Dynamic Simulation of a Tripod Based in Boltzmann-Hamel Equations

In this paper, authors show the results of performance simulation of a 3PRS lower-mobility parallel manipulator actuated by electronic devices. The simulation includes a mechatronic model of the actuators, the dynamic response of the mechanism found using the Boltzmann-Hamel equations, and a model of the control. The dynamics of the actuators is modelled using two transfer functions found by means of a test based identification method. Authors find the explicit Dynamic equations needed for simulation using analytical mechanics. Lagrange equations are convenient and systematic in open-loop serial kinematic chains. However, for closed-loop mechanisms are cumbersome, even with the help of Lagrange multipliers. Moreover, if spatial rotations are involved, generalized coordinates are very much coupled in the expressions of Lagrange functions to be differentiated. Boltzmann-Hamel equations come to help in this regard. By using Simulink, authors could evaluate the stability of the control and the bandwidth of the manipulator.