Determining the Set of Active Constraints When a Rigid Body Compliantly Interacts With Multiple Frictional Contacts

Abstract

In this paper, the motion of an elastically suspended rigid body unilaterally constrained by frictional contact at multiple locations is studied. In this problem, each individual contact may or may not constrain the body’s motion. The set of actual active constraints is determined by: 1) the commanded motion of the body’s compliant support, 2) the coefficient of friction at each contact point, 3) the number and geometry of all potentially constraining surfaces, and 4) the elastic properties of the support. Here, the investigated problem is restricted to quasistatic motion and the interaction is characterized by Coulomb friction. We show that, for a passive compliant system, if the coefficient of friction at each contact is upper bounded, the set of active constraints is unique. A procedure to determine both the set of active constraints and the motion of the constrained body is provided.