Dynamics analysis of planar multi-DOF mechanism with multiple revolute clearances and chaos identification of revolute clearance joints

  • Xiulong ChenEmail author
  • Shuai Jiang
  • Suyu Wang
  • Yu Deng


The clearance joint is one of the important factors which influence system performance and dynamic characteristics. Traditional studies are mainly focused on the planar single degree of freedom (DOF) simple mechanism with one joint clearance, only few researchers investigated mechanisms with more than one DOF considering more than one clearance joint as an object, and few studies systematically analyzed nonlinear characteristics of the clearance joints. This article is devoted to analyzing the effect of multiple clearances and different friction models on the dynamic behavior of a planar multi-DOF mechanism. The 2 DOFs nine bar planar mechanism is selected as the research object. The dynamic model of the planar mechanism with two revolute clearances is built by considering Lagrange equation. The influence of LuGre model and modified Coulomb friction model on the dynamic response of the nine bar mechanism is studied. The effects of the number of clearance joints, clearance values, driving speeds and friction coefficients on the dynamic responses of the mechanism are analyzed. The chaos phenomenon existing in the clearance revolute joints is identified by phase diagram, Poincaré map and largest Lyapunov exponent (LLE). Bifurcation diagrams of revolute clearance joints with changing clearance values, driving speeds and friction coefficients are also drawn. A virtual prototype model of 2 DOF nine bar mechanism containing two revolute clearances is built by using ADAMS software to verify the correctness of the numerical results. This research can provide theoretical basis for grasping the dynamic behavior of the planar rigid-body mechanism with clearances and identifying chaos of clearance joints.


Planar mechanism Clearance Dynamic response Chaos Bifurcation 



This research is supported by the Natural Science Foundation of Shandong Province (Grant No. ZR2017MEE066), Tai Shan Scholarship Project of Shandong Province (No. tshw2013095).


This manuscript has not been published, simultaneously submitted or already accepted for publication elsewhere. All authors have read and approved the manuscript. There is no conflict of interest related to individual authors’ commitments and any project support. All acknowledged persons have read and given permission to be named. Xiulong Chen et al. have nothing to disclose.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.College of Mechanical and Electronic EngineeringShandong University of Science and TechnologyQingdaoChina
  2. 2.College of TransportationShandong University of Science and TechnologyQingdaoChina

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