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.
Issue Section:
Technical Papers
1.
Fayet
, M.
, 1995
, “Me´canismes multiboucles III-Hyperstatisme au sens de la Dynamique et au sens de la cine´matique- Dualite´
,” Mech. Mach. Theory
, 30
, pp. 233
–251
.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
.6.
Fayet
, M.
, 1995
, “Me´canismes multiboucles I-De´termination des espaces de torseurs cine´matiques dans un me´canisme
,” Mech. Mach. Theory
, 30
, pp. 201
–217
.7.
Lipkin, H., and Duffy, J., 1982, “Analysis of Industial Robots via the Theory of Screws,” Proceedings of the 4th International Symposium on Theory and Practice of Robots Manipulators, Paris, pp. 359–370.
8.
Lipkin, H., and Duffy, J., 1984, “On the Geometry of Orthogonal and Reciprocal Screws,” 5th Symposium on Theory and Practice of Robots Manipulators, Udine Italy, June.
9.
Lipkin
, H.
, Duffy
, J.
, 1985, “The Elliptic Polarity of Screws,” ASME J. Mech., Transm., Autom. Des., 107.10.
Holzmann
, W.
, and Mac Carthy
, M.
, 1985, “Computing the Friction Forces Associated with a Three-Fingered Grasp,” IEEE J. Rob. Autom., RA-1(4).11.
Kerr, D. R., 1984, “An Analysis of Multi-Fingered Hand,” Ph.D. dissertation. Department of Mechanical Engineering. Stanford University.
12.
Romdhane
, L.
, and Duffy
, J.
, 1990, “Kinestatic Analysis of Multi-Fingered Hands,” Int. J. Robot. Res., 9(6).13.
Loncaric
, J.
, 1982, “Normal Forms of Stiffness and Compliance Matrices,” IEEE J. Rob. Autom., RA-3(6).14.
Fayet
, M.
, and Bonnet
, P.
, 1995
, “Me´canismes multiboucles II-Processus de de´termination du rang des e´quations de liaison. Distribution des mobilite´s
,” Mech. Mach. Theory
, 30
, pp. 219
–232
.Copyright © 2003
by ASME
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