Kinematics and Workspace of a Spherical Engraving Machine with the RPR/RRPR Parallel Configuration

  • Ruiqin LiEmail author
  • Shijie Liang
  • Maorong Zhang
  • Jianwei Zhang
  • Shaoping Bai
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


A spherical engraving machine based on RPR/RRPR spherical parallel mechanism (SPM) is presented. The mathematical model of the RPR/RRPR SPM is established. The forward kinematics and inverse kinematics of the SPM are analyzed. The reachable workspaces of the output reference point of the SPM are solved based on the kinematic analysis and Matlab software. The variation of the reachable workspace under reconfiguration is analyzed. A spherical engraving machine is designed based on the RPR/RRPR spherical parallel configuration for engraving patterns on spherical surfaces of variable diameters.


Spherical engraving machine RPR/RRPR Spherical parallel mechanism (SPM) Forward and inverse kinematics Workspace 


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This research was funded by the Key Research and Development Program of Shanxi Province of China (Grant Nos. 201803D421027, 201803D421028) and the Foundation of Shanxi Key Laboratory of Advanced Manufacturing Technology of China (Grant No. XJZZ201702).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ruiqin Li
    • 1
    Email author
  • Shijie Liang
    • 1
  • Maorong Zhang
    • 1
  • Jianwei Zhang
    • 2
  • Shaoping Bai
    • 3
  1. 1.School of Mechanical EngineeringNorth University of ChinaTaiyuanChina
  2. 2.Department of InformaticsUniversity of HamburgHamburgGermany
  3. 3.Department of Mechanical and Manufacturing EngineeringAalborg UniversityAalborgDenmark

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