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Workspace analysis and size optimization of planar 3-DOF redundantly actuated parallel mechanism

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Parallel mechanism is widely used due to its high stiffness, strong bearing capacity, small accumulated error, and good dynamic performance. In this paper, a planar three-degree-of-freedom (3-DOF) redundantly actuated parallel mechanism is proposed. Firstly, the position constraint equation is investigated and the inverse position solution is derived. The center velocity mapping model of the moving platform is established and the Jacobian matrix of the mechanism is obtained. The theoretical model based on Mathematica and the simulation model based on ADAMS are compared to validate the correctness of the theoretical results, and the peak deviation of the results is within 5 %. Then, the constraint conditions are conducted, and the workspace of the mechanism is solved by numerical method. Finally, the influence relationship curves of rod parameters on the proportion of workspace are obtained respectively. And the size parameters are optimized to carry out a comparative analysis of the workspace.

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Degrees of freedom


Computer numerical control


  1. X. W. Wang, B. Tang and X. S. Gu, Research on obstacle avoidance strategy for welding robot, J. of Mechanical Engineering, 55(17) (2019) 77–84.

    Article  Google Scholar 

  2. X. D. Jin, Y. Fang and D. Zhang, Design of dexterous hands based on parallel finger structures, Mechanism and Machine Theory, 152 (2020) 103952.

    Article  Google Scholar 

  3. D. Liang, J. Liu, B. Y. Chang and G. G. Jin, Design and performance optimization of 3-DOF translational parallel mechanism with hinged end structure, Transactions of the Chinese Society for Agricultural Machinery, 53(10) (2022) 446–458.

    Google Scholar 

  4. B. X. Ding, Y. A. Li and Y. R. Tang, Workspace analysis for a 3-DOF compliant parallel mechanism based on simmechanics, Proceedings of the 2015 7th IEEE International Conference on Cybernetics and Intelligent Systems and Robotics, Automation and Mechatronics, Cambodia (2015) 48–53.

  5. J. A. Saglia, J. S. Dai and D. G. Caldwell, Geometry, and kinematic analysis of a redundantly actuated parallel mechanism that eliminates singularities and improves dexterity, Journal of Mechanical Design, 130(12) (2008) 124501.

    Article  Google Scholar 

  6. D. Zhang and B. Wei, Stiffness analysis and optimization for a bio-inspired 3-DOF hybrid manipulator, Mechatronics and Robotics Engineering for Advanced and Intelligent Manufacturing, Springer International Publishing, Berlin/Heidelberg, Germany (2017) 341–350.

    Chapter  Google Scholar 

  7. C. A. Nelson, L. Nouaille and G. A. Poisson, Redundant rehabilitation robot with a variable stiffness mechanism, Mechanism and Machine Theory, 150 (2020) 103862.

    Article  Google Scholar 

  8. W. Ye, L. Hu, D. Xia and Z. Zhou, Performance analysis and optimization of redundantly actuated three translational parallel mechanism, Transactions of the Chinese Society for Agricultural Machinery, 52(11) (2021) 421–430.

    Google Scholar 

  9. M. Ceccarelli, A new 3-DOF parallel spatial mechanism, Mechanism and Machine Theory, 32(8) (1997) 895–902.

    Article  MathSciNet  Google Scholar 

  10. Z. H. Chen, J. H. Li, S. K. Wang, J. Z. Wang and L. L. Ma, Flexible gait transition for six wheel-legged robot with unstructured terrains, Robotics and Autonomous Systems, 150 (2022) 103989.

    Article  Google Scholar 

  11. Z. H. Chen, J. H. Li, J. Z. Wang, S. K. Wang, J. B. Zhao and J. Li, Towards hybrid gait obstacle avoidance for a six wheel-legged robot with payload transportation, Journal of Intelligent & Robotic Systems, 102(3) (2021) 60.

    Article  Google Scholar 

  12. J. P. Merlet, Redundant parallel manipulators, Laboratory Robotics and Automation, 8(1) (1996) 17–24.

    Article  Google Scholar 

  13. L. T. Schreiber and C. Gosselin, Kinematically redundant planar parallel mechanisms: kinematics, workspace, and trajectory planning, Mechanism and Machine Theory, 119 (2018) 91–105.

    Article  Google Scholar 

  14. X. F. Liu, Y. Liu, Y. He, B. Wan, Y. Liu and Y. S. Zhao, Kinematic analysis, and dimension optimization of multi-redundantly actuated parallel mechanism 2RPU+2UPR+RPR, Transactions of the Chinese Society for Agricultural Machinery, 54(3) (2023) 440–450.

