Generalized Mobility and Decoupling Conditions of Closed-Loop Mechanism

  • Fan ZhangEmail author
  • Guohua Cui
  • Dan Zhang
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


This paper purposes a new kinematic analysis approach of closed-loop mechanisms based on the linear dependence of twists. First, the generalized velocity equation of closed-loop mechanisms is established by means of the exponential product form of rigid body motion. Second, the condition of the decoupling of closed-loop mechanism is obtained. Third, a simple analysis approach for decoupling analysis of the mechanism is proposed. Next, the approach is proven by the analysis of the decoupling mechanism and partial decoupling mechanisms and the synthesis of a decoupling spherical mechanism. The examples indicate that the actuation wrench is related with the linear dependence of the kinematic joints of the close-loop mechanism. This broadens the traditional knowledge about the actuation wrenches based on the reciprocal screw theory.


Closed-loop mechanism Decoupling Motion Linear dependence Mobility analysis 


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The research work is supported by the Science and Technology Commission of Shanghai Municipality under Grant No. 17441901200.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Intelligent Robot Research CenterShanghai University of Engineering ScienceShanghaiChina
  2. 2.Kaneff Department in Advanced Robotics and MechatronicsYork UniversityTorontoTaiwan

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