Fine manipulation with multifinger hands

The existence of two- and three-finger grasps in the presence of arbitrarily small friction is shown for 2D and 3D smooth objects using a simple technique. No convexity of the objects is assumed. The existence of finger gaits for rotating a planar object using three and four fingers is proved. Additional results for smooth convex objects which describe two different finger gaits using four fingers are presented. The purpose is to move one or more fingers at any one time and at the same time to maintain a grip with the others, and thereby to move the object further than or in other ways than it could be moved with a fixed grip