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TECHNICAL PAPERS

Energy Analysis and Decoupling in Three-Dimensional Impacts of Multibody Systems

[+] Author and Article Information
Seyed Ali Modarres Najafabadi

Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canadasmodar@cim.mcgill.ca

József Kövecses

Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canadajozsef.kovecses@mcgill.ca

Jorge Angeles

Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canadaangeles@cim.mcgill.ca

For a full row rank matrix S, the right Moore-Penrose generalized inverse can be expressed as S=ST(SST)1.

J. Appl. Mech 74(5), 845-851 (Dec 20, 2006) (7 pages) doi:10.1115/1.2712226 History: Received November 07, 2005; Revised December 20, 2006

This paper discusses an exact decomposition of the kinetic energy to determine the energy content that influences the dynamics of unilateral contacts in multibody systems. This decomposition essentially divides the kinetic energy of the whole multibody system into two completely decoupled parts associated with the constrained and admissible directions of unilateral contacts. This will provide a picture of how the energy absorption/dissipation during impacts is related to the variation of the generalized velocities and the configuration of multibody systems. Potential applications of such a decoupling are highlighted.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

General unilaterally constrained multibody system

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Figure 2

Unilaterally constrained three-link planar manipulator

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Figure 3

Displacement and velocity of the end-point in the normal direction of contact

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Figure 4

Generalized velocities associated with admissible and constrained motions

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Figure 5

Kinetic energies of constrained Tc and admissible Ta motions

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Figure 6

Total mechanical energy of the manipulator

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