Lecture 26 ME 231: Dynamics
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- Shauna Manning
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1 Genea Pane Motion Letue 6 ME : Dnai
2 What Additiona Step Ae Requied fo Invee Dnai?. Ceate fee bod diaa Reation foe & oent Ditane foe & oent. Hint: kineati. Hint: kineti Reation foe at hip due to ue T F ME : Dnai Kineati: tud of otion of a bod without onidein foe that aue that otion Kineti: tud of how etena foe ontibute to the otion of a bod Dnai = kineati kineti Reation oent at hip due to ue Ditane foe at a ente due to avit
3 What Additiona Step Ae Requied fo Invee Dnai?. Ceate fee bod diaa Reation foe & oent Ditane foe & oent Inetia foe & oent. Fo otion quantitie (kineati) Poition (,, ) Veoitie (,, ) Aeeation,,. App Newton nd Law (kineti) Foe ( Σ = ), ( ΣF = ) Moent ΣM = I Reation foe at hip due to ue T F ME : Dnai Kineati: tud of otion of a bod without onidein foe that aue that otion Kineti: tud of how etena foe ontibute to the otion of a bod Dnai = kineati kineti Reation oent at hip due to ue I, I Ditane foe at a ente due to avit
4 Pan fo Toda Foe Moent Aeeation Veoitie. Muuokeeta Muti-Joint d d Geoet Dnai dt dt Ane Poition Data Foe Data Quik eview of the invee dnai pobe T I, I F,,,,,, Σ Σ F F = = ΣT = I tep fo invee dnai Fee bod diaa Kineati Kineti Majo eteno Majo feo Gatoneiu Tibiai anteio ta Soeu Eteno diitou ed tp Tibiai poteio Ditibution pobe Net anke oent M a ME : Dnai 4
5 The Invee Dnai Pobe Foe Muuokeeta Geoet Moent Aeeation Veoitie. Muti-Joint Dnai d dt d dt Ane Poition Data Foe Data Identif quetion that ou wi ue invee dnai to anwe Baed on quetion, deteine DOF to be eaued and odeed Meaue joint kineati Fite and diffeentiate kineati data ME : Dnai 5
6 The Invee Dnai Pobe Foe Muuokeeta Geoet Moent Aeeation Veoitie. Muti-Joint Dnai d dt d dt Ane Poition Data Foe Data Deive equation of otion fo ode of te Sove equation of otion with and without etena foe Ue uuokeeta eoet and auption about foe ditibution to etiate individua ue foe ME : Dnai 6
7 A Poibe Quetion What ae the aitta pane oent about the anke, knee, and hip duin a aiu heiht jup? Epeienta et-up ME : Dnai 7
8 The Epeienta Reut Epeient povide joint ane, anua veoitie, and ound eation foe duin oveent ME : Dnai 8
9 Mode of Ste Mut inude eent ae eent enth inetia popetie How do we et thee vaue? ME : Dnai Zaja & Godon, 989 9
10 Ue Invee Dnai to Cauate Net Joint Moent Joint Moent (N-) knee anke hip Peent Jup ME : Dnai
11 Step to Invee Dnai. Ceate fee bod diaa Reation foe & oent Ditane foe & oent Inetia foe & oent. Fo otion quantitie (kineati) Poition (,, ) Veoitie (,, ) Aeeation,,. App Newton nd Law (kineti) Foe ( Σ = ), ( ΣF = ) Moent ΣM = I I T F, I ME : Dnai
12 Eape Pobe Pana deee of feedo Poition (oientation) in oba oodinate te Seent enth = i Ditane to a ente = i Moent of inetia about a ente Foot ha no a and eain on ound, I, I, I ME : Dnai
