The Motion of a Compliantly Suspended Rigid Body Constrained by a Frictional Surface

In this paper, the quasistatic motion of an elastically suspended, unilaterally constrained rigid body is studied. The motion of the rigid body is determined, in part, by the position controlled motion of its support base and the behavior of the elastic suspension that couples the part to the support. The motion is also determined, in part, by contact with a frictional surface that both couples the rigid body to unilateral constraint surfaces and generates a friction force. The unknown friction force, however, is determined in part by the unknown direction of the rigid body motion. We derive a solvable set of equations that simultaneously determines both the friction force and the resulting rigid body motion. This set of equations requires that the friction and motion at the point of contact are oppositely directed. Solution involves the use of rigid body kinematics, the Coulomb friction coefficient, the commanded motion of the support, and the spatial elastic behavior of the coupling.