On the Symmetric Molecular Conjectures

Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 15)


A molecular linkage consists of a set of rigid bodies pairwise connected by revolute hinges where all hinge lines of each body are concurrent. It is an important problem in biochemistry, as well as in robotics, to efficiently analyze the motions of such linkages. The theory of generic rigidity of body-bar frameworks addresses this problem via fast combinatorial algorithms. However, recent work has shown that symmetry (a common feature of many molecular and mechanical structures) can lead to additional motions. These motions typically maintain the original symmetry of the structure throughout the path, and they can often be detected via simple combinatorial counts. In this paper, we outline how these symmetry-based mathematical counts and methods can be used to efficiently predict the motions of symmetric molecular linkages, and we numerically analyze configuration spaces supporting the symmetric Molecular Conjectures formulated herein.


Rigidity Flexibility Symmetry Molecular linkage Configuration space 



This work has been partially supported by the Spanish Ministry of Economy and Competitiveness under project DPI2010-18449.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Institut de Robòtica i Informàtica Industrial, UPC-CSICBarcelonaSpain
  2. 2.Department of Mathematics and StatisticsUniversity of LancasterLancasterUK
  3. 3.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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