13 Seent (foot) i Gound. Ceate fee bod diaa (tati NOT dnai) Reation foe & oent h ME : Dnai
14 Seent (foot) i Gound. Ceate fee bod diaa (tati NOT dnai) Reation foe & oent F T h ME : Dnai F 4
15 Seent (foot) i Gound. Ceate fee bod diaa (tati NOT dnai) Reation foe & oent. App Newton t Law (a = ) Foe Moent F T h ME : Dnai F 5
16 Seent (foot) i Gound. Ceate fee bod diaa (tati NOT dnai) Reation foe & oent. App Newton t Law (a = ) Foe Moent Σ = ΣF = = F F = ΣM = I h F T = F F T = F h F ME : Dnai F T h 6
17 Eape Pobe Pana deee of feedo Poition (oientation) in oba oodinate te Seent enth = i Ditane to a ente = i Moent of inetia about a ente Foot ha no a and eain on ound, I, I, I ME : Dnai 7
18 Seent (hank). Ceate fee bod diaa Reation foe & oent Ditane foe & oent Inetia foe & oent, I ME : Dnai 8
19 Seent (hank). Ceate fee bod diaa Reation foe & oent Ditane foe & oent Inetia foe & oent T I, I F T F ME : Dnai 9
20 Seent (hank). Fo otion quantitie (kineati) Poition Veoitie Aeeation T I, I F T F ME : Dnai o in
21 Seent (hank). Fo otion quantitie (kineati) Poition = = Veoitie = = Aeeation = = ( ) T I, I F T F ME : Dnai o in
22 Seent (hank). App Newton nd Law (kineti) Foe T I, I F T F ME : Dnai
23 Seent (hank). App Newton nd Law (kineti) = = Foe Σ = T ( ) I, I F = F F Σ = F F = ( ) F T F ME : Dnai
24 Seent (hank). App Newton nd Law (kineti) = = Foe Σ = ( ) F = F F Σ = F F = ( ) F F = ( ) ME : Dnai 4
25 Seent (hank). App Newton nd Law (kineti) Moent T F T I F, I ME : Dnai o ( ) in ( ) o in 5
26 Seent (hank). App Newton nd Law (kineti) Moent ΣM = I T T F F = ( ) ( ) I T F T I F, I ME : Dnai o ( ) in ( ) o in 6
27 7 ME : Dnai Seent (hank). App Newton nd Law (kineti) Moent = I T T F F ΣM = I I F F T T =
28 Eape Pobe Pana deee of feedo Poition (oientation) in oba oodinate te Seent enth = i Ditane to a ente = i Moent of inetia about a ente Foot ha no a and eain on ound, I, I, I ME : Dnai 8
29 Seent (thih). Ceate fee bod diaa Reation foe & oent Ditane foe & oent Inetia foe & oent, I ME : Dnai 9
30 Seent (thih). Ceate fee bod diaa Reation foe & oent Ditane foe & oent Inetia foe & oent I F T T F, I ME : Dnai
31 Seent (thih). Fo otion quantitie (kineati) Poition Veoitie Aeeation T F I, I F T ME : Dnai o o in in
32 Seent (thih). Fo otion quantitie (kineati) Poition = Veoitie = Aeeation = ( ) T F I, I F T ( ) ME : Dnai o = = = ( ) o in in
33 Seent (thih). App Newton nd Law (kineti) Foe F I T T F, I ME : Dnai
34 Seent (thih). App Newton nd Law (kineti) Foe = = Σ ( ) ( ) = 4 F ΣF = F F = F F = ( ) ( ) 5 I T T F, I ME : Dnai 4
35 5 ME : Dnai Seent (thih). App Newton nd Law (kineti) Foe = Σ = = F = Σ F F = = F F 5 4 = I F T T F F 4 5
36 Seent (thih). App Newton nd Law (kineti) Moent T F I, I F T ME : Dnai o ( ) in ( ) o in 6
