On computing three-finger force-closure grasps of polygonal objects

This paper presents a new approach to the computation of stable grasps of polygonal objects. The authors consider the case of a hand equipped with three hard fingers and assume point contact with friction. They prove a sufficient condition for force-closure grasps that leads to a system of linear constraints in the position of the fingers along the polygonal edges. All regions satisfying these constraints are found by a new projection algorithm based on linear parameter elimination accelerated by simplex techniques. Maximal object segments where fingers can be positioned independently are found by linear optimization within the grasp regions. The approach has been implemented and examples are presented.<>