A UNIFIED GRAPH - THEORETIC APPROACH TO FORMULATING MULTIBODY DYNAMICS EQUATIONS IN ABSOLUTE OR JOINT COORDINATES

The objective of this paper is to show how a single linear graph repre sentation of a multibody system can be used to automatically derive th e complete set of equations of motion in either absolute or joint coor dinates, depending upon the elements selected into the spanning tree o f the linear graph. Criteria for selecting a tree that produces the de sired set of equations are given and the systematic nature of this gra ph-theoretical procedure is demonstrated by means of two planar exampl es. The first is an open-loop compound pendulum, and the second is a c losed-loop four-bar mechanism driven by a time-varying torque. (C) 199 7 Published by Elsevier Science Ltd.