37 Seent (thih). App Newton nd Law (kineti) Moent ΣM = I T T F F = ( ) ( ) I 6 T F I, I F T ME : Dnai o ( ) in ( ) o in 7
38 8 ME : Dnai Seent (thih). App Newton nd Law (kineti) Moent = I I T F T T F F ΣM = I I F F T T = 6
39 Eape Pobe Pana deee of feedo Poition (oientation) in oba oodinate te Seent enth = i Ditane to a ente = i Moent of inetia about a ente Foot ha no a and eain on ound, I, I, I ME : Dnai 9
40 Seent (head, a, & tunk). Ceate fee bod diaa Reation foe & oent Ditane foe & oent Inetia foe & oent, I ME : Dnai 4
41 Seent (head, a, & tunk). Ceate fee bod diaa Reation foe & oent Ditane foe & oent Inetia foe & oent I, I F T ME : Dnai 4
42 Seent (head, a, & tunk). Fo otion quantitie (kineati) Poition Veoitie Aeeation I, I in T F o ME : Dnai o o in in 4
43 4 ME : Dnai, I F I. Fo otion quantitie (kineati) Poition Veoitie Aeeation = = = = = = Seent (head, a, & tunk) T
44 Seent (head, a, & tunk). App Newton nd Law (kineti) Foe I, I F T ME : Dnai 44
45 Seent (head, a, & tunk). App Newton nd Law (kineti) = = Σ = Foe ( ) ( ) ( I, I ) 7 F = F = Σ F = ( ) ( ) ( ) 8 F T ME : Dnai 45
46 46 ME : Dnai Seent (head, a, & tunk). App Newton nd Law (kineti) Foe 8 F = Σ F = = F 7 = Σ = = = I I T F T T F F
47 Seent (head, a, & tunk). App Newton nd Law (kineti) Moent I, I F ( ) in ( ) o in o T ME : Dnai 47
48 Seent (head, a, & tunk). App Newton nd Law (kineti) Moent ΣM = I T F = I 9 I, I F ( ) in ( ) o in o T ME : Dnai 48
49 49 ME : Dnai Seent (head, a, & tunk). App Newton nd Law (kineti) Moent = I I I T F T T F F ΣM = I I F T = 9
50 Noa Gait: Joint Kineati & Kineti a/faq/eiabiit/ ME : Dnai 5
51 The Invee Dnai Pobe Foe Muuokeeta Geoet Moent Aeeation Veoitie. Muti-Joint Dnai d dt d dt Ane Poition Data Foe Data Deive equation of otion fo ode of te Sove equation of otion with and without etena foe Ue uuokeeta eoet and auption about foe ditibution to etiate individua ue foe ME : Dnai 5
52 Net Joint Moent fo Mue Foe Net joint oent ae podued b utipe ue (peviou aued to be idea toque atuato) What fato wi affet how uh a ue ontibute to the net oent? Majo feo Tibiai anteio ta Eteno diitou Majo eteno ed Gatoneiu tp Soeu Tibiai poteio Net anke oent M a ME : Dnai 5
53 The Ditibution Pobe M j nube of feo M j = ue oent oent due to othe tutue = nf F f = f f feion oent Anke eape ne F e= e e etenion oent nube of eteno oent a equation with n f n e unknown Majo feo ( F F ) ( F F F ) M = a ta ta ed ed Can we edue the nube of unknown? Can we ineae the nube of equation? tp tp Tibiai anteio ta Eteno diitou Net anke oent Majo eteno ed Gatoneiu tp Soeu Tibiai poteio M a ME : Dnai 5
54 Stati Optiiation Seet a iteion to iniie o aiie ubjet to a et of ontaint Citeion and ontaint ae a funtion of ue foe Citeion attept to aptue the oa of the neua onto te Miniie ue foe? Miniie ue te? Majo feo Tibiai anteio ta Eteno diitou Majo eteno ed Gatoneiu tp Soeu Tibiai poteio Net anke oent M a ME : Dnai 54
