Redundant grasps, redundant manipulators, and their dual relationships

Abstract

Abstract This article presents a meaningful, practical, and theoretically sound solution that solves the problem of grasping a rigid object with a hand that has redundant (>6) grasping contacts. This is accomplished by introducing compliance at each contact point in such a way as to provide the engineer with the capabilities of object manipulation via controlled forces at the contact points. This method of solution is adapted straight‐away to compute the static forces generated in the legs of a redundant in‐parallel manipulator that equilibrates a wrench applied to the moving/platform or end‐effector. In a way similar to the redundant grasping problem, this is accomplished by introducing the knowledge of the compliances that exist in the legs. The solution thus obtained stems from physical parameters that model the in‐parallel manipulator. The in‐depth study of the duality between the statics of in‐parallel manipulators and the kinematics of serial manipulators reveals a meaningful, practical, and theoretically sound solution for the inverse kinematics of a redundant serial manipulator. This is accomplished by incorporating the knowledge of the compliances that exist or are desired to exist in the joints of the manipulator. (For instance, the torsional compliance in revolute joints or the linear compliance in prismatic joints.) Such information provides a physically meaningful model of the serial manipulator that in turn yields a physically meaningful set of joint increments for a given end‐effector twist. © 1992 John Wiley & Sons, Inc.