Dynamic force/torque closure for 2D and 3D objects by means of rolling contacts with robot fingers

This paper is concerned with problems of force/torque closure for 2D and 3D objects in a dynamic sense by using a pair of robot fingers with spherical ends that induce rolling contacts with object surfaces. In case of the use of frictionless fingers it is well known that three fingers suffice to immobilize (realize form closure of) any 2D object with triangular shape but four fingers are needed for immobilizing a parallelepiped. In contrast, the paper shows that only two fingers with spherical ends are enough to realize force/torque closure for any convex polygonal objects under the effect of gravity force. Moreover, the force/torque closure can be achieved in a dynamic sense by controlling locations of contact points on object surfaces through rollings between finger ends and object surfaces without knowing location of the object mass center. These discussions are extended to a class of problems of force/torque closure for 1) 3D objects with two flat parallel surfaces and 2) with two flat but non-parallel surfaces.