Abstract
We prove that a robot hand whose fingers make frictionless contact with a convex polyhedral object will be able to find a grasp where the hand can exert any desired force-torque on the object provided the hand has seven fingers. We present an algorithm for grasping any convex polyhedron and we prove rigorously that it works for any convex polyhedron. The algorithm requiresO(n 3/2√logn) steps (in the worst case) wheren is the number of vertices.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Aggrawal. Personal Communication, 1990.
K. L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry.Discrete and Computational Geometry,4(5):387–422, 1989.
M. E. Dyer. Linear time algorithm for two- and three-variable linear programs.SIAM Journal on Computing,13(1):31–45, February 1984.
A. J. Goldman. Resolution and separation. InLinear Inequalities and Related Systems, pp. 41–51, ed. by Kuhn, H. W., and Tucker, A. W. Princeton University Press, Princeton, NJ, 1956.
A. J. Goldman and A. W. Tucker. Polyhedral cones. InLinear Inequalities and Related Systems, pp. 19–40, ed. by Kuhn, H. W., and Tucker, A. W. Princeton University Press, Princeton, NJ, 1956.
B. Grunbaum.Convex Polytopes. Wiley Interscience, New York, 1967.
K. Lakshminarayama. Mechanics of form closure. ASME Paper 78-DET-32, 1978.
L. A. Lyusternik.Convex Figures and Polyhedra. Heath, Boston, 1966.
X. Markenscoff, L. Ni, and C. Papadimitriou. The geometry of form closure.International Journal of Robotics Research,9(1):61–74, February 1990.
N. Megiddo. Linear time algorithm for linear programming in r3 and related problems.SIAM Journal of Computing,12(4):759–776, November 1983.
B. Mishra, J. T. Schwartz, and M. Sharir. On the existence and synthesis of muitifinger positive grips.Algorithmica,2(4):541–558, November 1987.
B. Mishra and N. Silver. Some discussion of static gripping and its stability.IEEE Transactions on Systems, Man, and Cybernetics,19(4):783–796, July–August 1989.
V. -D. Nguyen. Construcing force-closure grasps.The International Journal of Robotics Research,7(3):3–16, June 1988.
F. P. Preparata and M. I. Shamos,Computational Geometry. Springer-Verlag, New York, 1985.
F. Reuleaux.Kinematics of Machinery. Dover, New York, 1875.
E. Steinitz. Bedingt konvergente reihen und konvexe systeme, i.J. Reine und Angewandte Mathematik,143:128–175, 1913.
E. Steinitz. Bedingt konvergente reihen und konvexe systeme, ii.J. Reine und Angewandte Mathematik,144:1–40, 1914.
E. Steinitz. Bedingt konvergente reihen und konvexe systeme, iii.J. Reine und Angewandte Mathematik,146:1–52, 1916.
Author information
Authors and Affiliations
Additional information
Communicated by John E. Hopcroft.
Rights and permissions
About this article
Cite this article
Meyer, W. Seven fingers allow force-torque closure grasps on any convex polyhedron. Algorithmica 9, 278–292 (1993). https://doi.org/10.1007/BF01190900
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01190900