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Mathematical Problems in Engineering
Volume 2009, Article ID 384071, 16 pages
Research Article

The Determination of the Velocities after Impact for the Constrained Bar Problem

1Center for Engineering, Modeling and Applied Social Sciences (CECS), Federal University of ABC (UFABC), Aerospace Engineering, Av. dos Estados, 5001. Bloco B/Sala 936, 09210-580 Santo André, SP, Brazil
2National Institute for Space Research—INPE, Av. dos Astronautas, 1758, 12201-940 São José dos Campos, SP, Brazil
3German Aerospace Center—DLR, Institute of Robotics and Mechatronics, 82234 Wessling, Germany

Received 27 May 2009; Accepted 23 November 2009

Academic Editor: Antonio Prado

Copyright © 2009 André Fenili et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A simple mathematical model for a constrained robotic manipulator is investigated. Besides the fact that this model is relatively simple, all the features present in more complex problems are similar to the ones analyzed here. The fully plastic impact is considered in this paper. Expressions for the velocities of the colliding bodies after impact are developed. These expressions are important in the numerical integration of the governing equations of motion when one must exchange the set of unconstrained equations for the set of constrained equation. The theory presented in this work can be applied to problems in which robots have to follow some prescribed patterns or trajectories when in contact with the environment. It can also de applied to problems in which robotic manipulators must handle payloads.