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Inverse dynamics for 3D upper limb movements : a critical evaluation from electromagnetic 6D data obtained in quadriplegic patients.

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(1)Inverse dynamics for 3D upper limb movements : a critical evaluation from electromagnetic 6D data obtained in quadriplegic patients. Matthieu Maesani, Gilles Dietrich, Gilles Hoffmann, Isabelle Laffont, Sylvain Hanneton, Agnès Roby-Brami. To cite this version: Matthieu Maesani, Gilles Dietrich, Gilles Hoffmann, Isabelle Laffont, Sylvain Hanneton, et al.. Inverse dynamics for 3D upper limb movements : a critical evaluation from electromagnetic 6D data obtained in quadriplegic patients.. ISB Symposium of 3D movement analysis, 2006, Valenciennes, France. �hal-00021114�. HAL Id: hal-00021114 https://hal.archives-ouvertes.fr/hal-00021114 Submitted on 17 Mar 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) Inverse dynamics for 3D upper limb movements..   

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(50) CL!Œ w ƒLD|œh w-ƒ:‘hzV¤XzFƒLza|X‘F’X}Vkw w yAM„L¦ — xzF‘Bƒx¨JœFy¨JwawqšX— ƒLƒLy||@=€:w~~ {€”y‘hw y¦w ƒ‚z4„”|X€‘=¨Jwt~ƒL€”y‘y:w xX— Aͦ]w]y:}ùƒ‚y€Lw]za‘X‘o¦¦ —4=w „”¥)€ AͤBy‘Xy—— z¨JƒLƒ‚€‚|Xzaww]‘ùyN!z A=t{ƒ˜— y|XzF}[wè¦ ƒ˜w~zhœFw ‘=x€L¨èy~wíza{yy~€”z ‘é~’X|wèzazaxXy—4œ¦„œèw]¦]y‰x¤Xywƒ:—4z ¦P¨J}ۀw¨Ð¦4—Dza~j{xXxy„Lyz œJw ’Xœ¤Xwí¤FwJ}ƒLzF|‘—w ƒL¦ |—Fwt~ƒèywzF¦ yzFy¤FœF}+€‘B¦ [—ay~Zw€œA:xXw_„`“}Aw]¦‘=|~zzay~Z~w ‘$zF‘J~Z€“ƒLƒ:|w4w2~hx!z {FAV{X—w ƒLyƒ‚—a— ¦]yÍ|¨÷¨J¦ w]za‘Bxƒ„”œ¦ „L¤Xzwq~Zw@ „”ƒ:xz‰wqƒ:zF|‘ w ¤X~Z|zFza‘XxwF„L œ - ‘$¤Xw—aœFœ€:€ê~ƒ‚zF€LzF„L—]‘ƒ:š2w œ ƒL|w‰AyyzFza¨ ƒ‚—]ƒ:€Lz4Ä́L‘ìw RF€€L‘+zF‘ƒ‚²M|Xw w‰RFƒ:w]{‘yz4~Z€L‘Xz4z‘ ²~xƒ‚{|B€”— ‘S‘ —]@=ƒ:€L~ýza‘íƒ:z —RF€:— ~ ¥w ~jxy~Vy{zaAÍ{y6zF„Lw y"¨¨S~$—@w œ€”‘_w

(51) ‘胂¤B— ¨Jy:}è}§z ‘’X~Zww w ¨J‘=„Lw ~w]zF¦]‘BƒLŠy ƒ=€‘A͗ 2&€ y:RBƒ:ƒ‚ww |XAœâ—4w]¨J¦]z4ƒÍ‘â~šFšE— ƒL=t‘B|œwÛw)€”œB$~ƒ@z€:€”~6‘à‘XœBza—aT€ ƒ A*„LAÍ@z4€L‘X‘B¦]x Üz!„ê=ãƒXƒ‚|Xƒ˜ƒ‚ztwè|Xw‘_xx— „”‘¨J¨J— w]zaytyx€L¦]¦ ‘Fy—aƒow „~z!“ƒ} A  ¦ zF¨Ð{w ‘=~—]ƒ:wۃL|Xw ¨Jš¤Xw ¦ —xl~Zwhƒ‚|Xw4~wܗ ywà~M}~jƒ:w ¨è— ƒL€‚¦Üw]yÍyzay~P

