Different Dynamic Formulations for a Mechanism using Bond Graph

Abstract

For modeling dynamics of mechanisms, various classical formulations are available in the literature. The equations of dynamics given by various classical formulations can also be derived from the bond graph. The bond graph is a convenient graphical representation for modeling dynamics of physical systems in multi-energy domains.In this paper, various alternative causality assignment procedures in the bond graph are used to derive different classical formulations such as the Lagrange’s equations of the first kind (with multipliers), Lagrange’s formulation of the second kind, and Hamiltonian formulations. An example of the quick return mechanism has been modeled using the bond graph technique, and various alternative causality assignment procedures are applied to derive the various formulations. Simulation coding has been done using MATLAB and results have been analyzed and discussed. The purpose of this paper is to show how the various formulations can be obtained from bond graph using various alternative causality assignment procedures.