Abstract
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.
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Communicated by Chee-Keng Yap.
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.
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Mishra, B., Schwartz, J.T. & Sharir, M. On the existence and synthesis of multifinger positive grips. Algorithmica 2, 541–558 (1987). https://doi.org/10.1007/BF01840373
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DOI: https://doi.org/10.1007/BF01840373