Simulation of dynamic systems possessing unilateral frictional contacts is important to many industrial applications. While rigid body models are often employed, it is well established that friction can cause problems with the existence and uniqueness of the forward dynamics problem. In these situations, we argue that compliant contact models, while increasing the length of the state vector, successfully resolve these ambiguities. The simplicity and efficiency of rigid body models, however, provide strong motivation for their use during those portions of a simulation when the compliant contact model indicates a unique and stable solution. We use singular perturbation theory in combination with linear complementarity theory to establish conditions for the validity of the rigid body model with rolling and sliding unilateral contacts for planar systems. The results are illustrated with a simple example.

Previous work in rigid body dynamic simulation has relied on rigid body impact models to model collisions. The well-known models due to Newton, Poisson, and Brach, are each based on a definition of a coefficient of restitution for rigid body impact. The objective of this paper is to develop a new model that overcomes the deficiencies of these models in frictional impacts and to present a formulation to solve problems with multiple concurrent impacts. The model is based on simple mechanical elements that model energy storage and dissipation at each contact. We present an algorithm for simulating concurrent impacts between rigid bodies and illustrate its application with a variation of the peg-in-hole insertion problem.