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 2nd order mobility index for a body, B, in frictionless contact with finger bodies A_1, ..., A_k. The index captures the inherent mobility of B in an equilibrium grasp due to 2nd order, or surface curvature, effects. It differentiates between grasps which are deemed equivalent by the classical 1st order theories, but are physically different. In a companion paper we discuss applications and provide physical justification for using 2nd order immobility effects.