Recursive lnverse dynamics Procedure Summary (1) Kinematic Computation (Outward) Known: 0, 0, 0 y Compute t, t 62,62,62 (t1t1) Link 1 Link 2
Recursive Inverse Dynamics • Procedure Summary (1) Kinematic Computation (Outward) Known: Compute θ,θ,θ t t , 1 1 1 , , 2 2 2 , , 1 1 c , c 2 2 c , c 1 1 ω ,ω 2 2 ω ,ω ( , ) 1 1 t t ( , ) 2 2 t t … Link 1 Link 2
Recursive lnverse dynamics Procedure Summary (2) Dynamic Computation(Inward) Known: Kinematic quantities of each link(from outward recursion) Compute: Joint wrench and external wrench NE WEE(EE, nEE)+Wn(fn, nn)-+Wnl(fn1, nn1)
Recursive Inverse Dynamics • Procedure Summary (2) Dynamic Computation (Inward) Known: Kinematic quantities of each link (from outward recursion) Compute: Joint wrench and external wrench WEE (fEE, nEE) Wn (fn, nn) Wn-1 (fn-1, nn-1) … N.E
Recursive lnverse dynamics Outward Recursions- Kinematics Computation (i Angular velocity and acceleration swi-1+ei, if the ith joint is R (625a) w-1 if the ith joint is P Wi-1+wi-1 Biei +eiei, if the ith joint is R Wi-1, if the ith joint is P(6.25b) Expressed in(i+1) frame QT(wi-1+0iei), if the ith joint isR if the ith joint is P (626a) Q wi Qi-1+Wi-1 x e:+0,ei), if the ith joint isR Q-1 the讪 oint is103b Initial conditions o=0
Recursive Inverse Dynamics • Outward Recursions - Kinematics Computation (i) Angular velocity and acceleration Expressed in (i+1) frame Initial conditions
Recursive lnverse dynamics Outward Recursions - Kinematics Computation Computational complexity for angular velocity and acceleration Coordinate Transformation [rl+1=Qrl cos e sin a 01 71c06+72sin6 [r]+1=-A@i A cos e: Air2 uisin ]i -Hi cos 0i Ai Lr3 4r+入3 h三c0ap≡aina 7三T1sin-72co6 The extra term in wi computation ei [wi-1 x0 eli 6 Also [ojei] 000
Recursive Inverse Dynamics • Outward Recursions - Kinematics Computation Computational complexity for angular velocity and acceleration Coordinate Transformation The extra term in computation: Also