(52) ®6|Fx=~š =tw=t—4‘_ƒ`ƒ:zJ~ƒLyw4~~ƒL|w‘Xw w œ‹AzFy

(53) — ‘hw4~Mƒ:€¨è—]ƒ:€Lz4‘hz!A6ƒ‚|Xwt— ¨Szax‘Fƒ6— ‘œ ƒL¨J|wwۗD~~M|x—y€{‘Xwh Ü!z ƒ‚A|XwS$~ @{€”‘âz~¨J€êƒ:€‚z za’X‘çw ¨J!z Atw]‘Bƒ‚|Xƒ0wJ— y:¤Xƒ:zFw A‘F—4}§¦]ƒ„L`— ®6‘œF|B¨S€˜~q— ¦ *y @=zaxX~q„œâyw „”—a— ¦ ƒL|B€“’X€Lwwh’Xƒ˜w zܜۃL¤|} w ~Zw ‘=~zay~oƒ‚|Byz xX F|—t~w]ƒ=z!A

(54) ~ƒL— ƒL€‚¦&{z~ƒLxyw4~P œ¤XBy—]—aƒ:—A¦]¥t|¦ ¦]€f¦— zF—4‘¦]y‘XœƒÍz~€ƒÐ‘B¨è t¤X—4wçƒ:€”z‘x=„“ƒ‚}J|X~w"w —Fœü{~"y— ƒ˜waz+‘S~w]w ‘Fƒ:„“w4ƒX¤X~j— z!ƒJ‘=üƒ‚—a|X„“~}wçƒ:—]~Z€˜¤X|D~P€L}_šF„{€zaB4zaxw]ƒ:y6y|Xw €w4‘VRB~€:€:¬[~M~܃‚Z€‘XƒL| q—]° ƒJw zSRaƒL=t{|Xw]wwçy’f€w ¨Sƒ‚yy€‚š_w ¦‘_ƒ‚w|Fƒ‚{=—a€:~~ „ y¨Jw]¨èz ’X—4w€”¨J‘~Üw ‘F¨JƒÍ~+z~j€ƒÐ‘ù„”T€ |X@w]w — „“}X„”ƒ‚š |F}ïAyzF~¨ xF¤ >z wa¤=¦]~ZƒÍw W~ y:’XCj—]'‹ ƒ:DF€Lz4C“« ‘=DF~ÜC”S¬ z D¤BC“<› ƒ:D㗠€‘X—Fw ~ œ+=œFw x„Ly„§€‘—F ð~ã!« €”Z ‘ _zF‘Xx— „“}@œFyy€”w{œF„‚wx F¦€‚w4¦~t{w —*„“ƒ˜¤X€Lw]!z ‘F=öƒÍ~?w CÍRF‹*ƒ: <w D‘=F~Z¥ãzFy{~M—ƒ‚yÍy— w]„“‘}X _~ƒ‚€:|V~zS¤BAoxBƒáƒ:|—aw&„:~ƒ‚zÛy€L¦ €w]¨Ð{={~`w ¤BœByw4—4~t¦]|Xw €„“X¤X‘!z za= ƒ ~j~jƒ˜ƒ˜T€—]A*¤XA‘€„”wa€ ƒê~}÷~P ¦azaxw-„Lœ ƒ‚|_wxlR_~+{„”— {€‘ïyza{X~zzF~¨Sw-w탂|Bz!—]Aäƒãƒ:— |X‘ïw퀝¦ ¨q„L€”{‘y€L¦]z —4’X„Ûw ¨S¤Xw w ‘F‘XƒãwÀê!z ƒÍ~ãAAz!„L€A㨤— ¨èœBwx=’X~w ¦]„Lxza„L{äzaƒ:—Fw]~‘X~œF€:~M€‘Xƒ:€“za’Xxlw@~Ð~:}Xƒ‚y~— ƒ:‘w ~¨VAÍw ~Ðy œFCx‹y‹ €‘XDq §— ‘!¬ œçZé¦ ‘Bza—]xXƒL„‚xœây͗¤X„0|w ¨JAMxz ’Xyƒ‚w |X¨Jw]yèw‘Fx=ƒÍ~|~ w œâC‹P< ƒ:z D C‹]«D ¥ Ž tkv Y £ ª Z³ª‡àªv®0 wƒ:|— ‘E@  xl~~Zw „‚š%YèSZ€TB4€Lw]‘J— ‘Bœè‡ä_ˆ&wP’=zF„7AjzFyƒ‚|Xw]€y|Xw „”{ =t€”ƒ‚|ýƒ‚|Xw-{X—]ƒ‚€Lw]‘BƒM~PÜ‡ä ‡äâ€:~Þ~MxB{{zayMƒ˜wœé¤B}ïª"¦ zF„LwövzFy¨è— „Lw +. +. +. ;. :. :. +. X|„Fª