    CAS  ADS  Google Scholar 

  15. H. Jamshidifar, A. Khajepour, B. Fidan and M. Rushton, Kinematically-constrained redundant cable-driven parallel robots: modeling, redundancy analysis, and stiffness optimization, IEEE/ASME Transactions on Mechatronics, 22(2) (2016) 921–930.

    Article  Google Scholar 

  16. Y. X. Fu, X. M. Huo, Y. Qi, Y. M. Song, T. Sun and T. Zhang, Stiffness optimal design of a three-legged six-DoF parallel external fixation frame for bone fracture reduction, Journal of Tianjin University (Science and Technology), 56(4) (2023) 361–371.

    Google Scholar 

  17. S. J. Wang, W. Feng, T. J. Li, J. J. Zhang, D. Yang and J. Y. Liu, Kinematic performance analysis of spatial 2-DOF redundantly actuated parallel manipulator, Journal of Mechanical Eegineering, 58(23) (2022) 18–27.

    Google Scholar 

  18. J. H. Park, J. Kim and J. H. Jeong, Kinematics optimization of A 3-SPS parallel redundant motion mechanism using conformal geometric algebra, Applied Mechanics and Materials, 789 (2015) 889–895.

    Article  Google Scholar 

  19. Y. J. Wang, H. F. Zhang and Q. C. Li, Dynamics modeling, force optimization and force/position hybrid control for a Vex4 redundantly actuated parallel robot, Journal of Mechanical Engineering, 58(23) (2022) 65–74.

    Article  CAS  Google Scholar 

  20. H. B. Qu, L. Q. Hu, S. Guo and S. J. Li, Statics analysis of a planar parallel mechanism with kinematic redundancy and closed-loop limb, Journal of Central South University (Science and Technology), 51(10) (2020) 2758–2771.

    Google Scholar 

  21. Z. Dan and B. Wei, Optimization and stiffness performance analysis for 3-DOF spatial and spherical parallel mechanisms, ASME International Mechanical Engineering Congress and Exposition, Phoenix, USA (2016).

  22. Z. Gao and D. Zhang, Performance analysis, mapping, and multi-objective optimization of a hybrid robotic machine tool, IEEE Transactions on Industrial Electronics, 62(1) (2015) 423–433.

    Article  Google Scholar 

  23. G. M. Li, Sensitivity analysis of a kinematically redundant planar parallel manipulator, Master’s Thesis, Beijing Jiaotong University, China (2021).

    Google Scholar 

  24. S. Xu, J. J. You, P. D. Ye, C. G. Li and H. P. Shen, A reconfiguration 3-RRR planar parallel mechanism and its workspace analysis, Journal of Nanjing University of Aeronautics and Astronautics, 54(3) (2022) 466–472.

    Google Scholar 

  25. D. B. Wang, J. Zhang, H. W. Guo, R. Q. Liu and Z. M. Kou, Design of a 2T1R-type parallel mechanism: performance analysis and size optimization, Actuators, 11(9) (2022) 262.

    Article  CAS  Google Scholar 

  26. S. Min, Y. L. Hong and J. Dong, Workspace and dexterity optimization of 3-PRR planar parallel manipulator, Proceedings of the 12th International Conference of European Society for Precision Engineering and Nanotechnology, Stcholm, Sweden (2012) 360–363.

  27. Y. G. Cao, Y. R. Zhang and Y. Z. Ma, Workspace analysis and parameter optimization of 6-RSS parallel mechanism, J. of Mechanical Engineering, 44(1) (2008) 19–24.

    Article  Google Scholar 

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This work was supported by Open R&D Program of Haian Taiyuan University of Technology Advanced Manufacturing and Intelligent Equipment Industry Research Institute (Project No. 2023HA-TYUTKFYF026), National Key R&D Program of China (Project No. 2018YFB1307900), National Natural Science Foundation of China (Project No. 51835002).

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Correspondence to Jing Zhang.

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Jing Zhang, Ph.D., is an Associate Professor in Yanshan University. Her research interests include robotics and mechanism theory and mechatronics.

Dongbao Wang studied at Taiyuan University of Technology, Taiyuan. His research interests include robotic and control.

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Zhang, J., Wang, D., Song, Z. et al. Workspace analysis and size optimization of planar 3-DOF redundantly actuated parallel mechanism. J Mech Sci Technol 38, 957–967 (2024).

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