Dynamic Modeling and Simulation of a Parallel Planar Manipulator with Linear Electric Actuators Using Power Flow Approach

Abstract

This work presents the analytical form determination of the dynamic model of a parallel planar mechanism with three degrees of freedom 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 speeds are determined. Considering the power flow between the degrees of freedom, and also between these and the actuating elements (linear electric actuators) the equilibrium relations of the forces and torques are obtained. Accounting for inertial effects of system components, the stiffness and damping effects, the equations of motion or the state equations are analytically determined. Besides, the relation between the inverse kinematics and the direct dynamics is presented. The proposed methodology is generalized and applicable in any type of mechanism (open or closed, planar or spatial). Thus, this methodology (power flow) is more efficient to achieve the dynamic analytical (closed) models of parallel mechanisms. Simulations are performed to validate this approach, using the real data (geometry, inertia, damping, actuators forces, etc.) from a planar mechanism designed and built especially for the purpose to compare the simulated and experimental results. The analytical equations lead to a more efficient simulation process and real-time control of these systems.