%!PS-Adobe-3.0 %%Title: (small_slope3.tex) %%Creator: (Textures\252: LaserWriter 8 8.3.3) %%CreationDate: (12:21 PM Wednesday, July 29, 1998) %%For: (T&AM) %%Pages: 33 %%DocumentFonts: CMR17 CMR12 CMTI12 CMBX10 CMR10 CMTI10 CMMI10 CMR7 CMBX12 CMSY10 CMR8 CMMI8 CMEX10 CMBX8 CMSY8 MSAM7 Times-Roman Times-Italic Symbol Helvetica %%DocumentNeededFonts: Times-Roman Times-Italic Symbol Helvetica %%DocumentSuppliedFonts: CMR17 CMR12 CMTI12 CMBX10 CMR10 CMTI10 CMMI10 CMR7 CMBX12 CMSY10 CMR8 CMMI8 CMEX10 CMBX8 CMSY8 MSAM7 %%DocumentData: Clean7Bit %%PageOrder: Ascend %%Orientation: Portrait %%DocumentMedia: Default 612 792 0 () () %ADO_ImageableArea: 31 31 583 761 %%EndComments userdict begin/dscInfo 5 dict dup begin /Title(small_slope3.tex)def /Creator(Textures\252: LaserWriter 8 8.3.3)def /CreationDate(12:21 PM Wednesday, July 29, 1998)def /For(T&AM)def /Pages 33 def end def end save /version23-manualfeedpatch where { pop false } { true }ifelse % we don't do an explicit 'get' since product and version MAY % be in systemdict or statusdict - this technique gets the lookup % without failure statusdict begin product (LaserWriter) eq % true if LaserWriter version cvr 23.0 eq % true if version 23 end and % only install this patch if both are true and % true only if patch is not installed and is for this printer % save object and boolean on stack dup { exch restore }if % either true OR saveobject false dup { /version23-manualfeedpatch true def /oldversion23-showpage /showpage load def /showpage % this showpage will wait extra time if manualfeed is true {% statusdict /manualfeed known {% manualfeed known in statusdict statusdict /manualfeed get {% if true then we loop for 5 seconds usertime 5000 add % target usertime { % loop dup usertime sub 0 lt { exit }if }loop pop % pop the usertime off the stac }if }if oldversion23-showpage }bind def }if not{ restore }if /md 182 dict def md begin/currentpacking where {pop /sc_oldpacking currentpacking def true setpacking}if %%BeginFile: adobe_psp_basic %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /bd{bind def}bind def /xdf{exch def}bd /xs{exch store}bd /ld{load def}bd /Z{0 def}bd /T/true /F/false /:L/lineto /lw/setlinewidth /:M/moveto /rl/rlineto /rm/rmoveto /:C/curveto /:T/translate /:K/closepath /:mf/makefont /gS/gsave /gR/grestore /np/newpath 14{ld}repeat /$m matrix def /av 83 def /por true def /normland false def /psb-nosave{}bd /pse-nosave{}bd /us Z /psb{/us save store}bd /pse{us restore}bd /level2 /languagelevel where { pop languagelevel 2 ge }{ false }ifelse def /featurecleanup { stopped cleartomark countdictstack exch sub dup 0 gt { {end}repeat }{ pop }ifelse }bd /noload Z /startnoload { {/noload save store}if }bd /endnoload { {noload restore}if }bd level2 startnoload /setjob { statusdict/jobname 3 -1 roll put }bd /setcopies { userdict/#copies 3 -1 roll put }bd level2 endnoload level2 not startnoload /setjob { 1 dict begin/JobName xdf currentdict end setuserparams }bd /setcopies { 1 dict begin/NumCopies xdf currentdict end setpagedevice }bd level2 not endnoload /pm Z /mT Z /sD Z /realshowpage Z /initializepage { /pm save store mT concat }bd /endp { pm restore showpage }def /$c/DeviceRGB def /rectclip where { pop/rC/rectclip ld }{ /rC { np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K clip np }bd }ifelse /rectfill where { pop/rF/rectfill ld }{ /rF { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl fill gR }bd }ifelse /rectstroke where { pop/rS/rectstroke ld }{ /rS { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K stroke gR }bd }ifelse %%EndFile %%BeginFile: adobe_psp_colorspace_level1 %%Copyright: Copyright 1991-1993 Adobe Systems Incorporated. All Rights Reserved. /G/setgray ld /:F1/setgray ld /:F/setrgbcolor ld /:F4/setcmykcolor where { pop /setcmykcolor ld }{ { 3 { dup 3 -1 roll add dup 1 gt{pop 1}if 1 exch sub 4 1 roll }repeat pop setrgbcolor }bd }ifelse /:Fx { counttomark {0{G}0{:F}{:F4}} exch get exec pop }bd /:rg{/DeviceRGB :ss}bd /:sc{$cs :ss}bd /:dc{/$cs xdf}bd /:sgl{}def /:dr{}bd /:fCRD{pop}bd /:ckcs{}bd /:ss{/$c xdf}bd /$cs Z %%EndFile %%BeginFile: adobe_psp_customps %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /$t Z /$p Z /$s Z /$o 1. def /2state? false def /ps Z level2 startnoload /pushcolor/currentrgbcolor ld /popcolor/setrgbcolor ld /setcmykcolor where { pop/currentcmykcolor where { pop/pushcolor/currentcmykcolor ld /popcolor/setcmykcolor ld }if }if level2 endnoload level2 not startnoload /pushcolor { currentcolorspace $c eq { currentcolor currentcolorspace true }{ currentcmykcolor false }ifelse }bd /popcolor { { setcolorspace setcolor }{ setcmykcolor }ifelse }bd level2 not endnoload /pushstatic { ps 2state? $o $t $p $s $cs }bd /popstatic { /$cs xs /$s xs /$p xs /$t xs /$o xs /2state? xs /ps xs }bd /pushgstate { save errordict/nocurrentpoint{pop 0 0}put currentpoint 3 -1 roll restore pushcolor currentlinewidth currentlinecap currentlinejoin currentdash exch aload length np clippath pathbbox $m currentmatrix aload pop }bd /popgstate { $m astore setmatrix 2 index sub exch 3 index sub exch rC array astore exch setdash setlinejoin setlinecap lw popcolor np :M }bd /bu { pushgstate gR pushgstate 2state? { gR pushgstate }if pushstatic pm restore mT concat }bd /bn { /pm save store popstatic popgstate gS popgstate 2state? { gS popgstate }if }bd /cpat{pop 64 div setgray 8{pop}repeat}bd %%EndFile %%BeginFile: adobe_psp_basic_text %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /S/show ld /A{ 0.0 exch ashow }bd /R{ 0.0 exch 32 exch widthshow }bd /W{ 0.0 3 1 roll widthshow }bd /J{ 0.0 32 4 2 roll 0.0 exch awidthshow }bd /V{ 0.0 4 1 roll 0.0 exch awidthshow }bd /fcflg true def /fc{ fcflg{ vmstatus exch sub 50000 lt{ (%%[ Warning: Running out of memory ]%%\r)print flush/fcflg false store }if pop }if }bd /$f[1 0 0 -1 0 0]def /:ff{$f :mf}bd /MacEncoding StandardEncoding 256 array copy def MacEncoding 39/quotesingle put MacEncoding 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/space/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave /Oacute/Ocircumflex/apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron MacEncoding 128 128 getinterval astore pop level2 startnoload /copyfontdict { findfont dup length dict begin { 1 index/FID ne{def}{pop pop}ifelse }forall }bd level2 endnoload level2 not startnoload /copyfontdict { findfont dup length dict copy begin }bd level2 not endnoload md/fontname known not{ /fontname/customfont def }if /Encoding Z /:mre { copyfontdict /Encoding MacEncoding def fontname currentdict end definefont :ff def }bd /:bsr { copyfontdict /Encoding Encoding 256 array copy def Encoding dup }bd /pd{put dup}bd /:esr { pop pop fontname currentdict end definefont :ff def }bd /scf { scalefont def }bd /scf-non { $m scale :mf setfont }bd /ps Z /fz{/ps xs}bd /sf/setfont ld /cF/currentfont ld /mbf { /makeblendedfont where { pop makeblendedfont /ABlend exch definefont }{ pop }ifelse def }def %%EndFile /currentpacking where {pop sc_oldpacking setpacking}if end %%EndProlog %%BeginSetup md begin countdictstack[{ %%BeginFeature: *ManualFeed False statusdict /manualfeed false put %%EndFeature }featurecleanup countdictstack[{ %%BeginFeature: *InputSlot Cassette %%EndFeature }featurecleanup countdictstack[{ %%BeginFeature: *PageRegion LetterSmall lettersmall %%EndFeature }featurecleanup (T&AM)setjob /mT[1 0 0 -1 31 761]def /sD 16 dict def 300 level2{1 dict dup/WaitTimeout 4 -1 roll put setuserparams}{statusdict/waittimeout 3 -1 roll put}ifelse fc %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueID 5000795 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACDD6500ABDA5ED9835F6A016CFC8F00B6C052ED76A87856B50F4D80DFAEB508C97F8281F3F88B17E4D3B90C0F65EC379791AACDC162A66CBBC5BE2F53AAD8DE72DD113B55A022FBFEE658CB95F5BB32BA0357B5E050FDDF264A07470BEF1C52119B6FBD5C77EBED964AC5A2BBEC9D8B3E48AE5BB003A63D545774B922B9D5FF6B0066ECE43645A131879B032137D6D823385FE55F3402D557FD3B4486BE356C29C3AEC91EF17F5D31183B1E489F1FA559A6693FBDD04D4F7 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont fc %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACDD6500ABDA5ED9835F6A016CFC8F00B6C052ED76A87856B50F4D80DFAEB508C97F8281F3F88B17E4D3B90C0F65EC379791AACDC162A66CBBC5BE2F53AAD8DE72DD113B55A022FBFEE658CB95F5BB32BA0357B5E050FDDF264A07470BEF1C52119B6FBD5C77EBED964AC5A2BBEC9D8B3E48AE5BB003A63D545774B922B9D5FF6B0066ECE43645A131879B032137D6D823385FE55F3402D557FD3B4486858B2A4B5A0CC2E1BF4E2A4A0E748483C3BCF5DE47CC5260A3A967C 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont fc %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /sterling put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueID 5000829 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACEE583A5C939393E012707B47E0C1FA47D284A1EDC9D01A497D772BCA8C543388E6DC0D1E2C4944740470E0914F65EFB0737B0851B2BA713A9A00B36D07DA6BCB52920B9B59EFE587734027A3C5E6566AAD332FE6FBCCED1417802822A3B81D6187875263D6BBDA04BBCF6E4870FEEAD60F104BB3C5A766610DD11AEA64A6B107B0B04439FA2888B8CC39232BB83F7695ABA81F0260CD5248B9E649CD803271DC8BB1656323089E9E2BB50F2B9508887D31DC36E555668D9 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cleartomark %%EndFont fc %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec 8053514D28EC28DA1630165FAB262882D3FCA78881823C5537FE6C3DDA8EE5B897E17CB027F5C73FDBB56B0A7C25FC3512B55FE8F3ACFBFFCC7F4A382D8299CC8FD37D3CEA49DABDCA92847AF0560B404EF71134B0F3D99934FC9D0B4E602011B9CFB856C23F958F3C5A2FBE0EF8587D1F5774879C324E51FCB22888B74F241550D7401EB990D4F3A7AF635198422283CAC1B6CD446DDBCBD915DB9BFF88844E784C6BF7389803D9450B0C21756A017306462C563D51ECE66FCC9C831843ECAE1FEFC1A232E2724F7B 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont fc %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec 8053514D28EC28DA1630165FAB262882D3FCA78881823C5537FE6C3DDA8EE5B897E17CB027F5C73FDBB56B0A7C25FC3512B55FE8F3ACFBFFCC7F4A382D8299CC8FD37D3CEA49DABDCA92847AF0560B404EF71134B0F3D99934FC9D0B4E602011B9CFB856C23F958F3C5A2FBE0EF8587D1F5774879C324E51FCB22888B74F241550D7401EB990D4F3A7AF635198422283CAC1B6CD446DDBCBD915DB9BFF88844E784C6BF7389803D9450B0C21756A017306457C7E62C1D269F306BD3402E266DEFC3B5E7D8A8D2F5BF0 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont fc %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /sterling put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec 8053514D28EC28DA1630165FAB262882D3FFD20326947B1065649B533EB5E9E3A88A87FE987918A687950B26F647D6E08BF14D983ED1D4A8CA1E2DA8D985F9442EB916F5B6ED0697AC7C33E1E36A3BF460D34CE45F1631871097CB04F18E38894CF4AC1538EB19481311D24FE3BE7BEAA4A3730E8B4831FE59D6D9CE2E46116B629C7BA2F9CE3ECBA2F43BC162A5A077CA1B2882A42AFDCEC3F4B75B5D63E0BC8E5DC95257766D8EA467AD9CBAF47BE60F797580CCED6884B3A68F70C91F4FDF80FD00ED9139E7F480 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cleartomark %%EndFont fc %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.0 %%CreationDate: 1991 Aug 18 17:49:13 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 19 /iota put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 35 /theta1 put dup 36 /pi1 put dup 37 /rho1 put dup 38 /sigma1 put dup 39 /phi1 put dup 40 /arrowlefttophalf put dup 41 /arrowleftbothalf put dup 42 /arrowrighttophalf put dup 43 /arrowrightbothalf put dup 44 /arrowhookleft put dup 45 /arrowhookright put dup 46 /triangleright put dup 47 /triangleleft put dup 48 /zerooldstyle put dup 49 /oneoldstyle put dup 50 /twooldstyle put dup 51 /threeoldstyle put dup 52 /fouroldstyle put dup 53 /fiveoldstyle put dup 54 /sixoldstyle put dup 55 /sevenoldstyle put dup 56 /eightoldstyle put dup 57 /nineoldstyle put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 63 /star put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /flat put dup 92 /natural put dup 93 /sharp put dup 94 /slurbelow put dup 95 /slurabove put dup 96 /lscript put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /dotlessi put dup 124 /dotlessj put dup 125 /weierstrass put dup 126 /vector put dup 127 /tie put dup 128 /psi put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5000785 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACEE583A5C939393E012707B47E0C1FA47D284A1EDC9D01A497D772BCA8C543388E6DC0D1E2C4944740470E0914F65EFB0737B0851B2BA713A9A00B36D07DA6BCB52920B9B59EFE587734027A3C5E6566AAD332FE6FBCCED1417802822A3B81D6187875263D6BBDA04BBCF6E4870FEEAD60F104BB3C5A766610DD11AEA64A6B107B0B04439FA2888B8CC39232BB83F7695ABA81F0260CD5248B9E649CD800BCB325468C79FFACB9CD3036F2ED7BB65DCC88381923B6EF7F2C 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%%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACDD6500ABDA5ED9835F6A016CFC8F00B6C052ED76A87856B50F4D80DFAEB508C97F8281F3F88B17E4D3B90C0F65EC379791AACDC162A66CBBC5BE2F53AAD8DE72DD113B55A022FBFEE658CB95F5BB32BA0357B5E050FDDF264A07470BEF1C52119B6FBD5C77EBED964AC5A2BBEC9D8B3E48AE5BB003A63D545774B922B9D5FF6B0066ECE43645A131879B032137D6D823385FE55F3402D557FD3B448685940729E6E22F4BE0E08C6505CBA868F795093F556B64B808DD710 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont fc %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 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/eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont fc %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 94 /logicaland put dup 95 /logicalor put dup 96 /turnstileleft put dup 97 /turnstileright put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 108 /arrowbothv put dup 109 /arrowdblbothv put dup 110 /backslash put dup 111 /wreathproduct put dup 112 /radical put dup 113 /coproduct put dup 114 /nabla put dup 115 /integral put dup 116 /unionsq put dup 117 /intersectionsq put dup 118 /subsetsqequal put dup 119 /supersetsqequal put dup 120 /section put dup 121 /dagger put dup 122 /daggerdbl put dup 123 /paragraph put dup 124 /club put dup 125 /diamond put dup 126 /heart put dup 127 /spade put dup 128 /arrowleft put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def 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cleartomark %%EndFont fc %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACDD6500ABDA5ED9835F6A016CFC8F00B6C052ED76A87856B50F4D80DFAEB508C97F8281F3F88B17E4D3B90C0F65EC379791AACDC162A66CBBC5BE2F53AAD8DE72DD113B55A022FBFEE658CB95F5BB32BA0357B5E050FDDF264A07470BEF1C52119B6FBD5C77EBED964AC5A2BBEC9D8B3E48AE5BB003A63D545774B922B9D5FF6B0066ECE43645A131879B032137D6D823385FE55F3402D557FD3B4486858B2A4B5A0CC2E1BF4E2A4A0E748483C3BCF5DE47CC5260A3A967C 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont fc %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.0 %%CreationDate: 1991 Aug 18 17:51:11 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 19 /iota put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 35 /theta1 put dup 36 /pi1 put dup 37 /rho1 put dup 38 /sigma1 put dup 39 /phi1 put dup 40 /arrowlefttophalf put dup 41 /arrowleftbothalf put dup 42 /arrowrighttophalf put dup 43 /arrowrightbothalf put dup 44 /arrowhookleft put dup 45 /arrowhookright put dup 46 /triangleright put dup 47 /triangleleft put dup 48 /zerooldstyle put dup 49 /oneoldstyle put dup 50 /twooldstyle put dup 51 /threeoldstyle put dup 52 /fouroldstyle put dup 53 /fiveoldstyle put dup 54 /sixoldstyle put dup 55 /sevenoldstyle put dup 56 /eightoldstyle put dup 57 /nineoldstyle put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 63 /star put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /flat put dup 92 /natural put dup 93 /sharp put dup 94 /slurbelow put dup 95 /slurabove put dup 96 /lscript put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /dotlessi put dup 124 /dotlessj put dup 125 /weierstrass put dup 126 /vector put dup 127 /tie put dup 128 /psi put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5000783 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACEE583A5C939393E012707B47E0C1FA47D284A1EDC9D01A497D772BCA8C543388E6DC0D1E2C4944740470E0914F65EFB0737B0851B2BA713A9A00B36D07DA6BCB52920B9B59EFE587734027A3C5E6566AAD332FE6FBCCED1417802822A3B81D6187875263D6BBDA04BBCF6E4870FEEAD60F104BB3C5A766610DD11AEA64A6B107B0B04439FA2888B8CC39232BB83F7695ABA81F0260CD5248B9E649CD803271DC8BB1656323089E9E2BB50F2B9508887D31FA4BDCF3EB512 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cleartomark %%EndFont fc %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /parenleftbig put dup 162 /parenrightbig put dup 163 /bracketleftbig put dup 164 /bracketrightbig put dup 165 /floorleftbig put dup 166 /floorrightbig put dup 167 /ceilingleftbig put dup 168 /ceilingrightbig put dup 169 /braceleftbig put dup 170 /bracerightbig put dup 173 /angbracketleftbig put dup 174 /angbracketrightbig put dup 175 /vextendsingle put dup 176 /vextenddouble put dup 177 /slashbig put dup 178 /backslashbig put dup 179 /parenleftBig put dup 180 /parenrightBig put dup 181 /parenleftbigg put dup 182 /parenrightbigg put dup 183 /bracketleftbigg put dup 184 /bracketrightbigg put dup 185 /floorleftbigg put dup 186 /floorrightbigg put dup 187 /ceilingleftbigg put dup 188 /ceilingrightbigg put dup 189 /braceleftbigg put dup 190 /bracerightbigg put dup 191 /angbracketleftbigg put dup 192 /angbracketrightbigg put dup 193 /slashbigg put dup 194 /backslashbigg put dup 195 /parenleftBigg put dup 196 /arrowdblbt put dup 0 /parenleftbig put dup 1 /parenrightbig put dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 4 /floorleftbig put dup 5 /floorrightbig put dup 6 /ceilingleftbig put dup 7 /ceilingrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 10 /angbracketleftbig put dup 11 /angbracketrightbig put dup 12 /vextendsingle put dup 13 /vextenddouble put dup 14 /slashbig put dup 15 /backslashbig put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 22 /floorleftbigg put dup 23 /floorrightbigg put dup 24 /ceilingleftbigg put dup 25 /ceilingrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 28 /angbracketleftbigg put dup 29 /angbracketrightbigg put dup 30 /slashbigg put dup 31 /backslashbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 36 /floorleftBigg put dup 37 /floorrightBigg put dup 38 /ceilingleftBigg put dup 39 /ceilingrightBigg put dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 42 /angbracketleftBigg put dup 43 /angbracketrightBigg put dup 44 /slashBigg put dup 45 /backslashBigg put dup 46 /slashBig put dup 47 /backslashBig put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 50 /bracketlefttp put dup 51 /bracketrighttp put dup 52 /bracketleftbt put dup 53 /bracketrightbt put dup 54 /bracketleftex put dup 55 /bracketrightex put dup 56 /bracelefttp put dup 57 /bracerighttp put dup 58 /braceleftbt put dup 59 /bracerightbt put dup 60 /braceleftmid put dup 61 /bracerightmid put dup 62 /braceex put dup 63 /arrowvertex put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 66 /parenleftex put dup 67 /parenrightex put dup 68 /angbracketleftBig put dup 69 /angbracketrightBig put dup 70 /unionsqtext put dup 71 /unionsqdisplay put dup 72 /contintegraltext put dup 73 /contintegraldisplay put dup 74 /circledottext put dup 75 /circledotdisplay put dup 76 /circleplustext put dup 77 /circleplusdisplay put dup 78 /circlemultiplytext put dup 79 /circlemultiplydisplay put dup 80 /summationtext put dup 81 /producttext put dup 82 /integraltext put dup 83 /uniontext put dup 84 /intersectiontext put dup 85 /unionmultitext put dup 86 /logicalandtext put dup 87 /logicalortext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 91 /uniondisplay put dup 92 /intersectiondisplay put dup 93 /unionmultidisplay put dup 94 /logicalanddisplay put dup 95 /logicalordisplay put dup 96 /coproducttext put dup 97 /coproductdisplay put dup 98 /hatwide put dup 99 /hatwider put dup 100 /hatwidest put dup 101 /tildewide put dup 102 /tildewider put dup 103 /tildewidest put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 106 /floorleftBig put dup 107 /floorrightBig put dup 108 /ceilingleftBig put dup 109 /ceilingrightBig put dup 110 /braceleftBig put dup 111 /bracerightBig put dup 112 /radicalbig put dup 113 /radicalBig put dup 114 /radicalbigg put dup 115 /radicalBigg put dup 116 /radicalbt put dup 117 /radicalvertex put dup 118 /radicaltp put dup 119 /arrowvertexdbl put dup 120 /arrowtp put dup 121 /arrowbt put dup 122 /bracehtipdownleft put dup 123 /bracehtipdownright put dup 124 /bracehtipupleft put dup 125 /bracehtipupright put dup 126 /arrowdbltp put dup 127 /arrowdblbt put dup 128 /parenleftBigg put dup 160 /space put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont fc %%BeginFont: CMBX8 %!PS-AdobeFont-1.1: CMBX8 1.0 %%CreationDate: 1991 Aug 20 16:36:07 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMBX8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-59 -250 1235 750}readonly def /UniqueID 5000766 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACDD6500ABDA5ED9835F6A016CFC8F00B6C052ED76A87856B50F4D80DFAEB508C97F8281F3F88B17E4D3B90C0F65EC379791AACDC162A66CBBC5BE2F53AAD8DE72DD113B55A022FBFEE658CB95F5BB32BA0357B5E050FDDF264A07470BEF1C52119B6FBD5C77EBED964AC5A2BBEC9D8B3E48AE5BB003A63D545774B922B9D5FF6B0066ECE43645A131879B032137D6D823385FE55F3402D557FD3B4486BE1F91DA738298311C1360C8158D61CB734273C21BCE59B0F2E1D38 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont fc %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 94 /logicaland put dup 95 /logicalor put dup 96 /turnstileleft put dup 97 /turnstileright put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 108 /arrowbothv put dup 109 /arrowdblbothv put dup 110 /backslash put dup 111 /wreathproduct put dup 112 /radical put dup 113 /coproduct put dup 114 /nabla put dup 115 /integral put dup 116 /unionsq put dup 117 /intersectionsq put dup 118 /subsetsqequal put dup 119 /supersetsqequal put dup 120 /section put dup 121 /dagger put dup 122 /daggerdbl put dup 123 /paragraph put dup 124 /club put dup 125 /diamond put dup 126 /heart put dup 127 /spade put dup 128 /arrowleft put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont fc %%BeginFont: MSAM7 %!PS-AdobeFont-1.1: MSAM7 2.1 %%CreationDate: 1992 Oct 17 08:30:29 % Copyright (C) 1991, 1992 Blue Sky Research. All rights reserved. % Copyright (C) 1991, 1992 Y&Y. