On the Successive Constraint Imposition Approach to Multibody Mechanisms

Abstract

A method is described for the successive imposition of constraints on a free particle mechanism and the subsequent derivation of closed sets of differential equations for the evolution of the mechanism with time. Fundamental is the idea of ideal constraints as contained in d'Alembert's principle. In particular, it is shown how constraints may be added one or more at a time, thereby obtaining intermediate descriptions with more dynamic freedom than the final mechanism. As a simple example, it is shown that the rigid body is such an intermediate description. The method is also applied to the problem of a chain of n particles or n rigid rods. Both an inductive and a constructive approach are demonstrated in deriving the equations of motion for arbitrary n.