Dynamic Models of Parallel Mechanisms using Power Flow Approach

Allan Nogueira Albuquerque¹; Mauro Speranza Neto¹; Marco Antonio Meggiolaro¹

¹ Pontifical Catholic University of Rio de Janeiro

doi:10.20906/CPS/CON-2016-0225

Resumo

This paper presents a procedure for the determination of the analytical form of dynamic models of parallel - or closed kinematic chains - mechanisms through the characterization of the power flow between its components. From the geometrical relations associated to the displacement of their degrees of freedom, the kinematic relations associated to their velocities are determined. Considering the power flow between the degrees of freedom, and also, if necessary, between these and the actuating elements (e.g. electric motors or hydraulic actuators) the equilibrium relations of the forces and torques are obtained. Finally, accounting for inertial effects of system components and, if necessary, the stiffness and damping effects, the equations of motion or the state equations are analytically determined and represented in any reference frame, local or global. This approach adopts the same fundamentals, concepts and elements of the Bond Graph Technique. As an illustration, the procedure is applied in a parallel planar mechanism with three degrees of freedom. The analytical equations lead to a more efficient simulation process and real-time control of these systems.

Palavras-chave: Parallel Mechanisms Dynamics; Kinematic Relations; Power Flow; Equilibrium Relations; Bond Graphs