Dynamic Performance Evaluation of a Redundantly Actuated and Over-constrained Parallel Manipulator

  • Hai-Qiang Zhang
  • Hai-Rong FangEmail author
  • Bing-Shan Jiang
  • Shuai-Guo Wang
Research Article


This paper presents a redundantly actuated and over-constrained 2RPU-2SPR parallel manipulator with two rotational and one translational coupling degrees of freedom. The kinematics analysis is firstly carried out and the mapping relationship of the velocity, acceleration and the independent parameters between the actuator joint and the moving platform are deduced by using the vector dot product and cross product operation. By employing d′Alembert′s principle and the principle of virtual work, the dynamics equilibrium equation is derived, and the simplified dynamics mathematical model of the parallel manipulator is further derived. Simultaneously, the generalized inertia matrix which can characterize the acceleration performance between joint space and operation space is further separated, and the performance indices including the dynamics dexterity, inertia coupling characteristics, energy transmission efficiency and driving force/torque balance are introduced. The analysis results show that the proposed redundantly actuated and over-constrained 2RPU-2SPR parallel manipulator in comparison with the existing non-redundant one has better dynamic comprehensive performance, which can be demonstrated practically by the successful application of the parallel kinematic machine head module of the hybrid machine tool.


Redundantly actuated over-constrained parallel manipulator dynamics performance index 


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This work was supported by the Fundamental Research Funds for the Central Universities (Nos. 2018JBZ007, 2018YJS136 and 2017YJS158), and China Scholarship Council (CSC) (No. 201807090079) and National Natural Science Foundation of China (No. 51675037).


