A configuration space analysis of bodies in contact—I. 1st order mobility

• Published in: Mechanism and machine theory Vol. 30; no. 6; pp. 897 - 912
• Main Authors: Rimon, Elon, Burdick, Joel W.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1995; New York, NY Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; Mobility; Solid body; Quasi static theory; Trajectories; Mechanical contacts; Planning; Work holder; Grippers; Dynamical systems; Robotics
• ISSN: 0094-114X; 1873-3999
• DOI: 10.1016/0094-114X(95)00002-G

This paper introduces a novel configuration space method for analyzing the relative mobility of a body B, in frictionless quasi-static contact with rigid stationary bodies A 1, …, A d . We study the 1st order properties of Bs free motions and relate them to the reciprocal/repelling screws of Screw Theory. This analysis forms the basis for a 1st order mobility theory. We introduce a coordinate invariant mobility index that measures the effective 1st order mobility of B in an equilibrium grasp. This index is shown to be solely a function of the number of the contact points. Examples show that the 1st order mobility theory (and hence Screw Theory) cannot adequately differentiate between different equilibrium grasps involving the same number of fingers. This motivates the development of a 2nd order theory in the companion paper. The 2nd order analysis is facilitated by the configuration space approach developed herein.