Paper abstract

 Title:  Curvature Effects of Bodies in Contact--Part I: 
	A 2^nd Order Mobility Index
 Authors:  E. Rimon and J. Burdick
 In : Submitted to  IEEE Trans. on Robotics and Automation, 1994.

ABSTRACT

Using a configuration-space approach, this paper develops a novel 2^nd order mobility theory for bodies in contact. A major contribution of this paper is the development of a coordinate invariant $2^{nd}$ order mobility index for a body, B, in frictionless contact with finger bodies A_1,...,A_k. The index is an integer that 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 classical 1^st order theories, but are physically different. Next we investigate the nature of the contact forces generated by 2^nd order effects. We show by a paradox that the conventional rigid body idealization is inadequate to completely explain how contact forces are generated by 2^nd order effects. The resolution of this paradox is considered in the companion paper. We further show that 2^nd order effects can be used to lower the effective 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.