Kinematic Performance Comparison of Two Parallel Kinematics Machines

  • Chensheng Wang
  • Yanqin Zhao
  • Chenglin Dong
  • Qi Liu
  • Wentie Niu
  • Hantao Liu
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


Kinematics characteristic is the representation of the working performance of parallel kinematics machine (PKM). Two kinds of parallel kinematics machines, Trimule and Tricept, are studied for comparative kinematics analysis in this paper. Firstly, global coordinate system and moving coordinate system are established based on structures of Tricept and Trimule. Secend, generalized Jacobian matrix is formulated, and then the homegeneous Jacobian matrix is formulated for dimensional normalization. The condition number of dimensionally homogeneous Jacobian matrix is used as the local kinematics performance evaluation index to analyze the kinematics performance of two PKMs. Through comparative analysis with κmax, κmin, \({\bar{\kappa }}\) and \({\tilde{\kappa }}\) in the whole working domain, the results show that κ varies with x, y, and z. Trimule is more prominent in the extreme value of motion performance index, while Tricept’s motion performance is more balanced. Tricept has a larger envelope range than Trimule with the same κ value and has a larger optimal workspace.


3-UPS&UP Parallel kinematics machine Kinematic performance 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported by the National Key Research Project under Grant 2017ZX04013001.


  1. 1.
    Olazagoitia, J. L., & Wyatt, S. New pkm tricept T9000 and its application to flexible manufacturing at aerospace industry. Sae Technical Papers, 2142, 37-48 (2007).Google Scholar
  2. 2.
    C Dong, H Liu, W Yue, T Huang. Stiffness modeling and analysis of a novel 5-DOF hy-brid robot, Mechanism and Machine Theory (2018).Google Scholar
  3. 3.
    Olds, K. C. Global indices for kinematic and force transmission performance in parallel robots. IEEE Transactions on Robotics, 31(2), 494-500 (2015).CrossRefGoogle Scholar
  4. 4.
    W A Khan, J Angeles. The kinematic optimization of robotic manipulators: the inverse and direct problems. ASME Journal of Mechanical Design, 128(1), 168–178 (2006).CrossRefGoogle Scholar
  5. 5.
    H T Liu, T Huang, & Chetwynd, D G. A method to formulate a dimensionally homogeneous Jacobian of parallel manipulator. IEEE Transaction on Robotic, 27(1), 150–156 (2011).Google Scholar
  6. 6.
    Brinker, J., Corves, B., & Takeda, Y. Kinematic performance evaluation of high-speed delta parallel robots based on motion/force transmission indices. Mechanism & Machine Theory, 125 (2018).Google Scholar
  7. 7.
    Li, B., Li, Y., & Zhao, X. Kinematics analysis of a novel over-constrained three degree-of-freedom spatial parallel manipulator. Mechanism & Machine Theory, 104, 222-233 (2016).Google Scholar
  8. 8.
    Chen, X., Chen, C., & Liu, X. J. Evaluation of force/torque transmission quality for parallel manipulators. Journal of Mechanisms & Robotics, 7(4), 041013 (2015).Google Scholar
  9. 9.
    Zhang, L. M., Mei, J. P., Zhao, X. M., & Tian, H. Dimensional synthesis of the delta robot using transmission angle constraints dimensional synthesis of the delta robot using transmission angle constraints. Robotica, 30(3), 343-349 (2012).Google Scholar
  10. 10.
    BALL R S. A Treatise on the theory of screws. Cambridge University Press, Cambridge (1998).Google Scholar
  11. 11.
    Wu, G., Caro, S., & Wang, J. Design and transmission analysis of an asymmetrical spherical parallel manipulator. Mechanism & Machine Theory, 94, 119-131 (2015).Google Scholar
  12. 12.
    Chen, C., & Angeles, J. Generalized transmission index and transmission quality for spatial linkages. Mechanism & Machine Theory, 42(9), 1225-1237 (2007).Google Scholar
  13. 13.
    Wang, J., Wu, C., & Liu, X. J. Performance evaluation of parallel manipulators: motion/force transmissibility and its index. Mechanism & Machine Theory, 45(10), 1462-1476 (2010).Google Scholar
  14. 14.
    Chen, X., Xie, F., & Liu, X. Evaluation of the maximum value of motion/force transmission power in parallel manipulators. Journal of Mechanical Engineering, 50(3), 1. (2014).Google Scholar
  15. 15.
    Liu, H., Huang, T., Kecskeméthy, A., & Chetwynd, D. G. A generalized approach for computing the transmission index of parallel mechanisms. Mechanism & Machine Theory, 74(74), 245-256 (2014).Google Scholar
  16. 16.
    Marlow, K., Isaksson, M., Dai, J. S., & Nahavandi, S. Motion/force transmission analysis of parallel mechanisms with planar closed-loop subchains. Journal of Mechanical Design (2016).Google Scholar
  17. 17.
    Shao, Z. F., Mo, J., Tang, X. Q., & Wang, L. P. Transmission index research of parallel manipulators based on matrix orthogonal degree. Chinese Journal of Mechanical Engineering, 30(6), 1396-1405 (2017).Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Chensheng Wang
    • 1
  • Yanqin Zhao
    • 1
  • Chenglin Dong
    • 1
  • Qi Liu
    • 1
  • Wentie Niu
    • 1
  • Hantao Liu
    • 1
  1. 1.Key Laboratory of Mechanism Theory and Equipment Design of Ministry of EducationTianjin UniversityTianjinChina

Personalised recommendations