55 Stati Optiiation Eape iniie ubjet to f M F Funtion of ue foe [ ] ( t) = [ F ( t) ( t) F ( t) ( t) ] F ( t) ( t) F ( t) ( t) F ( t) ( t) a ta ta ed ed tp tp F ta ( t) 9N Fed( ( t) F( t) F t) 5 Ftp ( t) 8N 5N N 5N Majo feo Tibiai anteio ta Eteno diitou Majo eteno ed Gatoneiu tp Soeu Tibiai poteio Net anke oent M a ME : Dnai 55
56 Stati Optiiation Eape iniie ubjet to n = M F Tota ue foe [ ] ( t) = [ F ( t) ( t) F ( t) ( t) ] F ( t) ( t) F ( t) ( t) F ( t) ( t) a ta ta ed ed tp tp F ta ( t) 9N Fed( ( t) F( t) F t) 5 Ftp ( t) 8N 5N N 5N Majo feo Tibiai anteio ta Eteno diitou Majo eteno ed Gatoneiu tp Soeu Tibiai poteio Net anke oent M a ME : Dnai 56
57 Stati Optiiation Eape iniie ubjet to n = M F PCSA Tota ue te [ ] ( t) = [ F ( t) ( t) F ( t) ( t) ] F ( t) ( t) F ( t) ( t) F ( t) ( t) a ta ta ed ed tp tp F ta ( t) 9N Fed( ( t) F( t) F t) 5 Ftp ( t) 8N 5N N 5N Majo feo Tibiai anteio ta Eteno diitou Majo eteno ed Gatoneiu tp Soeu Tibiai poteio Net anke oent M a ME : Dnai 57
58 Stati Optiiation Eape iniie ubjet to n F = PCSA M t = F t Tota (ue te) ~ etaboi ene [ ] [ ( t) F ( t) ( t) ] F ( t) ( t) F ( t) ( t) F ( t) ( t) a ta ta ed ed tp tp F ta ( t) 9N Fed( ( t) F( t) F t) 5 Ftp ( t) 8N 5N N 5N Majo feo Tibiai anteio ta Eteno diitou Majo eteno ed Gatoneiu tp Soeu Tibiai poteio Net anke oent M a ME : Dnai 58
59 Conide Thee Funtion n = n = n = F F PCSA F PCSA Tota ue foe Tota ue te Tota (ue te) ~ etaboi ene Diffiut to define and vaidate a ood iteion Poibe vaidation Ue output to dive a fowad dnai iuation Copae quaitative to epeienta EMG Copae to eaued foe (intuented hip ipant, buke tandue in tendon) Majo feo Tibiai anteio ta Eteno diitou Net anke oent Majo eteno ed Gatoneiu tp Soeu Tibiai poteio M a ME : Dnai 59
60 Dnai Optiiation Intead of optiiin ove an intant an optiie a iteion fo a otion aiie heiht eahed duin a jup iniie etaboi ene duin ait iniie diffeene between iuated and deied otion Can take dnai popetie into aount foe-enth-veoit popetie of ue ativation dnai of ue Majo feo Tibiai anteio ta Eteno diitou Majo eteno ed Gatoneiu tp Soeu Tibiai poteio Net anke oent M a ME : Dnai 6
61 Main Point of the Da Foe Moent Aeeation Veoitie. Muuokeeta Muti-Joint d d Geoet Dnai dt dt Ane Poition Data Foe Data Invee dnai pobe i uefu to ove T I, I F,,,,,, Σ Σ F F = = ΣT = I tep ae equied fo invee dnai Ceate fee bod diaa Sove fo kineati Sove fo kineti Majo eteno Majo feo Gatoneiu Tibiai anteio ta Soeu Eteno diitou ed tp Tibiai poteio Net anke oent M a Mue foe ditibution i a pobe Moe ue than DOF Optiiation i uefu to find a oution ME : Dnai 6
62 Fo Net Tie Continue Hoewok #9 due on Wedneda (/6) Read Chapte, Atie /8 & /9 ME : Dnai 6
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