Dynamic modeling and comparative analysis of a 3-PRR parallel robot with multiple lubricated joints

  • Haodong Zhang
  • Xianmin ZhangEmail author
  • Zhenhui Zhan
  • Lixin Yang


This paper presents a methodology to study the dynamic response of a parallel robot with multiple lubricated joints. Based on Gümbel’s boundary conditions, the hydrodynamic force of the journal bearing is calculated with the Pinkus–Sternlicht model. Considering the dynamic loads on the multiple lubricated joints, the Pinkus–Sternlicht model is modified to ensure numerical stability of the solution of the system’s equations. A comparative analysis of four joint force models is presented to show the advantages of the modified model for a 3-PRR (P and R represent prismatic and revolute pairs respectively and the underline of the P represents the actuated joint) parallel robot. The improvement in the numerical stability of the modified Pinkus–Sternlicht model is proven. Subsequently, the dynamic behavior of the 3-PRR parallel robot with multiple lubricated joints is analyzed comprehensively, compared with the 3-PRR parallel robot with multiple dry clearance joints. Simulation results demonstrate the validity of the dynamic methodology containing the modified Pinkus–Sternlicht model for the 3-PRR parallel robot with multiple lubricated joints. This dynamic methodology can illustrate the better periodicity of such parallel robots considering lubricated joints.


Multibody dynamics Multiple lubricated joints 3-PRR parallel robot Hydrodynamic force 



This research was supported by the National Natural Science Foundation of China (Grant No. U1501247) and the Fundamental Research Funds for the Central Universities of China (2019MS068). These supports are greatly acknowledged.

Compliance with ethical standards

Conflict of interests

The authors declare that they have no conflicts of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Guangdong Key Laboratory of Precision Equipment and Manufacturing Technology, School of Mechanical and Automotive EngineeringSouth China University of TechnologyTianhe DistrictPeople’s Republic of China

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