Multibody dynamics formulations via Kane's equations

Abstract

Introduction T past decade has seen a rapidly growing interest in multibody dynamics. This interest has been spurred by three factors: 1) a desire to obtain comprehensive analyses of large dynamic systems; 2) advances in modeling and dynamic analysis procedures; and 3) increased availability of computer systems. The growing interest in multibody dynamics has stimulated many research efforts. Indeed, the activity in multibody dynamics research parallels that seen in the early development of finite-element methods. The desire to obtain comprehensive analyses of large systems stems from the realization that many physical systems of interest and of practical importance (such as chains, cables, robots, mechanisms, space stations, and biodynamic models) can be effectively modeled as multibody systems. The advances in modeling and analysis techniques are based on recent computer-oriented advances in dynamic analyses. Among these advances are the advent of Kane's equations, the development of body configuration arrays, the formulation of differentiation algorithms, the use of Euler parameters, and the use of orthogonal complement arrays. The access to computer systems is continuing to expand, including access to class VI supercomputers. Also, recent advances in computer graphics are leading to a higher level of input and output, including animation of the modeled physical systems. Surprisingly, however, with all of this activity and despite all of these developments, there is still disagreement among analysts about which