Dynamics of an elastic multibody chain: part a—body motion equations

Abstract

In this paper—the first of a series describing the dynamics of an arbitrary multibody system—motion equations governing a set of individual bodies in a chain configuration are discussed. A chain consisting entirely of rigid bodies is considered first. Motion equations for a typical body of arbitrary shape and arbitrary mass distribution are then briefly summarized. Finally, the geometrical constraints necessary to connect the individual bodies into a chain are derived. Large translational and rotational motions are permitted at the joints connecting contiguous bodies. In other words, both prismatic and revolute joints are included, alone and in combination. As well, the interbody force constraints required to ensure that equal but opposite forces and torques exist at each joint are developed. The resulting expressions are amenable to the introduction of constraint and control forces at the chain joints. This permits the number of actively controlled degrees of freedom at any specific joint to be arbitrari...