Forming Equivalent Subsystem Components to Facilitate the Modelling of Mechatronic Multibody Systems

This paper presents an approach that allows groups of components containing internal degrees of freedom and/or internal constraints to be modelled as single components, which we call “equivalent subsystem components” (ESCs). This ability to formulate and store the equations for a portion of a system allows the governing equations for complicated multibody systems to be formulated in a piecewise fashion. First, the symbolic equations governing the identified subsystems are generated, followed by the generation of the equations for the overall system. Such an approach results in decreased formulation times when repeated subsystems or parallel processing facilities are present. As well, this approach makes the modelling process faster and more intuitive, since single objects representing groups of components may be used to construct complicated systems. Since the methodology is based on the standard linear graph component model, all of the advantages inherent in a graph-theoretic approach (multi-domain, coordinate selection, systematic) are achieved. In addition, it is shown how symbolic models of complex subsystems, obtained with the user’s preferred formulation method, may be incorporated within this approach. To demonstrate the proposed approach, formulation times for an electromechanical RRR-planar parallel manipulator are compared using both standard and subsystem approaches.