A New Approach to Eliminate the Constraints Violation at the Position and Velocity Levels in Constrained Mechanical Multibody Systems

  • P. FloresEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 24)


In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is presented. This new approach is derived under the framework of multibody dynamics formulation The basic idea of this methodology 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. A planar four bar mechanism is used as a demonstrative example of application, which allows to show the effectiveness of presented method.


Constraints violation Equations of motion Multibody systems 


  1. 1.
    Wittenburg J (1977) Dynamics of systems of rigid bodies. B.G. Teubner, Stuttgart, GermanyCrossRefzbMATHGoogle Scholar
  2. 2.
    Nikravesh PE (1988) Computer-aided analysis of mechanical systems. Prentice Hall, Englewood Cliffs, New JerseyGoogle Scholar
  3. 3.
    Shabana AA (1989) Dynamics of multibody systems. Wiley, New YorkzbMATHGoogle Scholar
  4. 4.
    Schiehlen W (1990) Multibody systems handbook. Springer, BerlinCrossRefzbMATHGoogle Scholar
  5. 5.
    Rahnejat H (2000) Multi-body dynamics: historical evolution and application. Proc Inst Mech Eng Part C J Mech Eng Sci 214:149–173Google Scholar
  6. 6.
    Eberhard P, Schiehlen W (2006) Computational dynamics of multibody systems: history, formalisms, and applications. J Comput Nonlinear Dyn 1:3–12CrossRefGoogle Scholar
  7. 7.
    Schiehlen W (2007) Research trends in multibody system dynamics. Multibody SysDyn 18:3–13CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Nikravesh PE (2008) Newtonian-based methodologies in multi-body dynamics. Proc Inst Mech Eng Part K J Multi-body Dyn 222:277–288Google Scholar
  9. 9.
    Jalón JG, Bayo E (1994) Kinematic and dynamic simulations of multibody systems: the real-time challenge. Springer, New YorkCrossRefGoogle Scholar
  10. 10.
    Rosen A, Edelstein E (1997) Investigation of a new formulation of the Lagrange method for constrained dynamic systems. J Appl Mech 64:116–122CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Blajer W (2002) Elimination of constraint violation and accuracy aspects in numerical simulation of multibody systems. Multibody Sys Dyn 7:265–284CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Flores P (2011) A methodology for quantifying the position errors due to manufacturing and assemble tolerances. J Mech Eng 57(6):457–467CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of MinhoBragaPortugal

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