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.
Distribution of Wrench-Twist Duality in Over-Constrained Mechanisms
Contributed by the Mechanisms Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 2000; revised March 2002. Associate Editor: G. S. Chirikjian.
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Fayet, M. (March 21, 2003). "Distribution of Wrench-Twist Duality in Over-Constrained Mechanisms ." ASME. J. Mech. Des. March 2003; 125(1): 81–91. https://doi.org/10.1115/1.1541629
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