Dynamic Analysis of Systems With Varying Constraints

Abstract

This paper deals with constrained dynamical systems which are subject, during motion, to the replacement of one set of constraints with another. The theory of imposition and removal of constraints is used to formulate equations governing motions of such systems. To this end, the terms minimally constrained state (MCS), phase of motion, transition, and transition conditions are introduced. These terms are used to denote, respectively, state of a system subject only to constraints which are not removed throughout the motion, period of time during which an MCS system is subject to one set of constraints, event characterized by the instantaneous removal of one set of constraints and the imposition of another, and conditions, satisfaction of which initiate a transition. The indicated formulation enables the simulation of motions of the systems in question, including the evaluation of changes in the motion variables associated with the transitions. The formulation is particularly efficient in that the impulses arising during the transitions are automatically eliminated. The formulation is used to simulate motions of a number of systems, including a legged machine.