Chad Schmitke

Dynamic Modelling of Mechatronic Multibody Systems With Symbolic Computing and Linear Graph Theory

The application of linear graph theory to the modelling of flexible multibody systems is described. When combined with symbolic computing methods, linear graph theory leads to efficient dynamic models that facilitate real-time simulation of systems of rigid bodies and flexible beams. The natural extension of linear graphs to the modelling of mechatronic multibody systems is presented, along with a recently-developed theory for building complex system models from models of individual subsystems.

Using linear graph theory and the principle of orthogonality to model multibody, multi-domain systems

This paper presents a unified formulation capable of systematically generating the governing symbolic equations for multibody, multi-domain systems. The formulation is based on the principle of orthogonality, a powerful concept that serves as a generalization of the principle of virtual work and virtual power. Since it is a graph-theoretic approach, the formulation also provides significant flexibility with respect to the systems modeling variables. This allows the user to model the mechanical portion of the system using joint, absolute, absolute angular, or some hybrid set of coordinates. To demonstrate the robustness of the approach, the paper compares the algorithms results for a forward dynamic analysis of a flexible parking lot barrier to those in the literature. The parking lot barrier model includes a three-phase induction motor, a six bar mechanism and a flexible beam.

Unified modelling and real-time simulation of an electric vehicle

This paper describes the unified modelling of a mechatronic system by a single, graph-theoretic representation, with specific application to an electric vehicle with in-wheel motors. Using linear graph theory and symbolic computing, we present a systematic approach to formulating and simplifying the governing equations. An optimised computational sequence is generated in Maple/DynaFlexPro and exported to Matlab/Simulink to perform real-time dynamics simulations. Although applied to a vehicle model, the general methodology presented here is applicable to a wide range of mechatronic systems.