Force polytope and force ellipsoid for redundant manipulators

Evaluation of force/motion capabilities for a manipulator is useful both in the design phase and in the operational phase. Manipulability ellipsoids and polytopes are well-known tools used to represent these capabilities graphically. This article focuses on the evaluation of force capabilities for redundant manipulators, for which additional constraints must be imposed on the available joint torques to satisfy the static assumption. An algorithm to correctly evaluate the task space force polytope is given and a new definition of the force ellipsoid is proposed. The obtained results can be applied also to nonredundant manipulators in singular configurations. Numerical results are provided in the case of a planar redundant arm. ©1997 John Wiley & Sons, Inc.