Geometric Reformulation of 3-Fingered Force-Closure Condition

This paper addresses the problem of testing whether three contact points form a 3-fingered force-closure grasp in two dimensions. In particular, assuming frictional point contacts, we present a new necessary and sufficient condition for three fingers to form a force-closure grasp. The proposed condition is based on a technique for representing a friction cone as a line segment in a dual plane. This representation allows force-closure test to be formulated as the problem of intersection detection between a line segment and a convex polygon. The resulting geometric condition is presented along with an efficient algorithm for using the condition in force-closure test.