A minimum principle for the dynamic analysis of systems with frictional contacts

The dynamic analysis and simulation of manufacturing processes and robot systems with multiple, concurrent frictional contacts are addressed. When principles of rigid body dynamics are used with empirical models for friction, inconsistencies and ambiguities may result. One approach to resolving this is to incorporate a model of the compliance at the contacts into the dynamic model. The principle of virtual work is used to derive a minimum principle which relates the contact forces and local deformations to the state and the applied external forces. A simplified, lumped-parameter model that always yields unique solutions is presented. Closed-form expressions for the contact forces are derived, and a simple algorithm for determination of the slip at each contact is developed. The analysis of whole-arm enveloping grasps is discussed using this method