A Novel, Loop-Based Approach for Rigidity Detection for Systems with Multiple Spherical–Spherical Bars: The “Double-Banana” Case

  • F. SimrothEmail author
  • H. F. Ding
  • A. Kecskeméthy
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 24)


Rigidity detection is a very important tool for structural synthesis of mechanisms and the processing of CAD-generated models, as it helps to unveil possible sources of inconsistency in Grübler’s count of degrees of freedom (DOF) and thus to generate consistent kinematical models of complex mechanisms. This paper proposes a loop-based rigidity detection algorithm that is able to detect rigidity/mobility for special cases including multiple spherical–spherical pairs, such as the famous “double-banana” mechanism. To this end, the algorithm tracks “isolated” DOFs which are split into “fully isolated” and “transmitted isolated” DOFs. Using the independent loops as the basic building blocks, the kinematical network and its reduced loop connection graph are obtained, from which rigid sub-systems and the inherent “global” isolated rotational DOFs are recognized. The procedure is explained for the “double-banana” mechanism but is easily extended to other mechanisms.


Rigidity detection “Double-banana” mechanism Kinematical network Multiple spherical joint 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of Duisburg-EssenDuisburgGermany
  2. 2.Yanshan UniversityQinhuangdaoChina

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