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Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

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Volume 60, Issue 3


Joint reactions in rigid or flexible body mechanisms with redundant constraints

M. Wojtyra
  • Corresponding author
  • Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, 24 Nowowiejska St., 00-665 Warsaw, Poland
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ J. Frączek
  • Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, 24 Nowowiejska St., 00-665 Warsaw, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2012-12-22 | DOI: https://doi.org/10.2478/v10175-012-0073-y


The problem of joint reactions indeterminacy, in engineering simulations of rigid body mechanisms is most often caused by redundant constraints which are defined as constraints that can be removed without changing the kinematics of the system. In order to find a unique set of all joint reactions in an overconstrained system, it is necessary to reject the assumption that all bodies are rigid. Flexible bodies introduce additional degrees of freedom to the mechanism, which usually makes the constraint equations independent. Quite often only selected bodies are modelled as the flexible ones, whereas the other remain rigid. In this contribution it is shown that taking into account flexibility of selected mechanism bodies does not guarantee that unique joint reactions can be found. Problems typical for redundant constraints existence are encountered in partially flexible models, which are not overconstrained. A case study of a redundantly constrained spatial mechanism is presented. Different approaches to the mechanism modelling, ranging from a purely rigid body model to a fully flexible one, are investigated and the obtained results are compared and discussed.

Keywords : multibody system; redundant constraints; joint reactions; flexible bodies.

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About the article

Published Online: 2012-12-22

Published in Print: 2012-12-01

Citation Information: Bulletin of the Polish Academy of Sciences: Technical Sciences, Volume 60, Issue 3, Pages 617–626, ISSN (Print) 0239-7528, DOI: https://doi.org/10.2478/v10175-012-0073-y.

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