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Research Papers

A Fast Algorithm for Contact Dynamics of Multibody Systems Using the Box Friction Model

[+] Author and Article Information
Farnood Gholami

Department of Mechanical Engineering and
Centre for Intelligent Machines,
McGill University,
Montreal, QC H3A 2K6, Canada
e-mail: farnood.gholami@mail.mcgill.ca

Mostafa Nasri

Department of Mechanical Engineering and
Centre for Intelligent Machines,
McGill University,
Montreal, QC H3A 2K6, Canada
e-mail: m.nasri@uwinnipeg.ca

József Kövecses

Department of Mechanical Engineering and
Centre for Intelligent Machines,
McGill University,
Montreal, QC H3A 2K6, Canada
e-mail: jozsef.kovecses@mcgill.ca

Marek Teichmann

CM Labs Simulations, Inc.,
Montreal, QC H3C 1T2, Canada
e-mail: marek@cm-labs.com

1Present address: Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, MB R3B 2E9, Canada.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 17, 2016; final manuscript received July 25, 2016; published online September 16, 2016. Assoc. Editor: Dan Negrut.

J. Comput. Nonlinear Dynam 12(1), 011016 (Sep 16, 2016) (11 pages) Paper No: CND-16-1142; doi: 10.1115/1.4034396 History: Received March 17, 2016; Revised July 25, 2016

One of the major challenges in dynamics of multibody systems is to handle redundant constraints appropriately. The box friction model is one of the existing approaches to formulate the contact and friction phenomenon as a mixed linear complementarity problem (MLCP). In this setting, the contact redundancy can be handled by relaxing the constraints, but such a technique might suffer from certain drawbacks, specially in the case of large number of redundant constraints. Most of the common pivoting algorithms used to solve the resulting mixed complementarity problem might not converge when the relaxation terms are chosen as small as they should be. To overcome the aforementioned shortcoming, we propose a novel approach which takes advantage of the sparse structure of the formulated MLCP. This novel approach reduces the sensitivity of the solution of the problem to the relaxation terms and decreases the number of required pivots to obtain the solution, leading to shorter computational times. Furthermore, as a result of the proposed approach, much smaller relaxation terms can be used while the solution algorithms converge.

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Figures

Grahic Jump Location
Fig. 1

(a) Polyhedral approximation of the friction cone and (b) box approximation of the friction cone where dn is the contact Jacobian of the normal direction, and d1 and d2 are the contact Jacobians of the tangent directions

Grahic Jump Location
Fig. 2

(a) A cube moving on the ground and (b) stack of blocks moving on the ground

Grahic Jump Location
Fig. 3

(a) OTCM connected to the SPDM manipulator (courtesy of the Canadian Space Agency) [37] and (b) OTCM—orbit replaceable unit/tool changeout mechanism

Grahic Jump Location
Fig. 4

Simulated OTCM and fixture: (a) OTCM, jaws, and fixture and (b) jaws grasping the fixture

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