where W is the p × p diagonal matrix of non-zero singular values, P is the (3n -6) × p orthonormal matrix whose columns span the constrained subspace of q, Q is the (3n -6)×(3n-6-p) orthonormal matrix whose columns span the unconstrained subspace of q, and Ǔ and Ǔ are the l×p and l×(l-p) matrices whose columns are the left-singular vectors corresponding to P and Q respectively. The constraint-nonredundant Jacobian can be calculated from the constraint-Cartesian Jacobian and the singular values and right singular vectors of the redundant-Cartesian Jacobian from equation 1,