The kinematic decoupling of parallel manipulators using joint-sensor data

In this paper we decouple the translational and rotational degrees of freedom of the end-effector of parallel manipulators, and hence, decompose the direct kinematics problem into two simpler subproblems. Most of the redundant joint-sensor layouts produce a linear decoupling equation expressing the least-square solution of position for a given orientation of the end-effector. The resulting orientation problem can be cast as a linear algebraic system constrained by the proper orthogonality of the rotation matrix. Although this problem is nonlinear, we propose a procedure that provides what we term a decoupled polar least-square estimate. The resulting procedure is fast, robust to measurement noise, and produces estimates with about the same accuracy as a procedure for nonlinear systems if sufficient redundancy is used.