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Math Symbol fonts were designed by the American Mathematical Society) readonly def /FullName (MSAM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /squaredot put dup 162 /squareplus put dup 163 /squaremultiply put dup 164 /square put dup 165 /squaresolid put dup 166 /squaresmallsolid put dup 167 /diamond put dup 168 /diamondsolid put dup 169 /clockwise put dup 170 /anticlockwise put dup 173 /harpoonleftright put dup 174 /harpoonrightleft put dup 175 /squareminus put dup 176 /forces put dup 177 /forcesbar put dup 178 /satisfies put dup 179 /dblarrowheadright put dup 180 /dblarrowheadleft put dup 181 /dblarrowleft put dup 182 /dblarrowright put dup 183 /dblarrowup put dup 184 /dblarrowdwn put dup 185 /harpoonupright put dup 186 /harpoondownright put dup 187 /harpoonupleft put dup 188 /harpoondownleft put dup 189 /arrowtailright put dup 190 /arrowtailleft put dup 191 /arrowparrleftright put dup 192 /arrowparrrightleft put dup 193 /shiftleft put dup 194 /shiftright put dup 195 /squiggleright put dup 196 /circleminus put dup 0 /squaredot put dup 1 /squareplus put dup 2 /squaremultiply put dup 3 /square put dup 4 /squaresolid put dup 5 /squaresmallsolid put dup 6 /diamond put dup 7 /diamondsolid put dup 8 /clockwise put dup 9 /anticlockwise put dup 10 /harpoonleftright put dup 11 /harpoonrightleft put dup 12 /squareminus put dup 13 /forces put dup 14 /forcesbar put dup 15 /satisfies put dup 16 /dblarrowheadright put dup 17 /dblarrowheadleft put dup 18 /dblarrowleft put dup 19 /dblarrowright put dup 20 /dblarrowup put dup 21 /dblarrowdwn put dup 22 /harpoonupright put dup 23 /harpoondownright put dup 24 /harpoonupleft put dup 25 /harpoondownleft put dup 26 /arrowtailright put dup 27 /arrowtailleft put dup 28 /arrowparrleftright put dup 29 /arrowparrrightleft put dup 30 /shiftleft put dup 31 /shiftright put dup 32 /squiggleright put dup 33 /squiggleleftright put dup 34 /curlyleft put dup 35 /curlyright put dup 36 /circleequal put dup 37 /succeedsorequal put dup 38 /greaterorsimilar put dup 39 /greaterorapproxeql put dup 40 /multimap put dup 41 /therefore put dup 42 /because put dup 43 /equalsdots put dup 44 /defines put dup 45 /precedesorequal put dup 46 /lessorsimilar put dup 47 /lessorapproxeql put dup 48 /equalorless put dup 49 /equalorgreater put dup 50 /equalorpreceeds put dup 51 /equalorsucceeds put dup 52 /precedesorcurly put dup 53 /lessdblequal put dup 54 /lessorequalslant put dup 55 /lessorgreater put dup 56 /primereverse put dup 57 /axisshort put dup 58 /equaldotrightleft put dup 59 /equaldotleftright put dup 60 /succeedsorcurly put dup 61 /greaterdblequal put dup 62 /greaterorequalslant put dup 63 /greaterorless put dup 64 /squareimage put dup 65 /squareoriginal put dup 66 /triangleright put dup 67 /triangleleft put dup 68 /trianglerightequal put dup 69 /triangleleftequal put dup 70 /star put dup 71 /between put dup 72 /triangledownsld put dup 73 /trianglerightsld put dup 74 /triangleleftsld put dup 75 /arrowaxisright put dup 76 /arrowaxisleft put dup 77 /triangle put dup 78 /trianglesolid put dup 79 /triangleinv put dup 80 /ringinequal put dup 81 /lessequalgreater put dup 82 /greaterlessequal put dup 83 /lessdbleqlgreater put dup 84 /greaterdbleqlless put dup 85 /Yen put dup 86 /arrowtripleright put dup 87 /arrowtripleleft put dup 88 /check put dup 89 /orunderscore put dup 90 /nand put dup 91 /perpcorrespond put dup 92 /angle put dup 93 /measuredangle put dup 94 /sphericalangle put dup 95 /proportional put dup 96 /smile put dup 97 /frown put dup 98 /subsetdbl put dup 99 /supersetdbl put dup 100 /uniondbl put dup 101 /intersectiondbl put dup 102 /uprise put dup 103 /downfall put dup 104 /multiopenleft put dup 105 /multiopenright put dup 106 /subsetdblequal put dup 107 /supersetdblequal put dup 108 /difference put dup 109 /geomequivalent put dup 110 /muchless put dup 111 /muchgreater put dup 112 /rightanglenw put dup 113 /rightanglene put dup 114 /circleR put dup 115 /circleS put dup 116 /fork put dup 117 /dotplus put dup 118 /revsimilar put dup 119 /revasymptequal put dup 120 /rightanglesw put dup 121 /rightanglese put dup 122 /ironcross put dup 123 /complement put dup 124 /intercal put dup 125 /circlering put dup 126 /circleasterisk put dup 127 /circleminus put dup 128 /squiggleright put dup 160 /space put readonly def /FontBBox{0 -576 1569 1076}readonly def /UniqueID 5032012 def currentdict end currentfile eexec 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49/infinity pd 50/element pd 51/owner pd 52/triangle pd 53/triangleinv pd 54/negationslash pd 55/mapsto pd 56/universal pd 57/existential pd 58/logicalnot pd 59/emptyset pd 60/Rfractur pd 61/Ifractur pd 62/latticetop pd 63/perpendicular pd 64/aleph pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/union pd 92/intersection pd 93/unionmulti pd 94/logicaland pd 95/logicalor pd 96/turnstileleft pd 97/turnstileright pd 98/floorleft pd 99/floorright pd 100/ceilingleft pd 101/ceilingright pd 102/braceleft pd 103/braceright pd 104/angbracketleft pd 105/angbracketright pd 106/bar pd 107/bardbl pd 108/arrowbothv pd 109/arrowdblbothv pd 110/backslash pd 111/wreathproduct pd 112/radical pd 113/coproduct pd 114/nabla pd 115/integral pd 116/unionsq pd 117/intersectionsq pd 118/subsetsqequal pd 119/supersetsqequal pd 120/section pd 121/dagger pd 122/daggerdbl pd 123/paragraph pd 124/club pd 125/diamond pd 126/heart pd 127/.notdef pd 128/.notdef pd 161/minus pd 162/periodcentered pd 163/multiply pd 164/asteriskmath pd 165/divide pd 166/diamondmath pd 167/plusminus pd 168/minusplus pd 169/circleplus pd 170/circleminus pd 173/circlemultiply pd 174/circledivide pd 175/circledot pd 176/circlecopyrt pd 177/openbullet pd 178/bullet pd 179/equivasymptotic pd 180/equivalence pd 181/reflexsubset pd 182/reflexsuperset pd 183/lessequal pd 184/greaterequal pd 185/precedesequal pd 186/followsequal pd 187/similar pd 188/approxequal pd 189/propersubset pd 190/propersuperset pd 191/lessmuch pd 192/greatermuch pd 193/precedes pd 194/follows pd 195/arrowleft pd 196/spade pd :esr /f9_12 f9_1 12 scf /f10_1/CMR8 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 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pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f10_12 f10_1 12 scf /f11_1/CMMI8 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef 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93/sharp pd 94/slurbelow pd 95/slurabove pd 96/lscript pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/dotlessi pd 124/dotlessj pd 125/weierstrass pd 126/vector pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/alpha pd 175/beta pd 176/gamma pd 177/delta pd 178/epsilon1 pd 179/zeta pd 180/eta pd 181/theta pd 182/iota pd 183/kappa pd 184/lambda pd 185/mu pd 186/nu pd 187/xi pd 188/pi pd 189/rho pd 190/sigma pd 191/tau pd 192/upsilon pd 193/phi pd 194/chi pd 195/psi pd 196/tie pd :esr /f11_12 f11_1 12 scf /f12_1/CMEX10 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/.notdef pd 33/parenrightBigg pd 34/bracketleftBigg pd 35/bracketrightBigg pd 36/floorleftBigg pd 37/floorrightBigg pd 38/ceilingleftBigg pd 39/ceilingrightBigg pd 40/braceleftBigg pd 41/bracerightBigg pd 42/angbracketleftBigg pd 43/angbracketrightBigg pd 44/slashBigg pd 45/backslashBigg pd 46/slashBig pd 47/backslashBig pd 48/parenlefttp pd 49/parenrighttp pd 50/bracketlefttp pd 51/bracketrighttp pd 52/bracketleftbt pd 53/bracketrightbt pd 54/bracketleftex pd 55/bracketrightex pd 56/bracelefttp pd 57/bracerighttp pd 58/braceleftbt pd 59/bracerightbt pd 60/braceleftmid pd 61/bracerightmid pd 62/braceex pd 63/arrowvertex pd 64/parenleftbt pd 65/parenrightbt pd 66/parenleftex pd 67/parenrightex pd 68/angbracketleftBig pd 69/angbracketrightBig pd 70/unionsqtext pd 71/unionsqdisplay pd 72/contintegraltext pd 73/contintegraldisplay pd 74/circledottext pd 75/circledotdisplay pd 76/circleplustext pd 77/circleplusdisplay pd 78/circlemultiplytext pd 79/circlemultiplydisplay pd 80/summationtext pd 81/producttext pd 82/integraltext pd 83/uniontext pd 84/intersectiontext pd 85/unionmultitext pd 86/logicalandtext pd 87/logicalortext pd 88/summationdisplay pd 89/productdisplay pd 90/integraldisplay pd 91/uniondisplay pd 92/intersectiondisplay pd 93/unionmultidisplay pd 94/logicalanddisplay pd 95/logicalordisplay pd 96/coproducttext pd 97/coproductdisplay pd 98/hatwide pd 99/hatwider pd 100/hatwidest pd 101/tildewide pd 102/tildewider pd 103/tildewidest pd 104/bracketleftBig pd 105/bracketrightBig pd 106/floorleftBig pd 107/floorrightBig pd 108/ceilingleftBig pd 109/ceilingrightBig pd 110/braceleftBig pd 111/bracerightBig pd 112/radicalbig pd 113/radicalBig pd 114/radicalbigg pd 115/radicalBigg pd 116/radicalbt pd 117/radicalvertex pd 118/radicaltp pd 119/arrowvertexdbl pd 120/arrowtp pd 121/arrowbt pd 122/bracehtipdownleft pd 123/bracehtipdownright pd 124/bracehtipupleft pd 125/bracehtipupright pd 126/arrowdbltp pd 127/.notdef pd 128/.notdef pd 161/parenleftbig pd 162/parenrightbig pd 163/bracketleftbig pd 164/bracketrightbig pd 165/floorleftbig pd 166/floorrightbig pd 167/ceilingleftbig pd 168/ceilingrightbig pd 169/braceleftbig pd 170/bracerightbig pd 173/angbracketleftbig pd 174/angbracketrightbig pd 175/vextendsingle pd 176/vextenddouble pd 177/slashbig pd 178/backslashbig pd 179/parenleftBig pd 180/parenrightBig pd 181/parenleftbigg pd 182/parenrightbigg pd 183/bracketleftbigg pd 184/bracketrightbigg pd 185/floorleftbigg pd 186/floorrightbigg pd 187/ceilingleftbigg pd 188/ceilingrightbigg pd 189/braceleftbigg pd 190/bracerightbigg pd 191/angbracketleftbigg pd 192/angbracketrightbigg pd 193/slashbigg pd 194/backslashbigg pd 195/parenleftBigg pd 196/arrowdblbt pd :esr /f12_12 f12_1 12 scf /f13_1/CMBX8 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/dollar pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/exclamdown pd 61/equal pd 62/questiondown pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f13_12 f13_1 12 scf /f14_1/CMSY8 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/.notdef pd 33/arrowright pd 34/arrowup pd 35/arrowdown pd 36/arrowboth pd 37/arrownortheast pd 38/arrowsoutheast pd 39/similarequal pd 40/arrowdblleft pd 41/arrowdblright pd 42/arrowdblup pd 43/arrowdbldown pd 44/arrowdblboth pd 45/arrownorthwest pd 46/arrowsouthwest pd 47/proportional pd 48/prime pd 49/infinity pd 50/element pd 51/owner pd 52/triangle pd 53/triangleinv pd 54/negationslash pd 55/mapsto pd 56/universal pd 57/existential pd 58/logicalnot pd 59/emptyset pd 60/Rfractur pd 61/Ifractur pd 62/latticetop pd 63/perpendicular pd 64/aleph pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/union pd 92/intersection pd 93/unionmulti pd 94/logicaland pd 95/logicalor pd 96/turnstileleft pd 97/turnstileright pd 98/floorleft pd 99/floorright pd 100/ceilingleft pd 101/ceilingright pd 102/braceleft pd 103/braceright pd 104/angbracketleft pd 105/angbracketright pd 106/bar pd 107/bardbl pd 108/arrowbothv pd 109/arrowdblbothv pd 110/backslash pd 111/wreathproduct pd 112/radical pd 113/coproduct pd 114/nabla pd 115/integral pd 116/unionsq pd 117/intersectionsq pd 118/subsetsqequal pd 119/supersetsqequal pd 120/section pd 121/dagger pd 122/daggerdbl pd 123/paragraph pd 124/club pd 125/diamond pd 126/heart pd 127/.notdef pd 128/.notdef pd 161/minus pd 162/periodcentered pd 163/multiply pd 164/asteriskmath pd 165/divide pd 166/diamondmath pd 167/plusminus pd 168/minusplus pd 169/circleplus pd 170/circleminus pd 173/circlemultiply pd 174/circledivide pd 175/circledot pd 176/circlecopyrt pd 177/openbullet pd 178/bullet pd 179/equivasymptotic pd 180/equivalence pd 181/reflexsubset pd 182/reflexsuperset pd 183/lessequal pd 184/greaterequal pd 185/precedesequal pd 186/followsequal pd 187/similar pd 188/approxequal pd 189/propersubset pd 190/propersuperset pd 191/lessmuch pd 192/greatermuch pd 193/precedes pd 194/follows pd 195/arrowleft pd 196/spade pd :esr /f14_12 f14_1 12 scf /f15_1/MSAM7 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/.notdef pd 33/squiggleleftright pd 34/curlyleft pd 35/curlyright pd 36/circleequal pd 37/succeedsorequal pd 38/greaterorsimilar pd 39/greaterorapproxeql pd 40/multimap pd 41/therefore pd 42/because pd 43/equalsdots pd 44/defines pd 45/precedesorequal pd 46/lessorsimilar pd 47/lessorapproxeql pd 48/equalorless pd 49/equalorgreater pd 50/equalorpreceeds pd 51/equalorsucceeds pd 52/precedesorcurly pd 53/lessdblequal pd 54/lessorequalslant pd 55/lessorgreater pd 56/primereverse pd 57/axisshort pd 58/equaldotrightleft pd 59/equaldotleftright pd 60/succeedsorcurly pd 61/greaterdblequal pd 62/greaterorequalslant pd 63/greaterorless pd 64/squareimage pd 65/squareoriginal pd 66/triangleright pd 67/triangleleft pd 68/trianglerightequal pd 69/triangleleftequal pd 70/star pd 71/between pd 72/triangledownsld pd 73/trianglerightsld pd 74/triangleleftsld pd 75/arrowaxisright pd 76/arrowaxisleft pd 77/triangle pd 78/trianglesolid pd 79/triangleinv pd 80/ringinequal pd 81/lessequalgreater pd 82/greaterlessequal pd 83/lessdbleqlgreater pd 84/greaterdbleqlless pd 85/Yen pd 86/arrowtripleright pd 87/arrowtripleleft pd 88/check pd 89/orunderscore pd 90/nand pd 91/perpcorrespond pd 92/angle pd 93/measuredangle pd 94/sphericalangle pd 95/proportional pd 96/smile pd 97/frown pd 98/subsetdbl pd 99/supersetdbl pd 100/uniondbl pd 101/intersectiondbl pd 102/uprise pd 103/downfall pd 104/multiopenleft pd 105/multiopenright pd 106/subsetdblequal pd 107/supersetdblequal pd 108/difference pd 109/geomequivalent pd 110/muchless pd 111/muchgreater pd 112/rightanglenw pd 113/rightanglene pd 114/circleR pd 115/circleS pd 116/fork pd 117/dotplus pd 118/revsimilar pd 119/revasymptequal pd 120/rightanglesw pd 121/rightanglese pd 122/ironcross pd 123/complement pd 124/intercal pd 125/circlering pd 126/circleasterisk pd 127/.notdef pd 128/.notdef pd 161/squaredot pd 162/squareplus pd 163/squaremultiply pd 164/square pd 165/squaresolid pd 166/squaresmallsolid pd 167/diamond 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(kneed)s 79.625 (w)s 86.57 (alk)s 99.347 (er.)s 8 f 685.43 y 232.14 (1)s end endp %%Page: 2 2 %%BeginPageSetup initializepage (T&AM; page: 2 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f8_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 9 14.4 /CMBX12 findfont fdef 41 41 translate 72 72.27 div dup scale 9 f 16 y 0 (1)s 24.3 (In)s 38.883 (tro)s 60.35 (duction)s 8 f 48.604 y 0 (Since)s 27.722 (h)s 33.501 (umans)s 67.367 (and)s 87.789 (some)s 114.355 (p)s 120.743 (oten)s 141.122 (tially-useful)s 199.93 (rob)s 216.081 (ot)s 228.595 (designs)s 265.563 (use)s 283.613 (legged)s 316.201 (w)s 323.805 (alking)s 355.481 (motions,)s 399.255 (it)s 409.335 (is)s 419.476 (in)s 428.297 (teresting)s 70.364 y 0 (to)s 13.383 (consider)s 56.058 (the)s 74.916 (limits)s 105.394 (of)s 117.865 (p)s 124.252 (ossible)s 159.049 (p)s 165.436 (erformance)s 221.768 (of)s 234.239 (bip)s 249.752 (edal)s 272.868 (w)s 280.472 (alking)s 313.018 (mac)s 332.181 (hines.)s 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(osed)s 303.171 (to)s 317.564 (a)s 327.698 (simple)s 362.835 (motor)s 396.116 (appro)s 423.217 (ximation\051)s 505.565 y 0 (eliminates)s 51.769 (some)s 79.205 (arbitrariness,)s 145.726 (and)s 167.018 (simpli\257es)s 214.59 (sim)s 230.771 (ulation)s 267.88 (and)s 289.172 (ph)s 301.034 (ysical)s 331.207 (exp)s 348.241 (erimen)s 380.209 (tal)s 396.634 (v)s 402.109 (eri\257cation.)s 527.326 y 17 (In)s 30.348 (this)s 51.361 (pap)s 69.307 (er,)s 84.882 (w)s 92.486 (e)s 100.663 (address)s 139.409 (w)s 147.013 (alking)s 179.22 (p)s 185.607 (erformance)s 241.599 (issues)s 271.859 (in)s 284.294 (the)s 302.813 (con)s 318.934 (text)s 341.407 (of)s 353.538 (gra)s 368.472 (vit)s 381.247 (y-p)s 397.064 (o)s 402.235 (w)s 409.839 (ered)s 433.255 (w)s 440.859 (alking)s 549.086 y 0 (mac)s 19.163 (hines,)s 50.248 (also)s 72.209 (men)s 91.98 (tioning)s 129.088 (some)s 156.524 (other)s 185.146 (prop)s 207.381 (erties)s 236.672 (of)s 249.143 (these)s 277.187 (mac)s 296.35 (hines.)s 9 f 594.387 y 0 (2)s 24.3 (P)s 34.917 (assiv)s 68.172 (e)s 80.963 (Dynamic)s 149.405 (W)s 164.788 (alking)s 212.713 (Mac)s 242.705 (hines)s 8 f 626.99 y 0 (P)s 7.148 (assiv)s 29.778 (e)s 37.129 (dynamic)s 80.069 (w)s 87.673 (alking)s 119.053 (mac)s 138.216 (hines)s 165.095 (that)s 187.655 (w)s 195.259 (alk)s 212.04 (on)s 226.083 (shallo)s 253.215 (w)s 263.608 (ground-slop)s 319.97 (es)s 331.641 (w)s 339.245 (ere)s 355.752 (\257rst)s 377.186 (designed,)s 423.765 (sim)s 439.947 (ulated)s 648.75 y 0 (and)s 22.343 (built)s 49.552 (b)s 55.332 (y)s 65.812 (T)s 72.808 (ad)s 89.067 (McGeer,)s 134.592 (who)s 158.76 (w)s 166.364 (as)s 180.86 (inspired)s 223.369 (b)s 229.148 (y)s 239.628 (the)s 259.538 (\134ballistic\042)s 312.358 (double-)s 352.343 (and)s 374.686 (triple-p)s 410.304 (endulum)s 456.372 (leg)s 685.43 y 232.14 (2)s end endp %%Page: 3 3 %%BeginPageSetup initializepage (T&AM; page: 3 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f5_12 sf ( )S 6 0 :M f3_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 10 10.95 /CMTI10 findfont fdef 11 10.95 /CMBX10 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 0 (mo)s 14.904 (dels)s 38.238 (prop)s 60.472 (osed)s 86.239 (b)s 92.018 (y)s 102.82 (Mo)s 118.636 (c)s 123.199 (hon)s 145.863 (and)s 168.527 (McMahon)s 221.608 (\0501980\051.)s 264.051 (The)s 287.932 (McGeer-lik)s 340.659 (e)s 350.548 (passiv)s 379.262 (e-dynamic)s 433.255 (w)s 440.859 (alking)s 37.76 y 0 (mac)s 19.163 (hines)s 48.271 (consist)s 85.349 (of)s 98.885 (hinged)s 135.232 (rigid)s 161.877 (b)s 168.265 (o)s 174.044 (dies)s 197.07 (that)s 221.859 (mak)s 241.934 (e)s 251.515 (collisional)s 303.132 (and)s 325.489 (rolling)s 360.65 (con)s 376.771 (tact)s 400.344 (with)s 426.35 (a)s 436.54 (slop)s 455.763 (ed,)s 59.52 y 0 (rigid)s 25.58 (ground)s 62.719 (surface.)s 81.28 y 17 (The)s 40.925 (t)s 44.879 (w)s 52.483 (o-dimensional)s 123.311 (kneed)s 156.057 (w)s 163.661 (alking)s 197.624 (mac)s 216.786 (hine)s 241.928 (w)s 249.532 (e)s 259.466 (study)s 291.056 (here,)s 319.624 (essen)s 343.775 (tially)s 373.479 (a)s 384.021 (cop)s 400.142 (y)s 410.987 (of)s 424.875 (McGeer\047s)s 103.04 y 0 (design,)s 35.958 (is)s 46.216 (sho)s 61.789 (wn)s 78.678 (sc)s 87.56 (hematically)s 145.511 (in)s 157.533 (\257gure)s 187.227 (1.)s 200.359 (It)s 211.468 (consists)s 251.048 (of)s 262.765 (a)s 10 f 271.137 (swing)s 300.666 (le)s 307.942 (g)s 8 f 316.844 (\050not)s 339.816 (in)s 351.838 (con)s 367.959 (tact)s 389.714 (with)s 413.903 (the)s 432.008 (ground\051)s 124.8 y 0 (and)s 21.774 (a)s 10 f 31.381 (stanc)s 55.727 (e)s 65.125 (le)s 72.401 (g)s 8 f 82.539 (\050touc)s 107.176 (hing)s 131.992 (the)s 151.333 (ground\051,)s 196.375 (connected)s 247.957 (b)s 253.736 (y)s 263.648 (a)s 273.255 (frictionless)s 328.335 (hinge)s 358.018 (at)s 371.884 (the)s 10 f 391.224 (hip)s 8 f 405.776 (.)s 415.131 (Extra)s 446.517 (mass)s 146.561 y 0 (is)s 11.733 (generally)s 59.024 (added)s 91.988 (at)s 106.093 (the)s 125.674 (hip)s 145.255 (serving)s 183.481 (as)s 197.648 (a)s 207.495 (crude)s 238.056 (mo)s 252.96 (del)s 271.324 (of)s 284.518 (an)s 300.448 (upp)s 319.003 (er)s 332.53 (b)s 338.918 (o)s 344.697 (dy)s 355.647 (.)s 365.722 (Eac)s 383.212 (h)s 393.668 (leg)s 411.423 (is)s 423.157 (comp)s 449.011 (osed)s 168.321 y 0 (of)s 13.515 (a)s 23.685 (rigid)s 50.309 (thigh)s 79.946 (and)s 102.282 (shank.)s 141.063 (The)s 164.616 (stance)s 199.18 (knee)s 225.47 (is)s 237.525 (lo)s 246.346 (c)s 250.908 (k)s 256.383 (ed.)s 278.375 (F)s 284.61 (or)s 299.069 (kneed)s 331.442 (w)s 339.046 (alk)s 353.038 (ers,)s 374.51 (the)s 394.413 (swing)s 425.934 (knee)s 452.225 (is)s 464.28 (a)s 190.081 y 0 (frictionless)s 54.507 (hinge)s 83.615 (with)s 108.466 (a)s 117.5 (knee-stop)s 166.44 (prev)s 187.154 (en)s 197.8 (ting)s 220.217 (h)s 225.996 (yp)s 238.162 (erextension.)s 299.969 (The)s 322.386 (t)s 326.34 (w)s 333.945 (o)s 342.978 (legs)s 364.24 (are)s 382.429 (assumed)s 426.259 (iden)s 446.03 (tical.)s 211.841 y 0 (Straigh)s 34.401 (t-legged)s 75.841 (\050kneeless\051)s 126.224 (w)s 133.828 (alk)s 147.82 (ers)s 165.018 (ma)s 179.314 (y)s 188.817 (b)s 195.204 (e)s 203.794 (view)s 225.086 (ed)s 239.759 (as)s 253.277 (obtained)s 298.367 (from)s 324.325 (kneed)s 355.728 (w)s 363.332 (alk)s 377.324 (ers)s 394.522 (b)s 400.301 (y)s 409.804 (p)s 416.191 (ermanen)s 456.676 (tly)s 233.601 y 0 (lo)s 8.821 (c)s 13.383 (king)s 37.413 (the)s 56.271 (knees.)s 255.361 y 17 (A)s 28.957 (strob)s 53.686 (e)s 62.297 (photo)s 93.417 (of)s 105.982 (one)s 126.152 (of)s 138.717 (our)s 158.309 (w)s 165.913 (orking)s 199.801 (kneed)s 231.224 (ph)s 243.087 (ysical)s 273.355 (mo)s 288.259 (dels)s 310.314 (is)s 321.42 (sho)s 336.993 (wn)s 354.729 (in)s 367.599 (\257gure)s 398.141 (2.)s 411.808 (A)s 423.765 (sim)s 439.947 (ulated)s 277.121 y 0 (w)s 7.604 (alking)s 39.597 (cycle,)s 69.268 (using)s 97.368 (parameters)s 153.512 (measured)s 201.717 (from)s 227.049 (this)s 247.849 (mo)s 262.753 (del,)s 282.994 (is)s 293.452 (sho)s 309.025 (wn)s 326.114 (sc)s 334.996 (hematically)s 393.148 (in)s 405.37 (\257gure)s 435.264 (3.)s 448.463 (Step)s 298.881 y 0 (p)s 6.388 (erio)s 24.364 (d)s 34.855 (and)s 56.905 (stride)s 88.171 (length)s 122.388 (data)s 148.088 (from)s 174.731 (the)s 194.347 (ph)s 206.21 (ysical)s 237.141 (mo)s 252.046 (del)s 270.445 (matc)s 293.866 (hed)s 315.308 (our)s 335.563 (sim)s 351.745 (ulation)s 389.611 (results)s 425.197 (to)s 439.338 (within)s 320.641 y 0 (ab)s 11.863 (out)s 31.329 (5\045)s 49.579 (at)s 62.963 (this)s 84.315 (ground-slop)s 140.677 (e.)s 342.401 y 17 (Three)s 49.492 (remark)s 82.707 (able)s 106.651 (features)s 148.633 (that)s 173.186 (mak)s 193.261 (e)s 202.605 (the)s 222.291 (McGeer-lik)s 275.018 (e)s 284.363 (mo)s 299.267 (dels)s 322.056 (so)s 336.328 (in)s 345.149 (triguing)s 387.373 (for)s 404.961 (b)s 411.348 (oth)s 431.643 (rob)s 447.794 (otics)s 364.161 y 0 (and)s 21.292 (the)s 40.15 (understanding)s 112.025 (of)s 124.496 (animal)s 160.387 (gait)s 182.287 (are)s 200.568 (these:)s 394.921 y 13.383 (1.)s 11 f 27.375 (Existence)s 84.593 (of)s 99.539 (Gait.)s 8 f 133.896 (A)s 146.283 (mec)s 164.837 (hanism)s 203.14 (that)s 227.39 (resem)s 254.552 (bles)s 277.038 (h)s 282.818 (uman)s 313.76 (legs)s 335.637 (in)s 348.938 (o)s 354.108 (v)s 359.583 (erall)s 384.472 (la)s 392.685 (y)s 398.16 (out)s 418.152 (has)s 438.205 (an)s 453.938 (un-)s 416.682 y 27.375 (con)s 43.496 (trolled)s 79.314 (p)s 85.701 (erio)s 103.678 (dic)s 122.432 (motion)s 160.652 (that)s 185.49 (is)s 197.613 (rather)s 231.637 (an)s 242.891 (throp)s 269.384 (omorphic.)s 325.068 (A)s 338.042 (lo)s 346.863 (ok)s 362.879 (at)s 377.375 (video)s 407.383 (recordings)s 460.934 (of)s 438.442 y 27.375 (McGeer\047s)s 75.495 (kneed)s 106.414 (mac)s 125.577 (hines)s 153.211 (\050or)s 170.474 (our)s 189.561 (imitations)s 240.92 (of)s 252.981 (them\051,)s 287.937 (at)s 300.91 (passiv)s 329.624 (e-dynamic)s 381.835 (kneed)s 412.754 (sim)s 428.936 (ulations,)s 460.202 y 27.375 (or)s 40.728 (a)s 49.792 (comparison)s 107.614 (of)s 120.024 (passiv)s 148.738 (e-dynamic)s 201.298 (stic)s 217.479 (k-\257gure)s 257.295 (strob)s 282.023 (e)s 290.479 (shots)s 318.523 (with)s 343.404 (h)s 349.183 (uman)s 379.539 (data)s 404.42 (\050lo)s 416.891 (w)s 424.495 (er)s 437.24 (part)s 460.934 (of)s 481.962 y 27.375 (\257gure)s 57.822 (3\051)s 71.206 (certainly)s 116.557 (hin)s 131.461 (t)s 139.369 (at)s 152.753 (the)s 171.611 (role)s 192.933 (of)s 205.404 (passiv)s 234.117 (e-dynamics)s 291.057 (in)s 303.832 (h)s 309.612 (uman)s 340.028 (gait.)s 512.722 y 13.383 (2.)s 11 f 27.375 (E\261ciency)s 84.194 (of)s 98.286 (Gait.)s 8 f 130.995 (These)s 162.472 (mac)s 181.634 (hines)s 209.461 (can)s 229.319 (w)s 236.923 (alk)s 254.652 (do)s 265.906 (wn)s 283.331 (shallo)s 310.462 (w)s 321.804 (ground-slop)s 378.166 (es,)s 393.87 (indicating)s 444.752 (small)s 534.482 y 27.375 (energy)s 62.139 (cost)s 84.462 (for)s 100.976 (horizon)s 135.986 (tal)s 152.165 (transp)s 182.977 (ort.)s 204.825 (McGeer)s 245.749 (n)s 251.528 (umerically)s 304.542 (found)s 335.017 (w)s 342.621 (alking)s 374.921 (motions)s 416.103 (for)s 432.616 (ground-)s 556.242 y 27.375 (slop)s 46.598 (es)s 58.242 (as)s 70.494 (lo)s 78.707 (w)s 89.073 (as)s 101.325 (ab)s 113.188 (out)s 131.463 (0.005)s 158.862 (radians)s 196.087 (and)s 216.186 (w)s 223.791 (e)s 231.115 (will)s 250.607 (sho)s 266.18 (w)s 276.546 (here)s 299.11 (predictions)s 353.976 (for)s 369.543 (w)s 377.147 (alking)s 408.501 (at)s 420.693 (arbitrarily)s 578.002 y 27.375 (small)s 56.028 (ground-slop)s 112.39 (es.)s 608.762 y 13.383 (3.)s 11 f 27.375 (Stabilit)s 67.426 (y)s 79.49 (of)s 95.053 (Gait.)s 8 f 131.02 (F)s 137.255 (or)s 151.731 (certain)s 189.323 (parameter)s 242.762 (com)s 261.925 (binations,)s 313.805 (McGeer)s 356.035 (found)s 10 f 387.818 (stable)s 8 f 419.114 (limit)s 446.334 (cycle)s 630.522 y 27.375 (motions)s 70.125 (for)s 88.206 (b)s 94.594 (oth)s 115.382 (straigh)s 148.019 (t-legged)s 190.708 (and)s 213.321 (kneed)s 245.973 (w)s 253.577 (alk)s 267.568 (ers)s 286.015 (as)s 300.781 (Gosw)s 326.772 (ami)s 349.386 (et)s 363.483 (al.)s 380.013 (\0501996\051)s 415.402 (and)s 438.015 (Garcia)s 652.282 y 27.375 (et)s 40.28 (al.)s 55.619 (\0501998\051)s 89.816 (later)s 115.526 (rep)s 131.069 (eated)s 160.399 (for)s 177.289 (some)s 204.855 (straigh)s 237.492 (t-legged)s 278.989 (w)s 286.593 (alk)s 300.585 (ers,)s 320.914 (and)s 342.336 (w)s 349.94 (e)s 358.587 (rep)s 374.13 (eat)s 392.51 (and)s 413.932 (extend)s 449.65 (here)s 685.43 y 232.14 (3)s end endp %%Page: 4 4 %%BeginPageSetup initializepage (T&AM; page: 4 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f8_12 sf ( )S 7 0 :M f5_12 sf ( )S 10 0 :M f8_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 9 14.4 /CMBX12 findfont fdef 10 10.95 /CMTI10 findfont fdef 12 12 /CMBX12 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 27.375 (for)s 44.135 (kneed)s 75.464 (and)s 96.756 (straigh)s 129.393 (t-legged)s 170.759 (w)s 178.364 (alk)s 192.355 (ers.)s 46.76 y 0 (Recen)s 28.44 (t)s 36.169 (or)s 49.403 (curren)s 79.576 (t)s 87.305 (w)s 94.909 (ork)s 113.923 (is)s 124.754 (in)s 137.35 (progress)s 179.936 (b)s 185.715 (y)s 194.965 (F)s 201.201 (o)s 206.371 (wble)s 231.742 (and)s 252.854 (Kuo)s 276.4 (\0501996\051,)s 313.365 (Adolfsson)s 363.19 (et)s 375.786 (al.)s 390.815 (\0501998\051,)s 427.78 (Coleman)s 68.52 y 0 (and)s 20.722 (Ruina)s 52.546 (\0501998\051,)s 89.198 (and)s 109.92 (Garcia)s 144.74 (\0501998\051)s 178.237 (to)s 191.051 (extend)s 226.069 (McGeer\047s)s 274.029 (w)s 281.633 (ork)s 300.256 (on)s 314.895 (three-dimensional)s 402.625 (mo)s 417.529 (dels.)s 443.558 (All)s 460.934 (of)s 90.28 y 0 (the)s 18.764 (ab)s 30.627 (o)s 35.797 (v)s 41.272 (e)s 49.695 (w)s 57.299 (ork)s 76.398 (hin)s 91.302 (ts)s 103.435 (at)s 116.724 (the)s 135.488 (p)s 141.875 (ossible)s 176.578 (role)s 197.806 (of)s 210.182 (passiv)s 238.896 (e-dynamics)s 295.741 (in)s 308.422 (pro)s 324.573 (ducing)s 10 f 359.762 (and)s 8 f 380.668 (stabilizing)s 432.951 (e\261cien)s 465.497 (t)s 112.04 y 0 (uncon)s 28.288 (trolled)s 62.024 (motion.)s 103.067 (But)s 123.846 (ev)s 134.188 (en)s 147.818 (unstable)s 190.71 (limit)s 215.899 (cycle)s 242.001 (motions)s 282.459 (of)s 293.961 (mec)s 312.515 (hanical)s 349.262 (systems)s 388.93 (can)s 408.035 (\050in)s 424.099 (principle\051)s 133.8 y 0 (b)s 6.388 (e)s 13.996 (stabilized)s 61.816 (with)s 85.85 (minimal)s 127.526 (energetic)s 172.882 (cost,)s 197.766 (as)s 210.303 (has)s 228.922 (b)s 235.31 (een)s 253.869 (demonstrated)s 321.794 (for)s 337.646 (a)s 345.863 (three-dimensional)s 433.255 (w)s 440.859 (alking)s 155.561 y 0 (mo)s 14.904 (del)s 33.578 (b)s 39.357 (y)s 49.819 (F)s 56.054 (o)s 61.225 (wble)s 87.807 (and)s 110.131 (Kuo)s 134.889 (\0501996\051)s 169.988 (and)s 192.311 (implied)s 232.277 (b)s 238.056 (y)s 248.518 (McGeer)s 290.719 (\0501993\051.)s 332.141 (Th)s 345.828 (us,)s 364.213 (although)s 410.87 (the)s 430.761 (stabilit)s 463.976 (y)s 177.321 y 0 (feature)s 37.55 (of)s 50.736 (some)s 78.886 (passiv)s 107.6 (e-dynamic)s 160.936 (designs)s 199.489 (is)s 211.215 (in)s 220.036 (triguing)s 262.148 (and)s 284.155 (p)s 290.542 (ossibly)s 326.967 (useful,)s 362.292 (ev)s 372.634 (en)s 387.949 (unstable)s 432.525 (passiv)s 461.238 (e-)s 199.081 y 0 (dynamic)s 44.104 (motions)s 85.532 (could)s 114.732 (b)s 121.119 (e)s 129.636 (relev)s 151.871 (an)s 163.125 (t)s 171.033 (to)s 184.416 (animals)s 224.627 (or)s 238.041 (mac)s 257.204 (hines.)s 9 f 244.382 y 0 (3)s 24.3 (Preliminaries)s 12 f 277.625 y 0 (3.1)s 30.75 (McGeer\047s)s 91.575 (Recip)s 125.429 (e)s 8 f 306.457 y 0 (Our)s 21.682 (n)s 27.462 (umerical)s 71.044 (analysis)s 111.372 (follo)s 131.447 (ws)s 146.468 (the)s 164.47 (program)s 207.474 (of)s 219.088 (McGeer)s 259.401 (\0501990a\051)s 298.086 (in)s 310.005 (treating)s 350.546 (a)s 358.814 (step)s 381.135 (as)s 393.723 (a)s 401.991 (P)s 409.139 (oincar)s 438.066 (\266)s 438.37 (e)s 446.03 (map.)s 328.217 y 0 (This)s 24.364 (approac)s 61.807 (h)s 70.901 (is)s 81.273 (particularly)s 140.008 (w)s 147.612 (ell)s 161.573 (suited)s 193.237 (to)s 205.982 (the)s 224.201 (analysis)s 264.747 (of)s 276.579 (gait)s 297.84 (and)s 318.493 (is)s 328.865 (not)s 347.693 (limited)s 384.162 (to)s 396.907 (passiv)s 425.62 (e)s 433.498 (mo)s 448.402 (dels.)s 349.978 y 0 (The)s 22.508 (tec)s 36.196 (hnique)s 71.783 (is)s 82.794 (also)s 104.755 (describ)s 138.609 (ed)s 153.209 (in)s 165.984 (some)s 193.42 (detail)s 223.836 (b)s 229.616 (y)s 239.045 (Garcia)s 274.435 (et)s 287.21 (al.)s 302.418 (\0501998\051)s 336.485 (and)s 357.776 (Coleman)s 403.401 (et)s 416.176 (al.)s 431.385 (\0501997\051.)s 371.738 y 17 (A)s 28.163 (kneed)s 58.793 (w)s 66.398 (alking)s 10 f 98.245 (step)s 8 f 119.944 (starts)s 149.814 (just)s 170.772 (after)s 195.958 (a)s 204.384 (heelstrik)s 244.625 (e)s 252.443 (and)s 273.036 (ends)s 297.34 (after)s 322.526 (the)s 340.685 (next)s 364.624 (heelstrik)s 404.865 (e.)s 417.407 (W)s 427.749 (e)s 435.567 (assume)s 393.498 y 0 (that)s 24.557 (the)s 44.248 (swing)s 75.558 (knee)s 101.636 (is)s 113.48 (initially)s 154.766 (free)s 176.616 (to)s 190.832 (\260)s 196.916 (ex,)s 215.294 (and)s 237.418 (so)s 251.694 (w)s 259.298 (e)s 268.647 (sa)s 278.137 (y)s 288.399 (that)s 312.956 (the)s 332.647 (w)s 340.251 (alk)s 354.243 (er)s 367.881 (is)s 379.724 (in)s 10 f 393.331 (thr)s 406.623 (e)s 411.101 (e-link)s 442.088 (mo)s 456.08 (de)s 8 f 466.713 (.)s 415.258 y 0 (Starting)s 41.578 (with)s 65.484 (initial)s 96.081 (conditions)s 147.423 (righ)s 166.007 (t)s 172.88 (after)s 197.728 (heelstrik)s 237.97 (e,)s 248.699 (w)s 256.303 (e)s 263.784 (solv)s 282.095 (e)s 289.575 (the)s 307.398 (di\256eren)s 342.712 (tial)s 361.142 (equations)s 409.138 (of)s 420.573 (motion)s 456.645 (for)s 437.018 y 0 (the)s 18.19 (three-link)s 67.132 (mo)s 82.036 (de)s 95.967 (un)s 107.83 (til)s 121.153 (kneestrik)s 164.132 (e)s 171.981 (is)s 182.323 (detected.)s 230.159 (Using)s 260.272 (the)s 278.462 (angular-momen)s 352.405 (tum)s 374.854 (based)s 404.663 (v)s 410.138 (elo)s 423.826 (cit)s 435.688 (y-jump)s 458.778 y 0 (conditions)s 51.445 (that)s 74.238 (describ)s 108.092 (e)s 115.676 (the)s 133.602 (knee)s 157.915 (collision)s 199.019 (\050assumed)s 246.267 (to)s 258.718 (b)s 265.105 (e)s 272.689 (instan)s 301.646 (taneous)s 340.925 (and)s 361.284 (plastic\051,)s 402.574 (w)s 410.178 (e)s 417.762 (obtain)s 450.897 (new)s 480.538 y 0 (initial)s 30.873 (conditions)s 82.49 (for)s 98.49 (the)s 116.588 (start)s 142.077 (of)s 153.787 (the)s 171.886 (straigh)s 204.523 (t-leg)s 228.704 (or)s 10 f 241.357 (two-link)s 282.353 (mo)s 296.344 (de)s 8 f 310.69 (\050lik)s 326.507 (e)s 334.263 (McGeer,)s 377.866 (w)s 385.47 (e)s 393.226 (use)s 411.385 (suction)s 448.402 (cups)s 502.298 y 0 (with)s 25.067 (adjustable)s 77.874 (leaks)s 105.131 (to)s 118.639 (enforce)s 156.207 (the)s 175.191 (plastic)s 210.052 (knee)s 235.423 (collision)s 277.584 (in)s 290.485 (our)s 310.107 (ph)s 321.969 (ysical)s 352.268 (kneed)s 383.722 (mo)s 398.627 (dels\051.)s 429.48 (W)s 439.821 (e)s 448.463 (then)s 524.058 y 0 (solv)s 18.311 (e)s 27.247 (the)s 46.525 (equations)s 95.977 (of)s 108.867 (motion)s 146.395 (for)s 163.575 (this)s 185.347 (straigh)s 217.984 (t-leg)s 243.346 (phase)s 274.243 (\050with)s 303.863 (the)s 323.141 (knee)s 348.806 (lo)s 357.627 (c)s 362.19 (k)s 367.665 (ed\051)s 386.943 (un)s 398.805 (til)s 413.217 (heelstrik)s 453.458 (e)s 462.394 (is)s 545.818 y 0 (detected)s 43.61 (\050straigh)s 80.505 (t-legged)s 121.682 (w)s 129.286 (alk)s 143.278 (ers)s 160.212 (are)s 178.303 (alw)s 194.423 (a)s 199.594 (ys)s 213.152 (in)s 225.737 (t)s 229.691 (w)s 237.296 (o-link)s 267.826 (mo)s 282.73 (de,)s 300.22 (and)s 321.322 (ha)s 332.576 (v)s 338.051 (e)s 346.377 (no)s 361.395 (kneestrik)s 404.374 (e)s 412.701 (during)s 447.216 (their)s 567.578 y 0 (gait\051.)s 30.771 (A)s 38.68 (t)s 46.706 (the)s 65.683 (instan)s 94.639 (t)s 102.666 (of)s 115.255 (double-supp)s 173.412 (ort)s 191.202 (\050i.e.,)s 216.292 (con)s 232.412 (tact)s 255.039 (at)s 268.541 (b)s 274.928 (oth)s 294.513 (feet\051,)s 322.948 (heelstrik)s 363.19 (e)s 371.824 (o)s 377.604 (ccurs,)s 408.868 (whic)s 430.464 (h)s 440.315 (is)s 451.444 (also)s 589.338 y 0 (assumed)s 44.467 (to)s 58.396 (b)s 64.783 (e)s 73.846 (instan)s 102.802 (taneous)s 143.559 (and)s 165.396 (plastic.)s 206.026 (The)s 229.08 (assumption)s 287.539 (of)s 300.555 (a)s 310.226 (plastic)s 345.507 (collision)s 388.088 (seems)s 419.78 (reasonable)s 611.099 y 0 (for)s 17.666 (the)s 37.431 (ph)s 49.293 (ysical)s 80.373 (mo)s 95.277 (del)s 113.825 (where)s 146.395 (no)s 162.51 (macroscopic)s 224.949 (b)s 231.336 (ounce)s 263.268 (or)s 277.588 (slip)s 298.63 (is)s 310.547 (observ)s 341.055 (ed.)s 362.632 (A)s 370.541 (t)s 379.355 (heelstrik)s 419.597 (e,)s 432.288 (the)s 452.053 (legs)s 632.859 y 0 (exc)s 15.208 (hange)s 45.811 (stance)s 78.3 (and)s 98.562 (swing)s 128.009 (roles.)s 157.565 (Using)s 187.317 (the)s 205.145 (angular-momen)s 279.088 (tum)s 301.174 (based)s 330.621 (v)s 336.096 (elo)s 349.784 (cit)s 361.646 (y-jump)s 398.333 (conditions)s 449.68 (that)s 654.619 y 0 (describ)s 33.854 (e)s 42.945 (the)s 62.377 (fo)s 71.502 (ot)s 85.46 (collision)s 128.07 (and)s 149.935 (renaming)s 198.598 (v)s 203.769 (ariables)s 244.585 (to)s 258.542 (switc)s 282.632 (h)s 292.94 (legs,)s 318.052 (w)s 325.656 (e)s 334.746 (obtain)s 369.387 (the)s 388.82 (initial)s 421.027 (conditions)s 685.43 y 232.14 (4)s end endp %%Page: 5 5 %%BeginPageSetup initializepage (T&AM; page: 5 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f5_12 sf ( )S 6 0 :M f3_12 sf ( )S 10 0 :M f6_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 10 10.95 /CMTI10 findfont fdef 11 10.95 /CMBX10 findfont fdef 13 10.95 /CMMI10 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 0 (for)s 16.76 (the)s 35.618 (next)s 60.255 (three-link)s 109.865 (mo)s 124.769 (de.)s 37.76 y 17 (F)s 23.235 (ollo)s 39.965 (wing)s 66.796 (McGeer,)s 111.847 (w)s 119.451 (e)s 128.641 (assume)s 167.152 (in)s 180.6 (our)s 200.769 (sim)s 216.951 (ulations)s 259.051 (that)s 283.449 (during)s 318.827 (the)s 338.358 (heelstrik)s 378.6 (e)s 387.789 (collision,)s 433.708 (there)s 462.394 (is)s 59.52 y 0 (no)s 15.447 (impulse)s 55.896 (on)s 71.342 (the)s 90.439 (old)s 108.927 (stance)s 142.685 (fo)s 151.81 (ot.)s 170.166 (W)s 180.508 (e)s 189.263 (ha)s 200.517 (v)s 205.992 (e)s 214.747 (not)s 234.452 (tested)s 266.992 (this)s 288.583 (mo)s 303.487 (deling)s 335.967 (assumption)s 394.119 (with)s 419.299 (force)s 446.03 (plate)s 81.28 y 0 (measuremen)s 58.795 (ts,)s 75.924 (but)s 97.486 (it)s 109.923 (is)s 122.421 (self-consisten)s 184.654 (t)s 194.05 (and)s 216.829 (giv)s 230.82 (es)s 245.143 (sim)s 261.325 (ulation)s 299.921 (results)s 336.235 (whic)s 357.831 (h)s 369.052 (correctly)s 415.921 (predict)s 454.547 (the)s 103.04 y 0 (b)s 6.388 (eha)s 22.508 (vior)s 44.399 (of)s 56.526 (our)s 75.679 (exp)s 92.713 (erimen)s 124.681 (tal)s 140.762 (mo)s 155.666 (dels.)s 181.771 (The)s 203.935 (heelstrik)s 244.177 (e)s 252.349 (collision)s 294.042 (causes)s 327.278 (the)s 345.792 (knee)s 370.694 (on)s 385.559 (the)s 404.073 (new)s 426.238 (swing)s 456.372 (leg)s 124.8 y 0 (to)s 13.772 (unlo)s 34.759 (c)s 39.322 (k)s 49.139 (and)s 70.819 (\260)s 76.902 (ex,)s 94.725 (and)s 116.405 (the)s 135.652 (next)s 160.678 (step)s 184.244 (b)s 190.631 (egins.)s 223.49 (This)s 248.881 (yields)s 280.051 (one)s 300.514 (ev)s 310.552 (aluation)s 353.524 (of)s 366.383 (the)s 385.63 (\134stride)s 422.001 (function\042,)s 146.561 y 0 (McGeer\047s)s 48.53 (name)s 77.73 (for)s 94.489 (the)s 113.348 (nonlinear)s 161.437 (return)s 194.956 (map)s 219.289 (\050or)s 236.961 (P)s 244.109 (oincar)s 273.035 (\266)s 273.34 (e)s 281.856 (map\051)s 310.448 (whic)s 332.044 (h)s 341.777 (describ)s 375.631 (es)s 388.467 (one)s 408.542 (step.)s 168.321 y 17 (If)s 28.269 (the)s 47.446 (new)s 70.273 (initial)s 102.225 (conditions)s 154.921 (after)s 181.124 (one)s 201.518 (step)s 225.014 (are)s 243.613 (exactly)s 281.648 (the)s 300.825 (same)s 328.58 (as)s 342.342 (those)s 371.314 (of)s 384.103 (the)s 403.28 (previous)s 447.186 (step,)s 190.081 y 0 (w)s 7.604 (e)s 16.786 (ha)s 28.04 (v)s 33.515 (e)s 42.697 (found)s 74.082 (a)s 83.872 (p)s 90.26 (erio)s 108.236 (d-one)s 138.709 (limit-cycle)s 192.604 (\050also)s 219.488 (called)s 251.178 (a)s 260.968 (\257xed)s 288.095 (p)s 294.483 (oin)s 308.779 (t)s 317.352 (of)s 330.488 (the)s 350.011 (map,)s 378.217 (or)s 392.296 (a)s 10 f 402.086 (gait)s 424.245 (cycle)s 8 f 448.293 (\051.)s 462.455 (If)s 211.841 y 0 (gait)s 21.938 (cycles)s 53.366 (do)s 68.612 (exist,)s 97.616 (they)s 122.291 (migh)s 145.712 (t)s 153.658 (b)s 160.046 (e)s 168.6 (stable,)s 203.383 (in)s 216.196 (whic)s 237.792 (h)s 247.563 (case)s 270.778 (they)s 295.454 (can)s 315.566 (b)s 321.954 (e)s 330.508 (found)s 361.267 (b)s 367.046 (y)s 376.513 (direct)s 407.606 (sim)s 423.788 (ulation)s 460.934 (of)s 233.601 y 0 (the)s 19.064 (system)s 55.587 (o)s 60.758 (v)s 66.233 (er)s 79.243 (sev)s 93.904 (eral)s 115.432 (steps,)s 146.227 (pro)s 161.77 (vided)s 191.479 (the)s 210.543 (initial)s 242.382 (conditions)s 294.965 (c)s 299.527 (hosen)s 330.21 (are)s 348.696 (in)s 361.677 (the)s 380.74 (basin)s 409.598 (of)s 422.275 (attraction)s 255.361 y 0 (\050as)s 18.199 (in)s 31.47 (Gosw)s 57.461 (ami)s 79.25 (et)s 92.521 (al.)s 108.226 (\0501997\051\051.)s 152.298 (Whether)s 198.146 (or)s 212.056 (not)s 232.019 (the)s 251.374 (\257xed)s 278.333 (p)s 284.721 (oin)s 299.016 (ts)s 311.74 (are)s 330.517 (stable,)s 365.874 (they)s 391.007 (can)s 411.579 (b)s 417.966 (e)s 426.979 (found)s 458.197 (b)s 463.976 (y)s 277.121 y 0 (ro)s 10.068 (ot-\257nding)s 59.592 (algorithms)s 113.466 (applied)s 151.431 (to)s 164.455 (the)s 182.954 (return)s 216.114 (map,)s 243.202 (as)s 256.287 (in)s 268.703 (McGeer)s 309.512 (\0501990a\051)s 348.695 (\050also)s 374.554 (explained)s 423.166 (b)s 428.945 (y)s 438.015 (Garcia)s 298.881 y 0 (et)s 11.897 (al.)s 26.227 (\0501998\051\051.)s 68.518 (A)s 76.426 (t)s 83.456 (the)s 101.437 (\257xed)s 127.021 (p)s 133.409 (oin)s 147.704 (t,)s 157.952 (the)s 175.932 (eigen)s 199.961 (v)s 205.132 (alues)s 231.69 (of)s 243.283 (the)s 261.263 (Jacobian)s 306.162 (determine)s 356.414 (stabilit)s 389.629 (y)s 398.181 (\050all)s 416.769 (eigen)s 440.798 (v)s 445.969 (alues)s 320.641 y 0 (inside)s 31.884 (the)s 51.541 (unit)s 75.456 (circle)s 104.876 (implies)s 142.844 (linearized)s 192.947 (stabilit)s 226.162 (y\051,)s 243.889 (something)s 297.065 (that)s 321.588 (is)s 333.398 (of)s 346.667 (secondary)s 398.352 (in)s 407.173 (terest)s 438.479 (in)s 452.052 (this)s 342.401 y 0 (pap)s 17.946 (er.)s 364.161 y 17 (Although)s 66.507 (the)s 86.51 (ro)s 96.577 (ot-\257nding)s 147.605 (in)s 156.426 (v)s 161.901 (olv)s 175.893 (ed)s 191.637 (in)s 205.556 (\257nding)s 243.201 (a)s 253.47 (gait)s 276.514 (cycle)s 304.73 (in)s 313.55 (v)s 319.025 (olv)s 333.017 (es)s 346.997 (the)s 367 (n)s 372.779 (umerical)s 418.362 (solution)s 460.934 (of)s 13 f 385.921 y 0 (n)s 8 f 11.575 (equations)s 61.958 (in)s 13 f 76.085 (n)s 8 f 87.66 (unkno)s 116.86 (wns)s 140.173 (\050where)s 13 f 177.447 (n)s 8 f 189.022 (is)s 201.384 (the)s 221.595 (dimension)s 274.716 (of)s 288.539 (the)s 308.749 (return)s 343.621 (map\051)s 373.564 (there)s 402.93 (is)s 415.293 (no)s 10 f 431.853 (a)s 442.611 (priori)s 8 f 407.682 y 0 (guaran)s 32.576 (tee)s 50.052 (that)s 73.612 (an)s 84.866 (y)s 94.13 (gait)s 115.864 (cycles)s 147.088 (will)s 167.606 (exist)s 193.356 (for)s 209.95 (a)s 218.909 (giv)s 232.901 (en)s 247.335 (passiv)s 276.049 (e)s 284.4 (dynamic)s 328.338 (w)s 335.942 (alking)s 368.323 (mac)s 387.485 (hine)s 411.045 (\050i.e.,)s 435.854 (a)s 444.813 (giv)s 458.805 (en)s 429.442 y 0 (set)s 16.215 (of)s 27.807 (masses,)s 66.22 (lengths,)s 106.336 (etc.\051)s 132.201 (on)s 146.53 (a)s 154.777 (giv)s 168.768 (en)s 182.489 (ground-slop)s 238.851 (e)s 13 f 246.489 (\260)s 8 f 252.767 (.)s 260.382 (In)s 273.19 (practice,)s 316.926 (all)s 331.255 (searc)s 354.767 (hes)s 372.808 (with)s 396.87 (all)s 411.2 (designs)s 448.159 (ha)s 459.413 (v)s 464.888 (e)s 451.202 y 0 (found)s 30.508 (either)s 61.351 (zero,)s 87.37 (one,)s 110.317 (or)s 123.518 (t)s 127.472 (w)s 135.077 (o)s 143.989 (an)s 155.243 (throp)s 181.736 (omorphic)s 229.613 (p)s 236 (erio)s 253.977 (d-one)s 283.572 (solutions)s 329.107 (for)s 345.654 (giv)s 359.646 (en)s 374.033 (mac)s 393.196 (hine)s 416.708 (parameters)s 472.962 y 0 (and)s 21.771 (ground-slop)s 78.133 (e.)s 92.347 (Other)s 124.491 (non-an)s 157.037 (throp)s 183.53 (omorphic)s 232.098 (solutions)s 278.324 (ma)s 292.62 (y)s 302.529 (exist)s 328.924 (where)s 361.067 (the)s 380.405 (leg)s 397.918 (swings)s 433.194 (forw)s 453.908 (ard)s 494.722 y 0 (and)s 21.844 (bac)s 37.964 (kw)s 51.348 (ard)s 71.397 (more)s 99.354 (than)s 125.456 (once)s 150.95 (or)s 164.916 (the)s 184.326 (swing)s 215.355 (leg)s 232.941 (mak)s 253.016 (es)s 266.403 (full)s 286.118 (rev)s 300.748 (olutions)s 342.728 (\050as)s 360.982 (in)s 374.309 (Garcia)s 410.251 (et)s 423.578 (al.)s 439.338 (\0501998\051)s 516.482 y 0 (and)s 21.292 (Coleman)s 66.917 (\0501998\051\051)s 105.242 (but)s 125.317 (w)s 132.921 (e)s 141.438 (do)s 156.646 (not)s 176.113 (consider)s 218.787 (them)s 246.771 (here.)s 11 f 553.564 y 0 (3.1.1)s 38.477 (Aside)s 73.427 (On)s 94.08 (The)s 119.804 (Map)s 149.073 (Dimensions)s 8 f 582.396 y 0 (In)s 14.549 (general,)s 56.415 (one)s 77.352 (exp)s 94.385 (ects)s 117.208 (the)s 136.928 (dimension)s 189.558 (of)s 202.891 (the)s 222.611 (P)s 229.759 (oincar)s 258.685 (\266)s 258.989 (e)s 268.368 (map)s 293.563 (to)s 307.808 (b)s 314.195 (e)s 323.573 (one)s 344.51 (less)s 365.568 (than)s 391.98 (the)s 411.7 (order)s 441.214 (of)s 454.547 (the)s 604.156 y 0 (system.)s 40.739 (F)s 46.974 (or)s 60.442 (general)s 98.243 (straigh)s 130.881 (t-legged)s 172.302 (w)s 179.906 (alk)s 193.897 (ers,)s 214.131 (the)s 233.044 (map)s 257.432 (of)s 269.957 (the)s 288.869 (4th-order)s 337.043 (system)s 373.415 (\050t)s 381.627 (w)s 389.231 (o)s 398.411 (angles)s 431.376 (and)s 452.722 (t)s 456.676 (w)s 464.28 (o)s 625.917 y 0 (rates\051)s 30.445 (is)s 40.785 (generally)s 86.682 (three-dimensional.)s 179.016 (F)s 185.252 (or)s 197.995 (the)s 216.182 (sup)s 232.972 (er\257cially)s 276.436 (6th-order)s 323.884 (kneed)s 354.542 (w)s 362.146 (alk)s 376.138 (er)s 388.272 (\050three)s 419.873 (angles)s 452.113 (and)s 647.677 y 0 (three)s 28.397 (rates)s 55.638 (in)s 68.796 (three-link)s 118.788 (mo)s 133.692 (de\051,)s 156.071 (the)s 175.312 (map)s 200.029 (is)s 211.422 (also)s 233.766 (only)s 10 f 258.178 (thr)s 271.47 (e)s 275.948 (e-dimensional)s 8 f 347.152 (b)s 353.54 (ecause)s 388.05 (the)s 407.292 (kneed)s 439.004 (w)s 446.608 (alk)s 460.6 (er)s 685.43 y 232.14 (5)s end endp %%Page: 6 6 %%BeginPageSetup initializepage (T&AM; page: 6 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f5_12 sf ( )S 6 0 :M f3_12 sf ( )S 10 0 :M f8_12 sf ( )S 14 0 :M f6_12 sf ( )S 22 0 :M f9_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 10 10.95 /CMTI10 findfont fdef 11 10.95 /CMBX10 findfont fdef 12 12 /CMBX12 findfont fdef 13 10.95 /CMMI10 findfont fdef 14 10.95 /CMSY10 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 0 (is)s 11.989 (lik)s 23.548 (e)s 33.043 (a)s 43.147 (straigh)s 75.784 (t-legged)s 118.129 (w)s 125.733 (alk)s 139.725 (er)s 153.509 (for)s 171.247 (part)s 195.981 (of)s 209.431 (the)s 229.268 (swing-phase)s 291.201 (\050after)s 322.323 (kneestrik)s 365.302 (e\051.)s 385.271 (Th)s 398.958 (us,)s 417.276 (of)s 430.725 (the)s 450.562 (four)s 37.76 y 0 (n)s 5.779 (umerically-calculated)s 111.726 (eigen)s 135.755 (v)s 140.926 (alues)s 169.341 (of)s 182.791 (McGeer)s 224.939 (\0501990b\051)s 266.068 (\050)s 14 f 270.327 (\241)s 8 f 278.843 (0)s 13 f 284.318 (:)s 8 f 287.36 (001)s 13 f 303.785 (;)s 8 f 308.652 (0)s 13 f 314.127 (:)s 8 f 317.168 (073)s 13 f 333.593 (;)s 8 f 338.46 (0)s 13 f 343.935 (:)s 8 f 346.977 (261)s 14 f 366.488 (\247)s 8 f 378.09 (0)s 13 f 383.565 (:)s 8 f 386.607 (363)s 13 f 403.032 (i)s 8 f 406.804 (\051,)s 418.978 (the)s 438.815 (\257rst)s 462.394 (is)s 59.52 y 0 (actually)s 10 f 41.671 (exactly)s 8 f 78.793 (zero.)s 12 f 97.243 y 0 (3.2)s 30.75 (Realit)s 65.917 (y)s 77.542 (Chec)s 106.576 (ks)s 8 f 126.075 y 0 (Our)s 23.178 (n)s 28.957 (umerical)s 74.034 (sim)s 90.216 (ulations)s 132.282 (are)s 151.201 (based)s 182.318 (on)s 198.165 (the)s 217.662 (assumptions)s 280.533 (ab)s 292.395 (o)s 297.566 (v)s 303.041 (e)s 312.197 (and)s 334.127 (not)s 354.232 (a)s 363.996 (general)s 402.382 (purp)s 425.225 (ose)s 444.175 (rigid-)s 147.835 y 0 (b)s 6.388 (o)s 12.167 (dy)s 26.818 (sim)s 42.999 (ulation)s 79.246 (co)s 89.892 (de.)s 108.463 (Th)s 122.151 (us,)s 138.555 (some)s 165.13 (of)s 176.739 (the)s 194.736 (p)s 201.123 (erio)s 219.1 (dic)s 235.88 (solutions)s 280.765 (w)s 288.369 (e)s 296.024 (\257nd)s 317.062 (migh)s 340.483 (t)s 347.53 (violate)s 382.256 (v)s 387.427 (arious)s 418.898 (ph)s 430.761 (ysically-)s 169.595 y 0 (relev)s 22.235 (an)s 33.489 (t)s 41.501 (inequalit)s 82.868 (y)s 92.401 (conditions)s 144.882 (as)s 158.43 (discussed)s 206.167 (in)s 219.045 (McGeer)s 260.318 (\0501990b\051.)s 305.038 (F)s 311.274 (or)s 324.791 (the)s 343.753 (purp)s 366.596 (oses)s 389.33 (of)s 401.905 (this)s 423.361 (pap)s 441.307 (er,)s 457.284 (w)s 464.888 (e)s 191.355 y 0 (neglect)s 36.419 (those)s 64.382 (violations)s 113.333 (in)s 125.419 (order)s 153.382 (to)s 166.076 (ha)s 177.33 (v)s 182.805 (e)s 190.633 (solutions)s 235.69 (to)s 248.384 (study)s 277.869 (o)s 283.039 (v)s 288.514 (er)s 300.631 (the)s 318.8 (parameter)s 370.488 (range)s 399.638 (of)s 411.419 (in)s 420.24 (terest;)s 453.33 (but)s 213.115 y 0 (when)s 28.513 (building)s 71.018 (a)s 80.064 (ph)s 91.927 (ysical)s 122.022 (mo)s 136.926 (del,)s 157.546 (these)s 185.512 (issues)s 216.032 (are)s 234.234 (of)s 246.626 (in)s 255.447 (terest.)s 290.187 (In)s 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(this)s 179.253 (scu\261ng)s 218.805 (either)s 249.81 (with)s 274.702 (electromec)s 324.92 (hanically-retractable)s 426.826 (ankles)s 459.991 (or)s 330.915 y 27.375 (with)s 51.724 (tiles)s 74.308 (placed)s 107.782 (on)s 122.397 (the)s 140.662 (ground)s 177.208 (\050spaced)s 216.217 (for)s 232.384 (alternate)s 278.054 (stance-leg)s 328.014 (landings\051.)s 379.585 (A)s 390.854 (studen)s 422.244 (t)s 429.559 (group)s 460.022 (at)s 352.675 y 27.375 (Cornell)s 64.803 (Univ)s 87.615 (ersit)s 108.086 (y)s 116.587 (\050Lattanzio)s 169.345 (et)s 181.192 (al.)s 195.473 (\0501992\051\051)s 232.87 (o)s 238.041 (v)s 243.516 (ercame)s 279.727 (this)s 300.152 (di\261cult)s 336.348 (y)s 344.849 (using)s 372.574 (a)s 380.771 (passiv)s 409.484 (e)s 417.073 (mec)s 435.627 (hanism)s 374.435 y 27.375 (that)s 51.465 (sligh)s 73.122 (tly)s 90.216 (retracted)s 137.483 (the)s 156.707 (swing)s 187.549 (leg.)s 209.936 (Kneed)s 244.368 (w)s 251.972 (alk)s 265.963 (ers)s 283.453 (ma)s 297.749 (y)s 302.615 (,)s 309.763 (but)s 330.203 (do)s 345.777 (not)s 365.608 (necessarily)s 415.644 (,)s 422.792 (a)s 427.962 (v)s 433.437 (oid)s 452.052 (this)s 396.196 y 27.375 (scu\261ng)s 67.992 (b)s 73.771 (y)s 84.214 (su\261cien)s 122.296 (tly)s 140.039 (\260)s 146.122 (exing)s 176.032 (the)s 195.904 (swing)s 227.396 (knee)s 253.655 (at)s 268.053 (mid)s 290.967 (stride.)s 328.775 (F)s 335.01 (or)s 349.438 (3-D)s 371.59 (w)s 379.194 (alking)s 412.754 (mec)s 431.308 (hanisms)s 417.956 y 27.375 (\050e.g.,.)s 61.257 (F)s 67.492 (allis)s 90.811 (\0501888\051\051)s 129.885 (and)s 151.926 (p)s 158.314 (ossibly)s 194.772 (in)s 208.296 (part)s 232.801 (for)s 250.31 (h)s 256.089 (umans,)s 294.804 (fo)s 303.929 (ot)s 318.061 (scu\261ng)s 358.413 (can)s 379.238 (b)s 385.625 (e)s 394.891 (a)s 400.062 (v)s 405.537 (oided)s 435.486 (b)s 441.266 (y)s 451.444 (side)s 439.716 y 27.375 (to)s 40.925 (side)s 63.052 (ro)s 73.12 (c)s 77.682 (king.)s 106.468 (An)s 124.581 (unp)s 143.135 (o)s 148.306 (w)s 155.91 (ered)s 179.831 (scu\261ng)s 219.6 (solution)s 261.194 (could)s 290.56 (b)s 296.948 (e)s 305.631 (c)s 310.193 (hanged)s 348.076 (to)s 361.626 (a)s 370.917 (non-scu\261ng)s 431.977 (solution)s 461.476 y 27.375 (b)s 33.154 (y)s 42.323 (adding)s 77.954 (a)s 86.818 (small)s 115.21 (amoun)s 147.147 (t)s 154.795 (of)s 167.005 (actuation)s 215.411 (or)s 228.564 (a)s 237.428 (passiv)s 266.141 (e)s 274.397 (mec)s 292.951 (hanism)s 330.468 (to)s 343.591 (sligh)s 365.248 (tly)s 381.716 (retract)s 417.408 (alternating)s 483.236 y 27.375 (legs)s 48.728 (for)s 65.487 (clearance.)s 513.996 y 13.383 (2.)s 11 f 27.375 (P)s 35.633 (ositiv)s 65.085 (e)s 76.159 (knee-lo)s 115.685 (c)s 120.932 (king)s 149.67 (of)s 165.116 (the)s 188.082 (stance)s 227.734 (leg.)s 8 f 254.546 (In)s 269.194 (our)s 289.651 (ph)s 301.514 (ysical)s 332.648 (mo)s 347.552 (del,)s 369.436 (a)s 379.521 (join)s 397.163 (t-stop)s 429.818 (prev)s 450.532 (en)s 461.177 (ts)s 535.756 y 27.375 (knee)s 53.387 (h)s 59.166 (yp)s 71.333 (erextension,)s 132.911 (but)s 153.752 (nothing)s 194.668 (stops)s 223.539 (knee)s 249.551 (\260)s 255.634 (ex,)s 273.929 (except)s 309.066 (residual)s 350.682 (suction)s 389.225 (in)s 402.766 (the)s 422.391 (knee)s 448.402 (cups)s 557.516 y 27.375 (just)s 49.935 (after)s 76.723 (kneestrik)s 119.702 (e.)s 135.188 (In)s 149.779 (our)s 170.18 (sim)s 186.361 (ulations)s 228.692 (w)s 236.296 (e)s 245.717 (assume)s 284.459 (that)s 309.087 (the)s 328.849 (stance)s 363.272 (knee)s 389.421 (is)s 401.335 (lo)s 410.156 (c)s 414.719 (k)s 420.194 (ed)s 435.697 (un)s 447.56 (til)s 462.455 (it)s 579.276 y 27.375 (lea)s 40.454 (v)s 45.929 (es)s 59.091 (the)s 78.276 (ground.)s 120.653 (Naturally-arising)s 205.659 (torques)s 244.706 (at)s 258.416 (the)s 277.601 (knee)s 303.173 (prev)s 323.887 (en)s 334.533 (t)s 342.767 (unlo)s 363.755 (c)s 368.317 (king)s 392.673 (in)s 405.774 (some)s 433.537 (but)s 453.938 (not)s 601.036 y 27.375 (all)s 43.053 (solutions.)s 94.467 (The)s 117.444 (sim)s 133.626 (ulation)s 171.204 (sho)s 186.777 (wn)s 204.889 (in)s 218.133 (\257gure)s 249.05 (3)s 258.644 (has)s 278.641 (a)s 288.236 (sligh)s 309.893 (t)s 318.27 (stance-leg)s 369.292 (unlo)s 390.28 (c)s 394.842 (king)s 419.341 (impulse)s 460.022 (at)s 622.796 y 27.375 (kneestrik)s 70.354 (e)s 79.472 (whic)s 101.068 (h)s 111.403 (w)s 119.007 (e)s 128.126 (ignore)s 161.608 (in)s 174.985 (our)s 195.084 (sim)s 211.265 (ulations.)s 258.757 (The)s 281.867 (corresp)s 316.359 (onding)s 352.853 (ph)s 364.715 (ysical)s 395.49 (mo)s 410.395 (del)s 428.638 (do)s 440.501 (es)s 453.938 (not)s 644.557 y 27.375 (collapse,)s 72.174 (presumably)s 131.721 (b)s 138.108 (ecause)s 172.986 (the)s 192.595 (naturally-arising)s 275.897 (torques)s 315.368 (just)s 337.776 (after)s 364.411 (kneestrik)s 407.39 (e)s 416.657 (are)s 435.688 (enough)s 685.43 y 232.14 (6)s end endp %%Page: 7 7 %%BeginPageSetup initializepage (T&AM; page: 7 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f3_12 sf ( )S 7 0 :M f8_12 sf ( )S 11 0 :M f6_12 sf ( )S 19 0 :M f9_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 11 10.95 /CMBX10 findfont fdef 12 12 /CMBX12 findfont fdef 13 10.95 /CMMI10 findfont fdef 14 10.95 /CMSY10 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 27.375 (to)s 40.706 (re-engage)s 89.351 (the)s 108.157 (knee)s 133.351 (stop.)s 161.377 (But)s 183.073 (ev)s 193.415 (en)s 207.962 (if)s 217.948 (they)s 242.533 (migh)s 265.954 (t)s 273.81 (not)s 293.224 (b)s 299.612 (e,)s 311.128 (in)s 319.949 (termitten)s 364.692 (t)s 372.548 (lo)s 381.369 (c)s 385.931 (king)s 409.908 (of)s 422.327 (a)s 431.4 (rotating)s 37.76 y 27.375 (join)s 45.017 (t)s 52.925 (can)s 73 (b)s 79.388 (e)s 87.904 (p)s 94.292 (erformed)s 140.282 (with)s 165.224 (\050theoretically\051)s 236.733 (zero)s 259.88 (energy)s 294.89 (cost.)s 66.956 y 13.383 (3.)s 11 f 27.375 (P)s 35.633 (ositiv)s 65.085 (e)s 74.849 (stance)s 113.19 (con)s 131.729 (tact)s 157.233 (force)s 187.923 (and)s 212.028 (no)s 229.312 (slip.)s 8 f 256.576 (The)s 278.905 (sim)s 295.087 (ulations)s 336.336 (assume)s 373.996 (con)s 390.116 (tact)s 412.446 (b)s 418.834 (et)s 427.654 (w)s 435.259 (een)s 454.547 (the)s 88.716 y 27.375 (stance)s 61.265 (leg)s 78.668 (and)s 100.33 (the)s 119.559 (ground.)s 162.067 (There)s 194.101 (is)s 205.482 (no)s 221.061 (con)s 237.182 (tact)s 260.061 (tension)s 298.209 (in)s 311.354 (our)s 331.221 (sim)s 347.403 (ulations)s 389.201 (since)s 416.399 (all)s 431.978 (motions)s 110.476 y 27.375 (are)s 45.473 (w)s 53.077 (ell)s 67.494 (b)s 73.882 (elo)s 86.961 (w)s 98.337 (the)s 117.013 (sp)s 127.719 (eed)s 147.003 (range)s 176.66 (\050)s 13 f 180.918 (v)s 14 f 189.66 (\274)s 102.269 y 201.218 (p)s 13.068 .438 210.343 102.269 r 13 f 110.476 y 210.343 (g)s 215.959 (L)s 8 f 223.411 (\051)s 231.137 (where)s 262.618 (tension)s 300.213 (is)s 311.041 (required)s 353.807 (to)s 367.008 (k)s 372.483 (eep)s 391.767 (the)s 410.443 (stance)s 443.779 (leg)s 460.63 (in)s 132.236 y 27.375 (con)s 43.496 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(or)s 132.202 (extend)s 167.25 (at)s 180.092 (the)s 198.41 (knee.)s 227.734 (That)s 254.569 (this)s 275.381 (motion)s 311.949 (is)s 322.419 (not)s 341.345 (h)s 347.124 (yp)s 359.291 (erextension)s 416.329 (needs)s 445.658 (to)s 458.501 (b)s 464.888 (e)s 226.712 y 27.375 (c)s 31.938 (hec)s 47.45 (k)s 52.925 (ed.)s 71.783 (Some)s 100.983 (of)s 113.454 (our)s 132.951 (sim)s 149.133 (ulated)s 182.591 (gaits)s 208.81 (ha)s 220.065 (v)s 225.54 (e)s 234.056 (a)s 243.181 (small)s 271.834 (amoun)s 303.771 (t)s 311.68 (of)s 324.15 (this)s 345.503 (h)s 351.282 (yp)s 363.449 (erextension,)s 424.069 (esp)s 439.643 (ecially)s 248.472 y 27.375 (at)s 41.019 (near-zero)s 88.791 (ground-slop)s 145.153 (es.)s 163.029 (Allo)s 182.496 (w)s 190.1 (ance)s 215.302 (of)s 228.034 (suc)s 242.999 (h)s 252.993 (h)s 258.772 (yp)s 270.939 (erextension)s 328.778 (could)s 358.239 (b)s 364.626 (e)s 373.404 (designed)s 418.134 (in)s 426.954 (to)s 440.598 (a)s 449.984 (lo)s 458.197 (w-)s 270.232 y 27.375 (energy)s 62.385 (con)s 78.506 (troller.)s 299.427 y 13.383 (5.)s 11 f 27.375 (Ground)s 75.343 (release)s 118.028 (of)s 133.77 (the)s 157.032 (new)s 184.492 (swing)s 220.941 (leg.)s 8 f 248.524 (As)s 265.924 (a)s 276.266 (leg)s 294.518 (switc)s 318.608 (hes)s 338.744 (from)s 365.847 (stance)s 400.584 (to)s 415.185 (swing,)s 450.226 (it)s 462.394 (is)s 321.188 y 27.375 (released)s 69.919 (from)s 96.889 (the)s 116.833 (ground.)s 161.487 (W)s 171.828 (e)s 181.431 (assume)s 220.355 (that)s 245.165 (it)s 257.201 (do)s 269.064 (es)s 282.985 (not)s 303.537 (p)s 309.925 (enetrate)s 353.624 (the)s 373.568 (ground,)s 415.106 (but)s 436.266 (ground)s 342.948 y 27.375 (p)s 33.763 (enetration)s 86.11 (could)s 115.31 (also)s 137.271 (b)s 143.658 (e)s 152.175 (a)s 157.346 (v)s 162.821 (oided)s 192.021 (b)s 197.8 (y)s 207.229 (a)s 216.354 (lo)s 224.566 (w-energy)s 271.134 (con)s 287.255 (troller.)s 12 f 379.933 y 0 (3.3)s 30.75 (Measures)s 90.601 (Of)s 109.365 (P)s 118.213 (erformance)s 8 f 408.764 y 0 (The)s 22.508 (p)s 28.896 (erformance)s 85.228 (issues)s 115.827 (of)s 128.298 (in)s 137.118 (terest)s 167.626 (here)s 191.382 (are)s 209.662 (energetic)s 255.926 (cost)s 278.495 (and)s 299.787 (sp)s 310.494 (eed.)s 11 f 445.109 y 0 (3.3.1)s 38.477 (Slop)s 62.612 (e)s 72.581 (And)s 100.291 (Sp)s 114.632 (eci\257c)s 146.288 (Cost)s 175.74 (Of)s 193.245 (T)s 200.955 (ransp)s 231.571 (ort)s 8 f 473.941 y 0 (Since)s 30.157 (mo)s 44.453 (ving)s 70.048 (sidew)s 95.963 (a)s 101.134 (ys)s 116.448 (in)s 130.788 (a)s 141.479 (gra)s 156.413 (vitational)s 207.558 (\257eld)s 232.849 (is)s 245.425 (w)s 253.029 (orkless,)s 293.768 (a)s 304.458 (rational)s 346.813 (dimensionless)s 416.694 (measure)s 460.934 (of)s 495.701 y 0 (energetic)s 47.591 (e\261ciency)s 96.065 (is)s 108.403 (somewhat)s 160.891 (problematic)s 222.474 (for)s 240.561 (transp)s 271.373 (ort)s 290.373 (or)s 305.114 (lo)s 313.935 (comotion)s 362.712 (on)s 379.248 (lev)s 392.631 (el)s 405.517 (ground.)s 450.897 (The)s 517.461 y 0 (most)s 26.828 (reasonable)s 80.452 (measure)s 123.127 (of)s 135.598 (e\261ciency)s 538.12 y 141.909 (\050fundamen)s 193.009 (tal)s 209.434 (minim)s 239.546 (um)s 258.405 (energetic)s 304.669 (cost\051)s 185.937 .438 141.909 543.009 r 553.039 y 204.735 (\050actual)s 241.843 (cost\051)s 545.528 y 455.763 (\0501\051)s 573.595 y 0 (is)s 10.428 (zero)s 32.993 (for)s 49.17 (all)s 63.795 (but)s 83.288 (the)s 101.564 (most)s 127.809 (ideal)s 153.384 (mac)s 172.547 (hines,)s 203.167 (for)s 219.344 (whic)s 240.94 (h)s 250.09 (it)s 260.458 (is)s 270.886 (unde\257ned)s 320.187 (\0500)s 13 f 329.92 (=)s 8 f 335.395 (0\051.)s 352.843 (The)s 374.768 (common)s 417.986 (dimension-)s 595.355 y 0 (less)s 19.664 (measure)s 61.807 (of)s 73.745 (\050in\051e\261ciency)s 138 (for)s 154.228 (lo)s 163.049 (comotion)s 209.966 (is,)s 223.593 (ho)s 234.847 (w)s 242.451 (ev)s 252.793 (er,)s 268.214 (the)s 286.54 (\134sp)s 302.722 (eci\257c)s 329.565 (cost)s 351.601 (of)s 363.54 (transp)s 394.352 (ort\042)s 416.967 (or)s 429.848 (\134sp)s 446.03 (eci\257c)s 617.115 y 0 (resistance\042)s 13 f 645.181 y 131.482 (\264)s 8 f 140.354 (=)s 637.774 y 153.112 (\050mec)s 175.925 (hanical)s 213.641 (energy)s 248.651 (cost)s 271.22 (for)s 287.98 (transp)s 318.792 (ort\051)s 183.96 .438 153.112 642.663 r 652.692 y 171.286 (\050w)s 183.149 (eigh)s 202.311 (t\051)s 14 f 214.478 (\243)s 8 f 226.645 (\050distance)s 273.547 (tra)s 287.265 (v)s 292.74 (elled\051)s 645.181 y 455.763 (\0502\051)s 685.43 y 232.14 (7)s end endp %%Page: 8 8 %%BeginPageSetup initializepage (T&AM; page: 8 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f5_12 sf ( )S 6 0 :M f3_12 sf ( )S 10 0 :M f6_12 sf ( )S 18 0 :M f9_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 10 10.95 /CMTI10 findfont fdef 11 10.95 /CMBX10 findfont fdef 13 10.95 /CMMI10 findfont fdef 14 10.95 /CMSY10 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 0 (where)s 32.274 (the)s 51.742 (energy)s 87.362 (cost)s 110.541 (is)s 122.162 (also)s 144.733 (the)s 164.202 (energy)s 199.821 (dissipated.)s 257.131 (F)s 263.367 (or)s 277.391 (steady)s 312.433 (w)s 320.037 (alking)s 353.193 (motions,)s 398.424 (this)s 420.387 (reduces)s 460.022 (to)s 37.76 y 0 (\050McGeer)s 45.427 (\0501993\051\051)s 13 f 70.52 y 147.831 (\264)s 8 f 156.703 (=)s 63.112 y 178.358 (\050energy)s 217.626 (dissipated)s 268.848 (p)s 275.235 (er)s 288.041 (step\051)s 151.262 .438 169.461 68.002 r 78.031 y 169.461 (\050w)s 181.324 (alk)s 195.315 (er)s 208.121 (w)s 215.725 (eigh)s 234.888 (t\051)s 14 f 247.054 (\243)s 8 f 259.221 (\050step)s 286.657 (length\051)s 70.52 y 455.763 (\0503\051)s 103.28 y 0 (In)s 14.541 (the)s 34.254 (case)s 58.285 (of)s 71.61 (gra)s 86.544 (vitationally-p)s 151.332 (o)s 156.503 (w)s 164.107 (ered)s 188.716 (w)s 196.321 (alking,)s 232.976 (the)s 252.688 (energy)s 288.551 (dissipated)s 340.627 (is)s 352.492 (\050w)s 364.354 (eigh)s 383.517 (t\051)s 14 f 396.537 (\243)s 8 f 409.558 (\050heigh)s 439.062 (t)s 447.825 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116.106 (normal)s 153.244 (to)s 166.628 (the)s 185.486 (slop)s 204.709 (e)s 213.226 (as)s 226.67 (in)s 239.445 (\257gure)s 269.892 (4.)s 283.276 (See)s 302.742 (also)s 324.703 (Chatterjee)s 378.571 (and)s 399.863 (Garcia)s 435.253 (\0501998\051.)s 430.956 y 17 (Under)s 51.584 (the)s 71.842 (presumably)s 132.037 (reasonable)s 187.061 (assumption)s 246.373 (that)s 271.498 (no)s 288.105 (impulse)s 329.716 (from)s 357 (the)s 377.257 (ground)s 415.795 (acts)s 439.764 (at)s 454.547 (the)s 452.716 y 0 (trailing)s 38.355 (fo)s 47.48 (ot,)s 63.906 (the)s 82.764 (kinetic)s 118.351 (energy)s 153.361 (lost)s 174.105 (in)s 186.88 (the)s 205.739 (collision)s 247.774 (is)s 258.785 (equal)s 287.681 (to)s 301.064 (the)s 319.923 (pro)s 336.074 (duct)s 483.935 y 171.915 (1)s 5.475 .438 171.915 488.824 r 498.854 y 171.915 (2)s 17 f 479.188 y 180.415 (h)s 8 f 492.957 y 187.499 (\137)s 13 f 185.586 (x)s 8 f 199.896 (\137)s 13 f 197.928 (y)s 17 f 479.188 y 203.689 (i)s 469.333 y 210.685 (2)s 489.043 y 210.685 (4)s 13 f 482.077 y 217.985 (M)s 15 f 483.719 y 228.608 (11)s 13 f 482.077 y 247.608 (M)s 15 f 483.719 y 258.231 (12)s 13 f 503.837 y 217.985 (M)s 15 f 505.479 y 228.608 (21)s 13 f 503.837 y 247.608 (M)s 15 f 505.479 y 258.231 (22)s 17 f 469.333 y 267.231 (3)s 489.043 y 267.231 (5)s 514.679 y 210.685 (\174)s 22.068 1.314 215.613 514.679 r 514.679 y 237.681 (\173z)s 22.068 1.314 247.536 514.679 r 514.679 y 269.604 (\175)s 18 f 524.993 y 237.972 (M)s 17 f 469.333 y 276.356 (2)s 489.043 y 276.356 (4)s 8 f 482.077 y 285.569 (\137)s 13 f 283.656 (x)s 8 f 503.837 y 285.873 (\137)s 13 f 283.905 (y)s 17 f 469.333 y 289.915 (3)s 489.043 y 289.915 (5)s 8 f 491.342 y 455.763 (\0507\051)s 545.692 y 0 (where)s 11 f 30.983 (M)s 8 f 45.906 (is)s 56.236 (a)s 64.681 (2)s 14 f 73.125 (\243)s 8 f 84.612 (2,)s 96.234 (symmetric,)s 152.052 (p)s 158.439 (ositiv)s 184.05 (e)s 191.886 (semi-de\257nite)s 255.142 (matrix)s 290.079 (that)s 313.124 (dep)s 330.461 (ends)s 354.783 (on)s 369.311 (the)s 387.489 (mass)s 413.697 (distribution)s 567.452 y 0 (and)s 21.45 (geometry)s 69.392 (of)s 82.021 (the)s 101.037 (w)s 108.641 (alk)s 122.633 (er.)s 11 f 140.17 (M)s 8 f 155.932 (is)s 167.101 (also)s 189.219 (con\257guration)s 255.716 (dep)s 273.054 (enden)s 300.733 (t,)s 311.88 (i.e.,)s 332.761 (it)s 343.869 (dep)s 361.206 (ends)s 386.367 (on)s 13 f 401.733 (\265)s 19 f 563.478 y 407.178 (\244)s 16 f 570.159 y 406.873 (st)s 8 f 567.452 y 414.373 (.)s 422.755 (W)s 433.097 (e)s 441.772 (de\257ne)s 11 f 589.212 y 0 (M)s 8 f 11.954 (\0500\051)s 30.105 (as)s 11 f 44.059 (M)s 8 f 60.172 (in)s 73.457 (the)s 92.825 (limit)s 119.493 (as)s 13 f 133.447 (\265)s 19 f 585.239 y 138.891 (\244)s 16 f 591.919 y 138.587 (st)s 14 f 589.212 y 149.978 (!)s 8 f 164.819 (0.)s 179.732 (F)s 185.967 (or)s 199.891 (the)s 219.259 (discussion)s 271.051 (that)s 295.286 (follo)s 315.361 (ws,)s 334.917 (w)s 342.521 (e)s 351.547 (need)s 377.607 (not)s 397.583 (discuss)s 434.776 (explicit)s 610.972 y 0 (\050and)s 25.759 (complicated\051)s 91.059 (represen)s 130.418 (tation)s 162.868 (of)s 11 f 175.548 (M)s 8 f 191.36 (in)s 204.343 (terms)s 235.06 (of)s 247.739 (the)s 266.806 (mass)s 293.903 (distribution)s 353.82 (and)s 375.32 (con\257guration)s 441.867 (of)s 454.547 (the)s 632.732 y 0 (link)s 17.338 (age.)s 40.849 (The)s 62.716 (only)s 86.105 (exception)s 134.435 (is)s 144.805 (for)s 160.923 (a)s 169.407 (simple)s 202.894 (\257rst-order)s 253.505 (appro)s 280.606 (ximation)s 325.895 (of)s 11 f 337.725 (M)s 8 f 352.687 (in)s 364.821 (subsection)s 417.227 (6.3.2;)s 445.999 (more)s 654.492 y 0 (discussion)s 51.283 (is)s 62.293 (found)s 93.014 (in)s 105.789 (a)s 114.914 (companion)s 170.273 (pap)s 188.219 (er)s 201.024 (b)s 206.803 (y)s 216.232 (Chatterjee)s 270.1 (and)s 291.392 (Garcia)s 326.782 (\0501998\051.)s 685.43 y 232.14 (9)s end endp %%Page: 10 10 %%BeginPageSetup initializepage (T&AM; page: 10 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f8_12 sf ( )S 7 0 :M f5_12 sf ( )S 10 0 :M f3_12 sf ( )S 14 0 :M f6_12 sf ( )S 22 0 :M f9_12 sf ( )S 34 0 :M f10_12 sf ( )S f11_12 sf ( )S 46 0 :M f14_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 9 14.4 /CMBX12 findfont fdef 10 10.95 /CMTI10 findfont fdef 11 10.95 /CMBX10 findfont fdef 13 10.95 /CMMI10 findfont fdef 14 10.95 /CMSY10 findfont fdef 15 8 /CMR8 findfont fdef 16 8 /CMMI8 findfont fdef 19 8 /CMSY8 findfont fdef 41 41 translate 72 72.27 div dup scale 9 f 16 y 0 (4)s 24.3 (The)s 57.358 (Simplest)s 123.34 (W)s 138.723 (alking)s 186.648 (Mo)s 210.565 (del)s 8 f 48.604 y 0 (An)s 18.236 (extreme)s 60.227 (simpli\257cation)s 128.103 (of)s 140.864 (a)s 150.279 (straigh)s 182.916 (t-legged)s 224.573 (w)s 232.177 (alk)s 246.169 (er)s 259.265 (is)s 270.566 (the)s 289.714 (\134minimal)s 338.062 (bip)s 353.575 (ed\042)s 373.94 (of)s 386.701 (Alexander)s 439.338 (\0501995\051)s 70.364 y 0 (\050a)s 14.647 (hip-mass)s 61.658 (on)s 78.13 (massless)s 122.829 (legs\051,)s 153.061 (made)s 183.525 (deterministic)s 250.58 (b)s 256.359 (y)s 267.052 (the)s 287.174 (addition)s 331.63 (of)s 345.364 (in\257nitesimal)s 408.739 (p)s 415.127 (oin)s 429.422 (t-masses)s 92.124 y 0 (at)s 14.004 (the)s 33.482 (feet.)s 60.589 (This)s 86.212 (\134simplest)s 135.012 (w)s 142.616 (alk)s 156.608 (er\042)s 175.509 (w)s 183.113 (as)s 197.178 (studied)s 236.184 (in)s 249.579 (some)s 277.635 (detail)s 308.672 (in)s 322.068 (Garcia)s 358.078 (et)s 371.473 (al.)s 387.302 (\0501998\051)s 421.989 (with)s 447.551 (b)s 453.938 (oth)s 113.884 y 0 (p)s 6.388 (erturbation)s 65.187 (metho)s 95.3 (ds)s 110.3 (and)s 132.539 (n)s 138.318 (umerical)s 183.704 (sim)s 199.885 (ulation.)s 244.094 (The)s 267.549 (k)s 273.024 (ey)s 288.267 (results)s 324.042 (of)s 337.46 (that)s 362.132 (study)s 393.253 (are)s 412.48 (summarized)s 135.644 y 0 (b)s 6.388 (elo)s 19.467 (w.)s 157.404 y 17 (The)s 40.816 (simplest)s 84.83 (p)s 91.217 (oin)s 105.513 (t-fo)s 122.546 (ot)s 137.238 (mo)s 152.142 (del)s 171.092 (has)s 191.927 (t)s 195.882 (w)s 203.486 (o)s 213.919 (gaits)s 241.446 (\050t)s 249.659 (w)s 257.263 (o)s 267.696 (\257xed)s 295.466 (p)s 301.854 (oin)s 316.15 (ts\051)s 333.944 (at)s 348.635 (arbitrarily)s 402.656 (small)s 432.616 (ground-)s 179.164 y 0 (slop)s 19.223 (es.)s 37.028 (Of)s 52.777 (these,)s 84.159 (the)s 103.254 (long-step)s 150.393 (gait)s 172.53 (is)s 183.778 (stable)s 215.709 (at)s 229.329 (su\261cien)s 267.411 (tly)s 284.377 (small)s 313.266 (ground-slop)s 369.628 (es)s 382.701 (\050)s 13 f 386.959 (\260)s 396.673 (\074)s 8 f 408.626 (0)s 13 f 414.101 (:)s 8 f 417.142 (015\051,)s 444.813 (while)s 200.924 y 0 (the)s 19.74 (short-step)s 71.873 (gait)s 94.654 (is)s 106.546 (unstable)s 151.288 (at)s 165.553 (all)s 181.642 (ground-slop)s 238.005 (es.)s 257.742 (\050In)s 276.569 (Garcia)s 312.84 (et)s 326.497 (al.)s 342.586 (\0501998\051)s 377.534 (these)s 406.46 (t)s 410.414 (w)s 418.018 (o)s 428.024 (gaits)s 455.124 (are)s 222.684 y 0 (called)s 32.028 (the)s 51.889 (\134long-p)s 87.477 (erio)s 105.453 (d\042)s 121.665 (and)s 143.959 (\134short-p)s 183.896 (erio)s 201.873 (d\042)s 218.084 (gaits,)s 248.599 (p)s 254.986 (ossibly)s 291.698 (incorrectly)s 347.208 (in)s 356.029 (timating)s 401.44 (that)s 426.169 (the)s 446.03 (long-)s 244.444 y 0 (p)s 6.388 (erio)s 24.364 (d)s 34.785 (gait)s 57.372 (is)s 69.07 (generally)s 116.326 (slo)s 128.857 (w)s 136.462 (er)s 149.954 (than)s 176.192 (the)s 195.738 (short-p)s 230.2 (erio)s 248.176 (d)s 258.597 (gait.\051)s 291.076 (As)s 13 f 307.945 (\260)s 14 f 318.41 (!)s 8 f 333.547 (0,)s 346.573 (the)s 366.119 (long-step)s 413.709 (gait)s 436.297 (motion)s 266.204 y 0 (approac)s 37.443 (hes)s 57.691 (a)s 68.146 (symmetric)s 122.796 (motion)s 161.233 (that)s 186.288 (has)s 207.145 (normal)s 245.613 (heelstrik)s 285.854 (e)s 295.7 (collisions)s 343.384 (\050)s 349.555 (\137)s 13 f 347.643 (x)s 8 f 359.158 (=)s 372.932 (0)s 383.386 (in)s 397.491 (\257gure)s 429.267 (4\051.)s 450.897 (The)s 287.965 y 0 (short-step)s 51.265 (solution)s 92.706 (do)s 104.568 (es)s 117.417 (not)s 136.897 (ha)s 148.151 (v)s 153.626 (e)s 162.156 (this)s 183.521 (symmetry)s 234.725 (and)s 256.03 (the)s 274.901 (\050quasi-massless\051)s 355.215 (fo)s 364.34 (ot)s 377.736 (has)s 397.276 (a)s 406.414 (collision)s 448.463 (with)s 309.725 y 0 (a)s 9.125 (non-zero)s 53.564 (tangen)s 85.501 (tial)s 104.968 (comp)s 130.822 (onen)s 153.026 (t)s 160.935 (at)s 174.318 (heelstrik)s 214.559 (e.)s 331.485 y 17 (F)s 23.235 (or)s 36.157 (this)s 57.017 (w)s 64.621 (alk)s 78.613 (er,)s 94.066 (b)s 100.454 (oth)s 119.428 (gait)s 140.836 (cycles)s 171.734 (w)s 179.338 (ere)s 196.518 (found)s 226.747 (to)s 239.638 (ha)s 250.892 (v)s 256.367 (e)s 264.392 (stance)s 297.419 (angle)s 13 f 325.518 (\265)s 16 f 333.127 y 330.658 (st)s 8 f 331.485 y 341.316 (or)s 354.238 (step-length)s 410.382 (prop)s 432.616 (ortional)s 353.245 y 0 (to)s 13 f 13.343 (\260)s 15 f 349.271 y 19.621 (1)s 16 f 23.871 (=)s 15 f 28.121 (3)s 8 f 353.245 y 36.481 (at)s 49.825 (small)s 78.437 (ground-slop)s 134.8 (es)s 147.595 (\050see)s 169.516 (curv)s 190.23 (es)s 203.026 (D)s 215.001 (in)s 227.736 (\257gure)s 258.143 (9\051,)s 274.536 (while)s 303.088 (the)s 321.907 (step)s 345.044 (p)s 351.432 (erio)s 369.408 (ds)s 383.421 (tend)s 408.323 (to)s 421.666 (\050di\256eren)s 461.238 (t\051)s 375.005 y 0 (nonzero)s 42.186 (constan)s 78.443 (ts)s 92.067 (as)s 106.909 (the)s 127.165 (step)s 151.739 (length)s 186.595 (go)s 197.849 (es)s 212.082 (to)s 226.863 (zero.)s 258.46 (This)s 284.86 (implies)s 323.426 (a)s 333.948 (w)s 341.553 (alking)s 375.496 (p)s 381.883 (o)s 387.054 (w)s 394.658 (er)s 408.861 (consumption)s 396.765 y 0 (prop)s 22.235 (ortional)s 63.023 (to)s 76.407 (the)s 95.265 (fourth)s 128.45 (p)s 134.837 (o)s 140.008 (w)s 147.612 (er)s 160.418 (of)s 172.889 (sp)s 183.595 (eed)s 203.062 (\050for)s 224.08 (lo)s 232.292 (w)s 243.851 (sp)s 254.557 (eeds\051,)s 285.643 (for)s 10 f 302.403 (b)s 306.88 (oth)s 8 f 325.361 (gaits:)s 428.177 y 176.162 (P)s 183.31 (o)s 188.481 (w)s 196.085 (er)s 14 f 208.282 (/)s 13 f 219.84 (mv)s 15 f 423.656 y 235.155 (4)s 13 f 428.177 y 239.905 (g)s 19 f 423.656 y 245.521 (\241)s 15 f 252.132 (1)s 16 f 256.382 (=)s 15 f 260.632 (2)s 13 f 428.177 y 265.382 (l)s 19 f 423.656 y 268.865 (\241)s 15 f 275.476 (3)s 16 f 279.726 (=)s 15 f 283.976 (2)s 13 f 428.177 y 288.726 (;)s 8 f 455.763 (\0508\051)s 459.589 y 0 (where)s 13 f 31.715 (m)s 8 f 45.03 (is)s 56.092 (the)s 75.002 (w)s 82.606 (alk)s 96.598 (er)s 109.454 (mass,)s 13 f 139.448 (v)s 8 f 148.85 (is)s 159.912 (the)s 178.822 (a)s 183.992 (v)s 189.467 (erage)s 218.141 (w)s 225.745 (alking)s 258.342 (v)s 263.817 (elo)s 277.504 (cit)s 289.367 (y)s 294.234 (,)s 13 f 300.989 (g)s 8 f 310.306 (is)s 321.368 (the)s 340.278 (gra)s 355.212 (vitational)s 404.843 (constan)s 441.099 (t,)s 452.113 (and)s 13 f 481.349 y 0 (l)s 8 f 8.136 (is)s 20.149 (the)s 40.01 (w)s 47.615 (alk)s 61.606 (er\047s)s 82.775 (leg)s 100.811 (length.)s 141.537 (Equation)s 189.837 (8)s 199.965 (mak)s 220.04 (es)s 233.879 (the)s 253.74 (unin)s 274.728 (tuitiv)s 300.886 (e)s 310.406 (prediction)s 363.147 (that)s 387.875 (cost)s 411.447 (of)s 424.921 (transp)s 455.733 (ort)s 503.109 y 0 (increases)s 45.777 (with)s 70.719 (decreasing)s 123.735 (gra)s 138.67 (vit)s 151.445 (y)s 160.874 (and)s 182.166 (leg)s 199.199 (length.)s 524.869 y 17 (This)s 42.831 (scaling)s 79.612 (also)s 102.401 (follo)s 122.476 (ws)s 139.182 (from)s 165.895 (the)s 185.582 (energy)s 221.42 (balance)s 261.79 (b)s 268.178 (et)s 276.999 (w)s 284.603 (een)s 304.898 (collision)s 347.762 (losses)s 378.582 (and)s 400.702 (used-up)s 442.349 (gra)s 457.284 (vi-)s 546.63 y 0 (tational)s 41.003 (p)s 47.39 (oten)s 67.769 (tial)s 87.48 (energy)s 117.927 (,)s 124.924 (rather)s 158.079 (lik)s 169.638 (e)s 178.399 (for)s 195.403 (the)s 214.505 (rimless)s 251.402 (wheel)s 282.062 (describ)s 315.916 (ed)s 330.761 (b)s 336.54 (y)s 346.213 (McGeer)s 387.626 (\0501990a\051.)s 432.159 (F)s 438.395 (or)s 452.053 (this)s 568.39 y 0 (sp)s 10.707 (ecial)s 35.82 (case,)s 11 f 62.253 (M)s 8 f 74.207 (\0500\051)s 92.02 (of)s 104.662 (equation)s 149.546 (9)s 158.843 (is)s 170.025 (singular,)s 214.739 (and)s 236.202 (the)s 255.232 (only)s 279.432 (energy)s 314.613 (dissipation)s 369.656 (term)s 396.017 (comes)s 428.491 (from)s 454.547 (the)s 590.15 y 1.968 (\137)s 13 f 0 (y)s 8 f 9.567 (or)s 23.137 (normal)s 60.432 (comp)s 86.286 (onen)s 108.49 (t)s 116.554 (of)s 129.181 (the)s 148.196 (fo)s 157.321 (ot)s 170.86 (v)s 176.335 (elo)s 190.022 (cit)s 201.885 (y)s 211.47 (at)s 225.009 (heelstrik)s 265.251 (e,)s 277.004 (for)s 293.919 (b)s 300.307 (oth)s 319.93 (gaits.)s 350.875 (As)s 367.213 (explained)s 416.339 (partially)s 460.63 (in)s 611.91 y 0 (Alexander)s 53.088 (\0501980\051)s 87.896 (and)s 109.928 (for)s 127.429 (this)s 149.522 (mo)s 164.427 (del)s 182.809 (in)s 196.325 (Garcia)s 232.456 (et)s 245.972 (al.)s 261.921 (\0501998\051,)s 299.956 (the)s 319.555 (normal)s 357.435 (v)s 362.91 (elo)s 376.597 (cit)s 388.46 (y)s 398.63 (is)s 410.382 (prop)s 432.616 (ortional)s 