The Motion of a Compliantly Suspended Rigid Body Constrained by Multipoint Frictional Contact

This paper addresses methods for determining the motion of an elastically suspended rigid body in frictional contact at multiple distinct locations. The methods developed assume that: (1) The motion of the support from which the body is suspended and the elastic behavior of the suspension are known; (2) inertial forces are negligible (motion is quasi-static); and (3) the contact is characterized by Coulomb friction. The derived coupled set of spatial rigid body equations is used to determine both the unknown direction of the friction force (at each point of contact) and the unknown motion of the rigid body. The uniqueness of the set of active constraints when considering multipoint contact is also addressed. We show that, for any 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