A configuration space analysis of bodies in contact—II. 2ND order mobility

Abstract

Using a configuration space approach, this paper develops a 2nd order mobility theory for a body B, in frictionless quasi-static contact with rigid stationary bodies A 1,…, A d . This analysis ultimately leads to a coordinate invariant 2nd order mobility index, an integer that captures the inherent mobility of B in an equilibrium grasp. The 2nd order index differentiates between grasps which are deemed equivalent by 1st order, or instantaneous, theories, but are physically different. We further show that 2nd order effects can be used to lower the effective mobility of an equilibrium grasp, and hence can be used to prove new lower bounds on the number of contacting bodies needed to immobilize an object.