633.67 y 0 (to)s 13.807 (b)s 20.194 (oth)s 40.084 (stance)s 74.026 (angle)s 103.041 (and)s 124.756 (stance)s 158.698 (angle)s 187.713 (rate.)s 215.78 (Since)s 244.795 (for)s 261.977 (small)s 291.053 (motions,)s 336.051 (the)s 355.333 (p)s 361.72 (erio)s 379.696 (d)s 389.853 (is)s 401.287 (appro)s 428.388 (ximately)s 655.43 y 0 (indep)s 26.463 (enden)s 54.142 (t)s 62.182 (of)s 74.785 (amplitude)s 126.626 (and)s 148.05 (the)s 167.041 (sp)s 177.748 (eeds)s 201.666 (are)s 220.078 (prop)s 242.313 (ortional)s 283.234 (to)s 296.75 (amplitude,)s 351.665 (the)s 370.656 (kinetic)s 406.376 (energy)s 441.518 (lost)s 462.394 (is)s 685.43 y 229.402 (10)s end endp %%Page: 11 11 %%BeginPageSetup initializepage (T&AM; page: 11 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f8_12 sf ( )S 7 0 :M ( )S 11 0 :M f6_12 sf ( )S 19 0 :M f9_12 sf ( )S 31 0 :M f10_12 sf ( )S f11_12 sf ( )S 43 0 :M f15_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 9 14.4 /CMBX12 findfont fdef 12 12 /CMBX12 findfont fdef 13 10.95 /CMMI10 findfont fdef 14 10.95 /CMSY10 findfont fdef 15 8 /CMR8 findfont fdef 16 8 /CMMI8 findfont fdef 21 9.144 /MSAM7 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 0 (prop)s 22.235 (ortional)s 63.494 (to)s 77.348 (the)s 96.676 (fourth)s 130.331 (p)s 136.719 (o)s 141.89 (w)s 149.494 (er)s 162.77 (of)s 175.711 (step)s 199.359 (amplitude.)s 256.737 (The)s 279.716 (gra)s 294.65 (vitational)s 344.7 (p)s 351.087 (o)s 356.258 (w)s 363.862 (er)s 377.138 (a)s 382.309 (v)s 387.48 (ailable)s 422.625 (is)s 434.107 (prop)s 456.341 (or-)s 37.76 y 0 (tional)s 30.874 (to)s 44.107 (step)s 67.134 (amplitude)s 118.691 (and)s 139.832 (ground-slop)s 196.194 (e.)s 208.919 (Th)s 222.607 (us,)s 239.58 (\050step)s 266.865 (amplitude\051)s 15 f 33.786 y 319.182 (4)s 14 f 37.76 y 326.974 (/)s 8 f 338.99 (\050step)s 366.275 (amplitude\051)s 14 f 422.091 (\243)s 8 f 434.107 (\050slop)s 457.588 (e\051,)s 59.52 y 0 (and)s 21.292 (so)s 34.736 (\050step)s 62.172 (amplitude\051)s 14 f 118.138 (/)s 8 f 130.305 (\050slop)s 153.787 (e\051)s 15 f 55.547 y 162.912 (1)s 16 f 167.162 (=)s 15 f 171.412 (3)s 8 f 59.52 y 176.162 (.)s 81.28 y 17 (Bet)s 33.577 (w)s 41.181 (een)s 60.686 (ground-slop)s 117.048 (es)s 129.922 (of)s 13 f 142.431 (\260)s 14 f 151.813 (\274)s 13 f 163.435 (:)s 8 f 166.477 (015)s 186.59 (to)s 13 f 200.011 (\260)s 14 f 209.393 (\274)s 13 f 221.015 (:)s 8 f 224.057 (019)s 244.17 (a)s 253.333 (p)s 259.72 (erio)s 277.696 (d-doubling)s 332.485 (route)s 361.145 (to)s 374.566 (c)s 379.128 (haos)s 404.169 (w)s 411.773 (as)s 425.255 (observ)s 455.763 (ed.)s 103.04 y 0 (Aside)s 29.652 (from)s 55.015 (the)s 73.351 (p)s 79.739 (erio)s 97.715 (d)s 106.927 (doubling)s 151.422 (route)s 179.522 (to)s 192.384 (c)s 196.946 (haos,)s 224.573 (no)s 239.259 (other)s 267.36 (non)s 288.13 (p)s 294.517 (erio)s 312.494 (d-one)s 341.78 (gaits)s 367.478 (w)s 375.082 (ere)s 392.232 (sough)s 419.364 (t)s 426.75 (or)s 439.642 (found.)s 124.8 y 0 (Recen)s 28.44 (tly)s 40.606 (,)s 47.119 (Ho)s 60.502 (w)s 68.107 (ell)s 82.483 (and)s 103.551 (Baillieul)s 146.368 (\0501998\051)s 180.211 (disco)s 203.692 (v)s 209.167 (ered)s 232.699 (a)s 241.601 (stable)s 273.072 (p)s 279.459 (erio)s 297.435 (d-three)s 334.959 (gait)s 356.636 (at)s 369.795 (a)s 378.697 (slop)s 397.92 (e)s 406.214 (of)s 13 f 418.461 (\260)s 14 f 427.78 (\274)s 8 f 439.338 (0)s 13 f 444.813 (:)s 8 f 447.855 (0125)s 146.561 y 0 (and)s 21.292 (subsequen)s 69.472 (t)s 77.38 (p)s 83.768 (erio)s 101.744 (d-doublings)s 160.813 (\050p)s 171.459 (erio)s 189.435 (d-six,)s 219 (p)s 225.388 (erio)s 243.364 (d-t)s 257.052 (w)s 264.656 (elv)s 278.039 (e,)s 289.597 (etc.\051)s 315.756 (for)s 332.515 (this)s 353.868 (mo)s 368.772 (del.)s 168.321 y 17 (In)s 30.922 (the)s 50.015 (rest)s 71.633 (of)s 84.338 (this)s 105.925 (pap)s 123.871 (er)s 136.911 (w)s 144.516 (e)s 153.267 (describ)s 187.121 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(hip.)s 25.632 (When)s 58.407 (the)s 78.104 (feet)s 99.93 (ha)s 111.184 (v)s 116.659 (e)s 126.014 (\257nite)s 154.836 (mass,)s 185.814 (ho)s 197.068 (w)s 204.672 (ev)s 215.014 (er,)s 231.909 (the)s 251.605 (fo)s 260.73 (ot)s 274.952 (masses)s 311.864 (also)s 334.664 (lose)s 356.854 (energy)s 392.702 (at)s 406.924 (heelstrik)s 447.165 (e.)s 462.455 (If)s 197.153 y 0 (the)s 19.327 (striking)s 59.734 (fo)s 68.859 (ot)s 82.711 (hits)s 104.532 (the)s 123.86 (ground)s 161.468 (with)s 186.878 (no)s 202.556 (tangen)s 234.493 (tial)s 254.429 (v)s 259.904 (elo)s 273.591 (cit)s 285.454 (y)s 290.321 (,)s 297.598 (the)s 316.926 (loss)s 338.2 (scales)s 369.207 (as)s 383.12 (step)s 406.767 (length)s 440.694 (to)s 454.547 (the)s 218.913 y 0 (fourth)s 32.439 (p)s 38.827 (o)s 43.997 (w)s 51.601 (er,)s 66.852 (giving)s 98.652 (a)s 107.032 (step)s 129.464 (length)s 162.176 (prop)s 184.411 (ortional)s 224.454 (to)s 13 f 237.092 (\260)s 15 f 214.939 y 243.369 (1)s 16 f 247.619 (=)s 15 f 251.869 (3)s 8 f 218.913 y 256.619 (.)s 264.279 (With)s 291.821 (non-negligible-fo)s 370.905 (ot-mass,)s 413.621 (a)s 422.001 (tangen)s 453.938 (tial)s 240.673 y 0 (v)s 5.475 (elo)s 19.163 (cit)s 31.025 (y)s 40.454 (comp)s 66.308 (onen)s 88.513 (t)s 96.421 (at)s 109.804 (heelstrik)s 150.046 (e)s 158.562 (can)s 178.637 (c)s 183.2 (hange)s 214.833 (the)s 233.691 (energy-loss)s 289.506 (scaling.)s 262.433 y 17 (This)s 41.655 (is)s 52.319 (demonstrated)s 120.804 (in)s 133.232 (\257gure)s 163.332 (5,)s 175.22 (whic)s 196.816 (h)s 206.202 (sho)s 221.775 (ws)s 237.305 (stance)s 270.477 (angle)s 298.722 (as)s 311.818 (a)s 320.596 (function)s 363.136 (of)s 13 f 375.26 (\260)s 8 f 384.84 (for)s 401.252 (t)s 405.206 (w)s 412.81 (o)s 421.588 (w)s 429.192 (alk)s 443.184 (ers)s 459.961 (as)s 284.193 y 0 (describ)s 33.854 (ed)s 47.91 (ab)s 59.772 (o)s 64.943 (v)s 70.418 (e.)s 83.012 (F)s 89.247 (or)s 102.117 (the)s 120.431 (long-step)s 166.79 (solution,)s 210.824 (the)s 229.138 (stance)s 262.113 (angle)s 290.161 (remains)s 330.466 (prop)s 352.701 (ortional)s 392.946 (to)s 405.785 (the)s 424.099 (cub)s 441.437 (e-ro)s 460.022 (ot)s 305.953 y 0 (of)s 13.658 (the)s 33.703 (ground-slop)s 90.065 (e.)s 106.4 (Unlik)s 132.254 (e)s 141.957 (the)s 162.002 (simplest)s 205.894 (w)s 213.498 (alk)s 227.49 (er,)s 244.82 (the)s 264.865 (stance)s 299.571 (angle)s 329.35 (for)s 347.296 (the)s 367.341 (short-step)s 419.78 (solution)s 462.394 (is)s 327.713 y 0 (linearly)s 38.758 (prop)s 60.993 (ortional)s 101.271 (to)s 13 f 114.145 (\260)s 8 f 123.562 (at)s 136.435 (v)s 141.91 (ery)s 159.985 (small)s 188.127 (ground-slop)s 244.49 (es,)s 259.959 (and)s 280.741 (prop)s 302.975 (ortional)s 343.254 (to)s 13 f 356.127 (\260)s 15 f 323.739 y 362.405 (1)s 16 f 366.655 (=)s 15 f 370.905 (3)s 8 f 327.713 y 378.795 (at)s 391.668 (somewhat)s 442.319 (larger)s 349.473 y 0 (slop)s 19.223 (es.)s 36.369 (There)s 68.05 (is)s 79.078 (some)s 106.53 (transition)s 156.522 (region)s 189.42 (where)s 221.101 (the)s 239.976 (short-step)s 291.245 (scaling)s 327.215 (c)s 331.777 (hanges)s 367.747 (b)s 374.134 (et)s 382.955 (w)s 390.559 (een)s 410.043 (the)s 13 f 428.919 (\260)s 15 f 345.499 y 435.196 (1)s 16 f 439.446 (=)s 15 f 443.696 (3)s 8 f 349.473 y 452.113 (and)s 371.233 y 0 (the)s 13 f 19.161 (\260)s 8 f 29.391 (scaling.)s 70.509 (So)s 86.02 (for)s 103.082 (the)s 122.243 (long-step)s 169.448 (gait,)s 194.768 (whic)s 216.364 (h)s 226.4 (is)s 237.713 (stable,)s 272.827 (p)s 279.215 (o)s 284.386 (w)s 291.99 (er)s 14 f 305.098 (/)s 8 f 317.567 (\050sp)s 332.532 (eed\051)s 15 f 367.26 y 352.607 (4)s 8 f 371.233 y 357.357 (,)s 364.427 (while)s 393.321 (for)s 410.383 (the)s 429.544 (unstable)s 392.993 y 0 (short-step)s 51.262 (gait,)s 76.216 (p)s 82.604 (o)s 87.775 (w)s 95.379 (er)s 14 f 108.194 (/)s 8 f 120.371 (\050sp)s 135.336 (eed\051)s 15 f 389.02 y 155.411 (2)s 8 f 392.993 y 163.821 (b)s 170.208 (elo)s 183.287 (w)s 194.856 (the)s 213.724 (transition)s 263.708 (region)s 296.599 (and)s 14 f 317.901 (/)s 8 f 330.077 (\050sp)s 345.042 (eed\051)s 15 f 389.02 y 365.117 (4)s 8 f 392.993 y 373.527 (ab)s 385.39 (o)s 390.561 (v)s 396.036 (e)s 404.562 (the)s 423.43 (transition)s 414.753 y 0 (region.)s 11 f 451.836 y 0 (5.1.2)s 38.477 (The)s 64.202 (Short-Step)s 127.627 (T)s 135.338 (ransition)s 187.99 (Region)s 8 f 480.668 y 0 (The)s 22.061 (ground-slop)s 78.423 (e)s 86.492 (at)s 99.427 (the)s 117.838 (transition)s 167.364 (region)s 199.797 (is)s 210.36 (go)s 221.006 (v)s 226.481 (erned)s 255.872 (b)s 261.651 (y)s 270.632 (the)s 289.043 (ratio)s 314.784 (of)s 326.807 (the)s 345.217 (fo)s 354.342 (ot)s 367.278 (mass)s 393.718 (to)s 406.654 (the)s 425.064 (hip)s 443.475 (mass.)s 502.428 y 0 (If)s 10.903 (the)s 29.714 (fo)s 38.839 (ot)s 52.175 (mass)s 79.016 (is)s 13 f 89.98 (\275)s 8 f 99.244 (times)s 128.458 (the)s 147.269 (hip)s 166.08 (mass)s 192.922 (instead)s 230.652 (of)s 243.076 (b)s 249.463 (eing)s 272.533 (totally)s 307.465 (negligible,)s 359.136 (then)s 384.03 (w)s 391.634 (e)s 400.104 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9.319 (\074\074)s 29.394 (\275)s 15 f 563.734 y 35.055 (3)s 16 f 39.305 (=)s 15 f 43.556 (2)s 8 f 567.708 y 51.956 (\050see)s 73.916 (subsection)s 126.963 (6.3\051.)s 589.468 y 17 (Figure)s 51.022 (5)s 59.615 (sho)s 75.189 (ws)s 90.534 (t)s 94.489 (w)s 102.093 (o)s 110.686 (suc)s 125.651 (h)s 134.853 (transitions.)s 193.228 (W)s 203.569 (alk)s 217.561 (er)s 229.835 (E)s 240.405 (has)s 259.401 (a)s 267.994 (fo)s 277.119 (ot)s 289.971 (mass)s 316.328 (of)s 328.267 (0.1)s 345.377 (and)s 366.137 (a)s 374.731 (hip)s 393.057 (mass)s 419.414 (of)s 431.353 (0.8)s 448.463 (\050an)s 463.976 (y)s 611.228 y 0 (units\051)s 31.729 (and)s 53.056 (so)s 13 f 66.534 (\275)s 16 f 612.923 y 72.196 (E)s 8 f 611.228 y 82.473 (=)s 94.09 (0)s 13 f 99.565 (:)s 8 f 102.606 (125.)s 127.044 (W)s 137.386 (alk)s 151.377 (er)s 164.218 (F)s 175.05 (has)s 194.613 (a)s 203.772 (fo)s 212.897 (ot)s 226.316 (mass)s 253.239 (of)s 265.744 (0.05)s 288.896 (and)s 310.222 (a)s 319.382 (hip)s 338.275 (mass)s 365.199 (of)s 377.704 (0.9)s 395.381 (so)s 13 f 408.86 (\275)s 16 f 612.923 y 414.521 (F)s 8 f 611.228 y 424.68 (=)s 436.297 (0)s 13 f 441.772 (:)s 8 f 444.813 (0556.)s 632.988 y 0 (Using)s 29.677 (the)s 47.43 (ab)s 59.293 (o)s 64.463 (v)s 69.938 (e)s 77.35 (rule)s 98.176 (of)s 109.542 (th)s 119.579 (um)s 134.483 (b,)s 146.374 (w)s 153.978 (e)s 161.39 (exp)s 178.423 (ect)s 194.96 (the)s 212.714 (transition)s 261.583 (ground-slop)s 317.945 (e)s 325.357 (for)s 341.012 (w)s 348.616 (alk)s 362.608 (er)s 374.308 (E)s 384.304 (to)s 396.582 (b)s 402.97 (e)s 410.382 (prop)s 432.616 (ortional)s 654.748 y 0 (to)s 13 f 13.512 (\275)s 16 f 656.443 y 19.174 (E)s 15 f 650.775 y 26.351 (3)s 16 f 30.602 (=)s 15 f 34.852 (2)s 8 f 654.748 y 42.858 (=)s 54.631 (0)s 13 f 60.106 (:)s 8 f 63.148 (125)s 15 f 650.775 y 79.573 (3)s 16 f 83.823 (=)s 15 f 88.073 (2)s 14 f 654.748 y 96.08 (\274)s 8 f 107.853 (0)s 13 f 113.328 (:)s 8 f 116.37 (044)s 136.574 (and)s 157.994 (that)s 181.848 (of)s 194.448 (w)s 202.052 (alk)s 216.044 (er)s 228.979 (F)s 239.905 (to)s 253.418 (b)s 259.805 (e)s 268.451 (prop)s 290.685 (ortional)s 331.603 (to)s 13 f 345.115 (\275)s 16 f 656.443 y 350.777 (F)s 15 f 650.775 y 357.837 (3)s 16 f 362.087 (=)s 15 f 366.337 (2)s 8 f 654.748 y 374.343 (=)s 386.117 (0)s 13 f 391.592 (:)s 8 f 394.633 (0556)s 15 f 650.775 y 416.533 (3)s 16 f 420.783 (=)s 15 f 425.033 (2)s 14 f 654.748 y 433.04 (\274)s 8 f 444.813 (0)s 13 f 450.288 (:)s 8 f 453.33 (013)s 685.43 y 229.402 (12)s end endp %%Page: 13 13 %%BeginPageSetup initializepage (T&AM; page: 13 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f8_12 sf ( )S 7 0 :M f6_12 sf ( )S 15 0 :M f9_12 sf ( )S 27 0 :M f11_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 12 12 /CMBX12 findfont fdef 13 10.95 /CMMI10 findfont fdef 14 10.95 /CMSY10 findfont fdef 16 8 /CMMI8 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 0 (\050these)s 31.859 (v)s 37.03 (alues)s 64.022 (are)s 81.859 (mark)s 106.222 (ed)s 120.379 (in)s 132.71 (\257gure)s 162.714 (5\051.)s 180.207 (The)s 202.272 (ratio)s 228.017 (of)s 240.044 (the)s 258.459 (t)s 262.413 (w)s 270.017 (o)s 278.699 (critical)s 314.785 (slop)s 334.009 (es)s 346.401 (is)s 356.968 (equal)s 385.42 (to)s 398.36 (the)s 416.774 (ratio)s 442.52 (of)s 454.547 (the)s 37.76 y 0 (in)s 8.821 (tersection)s 59.242 (v)s 64.412 (alues)s 92.294 (of)s 105.211 (the)s 124.516 (extrap)s 155.571 (olated)s 188.867 (b)s 195.255 (est-\257t)s 226.787 (lines)s 252.235 (from)s 278.566 (eac)s 293.47 (h)s 303.65 (w)s 311.254 (alk)s 325.245 (er\047s)s 345.858 (linear-scaling)s 412.703 (regime)s 448.463 (with)s 59.52 y 0 (an)s 15.208 (arbitrary)s 61.837 (cub)s 79.175 (e-ro)s 97.759 (ot-scaling)s 147.095 (line,)s 170.82 (as)s 184.264 (sho)s 199.838 (wn)s 217.479 (in)s 230.254 (the)s 249.113 (\257gure.)s 12 f 97.243 y 0 (5.2)s 30.75 (Generic)s 80.944 (Kneed)s 123.333 (And)s 153.028 (Straigh)s 195.479 (t-Legged)s 251.16 (Mo)s 271.09 (dels)s 8 f 126.075 y 0 (What)s 31.928 (ab)s 43.79 (out)s 64.464 (w)s 72.068 (alk)s 86.06 (ers)s 104.391 (with)s 130.54 (more)s 159.152 (general)s 198.106 (mass-distribution,)s 289.253 (non-zero)s 334.898 (fo)s 344.023 (ot)s 358.614 (radii,)s 388.744 (and)s 411.243 (fo)s 420.368 (ot)s 434.958 (o\256sets\077)s 147.835 y 0 (Figure)s 34.685 (6)s 43.941 (sho)s 59.514 (ws)s 75.523 (stance)s 109.173 (angle)s 13 f 137.896 (\265)s 16 f 149.477 y 143.037 (st)s 8 f 147.835 y 154.318 (at)s 167.833 (gait)s 189.864 (cycles)s 221.385 (o)s 227.164 (ccurring)s 269.94 (at)s 283.454 (di\256eren)s 318.768 (t)s 326.808 (ground-slop)s 383.17 (es)s 13 f 396.137 (\260)s 8 f 406.195 (for)s 423.086 (the)s 442.076 (kneed)s 169.595 y 0 (w)s 7.604 (alk)s 21.596 (er)s 34.413 (of)s 46.896 (\257gure)s 77.356 (3.)s 90.775 (Stable)s 124.246 (solutions)s 170.005 (are)s 188.297 (denoted)s 229.676 (b)s 235.455 (y)s 244.897 (the)s 263.767 (hea)s 279.888 (vy)s 295.109 (line.)s 320.087 (The)s 342.607 (dashed)s 379.18 (curv)s 399.894 (e)s 408.423 (sho)s 423.996 (ws)s 439.886 (stance)s 191.355 y 0 (angle)s 27.64 (v)s 33.115 (ersus)s 59.691 (ground-slop)s 116.053 (e)s 123.618 (for)s 139.426 (the)s 157.332 (straigh)s 189.969 (t-legged)s 230.385 (v)s 235.86 (ersion)s 266.632 (\050the)s 288.798 (same)s 315.282 (w)s 322.886 (alk)s 336.878 (er)s 348.731 (but)s 367.855 (with)s 391.845 (the)s 409.751 (knees)s 438.365 (alw)s 454.486 (a)s 459.657 (ys)s 213.115 y 0 (lo)s 8.821 (c)s 13.383 (k)s 18.858 (ed,)s 13 f 36.5 (\265)s 16 f 214.899 y 41.64 (sh)s 14 f 213.115 y 54.011 (\264)s 13 f 65.569 (\265)s 16 f 214.899 y 70.71 (th)s 8 f 213.115 y 79.177 (\051.)s 91.344 (Some)s 120.544 (observ)s 150.748 (ations)s 183.05 (ab)s 194.913 (out)s 214.38 (the)s 233.238 (solutions)s 278.985 (in)s 291.76 (\257gure)s 322.207 (6)s 331.332 (are)s 349.612 (as)s 363.056 (follo)s 383.131 (ws:)s 243.875 y 13.383 (1.)s 27.375 (F)s 33.61 (or)s 48.255 (b)s 54.643 (oth)s 75.34 (kneed)s 107.9 (and)s 130.423 (straigh)s 163.06 (t-legged)s 205.657 (w)s 213.262 (alk)s 227.253 (ers)s 245.609 (there)s 274.853 (are)s 294.365 (ground-slop)s 350.727 (e)s 13 f 360.474 (\260)s 8 f 371.633 (regimes)s 412.497 (where)s 445.391 (there)s 265.635 y 27.375 (are)s 45.995 (either)s 77.389 (zero,)s 104.002 (one,)s 127.543 (or)s 141.296 (t)s 145.25 (w)s 152.854 (o)s 162.318 (solutions.)s 213.341 (This)s 238.682 (agrees)s 271.963 (with)s 297.243 (the)s 316.441 (observ)s 346.645 (ations)s 379.286 (and)s 400.917 (calculations)s 460.934 (of)s 287.395 y 27.375 (McGeer)s 68.544 (\0501990a\051)s 108.086 (and)s 129.377 (McGeer)s 170.546 (\0501990b\051.)s 318.155 y 13.383 (2.)s 27.375 (F)s 33.61 (or)s 46.987 (the)s 65.809 (parameters)s 122.468 (used)s 147.434 (here,)s 174.201 (none)s 200.323 (of)s 212.756 (the)s 231.578 (straigh)s 264.215 (t-legged)s 305.544 (solutions)s 351.254 (and)s 372.509 (only)s 396.501 (a)s 405.589 (section)s 442.113 (of)s 454.547 (the)s 339.915 y 27.375 (kneed)s 58.704 (solution-lo)s 108.953 (cus)s 127.872 (are)s 146.152 (stable.)s 370.675 y 13.383 (3.)s 27.375 (Along)s 60.738 (the)s 81.021 (kneed)s 113.775 (curv)s 134.489 (e,)s 147.828 (kneestrik)s 190.807 (e)s 200.749 (o)s 206.528 (ccurs)s 236.027 (later)s 263.033 (and)s 285.749 (later)s 312.755 (in)s 326.955 (the)s 347.238 (step,)s 375.238 (un)s 387.101 (til)s 402.518 (at)s 417.326 (one)s 438.826 (end)s 460.934 (of)s 392.435 y 27.375 (the)s 47.036 (curv)s 67.75 (e)s 77.069 (\050p)s 87.715 (oin)s 102.011 (t)s 110.722 (1\051,)s 128.15 (heelstrik)s 168.391 (e)s 177.71 (and)s 199.804 (kneestrik)s 242.783 (e)s 252.102 (o)s 257.882 (ccur)s 282.44 (sim)s 298.621 (ultaneously)s 352.215 (.)s 362.531 (The)s 385.842 (lo)s 394.663 (cus)s 414.385 (of)s 427.658 (solutions)s 414.196 y 27.375 (terminates)s 83.029 (here)s 108.206 (since)s 136.455 (w)s 144.059 (e)s 153.997 (do)s 170.626 (not)s 191.514 (in)s 200.335 (v)s 205.81 (estigate)s 247.442 (motions)s 290.291 (where)s 323.376 (heelstrik)s 363.617 (e)s 373.555 (precedes)s 418.868 (kneestrik)s 461.847 (e.)s 435.956 y 27.375 (In)s 42.328 (the)s 62.452 (analogous)s 114.271 (region)s 148.417 (on)s 164.891 (the)s 185.015 (dashed)s 222.842 (curv)s 243.555 (e)s 253.338 (for)s 271.363 (the)s 291.487 (straigh)s 324.124 (t-legged)s 366.757 (w)s 374.361 (alk)s 388.353 (er)s 402.424 (\050p)s 413.07 (oin)s 427.365 (t)s 436.539 (2\051,)s 454.547 (the)s 457.716 y 27.375 (heelstrik)s 67.616 (e)s 76.774 (collision)s 119.451 (b)s 125.838 (ecomes)s 163.648 (increasingly)s 224.301 (tangen)s 256.239 (tial)s 276.347 (in)s 289.763 (nature,)s 328.311 (un)s 340.173 (til)s 354.806 (the)s 374.305 (solution)s 416.374 (disapp)s 447.764 (ears.)s 479.476 y 27.375 (In)s 42.852 (this)s 65.994 (area,)s 95.028 (solutions)s 142.565 (and)s 165.646 (n)s 171.425 (umerics)s 213.456 (b)s 219.843 (ecome)s 254.483 (v)s 259.958 (ery)s 280.332 (unstable;)s 329.919 (w)s 337.523 (e)s 347.829 (b)s 354.217 (eliev)s 375.509 (e)s 385.815 (that)s 411.329 (the)s 431.977 (solution)s 501.236 y 27.375 (terminates)s 81.871 (at)s 95.517 (a)s 104.906 (ground-slop)s 161.268 (e)s 170.047 (of)s 182.781 (ab)s 194.644 (out)s 13 f 214.374 (\260)s 8 f 224.131 (=)s 236.128 (0)s 13 f 241.603 (:)s 8 f 244.644 (056)s 264.982 (based)s 295.723 (on)s 311.194 (n)s 316.974 (umerical)s 361.675 (evidence)s 406.043 (not)s 425.772 (discussed)s 522.996 y 27.375 (here.)s 553.756 y 13.383 (4.)s 27.375 (A)s 35.283 (t)s 44.267 (the)s 64.202 (other)s 93.899 (end)s 115.659 (of)s 129.205 (the)s 149.139 (long-step)s 197.118 (curv)s 217.831 (e,)s 230.734 (the)s 250.669 (gait)s 273.644 (cycles)s 306.11 (are)s 325.466 (approac)s 362.909 (hing)s 388.318 (initial)s 421.027 (conditions)s 575.516 y 27.375 (whic)s 48.971 (h)s 58.83 (approac)s 96.273 (h)s 106.132 (falling)s 139.412 (bac)s 155.532 (kw)s 168.916 (ards,)s 195.931 (i.e.,.)s 221.249 (the)s 240.233 (w)s 247.837 (alk)s 261.829 (er)s 274.76 (has)s 294.413 (just)s 316.196 (enough)s 354.038 (initial)s 385.797 (kinetic)s 421.51 (energy)s 456.645 (for)s 597.276 y 27.375 (the)s 46.284 (stance)s 79.854 (leg)s 96.938 (to)s 110.372 (mak)s 130.447 (e)s 139.014 (it)s 150.015 (past)s 173.851 (the)s 192.76 (v)s 198.235 (ertical)s 231.775 (p)s 238.162 (osition.)s 277.917 (The)s 300.476 (same)s 327.962 (thing)s 356.605 (o)s 362.384 (ccurs)s 390.509 (at)s 403.943 (the)s 422.852 (analogous)s 619.036 y 27.375 (p)s 33.763 (oin)s 48.058 (t)s 56.591 (on)s 72.423 (the)s 91.906 (dashed)s 129.091 (curv)s 149.805 (e)s 158.946 (for)s 176.329 (the)s 195.812 (straigh)s 228.449 (t-legged)s 270.44 (w)s 278.044 (alk)s 292.036 (er.)s 310.972 (In)s 325.284 (b)s 331.671 (oth)s 351.762 (cases,)s 383.081 (this)s 405.057 (is)s 416.692 (the)s 436.175 (slo)s 448.707 (w)s 456.311 (est)s 640.796 y 27.375 (gait)s 49.275 (found)s 79.996 (for)s 96.756 (the)s 115.614 (w)s 123.218 (alk)s 137.21 (ers.)s 685.43 y 229.402 (13)s end endp %%Page: 14 14 %%BeginPageSetup initializepage (T&AM; page: 14 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f8_12 sf ( )S 7 0 :M ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 9 14.4 /CMBX12 findfont fdef 12 12 /CMBX12 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 13.383 (5.)s 27.375 (All)s 45.889 (of)s 58.929 (the)s 78.355 (straigh)s 110.992 (t-leg)s 136.502 (solutions)s 182.817 (and)s 204.678 (some)s 232.682 (of)s 245.721 (the)s 265.148 (kneed)s 297.045 (solutions)s 343.36 (allo)s 360.09 (w)s 372.216 (the)s 391.643 (fo)s 400.768 (ot)s 414.72 (to)s 428.671 (scu\256)s 454.547 (the)s 37.76 y 27.375 (ground)s 64.514 (during)s 99.219 (the)s 118.078 (gait)s 139.978 (cycle.)s 68.52 y 13.383 (6.)s 27.375 (Eac)s 44.865 (h)s 54.281 (w)s 61.885 (alk)s 75.877 (er)s 88.365 (needs)s 117.917 (a)s 126.725 (minim)s 156.837 (um)s 175.378 (ground-slop)s 231.74 (e)s 239.94 (to)s 253.006 (sustain)s 289.919 (gait)s 311.501 (\050ab)s 327.622 (out)s 346.772 (0.016)s 375.046 (rad)s 394.226 (for)s 410.668 (the)s 429.21 (straigh)s 461.847 (t-)s 90.28 y 27.375 (leg)s 45.648 (w)s 53.252 (alk)s 67.244 (er)s 81.289 (and)s 103.82 (ab)s 115.683 (out)s 136.389 (0.02)s 160.745 (rad)s 181.482 (for)s 199.481 (the)s 219.579 (kneed)s 252.148 (w)s 259.752 (alk)s 273.743 (er\051.)s 298.784 (So,)s 318.584 (these)s 347.867 (w)s 355.472 (alk)s 369.463 (ers)s 387.827 (are)s 407.347 (not)s 428.054 (p)s 434.441 (erfectly)s 112.04 y 27.375 (e\261cien)s 59.921 (t)s 67.829 (b)s 73.608 (y)s 83.038 (the)s 101.896 (e\261ciency)s 149.042 (measures)s 196.036 (discussed)s 243.668 (earlier.)s 9 f 157.341 y 0 (6)s 24.3 (W)s 39.683 (alking)s 87.608 (A)s 99.392 (t)s 111.092 (Near-Zero)s 188.45 (Slop)s 219.5 (es)s 8 f 189.945 y 0 (As)s 15.645 (seen)s 38.894 (in)s 51.132 (the)s 69.454 (previous)s 112.504 (section,)s 151.678 (generic)s 188.28 (McGeer-lik)s 241.007 (e)s 248.987 (w)s 256.591 (alking)s 288.6 (mac)s 307.763 (hines)s 335.27 (will)s 355.417 (t)s 359.371 (ypically)s 399.593 (ha)s 410.847 (v)s 416.322 (e)s 424.302 (no)s 438.973 (steady)s 211.705 y 0 (w)s 7.604 (alking)s 41.939 (motions)s 85.155 (b)s 91.543 (elo)s 104.622 (w)s 117.969 (some)s 147.193 (nonzero)s 189.771 (ground-slop)s 246.133 (e;)s 260.374 (th)s 270.412 (us,)s 289.742 (they)s 316.168 (ha)s 327.422 (v)s 332.897 (e)s 343.203 (some)s 372.427 (nonzero)s 415.005 (ine\261ciency)s 466.713 (.)s 233.465 y 0 (But)s 22.223 (w)s 29.827 (e)s 38.819 (ha)s 50.073 (v)s 55.548 (e)s 64.54 (already)s 103.675 (seen)s 127.936 (that)s 152.137 (the)s 171.47 (p)s 177.858 (oin)s 192.153 (t-fo)s 209.187 (ot)s 223.045 (w)s 230.65 (alk)s 244.641 (er)s 257.922 (with)s 283.339 (or)s 297.228 (without)s 338.461 (negligible)s 387.603 (fo)s 396.728 (ot)s 410.587 (mass)s 437.951 (can)s 458.501 (b)s 464.888 (e)s 255.225 y 0 (p)s 6.388 (erfectly)s 46.179 (e\261cien)s 78.725 (t.)s 93.375 (Here)s 120.087 (w)s 127.691 (e)s 137.036 (in)s 145.857 (v)s 151.332 (estigate)s 192.37 (the)s 212.056 (p)s 218.444 (ossibilit)s 254.761 (y)s 265.018 (of)s 278.317 (more)s 306.55 (general)s 345.125 (straigh)s 377.762 (t-legged)s 419.956 (and)s 442.076 (kneed)s 276.985 y 0 (w)s 7.604 (alk)s 21.596 (ers)s 38.72 (capable)s 78.262 (of)s 90.733 (zero-slop)s 133.103 (e)s 141.62 (w)s 149.224 (alking.)s 12 f 314.708 y 0 (6.1)s 30.75 (Necessary)s 93.976 (Conditions)s 162.301 (On)s 184.44 (Mass)s 218.958 (Distribution)s 295.645 (F)s 303.006 (or)s 319.77 (Near-Zero-Slop)s 410.11 (e)s 420.77 (W)s 433.589 (alking)s 8 f 343.54 y 0 (Necessary)s 50.644 (conditions)s 103.021 (on)s 118.23 (the)s 137.088 (mass)s 163.976 (distribution)s 223.684 (for)s 240.444 (near-zero-slop)s 307.178 (e)s 315.695 (kneed)s 347.024 (w)s 354.628 (alk)s 368.62 (ers)s 385.745 (are)s 404.025 (as)s 417.469 (follo)s 437.544 (ws:)s 374.3 y 13.383 (1.)s 27.375 (As)s 44.841 (demonstrated)s 114.958 (in)s 129.018 (a)s 139.427 (companion)s 196.07 (pap)s 214.016 (er)s 228.106 (b)s 233.885 (y)s 244.598 (Chatterjee)s 299.751 (and)s 322.327 (Garcia)s 359.001 (\0501998\051,)s 397.715 (based)s 429.476 (on)s 445.969 (some)s 396.06 y 27.375 (reasonable)s 81.199 (assumptions,)s 