(55) xBw]„L{‘=œ(•]~w]y€L€LwP— Fx‘yw]wà F¨JyœB— w]‘Fwܑ_ƒƒ–`_— AÍxyy{€˜za~•]¨šy€L¥èw]x ƒLˆ)yt|X“w½w]² ƒ0œ"‡âwJ€˜~ۀ„”‘B—J~j€˜x~Mˆ0ƒ:{Xž]w z4y¦wyM|ƒ:w w]œ§yœ¦]w |X¤}wJ„z!—- AvJ£ FŽ ªxxRˆá„”wƒ‡äx¨yšt¤Xw šza³qxy°œ =w  ®6|B€˜1~ =zF$y @c=—F~"~Mx{B{zay:ƒ:w œ¤}q­`zF‘XœF—]ƒ:€Lz4‘2ª Zt­6 ˆN\ Œ \ 2 \ .`8 \ _ :. ). & %&*T2‘ ’ *  ?A =A  _  ’ Ž#62 2 A ?A?^ $ŽŽ+&** †’ ŽF$Ž ‘ )2   F Ž ‘&&&*5’ Ž /$Ž ‘.*%!: ! ’ #

(56) Ž&’"/&* A5. %-

(57) '*’! ojjo  F! A  o4 j oo(m . &    + Ž ' ’  * ( ‘2/-& 8  _ ‘2! /)- \ A; Ž6;! @/Ž+/&#’%F&/- Ž’"/&! o /$'Ž *.‘ O’ Ž 2‘ * Ž - O’   Ž ‘T& !,)2 G +)F$Ž ‘2* A $‘& 8 Ž ‘. !. '! C6 C ojjo B"B!" A B   O‘2/)-)# 8 AA  4 Ž'* ’   h. A ( A   _ ‘2)! &/)-$ A \ A ekojjAg 'A C +! ‘T= ’ %$’ Ž ‘ 2  +) /Ž F‘ /  Ž "‘ * !&A :"‘ -+’   ‘T$'Ž /&c G’ Ž 2‘ 3O& /*‘T’ 6?‘& D&@&* *6  O ’ Ž &*( B "  _  ’ Ž#%m  o@2 j ? )o1 m &!  '$Ž’"* "4 A54 ’ 13 /Ž+/&&*N’ Ž/ #Ž#‘.O!(%F! ’  # 

(58) Ž&’"/&*   6’ +Ž ?% ’ Ž$Ž ‘9$ŽHA Ž Ž% ’ ŽF#Ž ‘5) 2 $% /)-’ 6Ž  AV. 3O -

(59) +**’ % ! ojjj. 6  !$B%   "$* ? ) 1OŽ ‘  B; A  o = ’ $m Žo   \ A  4 ’  "’ $Ž  " 3 A  8  #6$)   A  = +**)! =A  2  F !  A  *  2 #

(60) $ = )G’  <HA 7’ Ž')*‘T’"/&*` )-6$Ž+*’ Ž$ŽC  ’ Ž ‘T’ Ž' G ) $Ž ‘2*`C ’ Ž ! 8 0D& & *’ '! & "’ / F*‘T"’ $Ž 2‘ * A_ ’ ŽF& ! 8 & *  ojjj F !6B$ B$*  "B o A ^  ;;$ŽŽ $ A  ? & 1O Ž ‘  ž; A  ^  Ž+Ž O‘Ž  /_ A2  #

(61) $ = O ’  < A  ^  $‡‘ + 2‘ /Ž'   ‘.-+)! #F$ $9’ ‘1-N $ $ †& F)O&!