  1. [1]
    M. Mazare, M. Taghizadeh, M. R. Najafi. Kinematic analysis and design of a 3–DOF translational parallel robot. International Journal of Automation and Computing, vol. 14, no. 4, pp. 432–441, 2017. DOI: 10.1007/s11633–017–1066–y.CrossRefGoogle Scholar
  2. [2]
    B. Siciliano. The Tricept robot: Inverse kinematics, ma–nipulability analysis and closed–loop direct kinematics algorithm. Robotica, vol. 17, no. 4, pp. 437–445, 1999. DOI: 10.1017/S0263574799001678.CrossRefGoogle Scholar
  3. [3]
    Z. M. Bi, Y Jin. Kinematic modeling of Exechon parallel kinematic machine. Robotics and Computer–integrated Manufacturing, vol. 27, no. 1, pp. 186–193, 2011. DOI: 10.1016/j.rcim.2010.07.006.CrossRefGoogle Scholar
  4. [4]
    N. Hennes, D. Staimer. Application of PKM in aerospace manufacturing–high performance machining centers ECOSPEED, ECOSPEED–F and ECOLINER. In Proceedings of 4th Chemnitz Parallel Kinematics Seminar, Chemnitz, Germany, pp. 557–577, 2004.Google Scholar
  5. [5]
    D. Zhang. Parallel Robotic Machine Tools. Boston, USA: Springer, 2010. DOI: 10.1007/978–1–4419–1117–9.CrossRefGoogle Scholar
  6. [6]
    D. S. Zhang, Y. D. Xu, J. T. Yao, Y. S. Zhao. Inverse dynamic analysis of novel 5–DoF hybrid manipulator. Transactions of the Chinese Society for Agricultural Machinery, vol. 48, no. 9, pp. 384–391, 2017. DOI: 10.6041/j.issn.1000–1298.2017.09.049. (in Chinese)Google Scholar
  7. [7]
    L. Carbonari. Simplified approach for dynamics estimation of a minor mobility parallel robot. Mechatronics, vol. 30, pp. 76–84, 2015. DOI: 10.1016/j.mechatronics. 2015.06.005.CrossRefGoogle Scholar
  8. [8]
    S. Staicu. Dynamics analysis of the Star parallel manipulator. Robotics and Autonomous Systems, vol. 57, no. 11, pp. 1057–1064, 2009. DOI: 10.1016/j.robot.2009.07.005.CrossRefzbMATHGoogle Scholar
  9. [9]
    Y. M. Li, S. Staicu. Inverse dynamics of a 3–PRC parallel kinematic machine. Nonlinear Dynamics, vol. 67, no. 2, pp. 1031–1041, 2011. DOI: 10.1007/s11071–011–0045–z.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    H. Abdellatif, B. Heimann. Computational efficient inverse dynamics of 6–DOF fully parallel manipulators by using the Lagrangian formalism. Mechanism and Machine Theory, vol. 44, no. 1, pp. 192–207, 2009. DOI: 10.1016/j. mechmachtheory.2008.02.003.CrossRefzbMATHGoogle Scholar
  11. [11]
    Y. M. Li, Q. S. Xu. Kinematics and inverse dynamics analysis for a general 3–prs spatial parallel mechanism. Robotica, vol. 23, no. 2, pp. 219–229, 2005. DOI: 10.1017/S0263574704000797.CrossRefGoogle Scholar
  12. [12]
    Y. W. Li, J. S. Wang, X. J. Liu, L. P. Wang. Dynamic performance comparison and counterweight optimization of two 3–DOF parallel manipulators for a new hybrid machine tool. Mechanism and Machine Theory, vol. 45, no. 11, pp. 1668–1680, 2010. DOI: 10.1016/j.mechmachtheory. 2010.06.009.CrossRefzbMATHGoogle Scholar
  13. [13]
    B. Dasgupta, P. Choudhury. A general strategy based on the Newton–Euler approach for the dynamic formulation of parallel manipulators. Mechanism and Machine Theory, vol. 34, no. 6, pp. 801–824, 1999. DOI: 10.1016/S0094–114X(98)00081–0.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    S. A. A. Moosavian, A. Pourreza, K. Alipour. Dynamics and stability of a hybrid serial–parallel mobile robot. Mathematical and Computer Modelling of Dynamical Systems, vol. 16, no. 1, pp. 35–56, 2010. DOI: 10.1080/13873951003676518.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    B. Dasgupta, T. S. Mruthyunjaya. Closed–form dynamic equations of the general Stewart platform through the newton–Euler approach. Mechanism and Machine Theory, vol. 33, no. 7, pp. 993–1012, 1998. DOI: 10.1016/S0094–114X(97)00087–6.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Y. Yun, Y. M. Li. Design and analysis of a novel 6–DOF redundant actuated parallel robot with compliant hinges for high precision positioning. Nonlinear Dynamics, vol. 61, no. 4, pp. 829–845, 2010. DOI: 10.1007/s11071–010–9690–x.CrossRefzbMATHGoogle Scholar
  17. [17]
    T. Yoshikawa. Dynamic manipulability of robot manipulators. In Proceedings of IEEE International Conference on Robotics and Automation, St. Louis, USA, pp. 1033–1038, 1985. DOI: 10.1109/ROBOT.1985.1087277.Google Scholar
  18. [18]
    H. Asada. Dynamic analysis and design of robot manipulators using inertia ellipsoids. In Proceedings of IEEE International Conference on Robotics and Automation, Atlanta, USA, pp. 94–102, 1984. DOI: 10.1109/ROBOT.1984. 1087211.Google Scholar
