Mobility of bodies in contact. I. A new 2nd order mobility index for multiple-finger grasps

Using a configuration-space approach, this paper develops a coordinate invariant 2^nd order mobility index for a body, B, in frictionless contact with finger bodies A₁,...,A_k . The index captures the inherent mobility of B in an equilibrium grasp due to 2^nd order, or surface curvature, effects. It differentiates between grasps which are deemed equivalent by the classical 1^st order theories, but are physically different. In a companion paper we discuss applications and provide physical justification for using 2^nd order immobility effects