146.723 (if)s 156.96 (w)s 164.564 (alking)s 197.309 (motions)s 238.936 (do)s 254.344 (o)s 260.123 (ccur)s 284.078 (at)s 297.661 (v)s 303.136 (ery)s 321.92 (small)s 350.772 (ground-slop)s 407.134 (es,)s 423.261 (these)s 451.505 (mo-)s 417.82 y 27.375 (tions)s 54.966 (will)s 76.413 (b)s 82.8 (e)s 92.081 (v)s 97.556 (ery)s 116.904 (slo)s 129.435 (w.)s 147.542 (F)s 153.778 (or)s 167.955 (these)s 196.763 (motions,)s 242.186 (gra)s 257.121 (vit)s 269.896 (y)s 280.089 (forces)s 311.664 (will)s 333.111 (b)s 339.498 (e)s 348.779 (m)s 357.599 (uc)s 368.245 (h)s 378.742 (bigger)s 412.386 (than)s 438.699 (inertia)s 439.58 y 27.375 (forces.)s 62.363 (As)s 78.297 (a)s 87.175 (result,)s 120.526 (the)s 139.137 (w)s 146.741 (alk)s 160.733 (er)s 173.291 (m)s 182.111 (ust)s 200.175 (b)s 206.562 (e)s 214.831 (close)s 240.803 (to)s 253.939 (static)s 283.561 (equilibrium)s 341.439 (at)s 354.575 (all)s 369.536 (times.)s 402.973 (In)s 416.413 (the)s 435.023 (limit)s 460.934 (of)s 461.34 y 27.375 (zero)s 50.15 (slop)s 69.373 (e,)s 80.634 (the)s 99.12 (w)s 106.724 (alk)s 120.715 (er)s 133.148 (con\257guration)s 199.115 (m)s 207.936 (ust)s 225.874 (approac)s 263.317 (h)s 272.678 (a)s 281.431 (static)s 310.927 (equilibrium,)s 371.798 (or)s 384.839 (standing)s 428.936 (solution.)s 483.1 y 27.375 (Th)s 41.063 (us)s 55.143 (the)s 74.029 (fo)s 83.154 (ot-normal)s 133.704 (at)s 147.115 (the)s 166.002 (near-zero-slop)s 232.736 (e)s 241.28 (w)s 248.884 (alking)s 281.458 (condition)s 329.544 (m)s 338.365 (ust)s 356.704 (b)s 363.091 (e)s 371.636 (directed)s 413.669 (to)s 423.098 (w)s 430.703 (ards)s 454.547 (the)s 504.86 y 27.375 (b)s 33.763 (o)s 39.542 (dy)s 55.054 (cen)s 70.567 (ter)s 87.631 (of)s 100.101 (mass.)s 535.62 y 13.383 (2.)s 27.375 (A)s 35.283 (t)s 44.494 (the)s 64.654 (instan)s 93.61 (t)s 102.82 (of)s 116.593 (double-supp)s 174.75 (ort,)s 197.091 (or)s 211.806 (heelstrik)s 252.048 (e,)s 265.233 (b)s 271.621 (oth)s 292.389 (legs)s 315.044 (are)s 334.626 (straigh)s 367.263 (t)s 376.473 (and)s 399.066 (sim)s 415.248 (ultaneously)s 557.381 y 27.375 (touc)s 47.754 (h)s 56.973 (the)s 75.316 (ground.)s 116.541 (As)s 132.208 (the)s 150.551 (ground-slop)s 206.913 (e)s 214.915 (\050hence,)s 252.219 (step)s 274.882 (length\051)s 312.084 (go)s 323.338 (es)s 335.658 (to)s 348.527 (zero,)s 374.303 (the)s 392.647 (spacing)s 431.126 (b)s 437.513 (et)s 446.334 (w)s 453.938 (een)s 579.141 y 27.375 (the)s 46.072 (legs)s 67.263 (at)s 80.485 (this)s 101.675 (instan)s 130.632 (t)s 138.379 (also)s 160.178 (go)s 171.432 (es)s 184.107 (to)s 197.328 (zero.)s 224.68 (In)s 238.206 (the)s 256.903 (limiting)s 297.5 (case,)s 323.589 (the)s 342.286 (fo)s 351.411 (ot)s 364.633 (con)s 380.754 (tact)s 403.101 (p)s 409.488 (oin)s 423.784 (t)s 431.531 (m)s 440.352 (ust)s 458.501 (b)s 464.888 (e)s 600.901 y 27.375 (that)s 51.588 (p)s 57.976 (oin)s 72.272 (t)s 80.668 (on)s 96.365 (the)s 115.711 (fo)s 124.836 (ot)s 138.708 (whic)s 160.304 (h)s 170.525 (is)s 182.025 (farthest)s 223.058 (from)s 249.431 (the)s 268.778 (hip.)s 293.359 (Th)s 307.047 (us)s 321.587 (the)s 340.934 (normal)s 378.561 (to)s 392.432 (the)s 411.779 (fo)s 420.904 (ot)s 434.776 (con)s 450.897 (tact)s 622.661 y 27.375 (p)s 33.763 (oin)s 48.058 (t)s 55.967 (m)s 64.788 (ust)s 83.098 (pass)s 106.945 (through)s 148.342 (the)s 167.201 (hip.)s 685.43 y 229.402 (14)s end endp %%Page: 15 15 %%BeginPageSetup initializepage (T&AM; page: 15 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f5_12 sf ( )S 6 0 :M f3_12 sf ( )S 10 0 :M f8_12 sf ( )S 14 0 :M f6_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 10 10.95 /CMTI10 findfont fdef 11 10.95 /CMBX10 findfont fdef 12 12 /CMBX12 findfont fdef 13 10.95 /CMMI10 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 13.383 (3.)s 27.375 (F)s 33.61 (rom)s 56.589 (\0501\051)s 74.671 (and)s 96.403 (\0502\051)s 114.485 (the)s 133.783 (line)s 154.907 (from)s 181.232 (the)s 200.53 (hip)s 219.828 (through)s 261.666 (the)s 280.964 (b)s 287.352 (o)s 293.131 (dy)s 309.084 (cen)s 324.596 (ter)s 342.1 (of)s 355.011 (mass)s 382.339 (m)s 391.16 (ust)s 409.911 (in)s 418.732 (tersect)s 454.547 (the)s 37.76 y 27.375 (fo)s 36.5 (ot)s 49.435 (curv)s 70.149 (e)s 78.218 (normally)s 123.729 (at)s 136.664 (the)s 155.074 (place)s 182.609 (that)s 205.886 (will)s 226.122 (b)s 232.509 (e)s 240.578 (the)s 258.988 (nominal)s 300.515 (con)s 316.635 (tact)s 338.696 (p)s 345.083 (oin)s 359.379 (t)s 366.839 (at)s 379.774 (zero-slop)s 422.145 (e)s 430.213 (w)s 437.817 (alking.)s 59.52 y 27.375 (F)s 33.61 (or)s 46.856 (circular)s 86.29 (feet)s 107.11 (this)s 128.294 (is)s 139.137 (equiv)s 164.078 (alen)s 183.241 (t)s 190.981 (to)s 204.196 (the)s 222.886 (collinearit)s 270.062 (y)s 279.323 (of)s 291.626 (the)s 310.316 (cen)s 325.829 (ter)s 342.724 (of)s 355.027 (mass)s 381.747 (of)s 394.05 (the)s 412.74 (whole)s 443.597 (b)s 449.984 (o)s 455.763 (dy)s 466.713 (,)s 81.28 y 27.375 (the)s 46.233 (hip,)s 68.133 (and)s 89.425 (the)s 108.283 (fo)s 117.408 (ot)s 130.792 (cen)s 146.304 (ter)s 163.368 (\050see)s 185.329 (\257gure)s 215.776 (7\051.)s 112.04 y 13.383 (4.)s 27.375 (F)s 33.61 (or)s 46.608 (the)s 65.05 (swing)s 95.111 (leg)s 111.728 (to)s 124.695 (b)s 131.083 (e)s 139.183 (in)s 151.542 (static)s 180.994 (equilibrium)s 238.704 (in)s 251.063 (three-link)s 300.256 (mo)s 315.16 (de)s 329.344 (and)s 350.219 (to)s 363.186 (ha)s 374.441 (v)s 379.916 (e)s 388.016 (zero)s 410.747 (knee-lo)s 444.813 (c)s 449.376 (king)s 133.8 y 27.375 (torque,)s 65.277 (the)s 84.502 (cen)s 100.014 (ter)s 117.445 (of)s 130.282 (mass)s 157.538 (of)s 170.375 (the)s 189.6 (shank)s 221.357 (m)s 230.178 (ust)s 248.856 (lie)s 263.823 (directly)s 304.066 (under)s 335.488 (the)s 354.713 (knee,)s 383.459 (in)s 396.601 (the)s 415.826 (straigh)s 448.463 (t-leg)s 155.561 y 27.375 (con\257guration)s 93.714 (\050see)s 115.675 (\257gure)s 146.122 (7\051.)s 186.321 y 0 (The)s 22.611 (simpli\257cation)s 90.3 (of)s 102.873 (these)s 131.02 (ideas)s 158.558 (for)s 175.421 (straigh)s 208.058 (t-legged)s 249.527 (w)s 257.131 (alk)s 271.123 (ers)s 288.35 (is)s 299.464 (describ)s 333.317 (ed)s 348.02 (b)s 353.799 (y)s 363.331 (item)s 388.375 (\0503\051)s 406.12 (ab)s 417.982 (o)s 423.153 (v)s 428.628 (e.)s 441.711 (These)s 208.081 y 0 (necessary)s 48.816 (statics-based)s 113.783 (conditions)s 166.462 (on)s 181.972 (the)s 201.132 (mass)s 228.321 (distribution)s 288.331 (do)s 303.84 (not)s 323.608 (guaran)s 356.185 (tee)s 374.128 (that)s 398.154 (near-zero-slop)s 464.888 (e)s 229.841 y 0 (w)s 7.604 (alking)s 39.8 (solutions)s 85.197 (exist.)s 115.254 (Although)s 163.267 (w)s 170.871 (e)s 179.038 (do)s 193.897 (not)s 213.013 (kno)s 230.047 (w)s 241.255 (general)s 278.653 (su\261cien)s 316.735 (t)s 324.293 (conditions,)s 379.433 (it)s 390.033 (is)s 400.694 (our)s 419.841 (exp)s 436.875 (erience)s 251.601 y 0 (that)s 23.328 (designs)s 60.769 (whic)s 82.365 (h)s 91.701 (meet)s 118.071 (these)s 145.718 (conditions)s 197.698 (and)s 218.593 (whose)s 250.498 (total)s 276.259 (cen)s 291.772 (ter)s 308.439 (of)s 320.512 (mass)s 347.004 (is)s 357.617 (close)s 383.439 (to)s 396.426 (the)s 414.887 (hip)s 433.348 (do)s 448.159 (ha)s 459.413 (v)s 464.888 (e)s 273.361 y 0 (w)s 7.604 (alking)s 40.15 (motions)s 81.578 (for)s 98.337 (arbitrarily)s 151.049 (small)s 179.702 (ground-slop)s 236.064 (es.)s 295.121 y 17 (The)s 40.13 (mac)s 59.292 (hines)s 87.958 (in)s 96.779 (v)s 102.254 (estigated)s 149.17 (b)s 154.949 (y)s 165 (Gosw)s 190.991 (ami)s 212.904 (et)s 226.301 (al.)s 242.13 (\0501996\051)s 276.819 (and)s 298.732 (Gosw)s 324.723 (ami)s 346.636 (et)s 360.033 (al.)s 375.863 (\0501997\051)s 410.551 (satisfy)s 445.361 (these)s 316.881 y 0 (necessary)s 48.515 (conditions,)s 103.934 (so)s 117.378 (will)s 138.061 (probably)s 184.021 (w)s 191.625 (alk)s 209.571 (at)s 222.954 (arbitrarily)s 275.667 (small)s 304.319 (ground-slop)s 360.681 (es.)s 338.641 y 17 (W)s 27.342 (alk)s 41.333 (ers)s 58.458 (satisfying)s 107.246 (the)s 126.105 (necessary)s 174.619 (conditions)s 226.997 (ab)s 238.859 (o)s 244.03 (v)s 249.505 (e)s 258.022 (ha)s 269.276 (v)s 274.751 (e)s 283.268 (an)s 11 f 298.476 (M)s 8 f 310.43 (\0500\051)s 328.071 (whic)s 349.667 (h)s 359.401 (is)s 370.411 (diagonal.)s 12 f 376.364 y 0 (6.2)s 30.75 (T)s 39.014 (uning)s 76.514 (Mass-Distribution)s 187.718 (F)s 195.079 (or)s 211.843 (Near)s 245.135 (Zero-Slop)s 302.183 (e)s 312.843 (W)s 325.663 (alking)s 8 f 405.196 y 0 (After)s 30.224 (adjusting)s 79.64 (the)s 100.1 (mass)s 128.59 (parameters)s 186.888 (\050)s 10 f 191.146 (tuning)s 8 f 221.368 (\051)s 230.878 (for)s 249.239 (the)s 269.698 (w)s 277.303 (alk)s 291.294 (ers)s 310.02 (of)s 324.093 (\257gures)s 360.46 (3)s 371.187 (and)s 394.08 (6)s 404.806 (to)s 419.791 (matc)s 443.212 (h)s 454.547 (the)s 426.956 y 0 (conditions)s 52.773 (for)s 69.929 (zero-slop)s 112.299 (e)s 121.211 (w)s 128.816 (alking)s 161.757 (\050\257gure)s 196.858 (7\051,)s 213.778 (w)s 221.382 (e)s 230.294 (found)s 261.411 (that)s 285.532 (b)s 291.919 (oth)s 311.782 (of)s 324.648 (these)s 10 f 353.088 (tune)s 373.236 (d)s 8 f 384.01 (w)s 391.614 (alk)s 405.606 (ers)s 423.126 (do)s 438.73 (indeed)s 448.716 y 0 (ha)s 11.254 (v)s 16.729 (e)s 26.892 (w)s 34.496 (alking)s 68.688 (motions)s 111.761 (at)s 126.79 (near-zero-slop)s 193.524 (es.)s 215.556 (Also,)s 245.354 (eac)s 260.258 (h)s 271.637 (w)s 279.241 (alk)s 293.233 (er)s 307.684 (no)s 318.938 (w)s 332.143 (has)s 10 f 353.316 (two)s 8 f 375.122 (w)s 382.726 (alking)s 416.918 (motions)s 459.991 (or)s 470.476 y 0 (gait)s 22.897 (cycles)s 55.283 (at)s 69.663 (all)s 85.868 (ground-slop)s 142.23 (es)s 156.062 (of)s 13 f 169.53 (\260)s 180.51 (\074)s 8 f 193.729 (0)s 13 f 199.204 (:)s 8 f 202.246 (04.)s 224.094 (The)s 247.598 (long-step,)s 298.788 (long-p)s 328.901 (erio)s 346.877 (d)s 357.607 (cycle)s 385.674 (is)s 397.682 (stable)s 430.373 (at)s 444.752 (small)s 492.236 y 0 (ground-slop)s 56.362 (es,)s 72.24 (while)s 100.831 (the)s 119.69 (short-step,)s 173.984 (short-p)s 208.446 (erio)s 226.422 (d)s 236.155 (cycle)s 263.226 (is)s 274.237 (unstable.)s 513.996 y 17 (Figure)s 51.528 (8)s 60.629 (compares)s 108.753 (the)s 127.587 (shap)s 149.852 (es)s 162.663 (of)s 175.109 (the)s 193.942 (solution)s 235.345 (families)s 275.227 (of)s 287.672 (the)s 306.506 (0\045)s 324.731 (tuned)s 355.731 (kneed)s 387.035 (w)s 394.64 (alk)s 408.631 (er)s 421.412 (of)s 433.858 (\257gure)s 464.28 (6)s 535.756 y 0 (to)s 13.169 (its)s 28.224 (100\045)s 57.21 (tuned)s 88.021 (cousin.)s 125.727 (A)s 137.376 (solution)s 178.589 (family)s 211.833 (is)s 222.63 (also)s 244.377 (sho)s 259.95 (wn)s 277.378 (after)s 303.048 (the)s 321.692 (0\045)s 339.728 (w)s 347.333 (alk)s 361.324 (er)s 373.916 (has)s 393.229 (b)s 399.617 (een)s 418.869 (25\045)s 442.38 (tuned)s 557.516 y 0 (to)s 13.459 (sho)s 29.033 (w)s 40.667 (ho)s 51.921 (w)s 63.556 (the)s 82.49 (long-step)s 129.468 (and)s 150.836 (short-step)s 202.164 (solution)s 243.668 (get)s 261.994 (closer)s 292.578 (at)s 306.037 (high)s 330.446 (ground-slop)s 386.809 (es)s 399.72 (and)s 421.088 (ev)s 431.43 (en)s 442.076 (tually)s 579.276 y 0 (merge)s 33.542 (in)s 42.363 (to)s 57.016 (one)s 78.361 (curv)s 99.075 (e.)s 115.66 (As)s 133.112 (the)s 153.24 (100\045)s 183.71 (tuned)s 216.005 (w)s 223.609 (alk)s 237.601 (er)s 251.676 (is)s 263.957 (de-tuned,)s 314.211 (the)s 334.339 (graphs)s 370.984 (c)s 375.547 (hange)s 408.45 (shap)s 430.715 (e)s 440.502 (in)s 454.547 (the)s 601.036 y 0 (follo)s 20.075 (wing)s 46.233 (w)s 53.838 (a)s 59.008 (ys.)s 631.796 y 13.383 (1.)s 27.375 (The)s 49.505 (cusp)s 74.128 (at)s 87.133 (the)s 105.613 (origin)s 136.289 (breaks)s 170.373 (and)s 191.286 (the)s 209.765 (t)s 213.72 (w)s 221.324 (o)s 230.07 (solutions)s 275.438 (separate.)s 322.853 (The)s 344.983 (long-step)s 391.507 (solution)s 432.555 (remains)s 653.557 y 27.375 (stable)s 59.344 (but)s 79.694 (shifts)s 108.987 (to)s 122.645 (the)s 141.779 (righ)s 160.363 (t)s 168.547 (and)s 190.113 (no)s 205.597 (longer)s 238.752 (extends)s 278.934 (to)s 292.592 (zero)s 316.015 (ground-slop)s 372.377 (e.)s 385.977 (Also,)s 414.061 (an)s 429.544 (unstable)s 685.43 y 229.402 (15)s end endp %%Page: 16 16 %%BeginPageSetup initializepage (T&AM; page: 16 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f5_12 sf ( )S 6 0 :M f6_12 sf ( )S 14 0 :M f9_12 sf ( )S 26 0 :M f10_12 sf ( )S 30 0 :M f11_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 10 10.95 /CMTI10 findfont fdef 13 10.95 /CMMI10 findfont fdef 14 10.95 /CMSY10 findfont fdef 15 8 /CMR8 findfont fdef 16 8 /CMMI8 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 27.375 (region)s 60.256 (app)s 78.201 (ears)s 100.801 (at)s 114.184 (v)s 119.659 (ery)s 138.244 (lo)s 146.456 (w)s 158.015 (sp)s 168.721 (eeds.)s 44.934 y 13.383 (2.)s 27.375 (The)s 50.715 (short-step)s 102.8 (solution)s 145.059 (also)s 167.852 (shifts)s 197.702 (to)s 211.917 (the)s 231.607 (righ)s 250.192 (t;)s 262.39 (the)s 282.08 (p)s 288.468 (oin)s 302.764 (t)s 311.504 (on)s 327.544 (this)s 349.729 (curv)s 370.443 (e)s 379.791 (where)s 412.287 (the)s 431.977 (solution)s 66.694 y 27.375 (terminates)s 81.691 (mo)s 95.986 (v)s 101.461 (es)s 114.38 (up)s 130.279 (along)s 159.562 (the)s 178.502 (curv)s 199.216 (e)s 207.815 (to)s 221.281 (the)s 240.222 (p)s 246.61 (oin)s 260.905 (t)s 268.896 (where)s 300.643 (heelstrik)s 340.884 (e)s 349.483 (and)s 370.857 (kneestrik)s 413.836 (e)s 422.435 (are)s 440.798 (sim)s 456.98 (ul-)s 88.454 y 27.375 (taneous.)s 117.387 y 13.383 (3.)s 27.375 (A)s 35.283 (t)s 43.672 (higher)s 77.641 (ground-slop)s 134.003 (es,)s 150.481 (the)s 169.82 (t)s 173.774 (w)s 181.378 (o)s 190.983 (solutions)s 237.21 (get)s 255.94 (closer)s 286.928 (and)s 308.7 (ev)s 319.042 (en)s 329.688 (tually)s 361.497 (merge)s 394.25 (as)s 408.174 (the)s 427.513 (w)s 435.117 (alk)s 449.109 (er)s 462.394 (is)s 139.147 y 27.375 (de-tuned.)s 77.231 (This)s 102.15 (merge)s 134.338 (p)s 140.726 (oin)s 155.022 (t)s 162.847 (has)s 182.291 (a)s 191.332 (sharp)s 221.149 (corner,)s 257.643 (and)s 278.851 (o)s 284.63 (ccurs)s 312.621 (at)s 325.921 (lo)s 334.134 (w)s 341.738 (er)s 354.46 (and)s 375.668 (lo)s 383.881 (w)s 391.485 (er)s 404.207 (ground-slop)s 460.569 (es)s 160.907 y 27.375 (as)s 41.686 (the)s 61.411 (w)s 69.015 (alk)s 83.007 (er)s 96.679 (is)s 108.557 (de-tuned)s 155.049 (further.)s 198.773 (This)s 224.642 (merging)s 267.515 (do)s 279.377 (es)s 293.08 (not)s 313.413 (seem)s 341.108 (to)s 355.358 (o)s 361.137 (ccur)s 385.759 (in)s 399.401 (straigh)s 432.038 (t-legged)s 182.667 y 27.375 (w)s 34.979 (alk)s 48.971 (ers.)s 208.861 y 17 (Figure)s 50.666 (9)s 58.904 (sho)s 74.478 (ws)s 89.468 (short-step)s 139.834 (and)s 160.238 (long-step)s 206.254 (gait)s 227.267 (solutions)s 272.127 (for)s 287.999 (the)s 305.971 (ab)s 317.833 (o)s 323.004 (v)s 328.479 (emen)s 353.117 (tioned)s 385.688 (tuned)s 415.826 (straigh)s 448.463 (t-leg)s 230.621 y 0 (\050A\051)s 21.083 (and)s 43.079 (kneed)s 75.113 (\050C\051)s 95.892 (w)s 103.496 (alk)s 117.487 (ers,)s 138.534 (the)s 158.097 (p)s 164.485 (oin)s 178.781 (t-fo)s 195.814 (ot)s 209.902 (w)s 217.506 (alk)s 231.498 (er)s 245.007 (of)s 258.183 (Garcia)s 294.277 (et)s 307.757 (al.)s 323.669 (\0501998\051)s 358.441 (\050D\051,)s 382.718 (whic)s 404.314 (h)s 414.752 (is)s 426.467 (tuned)s 458.197 (b)s 463.976 (y)s 252.381 y 0 (de\257nition,)s 52.459 (and)s 74.351 (t)s 78.305 (w)s 85.909 (o)s 95.635 (other)s 124.857 (tuned)s 156.483 (straigh)s 189.12 (t-leg)s 214.662 (mo)s 229.566 (dels)s 252.127 (\050B)s 268.391 (and)s 290.284 (E\051.)s 309.286 (The)s 332.395 (parameters)s 389.692 (for)s 407.052 (eac)s 421.956 (h)s 432.29 (of)s 445.361 (these)s 274.141 y 0 (tuned)s 31.025 (w)s 38.629 (alk)s 52.621 (ers)s 69.745 (are)s 88.026 (listed)s 117.287 (in)s 130.062 (table)s 157.437 (1.)s 170.82 (W)s 181.162 (e)s 189.678 (mak)s 209.753 (e)s 218.27 (the)s 237.128 (follo)s 257.204 (wing)s 283.362 (observ)s 313.566 (ations)s 345.868 (on)s 361.077 (their)s 387.265 (b)s 393.653 (eha)s 409.774 (vior.)s 300.335 y 13.383 (1.)s 27.375 (All)s 45.321 (of)s 57.792 (these)s 85.836 (w)s 93.44 (alk)s 107.432 (ers)s 124.556 (can)s 144.631 (w)s 152.236 (alk)s 170.181 (at)s 183.565 (arbitrarily)s 236.277 (small)s 264.929 (ground-slop)s 321.292 (es.)s 329.269 y 13.383 (2.)s 27.375 (The)s 49.745 (simplest)s 92.311 (w)s 99.915 (alking)s 132.322 (mo)s 147.226 (del)s 164.729 (\050D\051)s 185.121 (is)s 195.993 (the)s 214.713 (only)s 238.603 (one)s 258.54 (with)s 283.343 (b)s 289.73 (oth)s 309.058 (gaits)s 335.138 (ha)s 346.392 (ving)s 370.283 (a)s 379.269 (step)s 402.308 (length)s 14 f 435.627 (/)s 13 f 447.186 (\260)s 15 f 325.295 y 453.463 (1)s 16 f 457.713 (=)s 15 f 461.963 (3)s 8 f 329.269 y 466.713 (.)s 358.202 y 13.383 (3.)s 27.375 (A)s 35.283 (t)s 42.729 (the)s 61.124 (smallest)s 102.758 (ground-slop)s 159.12 (es,)s 174.627 (the)s 193.023 (tuned)s 223.585 (straigh)s 256.222 (t-leg)s 280.701 (w)s 288.305 (alk)s 302.297 (ers)s 318.958 (with)s 343.437 (\257nite)s 370.958 (fo)s 380.083 (ot)s 393.003 (mass)s 419.429 (\050A,)s 438.128 (B,)s 452.113 (and)s 379.962 y 27.375 (E\051)s 43.395 (eac)s 58.299 (h)s 68.692 (ha)s 79.946 (v)s 85.421 (e)s 94.598 (one)s 115.333 (gait)s 137.893 (solution)s 179.981 (with)s 205.582 (step)s 229.42 (length)s 14 f 263.538 (/)s 13 f 276.196 (\260)s 8 f 286.784 (\050the)s 310.56 (short-step)s 362.473 (gait\051)s 389.291 (and)s 411.243 (one)s 431.978 (solution)s 401.722 y 27.375 (with)s 51.925 (step)s 74.71 (length)s 14 f 107.776 (/)s 13 f 119.335 (\260)s 15 f 397.749 y 125.612 (1)s 16 f 129.862 (=)s 15 f 134.112 (3)s 8 f 401.722 y 142.12 (\050the)s 164.845 (long-step)s 211.355 (gait\051.)s 241.641 (A)s 249.55 (t)s 257.066 (steep)s 281.764 (er)s 294.178 (ground-slop)s 350.54 (es)s 362.984 (\050)s 13 f 367.242 (\260)s 376.561 (\076)s 8 f 388.119 (0)s 13 f 393.594 (:)s 8 f 396.636 (01\051,)s 418.222 (all)s 433.039 (the)s 451.505 (gait)s 423.482 y 27.375 (solutions)s 73.122 (ha)s 84.376 (v)s 89.851 (e)s 98.368 (step)s 121.545 (length)s 14 f 155.004 (/)s 13 f 166.562 (\260)s 15 f 419.509 y 172.839 (1)s 16 f 177.089 (=)s 15 f 181.339 (3)s 8 f 423.482 y 189.739 (as)s 203.184 (seen)s 226.969 (most)s 253.797 (clearly)s 288.807 (in)s 301.582 (\257gure)s 332.029 (9b.)s 452.416 y 13.383 (4.)s 27.375 (The)s 50.576 (tuned)s 82.293 (kneed)s 114.314 (w)s 121.919 (alking)s 155.157 (solutions)s 201.596 (\050C\051)s 10 f 222.362 (se)s 231.317 (em)s 8 f 249.651 (to)s 263.726 (follo)s 283.801 (w)s 296.052 (a)s 305.869 (similar)s 342.544 (pattern)s 382.2 (to)s 396.276 (the)s 415.826 (straigh)s 448.463 (t-leg)s 474.176 y 27.375 (solutions)s 74.791 (in)s 89.236 (\257gure)s 121.353 (9.)s 139.745 (Ho)s 153.128 (w)s 160.732 (ev)s 171.074 (er,)s 189.008 (the)s 209.536 (long-step)s 258.108 (lengths)s 297.555 (of)s 311.696 (the)s 332.224 (tuned)s 364.919 (kneed)s 397.917 (w)s 405.522 (alk)s 419.513 (er)s 433.988 (are)s 453.938 (not)s 495.936 y 27.375 (prop)s 49.61 (ortional)s 90.265 (to)s 13 f 103.514 (\260)s 15 f 491.962 y 109.792 (1)s 16 f 114.042 (=)s 15 f 118.292 (3)s 8 f 495.936 y 126.558 (at)s 139.808 (v)s 145.283 (ery)s 163.734 (small)s 192.253 (ground-slop)s 248.615 (es.)s 265.664 (\050Note)s 296.251 (ho)s 307.506 (w)s 318.93 (the)s 337.655 (\134)s 14 f 343.13 (\243)s 8 f 351.646 (\042)s 360.638 (sym)s 379.557 (b)s 385.944 (ols)s 402.296 (trail)s 425.918 (o\256)s 441.297 (at)s 454.547 (the)s 517.696 y 27.375 (left)s 46.716 (of)s 59.365 (the)s 78.402 (plot)s 101.088 (as)s 114.711 (if)s 124.927 (they)s 149.743 (w)s 157.347 (ere)s 175.197 (migrating)s 225.289 (to)s 234.718 (w)s 242.323 (ards)s 266.317 (the)s 285.354 (linear)s 13 f 315.979 (y)s 8 f 325.079 (=)s 13 f 336.935 (ax)s 8 f 352.81 (scaling.\051)s 397.814 (In)s 411.68 (fact,)s 436.54 (further)s 539.456 y 27.375 (n)s 33.154 (umerical)s 78.122 (results)s 113.478 (indicate)s 155.373 (that)s 179.627 (this)s 201.508 (solution)s 243.464 (slo)s 255.996 (wly)s 276.904 (c)s 281.467 (hanges)s 317.948 (to)s 331.86 (a)s 341.514 (linear)s 372.49 (scaling)s 408.971 (at)s 422.883 (extremely)s 561.216 y 27.375 (small)s 56.833 (ground-slop)s 113.195 (es)s 126.836 (\050)s 13 f 131.094 (\260)s 14 f 141.755 (\274)s 8 f 154.656 (0)s 13 f 160.131 (:)s 8 f 163.172 (00015\051.)s 205.129 (Strictly)s 245.203 (sp)s 255.909 (eaking)s 291.085 (then,)s 320.075 (for)s 337.64 (the)s 357.303 (kneed)s 389.438 (w)s 397.042 (alk)s 411.034 (er,)s 427.887 (b)s 434.275 (oth)s 454.547 (the)s 582.976 y 27.375 (long-step)s 73.946 (and)s 94.907 (short-step)s 145.828 (gaits)s 171.716 (ha)s 182.97 (v)s 188.445 (e)s 196.63 (step)s 219.476 (lengths)s 14 f 256.923 (/)s 13 f 268.481 (\260)s 8 f 274.759 (,)s 281.185 (although)s 326.479 (the)s 345.006 (longer)s 377.555 (p)s 383.943 (erio)s 401.919 (d)s 411.321 (gait)s 432.89 (c)s 437.452 (hanges)s 604.736 y 27.375 (its)s 42.644 (scaling)s 78.597 (at)s 91.98 (extremely)s 142.502 (small)s 171.155 (ground-slop)s 227.517 (es.)s 633.67 y 13.383 (5.)s 27.375 (Although)s 75.687 (it)s 86.586 (is)s 97.546 (not)s 116.962 (sho)s 132.536 (wn)s 150.127 (in)s 162.851 (the)s 181.658 (plots,)s 211.487 (all)s 226.645 (of)s 239.065 (the)s 257.873 (tuned)s 288.847 (long-step)s 335.699 (gaits)s 361.867 (ha)s 373.121 (v)s 378.596 (e)s 387.062 (a)s 396.137 (certain)s 432.616 (ground-)s 655.43 y 27.375 (slop)s 46.598 (e)s 55.115 (b)s 61.503 (elo)s 74.582 (w)s 86.14 (whic)s 107.736 (h)s 117.469 (the)s 136.328 (gait)s 158.228 (is)s 169.238 (stable)s 200.933 (\050do)s 216.445 (wn)s 234.087 (to)s 247.47 (zero)s 270.617 (slop)s 289.841 (e\051.)s 685.43 y 229.402 (16)s end endp %%Page: 17 17 %%BeginPageSetup initializepage (T&AM; page: 17 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f3_12 sf ( )S 7 0 :M f8_12 sf ( )S 11 0 :M f6_12 sf ( )S 19 0 :M f9_12 sf ( )S 31 0 :M f10_12 sf ( )S f11_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 11 10.95 /CMBX10 findfont fdef 12 12 /CMBX12 findfont fdef 13 10.95 /CMMI10 findfont fdef 14 10.95 /CMSY10 findfont fdef 15 8 /CMR8 findfont fdef 16 8 /CMMI8 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 17 (Our)s 38.671 (n)s 44.45 (umerical)s 88.021 (results)s 121.981 (indicate)s 162.48 (that)s 185.337 (a)s 193.594 (step)s 215.904 (length)s 248.495 (prop)s 270.729 (ortional)s 310.65 (to)s 13 f 323.166 (\260)s 15 f 12.026 y 329.443 (1)s 16 f 333.693 (=)s 15 f 337.944 (3)s 8 f 16 y 345.476 (is)s 355.619 (the)s 373.61 (longest)s 409.911 (step)s 432.221 (p)s 438.608 (ossible)s 37.76 y 0 (\050and)s 25.11 (hence)s 55.087 (the)s 73.506 (smallest)s 115.163 (p)s 121.551 (o)s 126.722 (w)s 134.326 (er)s 146.691 (consumption)s 210.796 (p)s 217.184 (ossible\051)s 255.799 (at)s 268.743 (v)s 274.218 (ery)s 292.363 (small)s 320.575 (ground-slop)s 376.938 (es)s 389.334 (\050i.e.,)s 413.924 (lo)s 422.136 (w)s 433.255 (w)s 440.859 (alking)s 59.52 y 0 (sp)s 10.707 (eeds\051.)s 81.28 y 17 (As)s 33.917 (compared)s 84.567 (to)s 98.686 (w)s 106.29 (alk)s 120.282 (ers)s 138.142 (whic)s 159.738 (h)s 170.207 (do)s 186.151 (not)s 206.354 (meet)s 233.856 (the)s 253.451 (criteria)s 291.964 (in)s 305.475 (\257gure)s 336.658 (7)s 346.518 (ab)s 358.381 (o)s 363.552 (v)s 369.027 (e,)s 381.505 (tuned)s 413.266 (w)s 420.87 (alk)s 434.861 (ers)s 452.722 (will)s 103.04 y 0 (ha)s 11.254 (v)s 16.729 (e)s 24.611 (a)s 33.101 (longer)s 65.347 (step)s 87.89 (length)s 120.714 (at)s 133.462 (a)s 141.952 (giv)s 155.944 (en)s 169.909 (small)s 197.927 (ground-slop)s 254.289 (e)s 262.171 (\050assuming)s 313.367 (other)s 341.354 (parameters)s 397.416 (suc)s 412.381 (h)s 421.48 (as)s 434.289 (masses,)s 124.8 y 0 (inertias,)s 42.283 (and)s 63.748 (leg)s 80.955 (lengths)s 118.905 (are)s 137.359 (held)s 161.257 (constan)s 197.514 (t\051.)s 214.459 (This)s 239.635 (is)s 250.819 (illustrated)s 303.4 (b)s 309.18 (y)s 318.782 (comparing)s 372.519 (\257gures)s 407.459 (9)s 416.757 (and)s 438.222 (6)s 447.52 (from)s 146.561 y 0 (section)s 38.245 (5.2.)s 