Sources of error in a rigid body simulation of rigid parts on a vibrating rigid plate

Abstract

We present a simulation study of an important rigid body contact problem. The system in question is composed of a rigid plate and a single rigid body (or particle). The plate follows a prescribed periodic motion of small amplitude and high frequency, such that the net force applied to the part appears to be from a time-independent, position-dependent velocity field in the plane of the plate. Theoretical results obtained by Vose et al. were found to be in good agreement with simulation results obtained with the Stewart-Trinkle time-stepping method. In addition, simulations were found to agree with the qualitative experimental results of Vose et al. After such verification of the simulation method, additional numerical studies were done that would have been impossible to carry out analytically. Specifically, we were able to demonstrate the convergence of the method with decreasing step size (as predicted theoretically by Stewart). Further analytical and numerical studies will be carried out in the future to develop and select robust simulation methods that best satisfy the speed and accuracy requirements of different applications.

A Complementarity Based Contact Model for Geometrically Accurate Treatment of Polytopes in Simulation

“…Robotics experiments tend to be exceedingly costly and time consuming, so that the ability to perform reliable experiments in simulation would be a great benefit. Although some work has been done regarding validation of simu-lation [3][4][5], the problem of measuring physical accuracy of simulation is a difficult one. Certainly we can say that convergence of a constraint solver is not a good metric alone, since the underlying constraints may be flawed.…”