Analysis and Simulation of Planar Mechanism Systems Using Bond Graphs

Abstract

A method is presented for incorporating planar mechanisms into dynamic system models using bond graphs. Through the use of stiff coupling springs at the mechanism joints, the nonlinear geometrical relationships are uniformly and simply described by displacement modulated transformers and the system state equations can be written with no algebraic complications. In contrast to the more elegant kinematic techniques for describing mechanism dynamics, the present method results in higher order systems of equations but the equations themselves are simpler and not densely coupled. In addition, coupling forces are available at the joints. An example demonstrates that the extra eigenvalues associated with the coupling springs can readily be found for any configuration so that the spring constants can be chosen to minimize computation time.