(62) +*$‘.O’"/&3+*-, 8 Ž ‘.*%!<:).’ Ž')*‘T’"/&* &S ’ ’ 'Ž 5’ Ž 8  8 "0D& & *’ +! &"’ /F*‘T"’ $Ž 2‘ * A#. 6 *3/"’ $Ž /&’ 0Ž %&** A = ’ &

(63) % F  \ A ( A  2 #

(64) ! = &’ <HA (ŒO!   < Ac< A / "  +- ‘&)’  A   ’+ Ž )*‘T"’ /&*% -%+$Ž‹) 2  &/$+Ž * .‘ ;G/O2‘ $ ;O *2F*‘T’ & !:.‘ O% C /0’ 6Ž *(

(65) +*2‘ )C  2&/  ’ +Ž 6* A @= ’  )/)- ojjj  F !BB21!*11$* A 8 -F$Ž!"( 2 A Œ A  8 ! )'*33 8 A \ A  / 8  Ž F’"! !"  ›A:0 A  2 

(66) ŽF! *3 b^ A A    45&  +Ž  XA656A ; Ž +&*‘T"’  *‘T’ Ž  G’ 'Ž C3&‘&’ & ! % '3 ‘T"’ &*N 9‘1-+ -%  Ž #FC 

(67) A 3 -F’7  < 2 ?  0<2  1"$*"  B" A ; *2-F’ )'’ C A UŒ m'Ž /‘T’ Ž & ! m $Ž*‘% 8

(68)  .‘ -' )! #F $9%/’ Ž ‘ $Ž' 1  ‘.-%&$F’  $+Ž *C ’ Ž% !+D$Ž ‘T’ ‘&*‘T’ 6 G$‘&’#Ž ŽF& !

(69) +*"’ * ‘"-+E&! # $:%$’ Ž ‘ A & ŽF& !    F$Ž 3 \ &.‘ -% &   "’ / < \ *** /$’ *‘T’Ž m 1"1; F !$*B1$111 A '  8 ' 2 A)' m›j /&33&2 $’ /) &+!! ‘ *1’ Ž&!/ O& * N ’ Ž-% (/

(70) A!5; ’ \S*2\/)\ - 0 OŒ$Ž+* .  *3.‘ 6O&& ! !_ )

(71) +2*& ‘ 2 /$)-FŽ ).‘ #F*% ’"! !F\ Ž+%!"! % $`’ 'Ž  m. =. ojj1m < &B A  ? 8  _ ^ = : 2. 2 > A ' +! /$&-+0

(72)   ‘= 5 ’ Ž  O‘ *6* 6&/‘’ +  &! *‘T’ Žk #C’"^ /&+*,‘_ ‘.OC’"/&3< +*<#ŽF)! ‘’ ‘& ‘1’"/)+A * O! #$ +‘2$Ž+*’ Ž’ Ž9‘2‘"&!"’  A $Ž  )  B 7 1 " '    ’"/ 4  ' '  1 ’o/ jCj A<*.o  A Ž ; Ž &!

(73) ‘Tm5 ’"/&!/  Ž ‘1O !O98 %**’"*‘T’ Ž'C' \  $&/)-F’ Ž+N’ Ž A -= 6 #Ž+* `$ ’ ‘1-  ’"* F# ’ ! ’ ‘T’"&* Ž  ’ Ž ‘23* C  O &  A.   ’ ‘&* ’ %F&/-  Ž’"/&* $ŽŽ+3O &! / Ž ‘.* %S! F&* ‘.62` $ŽF  ')$ Ž ‘ )? $ 4`&&  _ * ’ Ž+3 1( 3! % A  A *$B *&* A <*ojjj j 1 1"". mm  m›o.

(74)

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