Multibody System Dynamics

, Volume 14, Issue 1, pp 23–46 | Cite as

Joint Reaction Forces in Multibody Systems with Redundant Constraints



Redundant constraints are defined as those constraints which can be removed without changing the kinematics of the mechanism. They are usually eliminated from the mathematical model of a multibody system. For a given mechanism the set of redundant constraints can be chosen in many ways. Rigid body systems with redundant constraints do not have a unique solution to the problem of joint reaction forces calculation. If redundant constraints are present in the mechanical system, then the system is statically undetermined. If in the case of dynamics problem the constraints are consistent, all of them are frictionless and we are interested only in positions, velocities and accelerations of the bodies, then the calculation of joint reaction forces is not necessary. In many cases, however, e.g. when we want to take into account friction in joints, the calculation of joint reaction forces cannot be avoided. In some rigid body systems, despite the redundant constraints existence, reaction forces in selected joints can be uniquely determined. The paper presents three methods of finding the constraints for which reaction forces can be uniquely determined using rigid body model. Three different techniques of Jacobian matrix analysis are used.


redundant constraints joint reaction force 


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  1. 1.
    Haug, E. J., Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon, Boston, MA, 1989.Google Scholar
  2. 2.
    Nikravesh, P. E., Computer-Aided Analysis of Mechanical Systems, Prentice Hall, New York, 1988.Google Scholar
  3. 3.
    Garcia de Jalon, J. and Bayo, E., Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge, Springer, New York, 1994.Google Scholar
  4. 4.
    Park, T., Haug, E. J. and Yim, H. J., ‘Automated kinematic feasibility evaluation and analysis of mechanical systems’, Mechanisms and Machine Theory 23(5), 1988, 383–391.CrossRefGoogle Scholar
  5. 5.
    Haug, E. J., Intermediate Dynamics, Prentice Hall, 1992.Google Scholar
  6. 6.
    Blajer, W., ‘On the determination of joint reactions in multibody mechanisms’, ASME Journal of Mechanical Design 126(2), 2004, 341–350.CrossRefGoogle Scholar
  7. 7.
    Udwadia, F. E. and Kalaba, R. E., Analytical Dynamics: A New Approach, Cambridge University Press, Cambridge, 1996.Google Scholar
  8. 8.
    Corwin, L. J. and Szczarba, R. H., Multivariable Calculus, Marcel Dekker, New York, 1982.Google Scholar
  9. 9.
    Jungnickel, U., ‘Differential-algebraic equations in riemannian spaces and applications to multibody system dynamics’, ZAMM 74(9), 1994, 409–415.Google Scholar
  10. 10.
    Blajer, W., ‘A Geometrical interpretation and uniform matrix formulation of multibody system dynamics’, ZAMM 81(4), 2001, 247–259.CrossRefGoogle Scholar
  11. 11.
    Strang, G., Linear Algebra and Its Applications, Academic Press, New York, 1980.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Institute of Aeronautics and Applied MechanicsWarsaw University of TechnologyWarsawPoland

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