The objective of this paper is to show how a single linear graph representation of a multibody system can be used to derive the complete set of equations of motion in either absolute or relative coordinates, depending upon the elements selected into the spanning tree of the linear graph. Criteria for selecting a tree that gives the desired set of equations is given and the systematic nature of this graph-theoretical procedure, known as the Vector-Network Method, 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.

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