Mobility of Bodies in Contact - I: A New 2nd Order Mobility Index for Multiple-Finger Grasps

Using a con guration-space approach, this paper develops a novel 2nd order mobility theory for bodies in contact. A major contribution of this paper is the development of a coordinate invariant 2nd order mobility index for a body, B, in frictionless contact with nger bodies A1; : : : ;Ak. The index is an integer that captures the inherent mobility of B in an equilibrium grasp due to 2nd order, or surface curvature, e ects. It di erentiates between grasps which are deemed equivalent by classical 1st order theories, but are physically di erent. We further show that 2nd order e ects can be used to lower the e ective mobility of a grasped object, and discuss implications of this result for proving new lower bounds on the number of contacting bodies needed to immobilize an object. Physical interpretation and stability analysis of 2nd order e ects are taken up in the companion paper.