65.199 (A)s 73.108 (t)s 82.7 (an)s 93.955 (y)s 105.068 (ground-slop)s 161.431 (e)s 171.632 (where)s 204.98 (gaits)s 232.884 (exist)s 260.484 (for)s 278.928 (b)s 285.315 (oth)s 306.467 (tuned)s 339.176 (and)s 362.152 (un-tuned)s 410.679 (w)s 418.283 (alk)s 432.275 (ers,)s 454.547 (the)s 168.321 y 0 (tuned)s 31.643 (w)s 39.248 (alk)s 53.239 (ers)s 70.982 (ha)s 82.236 (v)s 87.711 (e)s 96.846 (a)s 106.59 (larger)s 138.294 (stance)s 172.431 (angle,)s 204.838 (and)s 226.748 (hence)s 257.783 (a)s 267.526 (longer)s 301.025 (step.)s 330.315 (Because)s 372.817 (the)s 392.294 (step)s 416.09 (p)s 422.478 (erio)s 440.454 (ds)s 455.125 (are)s 190.081 y 0 (appro)s 27.101 (ximately)s 72.756 (the)s 92.253 (same)s 120.327 (for)s 137.724 (similarly-scaled)s 215.469 (tuned)s 247.132 (and)s 269.062 (un-tuned)s 316.541 (w)s 324.146 (alk)s 338.137 (ers,)s 359.101 (tuned)s 390.764 (w)s 398.368 (alk)s 412.36 (ers)s 430.123 (will)s 451.444 (also)s 211.841 y 0 (b)s 6.388 (e)s 14.904 (faster)s 45.108 (than)s 70.658 (non-tuned)s 122.975 (w)s 130.579 (alk)s 144.571 (ers)s 161.695 (at)s 175.078 (a)s 184.203 (giv)s 198.195 (en)s 212.795 (ground-slop)s 269.157 (e.)s 12 f 249.563 y 0 (6.3)s 30.75 (Energy)s 77.16 (Calculations)s 154.11 (And)s 183.804 (Scaling)s 230.117 (F)s 237.478 (or)s 254.242 (Near-Zero-Slop)s 344.582 (e)s 355.242 (W)s 368.061 (alking)s 8 f 278.395 y 0 (Here,)s 29.891 (w)s 37.495 (e)s 46.784 (sho)s 62.357 (w)s 74.688 (that)s 99.184 (for)s 116.716 (general)s 155.235 (w)s 162.839 (alking)s 196.157 (mac)s 215.32 (hines)s 244.136 (that)s 268.633 (w)s 276.237 (alk)s 294.955 (at)s 309.11 (near-zero)s 357.393 (ground-slop)s 413.755 (es,)s 430.597 (the)s 450.227 (step)s 300.155 y 0 (length)s 34.711 (for)s 52.722 (small)s 82.627 (slop)s 101.851 (e)s 13 f 111.619 (\260)s 8 f 122.799 (is)s 135.062 (asymptotically)s 209.984 (prop)s 232.218 (ortional)s 274.259 (to)s 288.895 (either)s 13 f 321.203 (\260)s 15 f 296.182 y 327.48 (1)s 16 f 331.73 (=)s 15 f 335.98 (3)s 8 f 300.155 y 345.632 (or)s 360.298 (to)s 13 f 374.934 (\260)s 8 f 381.212 (.)s 392.877 (Th)s 406.564 (us)s 421.869 (far)s 439.881 (in)s 453.908 (our)s 321.915 y 0 (n)s 5.779 (umerical)s 50.636 (in)s 59.457 (v)s 64.932 (estigations,)s 122.759 (as)s 136.621 (seen)s 160.825 (from)s 187.128 (the)s 206.404 (n)s 212.183 (umerical)s 257.04 (results)s 292.285 (in)s 305.478 (\257gure)s 336.343 (9,)s 349.032 (w)s 356.636 (e)s 365.571 (\257nd)s 387.889 (that)s 412.032 (all)s 427.658 (solutions)s 343.675 y 0 (for)s 16.76 (zero-slop)s 59.13 (e-capable)s 107.188 (straigh)s 139.826 (t)s 147.734 (leg)s 164.767 (w)s 172.371 (alk)s 186.363 (ers)s 203.488 (apparen)s 241.539 (tly)s 258.268 (ob)s 270.131 (ey)s 284.427 (one)s 304.502 (of)s 316.972 (these)s 345.017 (t)s 348.971 (w)s 356.575 (o)s 365.7 (scalings.)s 11 f 380.758 y 0 (6.3.1)s 38.477 (Deriv)s 68.536 (ation)s 100.542 (Of)s 118.046 (Scaling)s 161.245 (Rule)s 191.152 (F)s 198.026 (or)s 213.706 (Straigh)s 253.346 (t-Legged)s 305.343 (W)s 317.312 (alk)s 333.228 (ers)s 8 f 409.59 y 0 (Consider)s 47.13 (a)s 57.669 (straigh)s 90.306 (t-legged)s 133.087 (w)s 140.691 (alk)s 154.683 (er,)s 172.297 (with)s 198.653 (curv)s 219.366 (ed)s 235.38 (feet,)s 261.177 (at)s 275.974 (the)s 296.246 (instan)s 325.203 (t)s 334.525 (prior)s 362.767 (to)s 377.564 (heelstrik)s 417.805 (e.)s 434.822 (A)s 442.73 (t)s 452.052 (this)s 431.35 y 0 (instan)s 28.957 (t,)s 13 f 39.66 (\265)s 16 f 432.992 y 44.8 (st)s 8 f 431.35 y 55.342 (=)s 13 f 66.9 (\265)s 16 f 433.134 y 72.04 (th)s 8 f 431.35 y 83.849 (\050ignore)s 13 f 120.679 (\265)s 16 f 433.134 y 125.82 (sh)s 8 f 431.35 y 138.49 (in)s 150.956 (\257gure)s 181.094 (1)s 189.91 (for)s 206.361 (the)s 224.91 (straigh)s 257.548 (t-leg)s 282.18 (case\051.)s 313.772 (The)s 335.971 (matrix)s 11 f 371.28 (M)s 8 f 386.575 (referred)s 426.811 (to)s 439.886 (earlier)s 453.11 y 0 (\050see)s 21.961 (equation)s 66.673 (7\051)s 80.057 (is)s 91.068 (actually)s 132.738 (a)s 141.863 (function)s 184.751 (of)s 13 f 197.222 (\265)s 16 f 454.752 y 202.362 (st)s 8 f 453.11 y 209.862 (,)s 216.554 (but)s 236.629 (since)s 13 f 263.457 (\265)s 16 f 454.752 y 268.597 (st)s 8 f 453.11 y 279.747 (is)s 290.758 (small)s 319.41 (w)s 327.015 (e)s 335.531 (write)s 11 f 485.87 y 174.748 (M)s 8 f 186.701 (\050)s 13 f 190.96 (\265)s 16 f 487.513 y 196.1 (st)s 8 f 485.87 y 203.6 (\051)s 210.9 (=)s 11 f 222.458 (M)s 8 f 234.412 (\0500\051)s 250.837 (+)s 14 f 261.787 (O)s 8 f 270.809 (\050)s 13 f 275.067 (\265)s 16 f 487.513 y 280.207 (st)s 8 f 485.87 y 287.707 (\051)s 13 f 291.966 (:)s 8 f 455.763 (\0509\051)s 518.63 y 0 (F)s 6.235 (or)s 19.827 (the)s 38.863 (presen)s 69.067 (t)s 77.154 (discussion,)s 131.7 (w)s 139.304 (e)s 147.999 (men)s 167.77 (tion)s 190.456 (that)s 214.359 (for)s 231.297 (zero-slop)s 273.667 (e-capable)s 321.903 (w)s 329.508 (alk)s 343.499 (ers,)s 11 f 363.888 (M)s 8 f 375.842 (\0500\051)s 393.661 (will)s 414.523 (b)s 420.91 (e)s 429.605 (diagonal)s 540.39 y 0 (when)s 29.718 (expressed)s 79.968 (in)s 93.87 (the)s 113.855 (co)s 124.501 (ordinate)s 168.85 (system)s 206.294 (implicit)s 247.571 (in)s 261.472 (\257gure)s 293.046 (4)s 303.298 (and)s 325.716 (equation)s 371.555 (7.)s 388.319 (In)s 403.133 (particular,)s 458.136 (its)s 562.15 y 0 (elemen)s 32.546 (t)s 13 f 41.114 (M)s 15 f 563.793 y 51.737 (11)s 8 f 562.15 y 65.046 (will)s 86.389 (b)s 92.777 (e)s 101.953 (equal)s 131.508 (to)s 145.551 (the)s 165.069 (total)s 191.887 (mass)s 219.435 (of)s 232.565 (the)s 252.083 (w)s 259.687 (alk)s 273.679 (er,)s 290.35 (while)s 319.601 (elemen)s 352.147 (t)s 13 f 360.715 (M)s 15 f 563.793 y 371.338 (22)s 8 f 562.15 y 384.648 (will)s 405.991 (b)s 412.378 (e)s 421.554 (smaller)s 460.022 (\050a)s 583.91 y 0 (function)s 43.443 (of)s 56.47 (mass)s 83.914 (distribution)s 144.178 (and)s 166.026 (w)s 173.63 (alk)s 187.622 (er)s 200.983 (geometry\051.)s 258.952 (Finally)s 291.65 (,)s 299.036 (for)s 316.352 (a)s 326.033 (straigh)s 358.67 (t-leg,)s 387.348 (p)s 393.735 (oin)s 408.031 (t-fo)s 425.065 (ot)s 439.004 (w)s 446.608 (alk)s 460.6 (er)s 605.67 y 0 (with)s 24.873 (a)s 33.929 (small)s 62.513 (fo)s 71.638 (ot)s 84.953 (mass)s 111.773 (\050as)s 129.406 (considered)s 182.962 (in)s 195.669 (subsection)s 248.647 (5.1\051,)s 13 f 273.533 (M)s 15 f 607.313 y 284.156 (22)s 8 f 605.67 y 296.738 (is)s 307.68 (appro)s 334.781 (ximately)s 379.729 (equal)s 408.557 (\050asymptotic\051)s 627.431 y 0 (to)s 13.383 (the)s 32.242 (fo)s 41.367 (ot)s 54.75 (mass.)s 649.191 y 17 (Recall)s 49.929 (\257gure)s 80.303 (4.)s 93.663 (No)s 107.046 (w)s 118.531 (w)s 126.135 (e)s 134.579 (express)s 174.592 (\137)s 13 f 172.679 (x)s 8 f 182.515 (and)s 205.702 (\137)s 13 f 203.733 (y)s 8 f 213.072 (in)s 225.774 (terms)s 256.209 (of)s 646.301 y 270.721 (\137)s 13 f 649.191 y 268.607 (\265)s 16 f 650.833 y 273.748 (st)s 8 f 649.191 y 284.825 (and)s 646.301 y 308.158 (\137)s 13 f 649.191 y 306.044 (\265)s 16 f 650.975 y 311.184 (th)s 8 f 649.191 y 319.652 (,)s 326.285 (at)s 339.596 (the)s 358.381 (heelstrik)s 398.622 (e)s 407.066 (con\257guration)s 685.43 y 229.402 (17)s end endp %%Page: 18 18 %%BeginPageSetup initializepage (T&AM; page: 18 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f5_12 sf ( )S 6 0 :M f3_12 sf ( )S 10 0 :M f6_12 sf ( )S 18 0 :M f9_12 sf ( )S 30 0 :M f10_12 sf ( )S 34 0 :M f11_12 sf ( )S 42 0 :M f12_12 sf ( )S 51 0 :M f14_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 10 10.95 /CMTI10 findfont fdef 11 10.95 /CMBX10 findfont fdef 13 10.95 /CMMI10 findfont fdef 14 10.95 /CMSY10 findfont fdef 15 8 /CMR8 findfont fdef 16 8 /CMMI8 findfont fdef 17 10.95 /CMEX10 findfont fdef 19 8 /CMSY8 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 0 (but)s 20.287 (just)s 42.155 (b)s 48.543 (efore)s 75.247 (heelstrik)s 115.489 (e)s 124.217 (\050)s 13 f 128.476 (\265)s 19 f 12.026 y 133.92 (\244)s 16 f 19.334 y 133.616 (th)s 8 f 16 y 145.478 (=)s 14 f 157.389 (\241)s 13 f 165.906 (\265)s 19 f 12.026 y 171.351 (\244)s 16 f 18.707 y 171.046 (st)s 8 f 16 y 178.547 (\051.)s 191.349 (W)s 201.69 (e)s 210.419 (de\257ne)s 242.264 (the)s 261.334 (length)s 13 f 295.004 (l)s 8 f 302.348 (to)s 315.944 (b)s 322.331 (e)s 331.06 (the)s 350.13 (distance)s 392.986 (b)s 399.373 (et)s 408.194 (w)s 415.798 (een)s 435.477 (the)s 454.547 (hip)s 37.76 y 0 (and)s 21.292 (the)s 40.15 (fo)s 49.275 (ot)s 62.658 (cen)s 78.171 (ter.)s 99.493 (W)s 109.835 (e)s 118.351 (obtain:)s 64.992 y 141.625 (\137)s 13 f 139.713 (x)s 8 f 155.971 (=)s 13 f 174.488 (R)s 8 f 182.886 (\050)s 62.102 y 189.259 (\137)s 13 f 64.992 y 187.145 (\265)s 16 f 66.635 y 192.285 (st)s 14 f 64.992 y 202.218 (\241)s 8 f 62.102 y 215.282 (\137)s 13 f 64.992 y 213.168 (\265)s 16 f 66.776 y 218.309 (th)s 8 f 64.992 y 226.777 (\051)s 233.468 (+)s 13 f 244.418 (l)s 8 f 249.726 (cos)s 13 f 266.212 (\265)s 19 f 61.018 y 271.656 (\244)s 16 f 67.699 y 271.352 (st)s 8 f 64.992 y 278.852 (\050)s 62.102 y 285.224 (\137)s 13 f 64.992 y 283.111 (\265)s 16 f 66.635 y 288.251 (st)s 14 f 64.992 y 298.184 (\241)s 8 f 62.102 y 311.248 (\137)s 13 f 64.992 y 309.134 (\265)s 16 f 66.776 y 314.275 (th)s 8 f 64.992 y 322.742 (\051)s 13 f 327.001 (;)s 8 f 86.752 y 142.178 (\137)s 13 f 140.209 (y)s 8 f 155.971 (=)s 14 f 174.488 (\241)s 13 f 183.004 (l)s 8 f 188.312 (sin)s 13 f 203.581 (\265)s 19 f 82.778 y 209.026 (\244)s 16 f 89.459 y 208.721 (st)s 8 f 86.752 y 216.222 (\050)s 83.863 y 222.594 (\137)s 13 f 86.752 y 220.48 (\265)s 16 f 88.395 y 225.62 (st)s 8 f 86.752 y 235.554 (+)s 83.863 y 248.618 (\137)s 13 f 86.752 y 246.504 (\265)s 16 f 88.536 y 251.644 (th)s 8 f 86.752 y 260.112 (\051)s 13 f 264.37 (:)s 8 f 74.258 y 450.288 (\05010\051)s 113.493 y 0 (Assume)s 41.168 (that)s 65.484 (as)s 13 f 79.52 (\260)s 14 f 89.825 (!)s 8 f 104.803 (0,)s 117.71 (the)s 137.16 (gait)s 159.651 (cycle)s 187.314 (step)s 211.083 (length)s 13 f 245.133 (\265)s 19 f 109.519 y 250.578 (\244)s 16 f 116.2 y 250.274 (st)s 8 f 113.493 y 262.016 (is)s 273.618 (asymptotically)s 347.879 (of)s 14 f 360.942 (O)s 8 f 369.963 (\050)s 13 f 374.222 (\260)s 16 f 109.519 y 380.499 (p)s 8 f 113.493 y 385.278 (\051)s 393.778 (for)s 411.129 (some)s 13 f 439.157 (p)s 448.694 (\076)s 8 f 461.238 (0.)s 135.253 y 0 (During)s 36.378 (the)s 54.627 (w)s 62.231 (alking)s 94.168 (step,)s 119.9 (the)s 138.149 (angular)s 177.112 (rates)s 132.363 y 205.475 (\137)s 13 f 135.253 y 203.361 (\265)s 16 f 136.895 y 208.501 (st)s 8 f 135.253 y 219.042 (and)s 132.363 y 241.839 (\137)s 13 f 135.253 y 239.725 (\265)s 16 f 137.037 y 244.865 (th)s 8 f 135.253 y 256.374 (m)s 265.195 (ust)s 282.896 (also)s 304.248 (b)s 310.635 (e)s 14 f 318.543 (O)s 8 f 327.565 (\050)s 13 f 331.823 (\260)s 16 f 131.279 y 338.1 (p)s 8 f 135.253 y 342.879 (\051.)s 354.843 (Moreo)s 384.682 (v)s 390.157 (er,)s 405.516 (at)s 418.291 (the)s 436.54 (instan)s 465.497 (t)s 157.013 y 0 (of)s 12.462 (heelstrik)s 52.703 (e,)s 64.255 (one)s 84.321 (or)s 97.726 (b)s 104.114 (oth)s 123.572 (of)s 136.034 (these)s 164.069 (rates)s 190.918 (m)s 199.739 (ust)s 218.041 (also)s 239.993 (b)s 246.381 (e)s 254.889 (of)s 267.351 (the)s 286.201 (same)s 313.628 (order)s 342.272 (of)s 354.734 (magnitude)s 14 f 408.867 (O)s 8 f 417.888 (\050)s 13 f 422.147 (\260)s 16 f 153.039 y 428.424 (p)s 8 f 157.013 y 433.203 (\051)s 441.102 (\050these)s 178.773 y 0 (claims)s 33.393 (are)s 51.546 (pro)s 67.089 (v)s 72.564 (ed)s 87.038 (b)s 92.817 (y)s 102.119 (con)s 118.24 (tradiction)s 168.636 (in)s 181.284 (Chatterjee)s 235.025 (and)s 256.19 (Garcia)s 291.454 (\0501998\051\051.)s 333.995 (Note)s 360.331 (that)s 383.929 (one)s 403.877 (w)s 411.482 (ould)s 435.688 (exp)s 452.722 (ect,)s 200.533 y 0 (from)s 25.885 (eq.)s 43.222 (10,)s 60.864 (that)s 86.501 (\137)s 13 f 84.589 (x)s 8 f 93.889 (=)s 14 f 105.447 (O)s 8 f 114.469 (\050)s 13 f 118.727 (\260)s 16 f 196.559 y 125.004 (p)s 8 f 200.533 y 129.783 (\051,)s 140.733 (while)s 171.293 (\137)s 13 f 169.325 (y)s 8 f 178.128 (=)s 14 f 189.686 (O)s 8 f 198.708 (\050)s 13 f 202.966 (\260)s 15 f 196.559 y 209.244 (2)s 16 f 213.494 (p)s 8 f 200.533 y 218.272 (\051.)s 222.293 y 17 (T)s 24.604 (ypically)s 60.8 (,)s 67.204 (at)s 80.228 (heelstrik)s 120.47 (e,)s 133.653 (\137)s 13 f 131.741 (x)s 14 f 141.04 (6)s 8 f 141.04 (=)s 152.599 (0)s 161.364 (in)s 173.78 (Eq.)s 193.344 (10,)s 210.698 (i.e.,)s 219.404 y 233.208 (\137)s 13 f 222.293 y 231.094 (\265)s 16 f 223.936 y 236.234 (st)s 14 f 222.293 y 245.449 (\241)s 8 f 219.404 y 257.795 (\137)s 13 f 222.293 y 255.681 (\265)s 16 f 224.077 y 260.821 (th)s 14 f 222.293 y 272.33 (6)s 8 f 272.33 (=)s 283.889 (0.)s 297.152 (As)s 312.975 (a)s 321.74 (result,)s 355.002 (for)s 371.403 (small)s 13 f 399.696 (\260)s 8 f 405.973 (,)s 412.378 (w)s 419.982 (e)s 428.139 (\257nd)s 449.68 (that)s 244.053 y 0 (the)s 19.629 (energy)s 55.409 (dissipation)s 111.051 (p)s 117.438 (er)s 131.014 (step)s 154.962 (is)s 166.744 (prop)s 188.978 (ortional)s 230.537 (to)s 246.604 (\137)s 13 f 244.691 (x)s 15 f 240.08 y 250.949 (2)s 8 f 244.053 y 260.12 (\050see)s 282.851 (Eq.)s 303.544 (7\051,)s 320.932 (or)s 14 f 335.117 (O)s 8 f 344.138 (\050)s 13 f 348.397 (\260)s 15 f 240.08 y 354.674 (2)s 16 f 358.924 (p)s 8 f 244.053 y 363.703 (\051.)s 378.181 (Since)s 407.543 (the)s 427.172 (p)s 433.559 (oten)s 453.938 (tial)s 265.813 y 0 (energy)s 35.751 (a)s 40.922 (v)s 46.093 (ailable)s 81.51 (p)s 87.897 (er)s 101.444 (step)s 125.363 (is)s 14 f 137.116 (O)s 8 f 146.137 (\050)s 13 f 150.396 (\260)s 16 f 261.84 y 156.673 (p)s 15 f 160.952 (+1)s 8 f 265.813 y 172.313 (\051)s 180.963 (\050step)s 209.14 (length)s 14 f 243.34 (\243)s 8 f 256.249 (slop)s 275.472 (e\051,)s 292.216 (w)s 299.82 (e)s 309.078 (\257nd)s 331.72 (that)s 356.186 (energy)s 391.938 (balance)s 432.221 (requires)s 287.573 y 0 (that)s 23.725 (2)s 13 f 29.2 (p)s 8 f 37.751 (=)s 13 f 49.309 (p)s 8 f 57.252 (+)s 68.202 (1,)s 80.368 (or)s 13 f 93.782 (p)s 8 f 102.333 (=)s 113.891 (1,)s 126.058 (i.e.,)s 146.741 (the)s 165.6 (step)s 188.777 (length)s 222.235 (is)s 233.246 (prop)s 255.481 (ortional)s 296.27 (to)s 13 f 309.653 (\260)s 8 f 315.931 (.)s 309.333 y 17 (On)s 35.372 (the)s 54.352 (other)s 83.096 (hand,)s 113.664 (for)s 130.546 (some)s 158.103 (gaits)s 184.444 (of)s 197.036 (some)s 224.594 (w)s 232.198 (alk)s 246.19 (ers,)s 266.508 (it)s 277.58 (ma)s 291.876 (y)s 301.427 (happ)s 325.456 (en)s 340.177 (that)s 365.937 (\137)s 13 f 364.024 (x)s 8 f 373.527 (=)s 385.288 (0)s 394.535 (at)s 408.04 (heelstrik)s 448.281 (e,)s 459.991 (or)s 328.204 y 2.114 (\137)s 13 f 331.094 y 0 (\265)s 16 f 332.736 y 5.14 (st)s 14 f 331.094 y 15.459 (\241)s 8 f 328.204 y 28.908 (\137)s 13 f 331.094 y 26.794 (\265)s 16 f 332.877 y 31.934 (th)s 8 f 331.094 y 44.407 (=)s 56.928 (0.)s 72.044 (In)s 86.31 (those)s 115.54 (cases,)s 146.8 (the)s 166.236 (energy)s 201.824 (dissipation)s 257.273 (p)s 263.661 (er)s 277.044 (step)s 300.799 (is)s 14 f 312.388 (O)s 8 f 321.409 (\050)s 327.636 (\137)s 13 f 325.668 (y)s 15 f 327.12 y 331.429 (2)s 8 f 331.094 y 336.179 (\051)s 344.665 (or)s 14 f 358.657 (O)s 8 f 367.678 (\050)s 13 f 371.937 (\260)s 15 f 327.12 y 378.214 (4)s 16 f 382.464 (p)s 8 f 331.094 y 387.243 (\051.)s 401.143 (As)s 417.902 (b)s 424.29 (efore,)s 454.547 (the)s 352.854 y 0 (p)s 6.388 (oten)s 26.767 (tial)s 46.869 (energy)s 82.515 (a)s 87.686 (v)s 92.857 (ailable)s 128.168 (p)s 134.555 (er)s 147.997 (step)s 171.81 (is)s 14 f 183.457 (O)s 8 f 192.479 (\050)s 13 f 196.737 (\260)s 16 f 348.88 y 203.015 (p)s 15 f 207.293 (+1)s 8 f 352.854 y 218.655 (\051.)s 232.73 (Energy)s 270.961 (balance)s 311.138 (therefore)s 357.764 (requires)s 399.585 (4)s 13 f 405.06 (p)s 8 f 414.671 (=)s 13 f 427.289 (p)s 8 f 435.656 (+)s 447.03 (1,)s 459.991 (or)s 13 f 374.614 y 0 (p)s 8 f 9.439 (=)s 21.885 (1)s 13 f 27.36 (=)s 8 f 32.835 (3,)s 45.668 (i.e.,)s 67.017 (the)s 86.409 (step)s 110.119 (length)s 10 f 144.11 (c)s 148.587 (an)s 8 f 164.523 (b)s 170.911 (e)s 179.96 (prop)s 202.195 (ortional)s 243.516 (to)s 13 f 257.433 (\260)s 15 f 370.64 y 263.71 (1)s 16 f 267.96 (=)s 15 f 272.21 (3)s 8 f 374.614 y 276.96 (.)s 286.467 (The)s 309.508 (same)s 337.477 (result)s 368.518 (holds)s 397.703 (true)s 421.383 (if)s 433.866 (\137)s 13 f 431.953 (x)s 8 f 442.395 (is)s 453.938 (not)s 396.374 y 0 (exactly)s 37.598 (zero,)s 63.691 (but)s 83.647 (a)s 92.653 (higher-order)s 154.675 (quan)s 177.791 (tit)s 189.046 (y)s 193.912 (,)s 200.508 (suc)s 215.473 (h)s 225.088 (that)s 393.484 y 250.807 (\137)s 13 f 396.374 y 248.693 (\265)s 16 f 398.016 y 253.834 (st)s 14 f 396.374 y 263.529 (\241)s 8 f 393.484 y 276.354 (\137)s 13 f 396.374 y 274.24 (\265)s 16 f 398.158 y 279.381 (th)s 8 f 396.374 y 290.89 (=)s 14 f 302.448 (O)s 8 f 311.47 (\050)s 13 f 315.728 (\260)s 15 f 392.4 y 322.006 (2)s 16 f 326.256 (p)s 8 f 396.374 y 331.035 (\051,)s 341.889 (or)s 355.184 (smaller.)s 397.21 (Th)s 410.898 (us,)s 427.897 (it)s 438.728 (is)s 449.619 (seen)s 418.134 y 0 (that)s 23.725 (the)s 42.583 (only)s 66.613 (t)s 70.567 (w)s 78.171 (o)s 87.296 (p)s 93.683 (ossibilities)s 146.183 (for)s 162.942 (step)s 186.12 (lengths)s 223.897 (prop)s 246.132 (ortional)s 286.921 (to)s 13 f 300.304 (\260)s 16 f 414.16 y 306.582 (p)s 8 f 418.134 y 315.01 (are)s 13 f 333.291 (p)s 8 f 341.842 (=)s 353.4 (1)s 362.525 (and)s 13 f 383.817 (p)s 8 f 392.367 (=)s 403.926 (1)s 13 f 409.401 (=)s 8 f 414.876 (3.)s 11 f 455.216 y 0 (6.3.2)s 38.477 (Predicting)s 100.017 (The)s 125.742 (Short-Step)s 189.168 (T)s 196.878 (ransition)s 249.531 (Slop)s 273.666 (e)s 8 f 484.048 y 0 (for)s 16.177 (P)s 23.325 (oin)s 37.62 (t-F)s 51.764 (o)s 57.543 (ot)s 70.344 (W)s 80.686 (alk)s 94.677 (ers.)s 115.866 (Short-step)s 168.299 (gaits)s 193.936 (for)s 210.112 (straigh)s 242.75 (t-legged)s 283.533 (w)s 291.138 (alk)s 305.129 (ers)s 321.671 (with)s 346.03 (non-negligible)s 415.405 (fo)s 424.53 (ot)s 437.331 (masses)s 505.808 y 0 (and)s 21.512 (p)s 27.899 (oin)s 42.195 (t-feet)s 71.311 (will)s 92.214 (t)s 96.168 (ypically)s 137.146 (exhibit)s 174.171 (a)s 183.515 (transition)s 233.71 (region)s 266.81 (b)s 273.198 (et)s 282.019 (w)s 289.623 (een)s 309.309 (the)s 328.388 (linear)s 359.055 (and)s 380.566 (cub)s 397.904 (e-ro)s 416.488 (ot)s 430.092 (scalings,)s 527.568 y 0 (as)s 13.702 (discussed)s 61.592 (in)s 74.624 (subsection)s 127.928 (5.1.2.)s 159.117 (Here,)s 188.365 (w)s 195.969 (e)s 204.743 (consider)s 247.675 (the)s 266.791 (e\256ect)s 295.944 (of)s 308.673 (adding)s 344.822 (a)s 354.204 (small)s 383.114 (but)s 403.447 (non-negligible)s 549.329 y 0 (fo)s 9.125 (ot)s 23.041 (mass)s 50.461 (of)s 13 f 63.464 (\275)s 8 f 73.308 (times)s 103.101 (the)s 122.492 (total)s 149.182 (mass)s 176.603 (\050here)s 205.149 (assumed)s 249.603 (nondimensionalized)s 346.921 (to)s 360.837 (unit)s 379.999 (y\051,)s 397.394 (to)s 411.309 (the)s 430.7 (simplest)s 571.089 y 0 (p)s 6.388 (oin)s 20.683 (t-fo)s 37.717 (ot)s 51.1 (w)s 58.704 (alk)s 72.696 (er.)s 592.849 y 17 (Assuming)s 13 f 68.557 (\265)s 16 f 594.491 y 73.697 (st)s 8 f 592.849 y 86.095 (is)s 98.353 (small,)s 131.607 (the)s 151.713 (kinetic)s 188.548 (energy)s 224.805 (dissipated)s 277.275 (in)s 291.297 (the)s 311.403 (collision)s 354.687 (is)s 366.945 (simply)s 403.233 (\050)s 11 f 407.491 (M)s 8 f 419.445 (\0500\051)s 438.334 (is)s 450.592 (no)s 461.847 (w)s 614.609 y 0 (diag[1)s 13 f 31.633 (\275)s 8 f 37.295 (];)s 47.028 (see)s 64.73 (discussion)s 116.013 (of)s 11 f 128.484 (M)s 8 f 140.438 (\0500\051)s 158.079 (ab)s 169.942 (o)s 175.113 (v)s 180.588 (e)s 189.104 (also\051)s 639.961 y 202.581 (1)s 5.475 .438 202.581 644.85 r 654.88 y 202.581 (2)s 17 f 638.499 y 211.081 (\241)s 8 f 647.369 y 218.068 (\137)s 13 f 216.099 (y)s 15 f 642.848 y 221.861 (2)s 8 f 647.369 y 229.044 (+)s 13 f 239.994 (\275)s 8 f 247.568 (\137)s 13 f 245.656 (x)s 15 f 642.848 y 251.914 (2)s 17 f 638.499 y 256.664 (\242)s 13 f 647.369 y 265.333 (:)s 8 f 685.43 y 229.402 (18)s end endp %%Page: 19 19 %%BeginPageSetup initializepage (T&AM; page: 19 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f3_12 sf ( )S 7 0 :M f6_12 sf ( )S 15 0 :M f9_12 sf ( )S 27 0 :M f10_12 sf ( )S 31 0 :M f11_12 sf ( )S 39 0 :M f14_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 11 10.95 /CMBX10 findfont fdef 13 10.95 /CMMI10 findfont fdef 14 10.95 /CMSY10 findfont fdef 15 8 /CMR8 findfont fdef 16 8 /CMMI8 findfont fdef 19 8 /CMSY8 findfont fdef 41 41 translate 72 72.27 div dup scale 8 f 16 y 0 (Assuming)s 50.309 (a)s 59.434 (step)s 82.612 (length)s 116.07 (comparable)s 174.501 (to)s 13 f 187.884 (\260)s 16 f 12.026 y 194.161 (p)s 8 f 16 y 202.59 (as)s 216.034 (b)s 222.422 (efore,)s 251.956 (w)s 259.561 (e)s 268.077 (\257nd)s 289.977 (that)s 313.702 (energy)s 348.712 (balance)s 388.254 (requires)s 13 f 48.76 y 180.588 (\260)s 16 f 44.239 y 186.865 (p)s 15 f 191.144 (+1)s 8 f 48.76 y 205.547 (=)s 14 f 217.105 (O)s 8 f 226.127 (\050)s 13 f 230.385 (\260)s 15 f 44.239 y 236.663 (4)s 16 f 240.913 (p)s 8 f 48.76 y 248.125 (+)s 13 f 259.075 (\275\260)s 15 f 44.239 y 271.013 (2)s 16 f 275.264 (p)s 8 f 48.76 y 280.042 (\051)s 13 f 286.126 (;)s 8 f 81.52 y 0 (or)s 13 f 103.28 y 180.073 (\260)s 15 f 98.759 y 186.35 (3)s 16 f 190.6 (p)s 19 f 194.879 (\241)s 15 f 201.49 (1)s 8 f 103.28 y 208.674 (+)s 13 f 219.624 (\275\260)s 16 f 98.759 y 231.562 (p)s 19 f 235.841 (\241)s 15 f 242.452 (1)s 8 f 103.28 y 250.244 (=)s 14 f 261.802 (O)s 8 f 270.824 (\0501\051)s 13 f 286.641 (:)s 8 f 131.54 y 0 (F)s 6.235 (or)s 13 f 20.015 (\275)s 8 f 29.692 (an)s 40.946 (y)s 50.741 (nonzero)s 91.895 (p)s 98.283 (ositiv)s 123.893 (e)s 132.776 (constan)s 169.032 (t,)s 180.439 (this)s 202.158 (expression)s 255.296 (implies)s 13 f 292.831 (p)s 8 f 301.991 (=)s 314.159 (1)s 323.649 (as)s 13 f 337.459 (\260)s 8 f 347.752 (b)s 354.14 (ecomes)s 391.675 (arbitrarily)s 444.752 (small)s 153.3 y 0 (\050i.e.,)s 25.599 (step)s 49.303 (length)s 14 f 83.288 (/)s 13 f 95.723 (\260)s 8 f 106.177 (at)s 120.087 (v)s 125.562 (ery)s 144.672 (small)s 173.851 (ground-slop)s 230.213 (es\051.)s 253.145 (On)s 271.921 (the)s 291.305 (other)s 320.454 (hand,)s 351.528 (for)s 368.814 (su\261cien)s 406.896 (tly)s 424.151 (small)s 453.33 (but)s 175.061 y 0 (\257xed)s 13 f 27.345 (\260)s 8 f 33.622 (,)s 41.417 (taking)s 76.062 (smaller)s 114.752 (and)s 136.926 (smaller)s 13 f 175.617 (\275)s 8 f 181.278 (,)s 189.073 (the)s 208.813 (scaling)s 245.648 (ev)s 255.99 (en)s 266.636 (tually)s 298.847 (rev)s 313.478 (erts)s 335.743 (to)s 13 f 350.009 (p)s 8 f 360.03 (=)s 373.059 (1)s 13 f 378.534 (=)s 8 f 384.009 (3.)s 400.04 (The)s 423.43 (transition)s 196.821 y 0 (o)s 5.779 (ccurs)s 34.976 (when)s 64.691 (the)s 84.671 (t)s 88.626 (w)s 96.23 (o)s 106.477 (left)s 126.762 (hand)s 155.26 (side)s 178.343 (terms)s 209.974 (ab)s 221.836 (o)s 227.007 (v)s 232.482 (e)s 242.121 (are)s 261.524 (comparable,)s 324.4 (or)s 13 f 338.936 (\275)s 8 f 349.51 (=)s 14 f 362.939 (O)s 8 f 371.96 (\050)s 13 f 376.219 (\260)s 15 f 192.847 y 382.496 (2)s 16 f 386.746 (p)s 8 f 196.821 y 391.525 (\051,)s 403.878 (in)s 417.776 (whic)s 439.372 (h)s 450.227 (case)s 218.581 y 0 (clearly)s 13 f 35.796 (p)s 8 f 45.657 (=)s 58.526 (1)s 13 f 64.001 (=)s 8 f 69.476 (3.)s 85.217 (Th)s 98.905 (us,)s 116.982 (the)s 136.626 (transition)s 187.387 (o)s 193.166 (ccurs)s 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338.213 (al)s 350.679 (Engine)s 383.291 (ering)s 8 f 407.497 (,)s 414.397 (120\0502\051:281\173)s 59.52 y 21.9 (288.)s 90.28 y 0 (Garcia,)s 38.041 (M.,)s 57.422 (Ruina,)s 92.467 (A.,)s 110.023 (Coleman,)s 158.299 (M.,)s 177.68 (and)s 198.484 (Chatterjee,)s 255.003 (A.)s 269.42 (\0501996\051.)s 306.938 (P)s 314.086 (assiv)s 336.716 (e-dynamic)s 388.849 (mo)s 403.753 (dels)s 425.226 (of)s 437.209 (h)s 442.988 (uman)s 112.04 y 21.9 (gait.)s 10 f 47.934 (Pr)s 59.419 (o)s 64.456 (c)s 68.934 (e)s 73.411 (e)s 77.888 (dings)s 106.368 (of)s 119.177 (the)s 137.302 (Confer)s 169.343 (enc)s 185.013 (e)s 193.905 (on)s 209.512 (Biome)s 239.606 (chanics)s 278.719 (and)s 299.923 (Neur)s 323.033 (al)s 335.283 (Contr)s 362.566 (ol)s 374.816 (of)s 387.624 (Movement)s 8 f 436.899 (,)s 443.536 (pages)s 133.8 y 21.9 (32\17333.)s 164.561 y 0 (Gosw)s 25.991 (ami,)s 50.516 (A.,)s 68.654 (Espiau,)s 107.991 (B.,)s 125.673 (and)s 147.118 (Keramane,)s 202.698 (A.)s 217.756 (\0501997\051.)s 256.525 (Limit)s 286.639 (cycles)s 318.182 (in)s 331.111 (a)s 340.389 (passiv)s 369.102 (e)s 377.772 (compass)s 421.239 (gait)s 443.292 (bip)s 458.805 (ed)s 186.321 y 21.9 (and)s 43.192 (passivit)s 79.205 (y-mimic)s 117.53 (king)s 141.559 (con)s 157.68 (trol)s 178.394 (la)s 186.606 (ws.)s 10 f 206.73 (Journal)s 247.038 (of)s 259.91 (A)s 267.77 (utonomous)s 323.456 (R)s 330.884 (ob)s 340.958 (ots)s 8 f 354.67 (.)s 362.566 (In)s 376.253 (Press.)s 217.081 y 0 (Gosw)s 25.991 (ami,)s 50.176 (A.,)s 67.973 (Th)s 81.661 (uilot,)s 110.104 (B.,)s 127.446 (and)s 148.552 (Espiau,)s 187.55 (B.)s 201.812 (\0501996\051.)s 239.823 (Compass-lik)s 297.736 (e)s 306.067 (bip)s 321.58 (edal)s 344.511 (rob)s 360.662 (ot)s 373.86 (part)s 397.43 (I:)s 407.89 (Stabilit)s 442.87 (y)s 452.113 (and)s 238.841 y 21.9 (bifurcation)s 77.593 (of)s 90.064 (passiv)s 118.777 (e)s 127.294 (gaits.)s 10 f 157.759 (INRIA)s 194.387 (R)s 201.814 (ese)s 215.806 (ar)s 225.46 (ch)s 240.011 (R)s 247.439 (ep)s 257.513 (ort)s 275.282 (No.)s 296.294 (2996)s 8 f 318.681 (.)s 269.601 y 0 (Hatze,)s 35.216 (H.)s 50.796 (\0501989\051.)s 91.123 (Neurom)s 128.87 (uscular)s 167.354 (con)s 183.474 (trol)s 204.864 (systems)s 246.177 (mo)s 261.081 (deling:)s 298.933 (A)s 311.47 (critical)s 348.677 (surv)s 368.843 (ey)s 383.815 (of)s 396.961 (recen)s 421.629 (t)s 430.213 (dev)s 446.638 (elop-)s 291.361 y 21.9 (men)s 41.671 (ts.)s 10 f 58.145 (IEEE)s 88.567 (T)s 95.563 (r)s 99.62 (ansactions)s 153.628 (on)s 169.298 (A)s 177.158 (utomatic)s 222.771 (Contr)s 250.054 (ol)s 8 f 258.449 (,)s 265.141 (A)s 273.049 (C-25:375\173385.)s 322.121 y 0 (Ho)s 13.383 (w)s 20.987 (ell,)s 40.301 (G.)s 56.924 (W.)s 76.207 (and)s 98.837 (Baillieul,)s 146.591 (J.)s 160.247 (\0501998\051.)s 202.547 (Simple)s 239.776 (con)s 255.897 (trollable)s 300.457 (w)s 308.061 (alking)s 341.945 (mec)s 360.499 (hanisms)s 403.934 (whic)s 425.53 (h)s 436.601 (exhibit)s 343.881 y 21.9 (bifurcations.)s 85.802 (T)s 92.798 (o)s 101.705 (app)s 119.651 (ear)s 137.712 (in)s 10 f 150.269 (Pr)s 161.754 (o)s 166.791 (c)s 171.269 (e)s 175.746 (e)s 180.223 (dings)s 208.565 (of)s 221.236 (the)s 239.224 (37th)s 263.369 (IEEE)s 293.59 (Confer)s 325.631 (enc)s 341.301 (e)s 350.055 (on)s 365.524 (De)s 378.269 (cision)s 409.969 (and)s 431.035 (Contr)s 458.318 (ol)s 8 f 466.713 (.)s 374.641 y 0 (Katz,)s 30.331 (A.)s 45.653 (\0501994\051.)s 10 f 85.211 (Subsonic)s 131.207 (A)s 139.067 (irplane)s 176.529 (Performanc)s 232.368 (e)s 8 f 237.405 (.)s 246.546 (So)s 258.408 (ciet)s 275.137 (y)s 284.984 (of)s 297.873 (Automotiv)s 349.277 (e)s 358.212 (Engineers,)s 411.902 (W)s 422.244 (arrendale,)s 396.401 y 21.9 (P)s 28.44 (A.)s 427.161 y 0 (Lattanzio,)s 54.14 (H.,)s 73.756 (Kuenzler,)s 124.733 (G.,)s 144.729 (and)s 167.358 (Reading,)s 214.806 (M.)s 232.871 (\050Ma)s 252.338 (y)s 263.104 (1992\051.)s 301.142 (P)s 308.29 (assiv)s 330.92 (e)s 340.773 (dynamic)s 386.214 (w)s 393.818 (alking.)s 434.593 (Pro)s 452.417 (ject)s 448.921 y 21.9 (Rep)s 41.215 (ort,)s 61.928 (Human)s 100.558 (P)s 107.706 (o)s 112.876 (w)s 120.481 (er)s 133.286 (Lab.)s 158.38 (Cornell)s 196.735 (Univ)s 219.548 (ersit)s 240.018 (y)s 244.885 (.)s 479.682 y 0 (McGeer,)s 43.506 (T.)s 57.226 (\0501990a\051.)s 99.578 (P)s 106.726 (assiv)s 129.356 (e)s 136.993 (dynamic)s 180.216 (w)s 187.82 (alking.)s 10 f 223.177 (International)s 288.851 (Journal)s 328.349 (of)s 340.412 (R)s 347.839 (ob)s 357.913 (otics)s 383.127 (R)s 390.555 (ese)s 404.547 (ar)s 414.201 (ch)s 8 f 424.834 (,)s 430.822 (9:62\17382.)s 510.442 y 0 (McGeer,)s 44.059 (T.)s 58.469 (\0501990b\051.)s 102.557 (P)s 109.705 (assiv)s 132.335 (e)s 140.662 (w)s 148.266 (alking)s 180.622 (with)s 205.374 (knees.)s 10 f 238.876 (Pr)s 250.362 (o)s 255.399 (c)s 259.876 (e)s 264.353 (e)s 268.83 (dings)s 297.199 (of)s 309.897 (the)s 327.911 (IEEE)s 358.159 (Confer)s 390.2 (enc)s 405.87 (e)s 414.651 (on)s 430.147 (R)s 437.574 (ob)s 447.648 (otics)s 532.202 y 21.9 (and)s 43.167 (A)s 51.027 (utomation)s 8 f 99.438 (,)s 106.129 (2:1640\1731645.)s 562.962 y 0 (McGeer,)s 44.308 (T.)s 58.986 (\0501992\051.)s 97.532 (Principles)s 148.345 (of)s 160.894 (w)s 168.498 (alking)s 201.122 (and)s 222.492 (running.)s 267.759 (In)s 10 f 281.525 (A)s 289.104 (dvanc)s 315.968 (es)s 329.472 (in)s 342.976 (Comp)s 370.399 (ar)s 380.053 (ative)s 406.709 (and)s 428.048 (Envir)s 454.084 (on-)s 584.722 y 21.9 (mental)s 57.998 (Physiolo)s 97.607 (gy,)s 115.236 (V)s 122.536 (ol.)s 138.206 (11)s 8 f 149.4 (.)s 156.091 (Springer-V)s 207.252 (erlag,)s 237.091 (Berlin.)s 615.482 y 0 (McGeer,)s 44.58 (T.)s 59.476 (\0501993\051.)s 98.671 (Dynamics)s 149.671 (and)s 171.259 (con)s 187.38 (trol)s 208.389 (of)s 221.156 (bip)s 236.668 (edal)s 260.081 (lo)s 268.902 (comotion.)s 10 f 321.48 (Journal)s 362.06 (of)s 375.204 (The)s 393.113 (or)s 402.767 (etic)s 419.277 (al)s 431.862 (Biolo)s 456.36 (gy)s 8 f 466.713 (,)s 637.242 y 21.9 (163:277\173314.)s 685.43 y 229.402 (23)s end endp %%Page: 24 24 %%BeginPageSetup initializepage (T&AM; page: 24 of 33)setjob %%EndPageSetup gS 0 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(B.,)s 58.9 (Gosw)s 84.891 (ami,)s 108.79 (A.,)s 126.302 (and)s 147.051 (Espiau,)s 185.763 (B.)s 199.668 (\0501997\051.)s 237.096 (Bifurcation)s 293.919 (and)s 314.668 (c)s 319.23 (haos)s 343.69 (in)s 355.922 (a)s 364.504 (simple)s 398.089 (passiv)s 426.802 (e)s 434.776 (bip)s 450.288 (edal)s 142.8 y 21.9 (gait.)s 10 f 48.046 (IEEE)s 78.469 (International)s 144.953 (Confer)s 176.994 (enc)s 192.664 (e)s 201.619 (on)s 217.289 (R)s 224.717 (ob)s 234.791 (otics)s 260.815 (and)s 282.083 (A)s 289.942 (utomation)s 8 f 338.353 (.)s 173.561 y 0 (Win)s 20.075 (ter,)s 39.431 (D.)s 53.55 (A.)s 67.517 (\0501987\051.)s 10 f 104.303 (The)s 125.828 (Biome)s 155.922 (chanics)s 194.236 (and)s 214.641 (Motor)s 246.964 (Contr)s 274.247 (ol)s 285.698 (of)s 297.708 (Human)s 335.487 (Gait)s 8 f 356.551 (.)s 362.92 (Univ)s 385.732 (ersit)s 406.203 (y)s 414.695 (of)s 426.229 (W)s 436.57 (aterlo)s 464.28 (o)s 195.321 y 21.9 (Press.)s 226.081 y 0 (Y)s 7.3 (amaguc)s 43.496 (hi,)s 60.314 (G.)s 76.399 (T.)s 91.8 (and)s 113.892 (Za)s 126.667 (jac,)s 148.047 (F.)s 162.688 (E.)s 177.632 (\0501990\051.)s 218.332 (Restoring)s 268.651 (unassisted)s 321.951 (natural)s 361.107 (gait)s 383.808 (to)s 397.992 (paraplegics)s 455.459 (via)s 247.841 y 21.9 (functional)s 73.865 (neurom)s 109.483 (uscular)s 147.851 (stim)s 168.291 (ulation:)s 210.779 (A)s 223.202 (computer)s 272.46 (sim)s 288.641 (ulation)s 326.31 (study)s 351.921 (.)s 10 f 361.488 (IEEE)s 392.426 (T)s 399.421 (r)s 403.479 (ansactions)s 458.002 (on)s 269.601 y 21.9 (Biome)s 51.994 (dic)s 65.426 (al)s 77.739 (Engine)s 110.351 (ering)s 8 f 134.556 (,)s 141.248 (37:886\173902.)s 685.43 y 229.402 (24)s end endp %%Page: 25 25 %%BeginPageSetup initializepage (T&AM; page: 25 of 33)setjob %%EndPageSetup gS 0 0 552 730 rC 0 0 :M f4_12 sf ( )S 3 0 :M f6_12 sf ( )S 11 0 :M f11_12 sf ( )S 19 0 :M f16_12 sf ( )S f17_12 sf ( )S f18_12 sf ( )S f19_12 sf ( )S 0 0 :M initclip TeXdict begin 8 10.95 /CMR10 findfont fdef 13 10.95 /CMMI10 findfont fdef 16 8 /CMMI8 findfont fdef 41 41 translate 72 72.27 div dup scale 1.052 1.052 57.852 168.77 sps -139 -590 translate %%BeginDocument: kneed.config.eps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: Adobe Illustrator(TM) 5.5 %%For: (SRF) (LNS) %%Title: (kneed.config.eps) %%CreationDate: (7/9/98) (4:08 PM) %%BoundingBox: 139 590 481 745 %%HiResBoundingBox: 139.4053 590.2239 480.568 744.257 %%DocumentProcessColors: Black %%DocumentFonts: Helvetica %%+ Symbol %%+ Times-Italic %%+ Times-Roman %%DocumentSuppliedResources: procset Adobe_level2_AI5 1.0 0 %%+ procset Adobe_typography_AI5 1.0 0 %%+ procset Adobe_IllustratorA_AI5 1.0 0 %AI5_FileFormat 1.2 %AI3_ColorUsage: Black&White %AI3_TemplateBox: 306 396 306 396 %AI3_TileBox: 0 0 552 728 %AI3_DocumentPreview: Macintosh_ColorPic %AI5_ArtSize: 612 792 %AI5_RulerUnits: 2 %AI5_ArtFlags: 1 0 0 1 0 0 1 1 0 %AI5_TargetResolution: 800 %AI5_NumLayers: 1 %AI5_OpenToView: 54 768 2 826 581 18 1 1 3 40 %AI5_OpenViewLayers: 7 %%EndComments %%BeginProlog %%BeginResource: procset Adobe_level2_AI5 1.0 0 %%Title: (Adobe Illustrator (R) Version 5.0 Level 2 Emulation) %%Version: 1.0 %%CreationDate: (04/10/93) () %%Copyright: ((C) 1987-1993 Adobe Systems Incorporated All Rights Reserved) userdict /Adobe_level2_AI5 21 dict dup begin put /packedarray where not { userdict begin /packedarray { array astore readonly } bind def /setpacking /pop load def /currentpacking false def end 0 } if pop userdict /defaultpacking currentpacking put true setpacking /initialize { Adobe_level2_AI5 begin } bind def /terminate { currentdict Adobe_level2_AI5 eq { end } if } bind def mark /setcustomcolor where not { /findcmykcustomcolor { 5 packedarray } bind def /setcustomcolor { exch aload pop pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop setcmykcolor } def } if /gt38? mark {version cvx exec} stopped {cleartomark true} {38 gt exch pop} ifelse def userdict /deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt put userdict /level2? systemdict /languagelevel known dup { pop systemdict /languagelevel get 2 ge } if put level2? not { /setcmykcolor where not { /setcmykcolor { exch .11 mul add exch .59 mul add exch .3 mul add 1 exch sub setgray } def } if /currentcmykcolor where not { /currentcmykcolor { 0 0 0 1 currentgray sub } def } if /setoverprint where not { /setoverprint /pop load def } if /selectfont where not { /selectfont { exch findfont exch dup type /arraytype eq { makefont } { scalefont } ifelse setfont } bind def } if /cshow where not { /cshow { [ 0 0 5 -1 roll aload pop ] cvx bind forall } bind def } if } if cleartomark /anyColor? { add add add 0 ne } bind def /testColor { gsave setcmykcolor currentcmykcolor grestore } bind def /testCMYKColorThrough { testColor anyColor? } bind def userdict /composite? level2? { gsave 1 1 1 1 setcmykcolor currentcmykcolor grestore add add add 4 eq } { 1 0 0 0 testCMYKColorThrough 0 1 0 0 testCMYKColorThrough 0 0 1 0 testCMYKColorThrough 0 0 0 1 testCMYKColorThrough and and and } ifelse put composite? not { userdict begin gsave /cyan? 1 0 0 0 testCMYKColorThrough def /magenta? 0 1 0 0 testCMYKColorThrough def /yellow? 0 0 1 0 testCMYKColorThrough def /black? 0 0 0 1 testCMYKColorThrough def grestore /isCMYKSep? cyan? magenta? yellow? black? or or or def /customColor? isCMYKSep? not def end } if end defaultpacking setpacking %%EndResource %%BeginResource: procset Adobe_typography_AI5 1.0 1 %%Title: (Typography Operators) %%Version: 1.0 %%CreationDate:(03/26/93) () %%Copyright: ((C) 1987-1993 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_typography_AI5 54 dict dup begin put /initialize { begin begin Adobe_typography_AI5 begin Adobe_typography_AI5 { dup xcheck { bind } if pop pop } forall end end end Adobe_typography_AI5 begin } def /terminate { currentdict Adobe_typography_AI5 eq { end } if } def /modifyEncoding { /_tempEncode exch ddef /_pntr 0 ddef { counttomark -1 roll dup type dup /marktype eq { pop pop exit } { /nametype eq { _tempEncode /_pntr dup load dup 3 1 roll 1 add ddef 3 -1 roll put } { /_pntr exch ddef } ifelse } ifelse } loop _tempEncode } def /TE { StandardEncoding 256 array copy modifyEncoding /_nativeEncoding exch def } def % /TZ { dup type /arraytype eq { /_wv exch def } { /_wv 0 def } ifelse /_useNativeEncoding exch def pop pop findfont _wv type /arraytype eq { _wv makeblendedfont } if dup length 2 add dict begin mark exch { 1 index /FID ne { def } if cleartomark mark } forall pop /FontName exch def counttomark 0 eq { 1 _useNativeEncoding eq { /Encoding _nativeEncoding def } if cleartomark } { /Encoding load 256 array copy modifyEncoding /Encoding exch def } ifelse FontName currentdict end definefont pop } def /tr { _ax _ay 3 2 roll } def /trj { _cx _cy _sp _ax _ay 6 5 roll } def /a0 { /Tx { dup currentpoint 3 2 roll tr _psf newpath moveto tr _ctm _pss } ddef /Tj { dup currentpoint 3 2 roll trj _pjsf newpath moveto trj _ctm _pjss } ddef } def /a1 { /Tx { dup currentpoint 4 2 roll gsave dup currentpoint 3 2 roll tr _psf newpath moveto tr _ctm _pss grestore 3 1 roll moveto tr sp } ddef /Tj { dup currentpoint 4 2 roll gsave dup currentpoint 3 2 roll trj _pjsf newpath moveto trj _ctm _pjss grestore 3 1 roll moveto tr jsp } ddef } def /e0 { /Tx { tr _psf } ddef /Tj { trj _pjsf } ddef } def /e1 { /Tx { dup currentpoint 4 2 roll gsave tr _psf grestore 3 1 roll moveto tr sp } ddef /Tj { dup currentpoint 4 2 roll gsave trj _pjsf grestore 3 1 roll moveto tr jsp } ddef } def /i0 { /Tx { tr sp } ddef /Tj { trj jsp } ddef } def /i1 { W N } def /o0 { /Tx { tr sw rmoveto } ddef /Tj { trj swj rmoveto } ddef } def /r0 { /Tx { tr _ctm _pss } ddef /Tj { trj _ctm _pjss } ddef } def /r1 { /Tx { dup currentpoint 4 2 roll currentpoint gsave newpath moveto tr _ctm _pss grestore 3 1 roll moveto tr sp } ddef /Tj { dup currentpoint 4 2 roll currentpoint gsave newpath moveto trj _ctm _pjss grestore 3 1 roll moveto tr jsp } ddef } def /To { pop _ctm currentmatrix pop } def /TO { iTe _ctm setmatrix newpath } def /Tp { pop _tm astore pop _ctm setmatrix _tDict begin /W { } def /h { } def } def /TP { end iTm 0 0 moveto } def /Tr { _render 3 le { currentpoint newpath moveto } if dup 8 eq { pop 0 } { dup 9 eq { pop 1 } if } ifelse dup /_render exch ddef _renderStart exch get load exec } def /iTm { _ctm setmatrix _tm concat 0 _rise translate _hs 1 scale } def /Tm { _tm astore pop iTm 0 0 moveto } def /Td { _mtx translate _tm _tm concatmatrix pop iTm 0 0 moveto } def /iTe { _render -1 eq { } { _renderEnd _render get dup null ne { load exec } { pop } ifelse } ifelse /_render -1 ddef } def /Ta { pop } def /Tf { dup 1000 div /_fScl exch ddef % selectfont } def /Tl { pop 0 exch _leading astore pop } def /Tt { pop } def /TW { 3 npop } def /Tw { /_cx exch ddef } def /TC { 3 npop } def /Tc { /_ax exch ddef } def /Ts { /_rise exch ddef currentpoint iTm moveto } def /Ti { 3 npop } def /Tz { 100 div /_hs exch ddef iTm } def /TA { pop } def /Tq { pop } def /Th { pop pop pop pop pop } def /TX { pop } def /Tk { exch pop _fScl mul neg 0 rmoveto } def /TK { 2 npop } def /T* { _leading aload pop neg Td } def /T*- { _leading aload pop Td } def /T- { _hyphen Tx } def /T+ { } def /TR { _ctm currentmatrix pop _tm astore pop iTm 0 0 moveto } def /TS { currentfont 3 1 roll /_Symbol_ _fScl 1000 mul selectfont 0 eq { Tx } { Tj } ifelse setfont } def /Xb { pop pop } def /Tb /Xb load def /Xe { pop pop pop pop } def /Te /Xe load def /XB { } def /TB /XB load def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_IllustratorA_AI5 1.1 0 %%Title: (Adobe Illustrator (R) Version 5.0 Abbreviated Prolog) %%Version: 1.1 %%CreationDate: (3/7/1994) () %%Copyright: ((C) 1987-1994 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_IllustratorA_AI5_vars 70 dict dup begin put /_lp /none def /_pf { } def /_ps { } def /_psf { } def /_pss { } def /_pjsf { } def /_pjss { } def /_pola 0 def /_doClip 0 def /cf currentflat def /_tm matrix def /_renderStart [ /e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0 ] def /_renderEnd [ null null null null /i1 /i1 /i1 /i1 ] def /_render -1 def /_rise 0 def /_ax 0 def /_ay 0 def /_cx 0 def /_cy 0 def /_leading [ 0 0 ] def /_ctm matrix def /_mtx matrix def /_sp 16#020 def /_hyphen (-) def /_fScl 0 def /_cnt 0 def /_hs 1 def /_nativeEncoding 0 def /_useNativeEncoding 0 def /_tempEncode 0 def /_pntr 0 def /_tDict 2 dict def /_wv 0 def /Tx { } def /Tj { } def /CRender { } def /_AI3_savepage { } def /_gf null def /_cf 4 array def /_if null def /_of false def /_fc { } def /_gs null def /_cs 4 array def /_is null def /_os false def /_sc { } def /discardSave null def /buffer 256 string def /beginString null def /endString null def /endStringLength null def /layerCnt 1 def /layerCount 1 def /perCent (%) 0 get def /perCentSeen? false def /newBuff null def /newBuffButFirst null def /newBuffLast null def /clipForward? false def end userdict /Adobe_IllustratorA_AI5 74 dict dup begin put /initialize { Adobe_IllustratorA_AI5 dup begin Adobe_IllustratorA_AI5_vars begin discardDict { bind pop pop } forall dup /nc get begin { dup xcheck 1 index type /operatortype ne and { bind } if pop pop } forall end newpath } def /terminate { end end } def /_ null def /ddef { Adobe_IllustratorA_AI5_vars 3 1 roll put } def /xput { dup load dup length exch maxlength eq { dup dup load dup length 2 mul dict copy def } if load begin def end } def /npop { { pop } repeat } def /sw { dup length exch stringwidth exch 5 -1 roll 3 index mul add 4 1 roll 3 1 roll mul add } def /swj { dup 4 1 roll dup length exch stringwidth exch 5 -1 roll 3 index mul add 4 1 roll 3 1 roll mul add 6 2 roll /_cnt 0 ddef { 1 index eq { /_cnt _cnt 1 add ddef } if } forall pop exch _cnt mul exch _cnt mul 2 index add 4 1 roll 2 index add 4 1 roll pop pop } def /ss { 4 1 roll { 2 npop (0) exch 2 copy 0 exch put pop gsave false charpath currentpoint 4 index setmatrix stroke grestore moveto 2 copy rmoveto } exch cshow 3 npop } def /jss { 4 1 roll { 2 npop (0) exch 2 copy 0 exch put gsave _sp eq { exch 6 index 6 index 6 index 5 -1 roll widthshow currentpoint } { false charpath currentpoint 4 index setmatrix stroke } ifelse grestore moveto 2 copy rmoveto } exch cshow 6 npop } def /sp { { 2 npop (0) exch 2 copy 0 exch put pop false charpath 2 copy rmoveto } exch cshow 2 npop } def /jsp { { 2 npop (0) exch 2 copy 0 exch put _sp eq { exch 5 index 5 index 5 index 5 -1 roll widthshow } { false charpath } ifelse 2 copy rmoveto } exch cshow 5 npop } def /pl { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } def /setstrokeadjust where { pop true setstrokeadjust /c { curveto } def /C /c load def /v { currentpoint 6 2 roll curveto } def /V /v load def /y { 2 copy curveto } def /Y /y load def /l { lineto } def /L /l load def /m { moveto } def } { /c { pl curveto } def /C /c load def /v { currentpoint 6 2 roll pl curveto } def /V /v load def /y { pl 2 copy curveto } def /Y /y load def /l { pl lineto } def /L /l load def /m { pl moveto } def } ifelse /d { setdash } def /cf { } def /i { dup 0 eq { pop cf } if setflat } def /j { setlinejoin } def /J { setlinecap } def /M { setmiterlimit } def /w { setlinewidth } def /H { } def /h { closepath } def /N { _pola 0 eq { _doClip 1 eq { clip /_doClip 0 ddef } if newpath } { /CRender { N } ddef } ifelse } def /n { N } def /F { _pola 0 eq { _doClip 1 eq { gsave _pf grestore clip newpath /_lp /none ddef _fc /_doClip 0 ddef } { _pf } ifelse } { /CRender { F } ddef } ifelse } def /f { closepath F } def /S { _pola 0 eq { _doClip 1 eq { gsave _ps grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { _ps } ifelse } { /CRender { S } ddef } ifelse } def /s { closepath S } def /B { _pola 0 eq { _doClip 1 eq gsave F grestore { gsave S grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { S } ifelse } { /CRender { B } ddef } ifelse } def /b { closepath B } def /W { /_doClip 1 ddef } def /* { count 0 ne { dup type /stringtype eq { pop } if } if newpath } def /u { } def /U { } def /q { _pola 0 eq { gsave } if } def /Q { _pola 0 eq { grestore } if } def /*u { _pola 1 add /_pola exch ddef } def /*U { _pola 1 sub /_pola exch ddef _pola 0 eq { CRender } if } def /D { pop } def /*w { } def /*W { } def /` { /_i save ddef clipForward? { nulldevice } if 6 1 roll 4 npop concat pop userdict begin /showpage { } def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash /setstrokeadjust where {pop false setstrokeadjust} if newpath 0 setgray false setoverprint } def /~ { end _i restore } def /O { 0 ne /_of exch ddef /_lp /none ddef } def /R { 0 ne /_os exch ddef /_lp /none ddef } def /g { /_gf exch ddef /_fc { _lp /fill ne { _of setoverprint _gf setgray /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /G { /_gs exch ddef /_sc { _lp /stroke ne { _os setoverprint _gs setgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /k { _cf astore pop /_fc { _lp /fill ne { _of setoverprint _cf aload pop setcmykcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /K { _cs astore pop /_sc { _lp /stroke ne { _os setoverprint _cs aload pop setcmykcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /x { /_gf exch ddef findcmykcustomcolor /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /X { /_gs exch ddef findcmykcustomcolor /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /A { pop } def /annotatepage { userdict /annotatepage 2 copy known {get exec} {pop pop} ifelse } def /discard { save /discardSave exch store discardDict begin /endString exch store gt38? { 2 add } if load stopped pop end discardSave restore } bind def userdict /discardDict 7 dict dup begin put /pre38Initialize { /endStringLength endString length store /newBuff buffer 0 endStringLength getinterval store /newBuffButFirst newBuff 1 endStringLength 1 sub getinterval store /newBuffLast newBuff endStringLength 1 sub 1 getinterval store } def /shiftBuffer { newBuff 0 newBuffButFirst putinterval newBuffLast 0 currentfile read not { stop } if put } def 0 { pre38Initialize mark currentfile newBuff readstring exch pop { { newBuff endString eq { cleartomark stop } if shiftBuffer } loop } { stop } ifelse } def 1 { pre38Initialize /beginString exch store mark currentfile newBuff readstring exch pop { { newBuff beginString eq { /layerCount dup load 1 add store } { newBuff endString eq { /layerCount dup load 1 sub store layerCount 0 eq { cleartomark stop } if } if } ifelse shiftBuffer } loop } { stop } ifelse } def 2 { mark { currentfile buffer readline not { stop } if endString eq { cleartomark stop } if } loop } def 3 { /beginString exch store /layerCnt 1 store mark { currentfile buffer readline not { stop } if dup beginString eq { pop /layerCnt dup load 1 add store } { endString eq { layerCnt 1 eq { cleartomark stop } { /layerCnt dup load 1 sub store } ifelse } if } ifelse } loop } def end userdict /clipRenderOff 15 dict dup begin put { /n /N /s /S /f /F /b /B } { { _doClip 1 eq { /_doClip 0 ddef clip } if newpath } def } forall /Tr /pop load def /Bb {} def /BB /pop load def /Bg {12 npop} def /Bm {6 npop} def /Bc /Bm load def /Bh {4 npop} def end /Lb { 4 npop 6 1 roll pop 4 1 roll pop pop pop 0 eq { 0 eq { (%AI5_BeginLayer) 1 (%AI5_EndLayer--) discard } { /clipForward? true def /Tx /pop load def /Tj /pop load def currentdict end clipRenderOff begin begin } ifelse } { 0 eq { save /discardSave exch store } if } ifelse } bind def /LB { discardSave dup null ne { restore } { pop clipForward? { currentdict end end begin /clipForward? false ddef } if } ifelse } bind def /Pb { pop pop 0 (%AI5_EndPalette) discard } bind def /Np { 0 (%AI5_End_NonPrinting--) discard } bind def /Ln /pop load def /Ap /pop load def /Ar { 72 exch div 0 dtransform dup mul exch dup mul add sqrt dup 1 lt { pop 1 } if setflat } def /Mb { q } def /Md { } def /MB { Q } def /nc 3 dict def nc begin /setgray { pop } bind def /setcmykcolor { 4 npop } bind def /setcustomcolor { 2 npop } bind def currentdict readonly pop end currentdict readonly pop end setpacking %%EndResource %%EndProlog %%BeginSetup %%IncludeFont: Helvetica %%IncludeFont: Symbol %%IncludeFont: Times-Italic %%IncludeFont: Times-Roman Adobe_level2_AI5 /initialize get exec Adobe_IllustratorA_AI5_vars Adobe_IllustratorA_AI5 Adobe_typography_AI5 /initialize get exec Adobe_IllustratorA_AI5 /initialize get exec [ 39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex 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