EFFICIENT COMPUTER SIMULATION OF MOTIONS OF MULTIBODY SYSTEMS

The demands of spacecraft, robot, automobile and machinery design have motivated the development of general-purpose numerical multibody programs. Such programs enable an analyst to simulate, with minimal manual effort, the motions of large systems of interconnected rigid bodies, or to calculate the forces and torques that must be applied to cause a desired motion of a system. The elimination of arduous and error-prone manual formulation of equations allows the engineer to concentrate on the physical interpretation of computational results and on the design of a system and its associated controllers. In many cases, however, computational inefficiencies of numerical multibody programs lead to slow evaluation of actuator forces and torques and slows simulations of motions; and when computational inefficiencies become prohibitive, analysts generally are forced to formulate manually problem-specific equations of motion. In an attempt to combine the advantages of both these approaches, computer programs (hereafter called symbolic multibody programs) that automatically produce problem-specific (or custom) equations of motion in literal form have been developed. Unfortunately, many of these programs produce equations as computationally inefficient as the aforementioned numerical multibody programs.

In the present study, a new approach to symbolically deriving equations of motion is put forth and used to create a symbolic multibody program which can be run on computers as small as an IBM PC. This program leads to simulations (and force and torque evaluations), which are as efficient as, or more efficient than, any that can be performed with equations derived manually. The algorithms and techniques by which these levels of efficiency are obtained are explained in detail, and results of applying the symbolic multibody program to several mechanical systems are provided.