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Comparison of Different Methods to Control Constraints Violation in Forward Multibody Dynamics

[+] Author Affiliations
Paulo Flores

Universidade do Minho, Campus de Azurém, Guimarães, Portugal

Parviz E. Nikravesh

The University of Arizona, Tucson, AZ

Paper No. DETC2013-12591, pp. V07AT10A028; 9 pages
doi:10.1115/DETC2013-12591
From:
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 7A: 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5596-6
  • Copyright © 2013 by ASME

abstract

The dynamic equations of motion for constrained multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. It is known that the standard resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general review of the main methods commonly used to control or eliminate the violation of the constraint equations in the context of multibody dynamics formulation is presented and discussed. Furthermore, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is also presented. The basic idea of this approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations.

Copyright © 2013 by ASME

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