Distribution of Wrench-Twist Duality in Over-Constrained Mechanisms

Author:

Fayet M.1

Affiliation:

1. Equipe de Me´canique ge´ne´rale-Laboratoire de Me´canique des Solides, Ba^timent 302, INSA, 20 Ave A. Einstein, 69621 Villeurbanne Cedex-France

Abstract

First, a procedure is presented in order to build the space of statically admissible wrenches. The matrix which generates them is obtained in an intrinsic way. It uses intersection of spaces for the edges (of the associated graph) and the new operation of “triangular projection” for the vertices. From this matrix, the choice of any set of indeterminable contact forces is achieved via a very simple test. This matrix allows to determine also all the possible degrees of freedom to add to the over-constrained mechanism in order to transform it into a non over-constrained one. Wrench-twist duality arises clearly in this last procedure.

Publisher

ASME International

Subject

Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials

Reference14 articles.

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2. Philips, J. R., and Hunt, K. H., 1964, “On the Theorem of Three Axes in the Spatial Motion of Three Bodies,” Aust. Appl. Scie., 156, pp. 267–287.

3. Waldron, K. J. , 1966, “The Constraint Analysis of Mechanisms,” J. Mec., 1(2), pp. 101–104.

4. Davies, T. H., and Primerose, J. F., 1971, “An Algebra for the Screw System of Pairs of Bodies in a Kinematic Chain,” Third World Congress for the Theory of Machines and Mechanisms, Kupary, Yugoslavia, Vol. D, paper D. 14, pp. 199–212.

5. Baker, J. E. , 1980, “On the Relative Freedom Between Links in Kinematic Chains with Cross Jointing,” Mech. Mach. Theory, 15, pp. 397–413.

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