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Abstract: On Dynamic Multi-Rigid-Body Contact Problems with Coulomb Friction
On Dynamic Multi-Rigid-Body Contact Problems with Coulomb Friction
J.C. Trinkle
J.S. Pang
S. Sudarsky
G. Lo
Tech Report 95-003, Texas A&M University, Department of Computer Science
© 1995 TAMU.
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Abstract:
This paper is summary of a comprehensive study of the problem of
predicting the possible acceleration(s) of a set of rigid,
three-dimensional bodies in contact in the presence of Coulomb
friction. We begin with a brief introduction to this problem and a
survey of related work and previous approaches. This is followed by
the introduction of two novel complementarity formulations for the
contact problem under two friction laws: Coulomb's Law and an
analogous law in which Coulomb's quadratic friction cone is
approximated by a pyramid. Under a full column rank assumption on the
system Jacobian matrix, we establish the existence and uniqueness of a
solution to our new models in the case where the friction coefficients
are nonnegative and sufficiently small. For the model based on the
friction pyramid law, we also show that the classical Lemke
almost-complementary pivot algorithm and our new feasible interior
point method are guaranteed to compute a solution. Extensive
computational results are presented to demonstrate the effectiveness
and characteristics of these solution methods for solving the model
with friction pyramids. Finally, results are summarized and
conclusions are drawn.
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