Nonlinear Dynamics

, Volume 9, Issue 1–2, pp 73–90 | Cite as

On the use of linear graph theory in multibody system dynamics

  • J. J. McPhee
Article

Abstract

Multibody dynamics involves the generation and solution of the equations of motion for a system of connected material bodies. The subject of this paper is the use of graph-theoretical methods to represent multibody system topologies and to formulate the desired set of motion equations; a discussion of the methods available for solving these differential-algebraic equations is beyond the scope of this work. After a brief introduction to the topic, a review of linear graphs and their associated topological arrays is presented, followed in turn by the use of these matrices in generating various graph-theoretic equations. The appearance of linear graph theory in a number of existing multibody formulations is then discussed, distinguishing between approaches that use absolute (Cartesian) coordinates and those that employ relative (joint) coordinates. These formulations are then contrasted with formal graph-theoretic approaches, in which both the kinematic and dynamic equations are automatically generated from a single linear graph representation of the system. The paper concludes with a summary of results and suggestions for further research on the graph-theoretical modelling of mechanical systems.

Key words

Multibody dynamics linear graph theory absolute and joint coordinates 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • J. J. McPhee
    • 1
  1. 1.Systems Design EngineeringUniversity of WaterlooOntarioCanada

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