Planar sliding with dry friction Part 1. Limit surface and moment function

We present two geometric descriptions of the net frictional force and moment between a rigid body and a planar surface on which it slides. The limit surface, from classical plasticity theory, is the surface in load space which bounds the set of all possible frictional forces and moments that can be sustained by the frictional interface. Zhukovskii's moment function (N.E. Zhukovskii, Collected Works, Vol. 1, Gostekhizdat, Moscow, 1948, pp. 339–354) is the net frictional moment about the body's instantaneous center of rotation as a function of its location. Both of these descriptions implicitly contain the full relation between slip motion and frictional load. While Zhukovskii's moment function applies only to ordinary isotropic Coulomb friction, the limit surface applies to a wider class of friction laws that includes, for example, contact mediated by massless rigid wheels. Both the limit surface and the moment function can be used to deduce results concerning the motion of sliding rigid bodies.