Analysis of rigid-body dynamic models for simulation of systems with frictional contacts

The use of Coulomb's friction law with the principles of classical rigid-bo dy dynamics introduces mathematical inconsistencies. Specifically, the forw ard dynamics problem can have no solutions or multiple solutions. In these situations, compliant contact models, while increasing the dimensionality o f the state vector, can resolve these problems. The simplicity and efficien cy of rigid-body models, however, provide strong motivation for their use d uring those portions of a simulation when the rigid-body solution is unique and stable. In this paper, we use singular perturbation analysis in conjun ction with linear complementarity theory to establish conditions under whic h the solution is unique and stable. In this paper, we use singular perturb ation analysis in conjunction with linear complementarity theory to establi sh conditions under which the solution predicted by the rigid-body dynamic model is stable. We employ a general model of contact compliance to derive stability criteria for planar mechanical systems. In particular, we show th at for cases with one sliding contact, there is always at most one stable s olution. Our approach is not directly applicable to transition between roll ing and sliding where the Coulomb friction law is discontinuous. To overcom e this difficulty, we introduce a smooth nonlinear friction law, which appr oximates Coulomb friction. Such a friction model can also increase the effi ciency of both rigid-body and compliant contact simulation. Numerical simul ations for the different models and comparison with experimental results ar e also presented.