Global Stiffness and Well-Conditioned Workspace Optimization Analysis of 3UPU-UPU Robot Based on Pareto Front Theory

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9320)


In this paper, an approach based on the Pareto front theory is employed to conduct the multi-objective optimization of the global stiffness and well-conditioned workspace of 3UPU-UPU parallel mechanism. The inverse kinematic and Jacobian matrix of the 3UPU-UPU mechanism are first calculated. Then the stiffness model of the mechanism is derived and the sum of the diagonal elements of the stiffness matrix is used as a criterion to evaluate the global stiffness. Secondly, the Monte Carlo method is used to derive the global condition index of the mechanism which later is used as a criterion to evaluate the well-conditioned workspace of the mechanism. Normally, increasing the workspace of the mechanism will deteriorate the stiffness, here the global stiffness and well-conditioned workspace of the mechanism are optimized simultaneously based on the Pareto front theory, and the optimized results are displayed and compared.


Global stiffness Well-conditioned workspace Parallel robot Optimization Modelling 


  1. 1.
    Zhang, D., Bi, Z.M., Li, B.Z.: Design and kinetostatic analysis of a new parallel manipulator. Robot. Comput. Integr. Manuf. 25, 782–791 (2009)CrossRefGoogle Scholar
  2. 2.
    Zhang, D., Gao, Z., Fassi, I.: Design optimization of a spatial hybrid mechanism for micromanipulation. Int. J. Mech. Mater. Des. 7, 55–70 (2011)CrossRefGoogle Scholar
  3. 3.
    Gorie, N., Dolga, V., Biomechatronics recovery systems for persons with disabilities. In: Proceedings of International Conference on Innovations, Recent Trends and Challenges in Mechatronics, Mechanical Engineering and New High-Tech Products Development –MECAHITECH 2011, vol. 3 (2011)Google Scholar
  4. 4.
    Castelli, G., Ottaviano, E.: Modelling, simulation and testing of a reconfigurable cable-based parallel manipulator as motion aiding system. Appl. Bion. Biomech. 7(4), 253–268 (2010)CrossRefGoogle Scholar
  5. 5.
    Castelli, G., Ottaviano, E.: Modeling and simulation of a cable based parallel manipulator as an assisting device. In: Computational Kinematics: Proceedings of the 5th International Workshop on Computational Kinematics. Springer, pp. 17–24 (2010)Google Scholar
  6. 6.
    Pan, M.: Improved design of a three-degree of freedom hip exoskeleton based on biomimetic parallel structure. Master Thesis, University of Ontario Institute of Technology, Canada (2011)Google Scholar
  7. 7.
    Huang, X.G., He, G.P., Tan, X.L.: An introduction to parallel robot mechanism. J. North China Univ. Technol. 27(3), 25–31 (2009)Google Scholar
  8. 8.
    Yu, H.J.: Research on parallel robot based flexible fixtures for automotive sheet metal assembly. PhD thesis, Harbin Institute of Technology (2010)Google Scholar
  9. 9.
    Zhang, Y.W., Wei, B., Wang, N.: Kinematic performance analysis of 3-SPS-S spatial rotation parallel mechanism. Trans. Chin. Soc. Agri. Mach. 43(4), 212–215 (2012)Google Scholar
  10. 10.
    Zhang, D., Gao, Z.: Hybrid head mechanism of the groundhog-like mine rescue robot. Robot. Comput. Integr. Manuf. 27, 460–470 (2011)CrossRefGoogle Scholar
  11. 11.
    Konak, A., Coit, D.W., Smith, A.E.: Multi-objective optimization using genetic algorithms: a tutorial. Reliab. Eng. Syst. Saf. 91, 992–1007 (2006)CrossRefGoogle Scholar
  12. 12.
    Gao, Z.: Spatial three degree-of-freedom parallel mechanisms: configurations, performances and applications. PhD thesis, University of Science and Technology of China (2009)Google Scholar
  13. 13.
    Zhang, D., Gao, Z.: Forward kinematics, performance analysis, and multi-objective optimization of a bio-inspired parallel manipulator. Robot. Comput. Integr. Manuf. 28(4), 484–492 (2012)CrossRefGoogle Scholar
  14. 14.
    Lara-Molina, F.A., Rosario, J.M., Dumur, D.: Multi-objective design of parallel manipulator using global indices. Open Mech. Eng. J. 4, 37–47 (2010)CrossRefGoogle Scholar
  15. 15.
    Zhang, D.: Parallel Robotic Machine Tools. Springer, Berlin (2009)Google Scholar
  16. 16.
    Hu, X.L.: Design and analysis of a three degrees of freedom parallel kinematic machine. Master thesis. University of Ontario Institute of Technology (2008)Google Scholar
  17. 17.
    Stamper, R.E., Tsai, L.W., Walsh, G.C.: Optimization of a three DOF translational platform for well-conditioned workspace. In: Proceedings of the IEEE International Conference on Robotics and Automation. New Mexico, pp. 3250–3255 (1997)Google Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of Ontario Institute of TechnologyOshawaCanada

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