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 representation of a multibody system can be used to automatically derive the complete set of equations of motion in either absolute or joint coordinates, depending upon the elements selected into the spanning tree of the linear graph. Criteria for selecting a tree that produces the desired set of equations are given and the systematic nature of this graph-theoretical procedure is demonstrated by means of two planar examples. The first is an open-loop compound pendulum, and the second is a closed-loop four-bar mechanism driven by a time-varying torque.