On the Numerical Solution of the Inverse Kinematic Problem

Abstract

Solved in this paper is the inverse kinematic problem asso ciated with manipulators of arbitrary architecture. Its formu lation is based on invariants in the rotational part of the closure equations, which produces a formally overdetermined nonlinear algebraic system. In the translational part, a recur sive scheme similar to that of Horner's for polynomial evalu ation is introduced. This leads to a reduced number of com putations, which allows an efficient numerical solution of the problem. Velocity and acceleration kinematic inversions are also included. The procedure is illustrated with the analysis of a six-degree-of-freedom, revolute-coupled manipulator of an architecture that makes a closed-form solution difficult. This method has been successfully applied to the analysis of 7R spatial linkages as well. Appendix A lists the nomenclature and notation used in this paper.