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On the symmetric molecular conjectures

Research output: Contribution in Book/Report/ProceedingsPaper


Publication date2014
Host publicationComputational Kinematics: Proceedings of the 6th International Workshop on Computational Kinematics (CK2013)
EditorsFederico Thomas, Alba Perez Gracia
Place of publicationBerlin
PublisherSpringer Verlag
Number of pages10
ISBN (Electronic)9789400772144
ISBN (Print)9789400772137
Original languageEnglish

Publication series

NameMechanisms and Machine Science


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.