Classification of Singularities in Kinematics of Mechanisms

  • Samuli PiipponenEmail author
  • Teijo Arponen
  • Jukka Tuomela
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 15)


In this short article we will discuss methods of finding and classifying singularities of planar mechanisms. The key point is to observe that the configuration spaces of the mechanisms can be understood as analytic and algebraic varieties. The set of singular points of an algebraic variety is itself an algebraic variety and of lower dimension than the original one. The singular variety can be computed using the Jacobian criterion. Once the singular points are obtained their nature can be investigated by investigating the localization of the constraint ideal at the local ring at this point. This will tell us if the singularity is an intersection of several motion modes or a singularity of a particular motion mode. The nature of the singularity can be then analyzed further by computing the tangent cone at this point.


Kinematical singularities Planar mechanisms Algebraic geometry Local rings Tangent cone 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Samuli Piipponen
    • 1
    Email author
  • Teijo Arponen
    • 1
  • Jukka Tuomela
    • 1
  1. 1.Department of Physics and MathematicsUniversity of Eastern Finland KuopioFinland

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