Abstract

. This paper is summary of a comprehensive study of the problem of predicting the possible acceleration(s) of a set of rigid, three-dimensional bodies in contact in the presence of Coulomb friction. We begin with a brief introduction to this problem and a survey of related work and previous approaches. This is followed by the introduction of two novel complementarity formulations for the contact problem under two friction laws: Coulomb's Law and an analogous law in which Coulomb's quadratic friction cone is approximated by a pyramid. Under a full column rank assumption on the system Jacobian matrix, we establish the existence and uniqueness of a solution to our new models in the case where the friction coefficients are nonnegative and sufficiently small. For the model based on the friction pyramid law, we also show that the classical Lemke almost-complementary pivot algorithm and our new feasible interior point method are guaranteed to compute a solution. Extensive computational result...

Citations