Distributed Compliant Model for Efficient Dynamic Simulation of Systems With Frictional Contacts

The use of Coulomb’s friction law with the principles of classical rigid body dynamics introduces mathematical inconsistencies. Specifically, the forward dynamics problem can have no solutions or multiple solutions. In these situations an explicit model of the contact compliance at the contact point can resolve these difficulties. In this paper, we introduce a distributed compliant model for dynamic simulation. In contrast to the rigid body model and the lumped model, our approach models each contact as a finite patch and uses half space approximation to derive solutions for the small deformations and force distributions in the contact patch. This approach leads to a linear complementarity problem formulation for the contact dynamics. The existence of an unique solution can be proved for both the lumped model in the point contact case and the more accurate, distributed model. Simulation algorithm that incorporates compliant contact models and linear complementarity theory are created and demonstrated through numerical examples.