Single Exponential Motion and Its Kinematic Generators

  • Guanfeng LiuEmail author
  • Yuanqin Wu
  • Xin Chen
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 15)


Both constant velocity (CV) joints and zero-torsion parallel kinematic machines (PKMs) possess special geometries in their subchains. They are studied as two different subjects in the past literature. In this paper we provide an alternative analysis method based on the symmetric product on \(SE(3)\) (the Special Euclidean group). Under this theoretical framework CV joints and zero-torsion mechanisms are unified into single exponential motion generators (SEMG). The properties of single exponential motion are studied and sufficient conditions are derived for the arrangement of joint screws of a serial chain so that the motion pattern of the resulting mechanism is indeed a single exponential motion generator.


Constant velocity transmission Zero torsion Symmetric product Single exponential motion generator 



This research is supported by Talents Introduction Startup Funds of High Education of Guangdong Province (2050205) and supported by \(1000\) Young Investigator Plan of the Chinese Government.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Guangdong University of TechnologyGuangdongChina
  2. 2.Hong Kong University of Science and TechnologyHong KongChina

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