Nonlinear Dynamics

, Volume 94, Issue 4, pp 2625–2642 | Cite as

Chaotic characteristic analysis of spatial parallel mechanism with clearance in spherical joint

  • Xiulong Chen
  • Wenhua Gao
  • Yu Deng
  • Qing Wang
Original Paper


The spherical joint is one of the main motion pairs in spatial parallel mechanism, and the spherical clearance has a great effect on the nonlinear dynamic performance of parallel mechanism. Most previous studies mainly focused on planar mechanism with revolute joint, spatial parallel mechanism with spherical clearance researched rarely. In this paper, the chaotic characteristic analysis of spatial 4-UPS (universal joint-prismatic pair-spherical joint)-RPU (revolute joint-prismatic pair-universal joint) parallel mechanism with spherical clearance is investigated. The models of spherical joint with clearance are established, and then the nonlinear dynamics equation of the parallel mechanism with spherical clearance is derived by Lagrange method. The influence of clearance on displacement, velocity and acceleration of moving platform is both analyzed. And the influence of different clearance sizes on contact force and center trajectory of the spherical clearance is analyzed, and the chaotic characteristics of spherical joint and the mechanism are all studied by phase diagram, Poincare section mapping method and Lyapunov exponent. The results show that spherical clearance has great influence on the nonlinear dynamic performance of 4-UPS-RPU parallel mechanism, and chaos exists in the dynamic response of spherical clearance and the mechanism. As the clearance value increases, the stability of the mechanism is weakened. When the clearance value increases to 2.1 mm, chaotic motion appeared on the moving platform of the mechanism. This research is a useful attempt to study the nonlinear dynamics characteristic of parallel mechanisms with spherical clearance, which has guiding significance and practical value for further research on the design and chaotic control of parallel mechanism.


Parallel mechanism Chaotic characteristic Clearance Spherical joint 



This research is supported by the Natural Science Foundation of Shandong Province (Grant No. ZR2017MEE066), the Shandong Young Scientists Award Fund (Grant No. BS2012ZZ008), Taishan Scholarship Project of Shandong Province (No. tshw20130956).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

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

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