Friction and Part Curvature in Parallel-Jaw Grasping

When grasping a part with a parallel-jaw gripper, the part will generally rotate due to kinematic constraints. Predicting the part's final orientation is useful for grasping and for planning sequences of gripper motions to orient parts. For a given part geometry, the grasp function maps initial orientations to final orientations. Previously, we studied polygonal and algebraic parts in the absence of friction. This article considers how Coulomb friction affects the grasp function. We consider two models of Coulomb friction, For a deterministic model, we show that the grasp function of any polygonal part can be represented with a piecewise linear function that we call a step-ramp function. We then show that any step-ramp function is the grasp function of a curved part operating under zero friction. Both contain ranges of orientations where the part does not rotate when grasped. This yields our primary result, that any part with deterministic friction has equivalent grasp mechanics to a "dual" part under zero friction. We then apply previous results to derive grasp plans that orient parts in the presence of friction. We also give an algorithm for planning under a non-deterministic model of Coulomb friction, and give bounds on the friction coefficient needed to insure the existence of such plans. (C) 1995 John Wiley & Sons, Inc.