On the existence and synthesis of multifinger positive grips

We study the criteria under which an object can be gripped by a multifingered dexterous hand, assuming no static friction between the object and the fingers; such grips are calledpositive grips. We study three cases in detail: (i) the body is at equilibrium, (ii) the body is under some constant external force/torque, and (iii) the body is under a varying external force/torque. In each case we obtain tight bounds on the number of fingers needed to obtain grip.We also present efficient algorithms to synthesize such positive grips for bounded polyhedral/polygonal objects; the number of fingers employed in the grips synthesized by our algorithms match the above bounds. The algorithms run in time linear in the number of faces/sides.The paper may be of independent interest for its presentation of algorithms arising in the study of positive linear spaces.Work on this paper has been supported by Office of Naval Research Grant N00014-82-K.-0381, National Science Foundation Grant No. NSF-DCR-83-20085, and by grants from the Digital Equipment Corporation, and the IBM Corporation.