Natural Orthogonal Complement Constraint equation and Twist Shape Matrix-P Joint ai1 a bi Ci C Pitti, CiI (674a) =2-1+wa-1×(0-1+p1+be)+be (6.74b)
Natural Orthogonal Complement • Constraint equation and Twist Shape Matrix – P Joint Oi-1 Oi O'i Oi+1 Ci-1 Ci Oi i-1 ci-1 i ci bi ai ai+1
Natural Orthogonal Complement Constraint equation and Twist Shape Matrix-P Joint --1+R{w-be=0 (676) R≡D1+RL (675) D;_, is the cross-product matrix of vector di- Ri is the cross-product matrix of P i +b;ei E1(2-21-1+Rw)=0 (677) Regroup( 6. 74a)and (6.77) K,a-1t-1+Kt=0 (6.78 10 O一E ER Ei
Natural Orthogonal Complement • Constraint equation and Twist Shape Matrix – P Joint Regroup (6.74a) and (6.77):
Natural Orthogonal Complement Constraint equation and Twist Shape Matrix-P Joint If the first joint is prismatic, then where 10 K 11 o E Define partial Jacobian t=6tn+…+btk+…+bt 27 (6.83
Natural Orthogonal Complement • Constraint equation and Twist Shape Matrix – P Joint If the first joint is prismatic, then where Define partial Jacobian
Natural Orthogonal Complement Constraint equation and Twist Shape Matrix Compute T wi xe xei)xri+ei xii ifj≤ (6.84) 0 therwise Xa+…+“1Xa-1+ (6.85 If kth joint is prismatic, then 0 ek (6.86) Wk e
Natural Orthogonal Complement • Constraint equation and Twist Shape Matrix Compute If kth joint is prismatic, then