  19. [19]
    J. Wu, Y. Gao, B. B. Zhang, L. P. Wang. Workspace and dynamic performance evaluation of the parallel manipulators in a spray–painting equipment. Robotics and Computer–Integrated Manufacturing, vol. 44, pp. 199–207, 2017. DOI: 10.1016/j.rcim.2016.09.002.Google Scholar
  20. [20]
    G. H. Cui, D. Zhang, H. D. Zhou, Y. W. Zhang. Operating dexterity optimization and analysis of a 3–DOF parallel manipulator for a tunnel segment assembly system. International Journal of Mechanics and Materials in Design, vol. 11, no. 3, pp. 277–285, 2015. DOI: 10.1007/s10999–014–9268–8.CrossRefGoogle Scholar
  21. [21]
    J. Zhang, J. S. Dai, T. Huang. Characteristic equationbased dynamic analysis of a three–revolute prismatic spherical parallel kinematic machine. Journal of Computational and Nonlinear Dynamics, vol. 10, no. 2, Article Number 021017, 2015. DOI: 10.1115/1.4028416.Google Scholar
  22. [22]
    S. Lu, Y. M. Li. Dynamic dexterity evaluation of a 3–DOF 3–PUU parallel manipulator based on generalized inertia matrix. In Proceedings of IEEE International Conference on Robotics and Biomimetics, Zhuhai, China, pp. 1506–1511, 2016. DOI: 10.1109/ROBIO.2015.7418984.Google Scholar
  23. [23]
    M. Li, T. Huang, J. P. Mei, X. M. Zhao, D. G. Chetwynd, S. J. Hu. Dynamic formulation and performance comparison of the 3–DOF modules of two reconfigurable PKM–the tricept and the TriVariant. Journal of Mechanical Design, vol. 127, no. 6, pp. 1129–1136, 2005. DOI: 10.1115/1. 1992511.CrossRefGoogle Scholar
  24. [24]
    Y. J. Zhao. Dynamic optimum design of a three translational degrees of freedom parallel robot while considering anisotropic property. Robotics and Computer–Integrated Manufacturing, vol. 29, no. 4, pp. 100–112, 2013. DOI: 10.1016/j.rcim.2012.11.004.CrossRefGoogle Scholar
  25. [25]
    J. Wu, J. S. Wang, L. P. Wang, T. M. Li. Dynamic formulation of redundant and nonredundant parallel manipulators for dynamic parameter identification. Mechatronics, vol. 19, no.4, pp. 586–590, 2009. DOI: 10.1016/j.mechatronics. 2009.01.003.CrossRefGoogle Scholar
  26. [26]
    Y. J. Zhao, K. Qiu, S. X. Wang, Z. Q. Zhang. Inverse kinematics and rigid–body dynamics for a three rotational degrees of freedom parallel manipulator. Robotics and Computer–Integrated Manufacturing, vol. 31, pp. 40–50, 2015. DOI: 10.1016/j.rcim.2014.07.002.Google Scholar
  27. [27]
    Z. M. Chen, X. M. Liu, Y. Zhang, K. Huang, Z. Huang. Dynamics analysis of a symmetrical 2R1T 3–UPU parallel mechanism. Journal of Mechanical Engineering, vol. 21, pp. 46–53, 2017. (in Chinese)CrossRefGoogle Scholar
  28. [28]
    Y. Jiang, T. M. Li, L. P. Wang. Dynamic modeling and redundant force optimization of a 2–DOF parallel kinematic machine with kinematic redundancy. Robotics and Computer–Integrated Manufacturing, vol. 32, pp. 1–10, 2015. DOI: 10.1016/j.rcim.2014.08.001.CrossRefGoogle Scholar
  29. [29]
    H. Q. Zhang, H. R. Fang. Stiffness characteristics analysis of a novel 3–DOF parallel kinematic machine tool. International Journal of Engineering and Technology, vol. 10, no. 4, pp. 346–354, 2018. DOI: 10.7763/IJET.2018.V10. 1082.CrossRefGoogle Scholar
  30. [30]
    H. Ming, J. S. Shun. The kinematic analyses of the 3–DOF parallel machine tools. International Journal of Automation and Computing, vol. 8, no. 1, pp. 107–111, 2011. DOI: 10.1007/s11633–010–0561–1.CrossRefGoogle Scholar
  31. [31]
    D. Wang, J. Wu, L. P. Wang, X. J. Liu. Research on the inertia coupling property of a 3–PRS parallel robot. Chinese Journal of Theoretical and Applied Mechanics, vol. 48, no. 4, pp. 804–812, 2016. DOI: 10.6052/0459–1879–16–160. (in Chinese)Google Scholar
  32. [32]
    B. B. Zhang, L. P. Wang, J. Wu. Dynamic isotropic performance evaluation of a 3–DOF parallel manipulator. Journal of Tsinghua University (Science and Technology), vol. 57, no. 8, pp. 803–809, 2017. DOI: 10.16511/j.cnki.qhdxxb. 2017.22.041. (in Chinese)MathSciNetGoogle Scholar
  33. [33]
    H. E. Ghor, E. M. Aggoune. Energy efficient scheduler of aperiodic jobs for real–time embedded systems. International Journal of Automation and Computing, 2016. DOI: 10.1007/s11633–016–0993–3.Google Scholar

Copyright information

© Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical, Electronic and Control EngineeringBeijing Jiaotong UniversityBeijingChina
  2. 2.MH Robot & Automation Limited CompanyWeifangChina

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