Nonlinearity for a parallel kinematic machine tool and its application to interpolation accuracy analysis

  • Jinsong Wang
  • Zhonghua Wang
  • Tian Huang
  • D. J. Whitehouse


This paper is concerned with the kinematic nonlinearity measure of parallel kinematic machine tool (PKM), which depends upon differential geometry curvalure. The nonlinearity can be described by the curve of the solution locus and the equal interval input of joints mapping into inequable interval output of the end-effectors. Such curing and inequation can be measured by BW curvature. So the curvature can measure the nonlinearity of PKM indirectly. Then the distribution of BW curvature in the local area and the whole workspace are also discussed. An example of application to the interpolation accuracy analysis of PKM is given to illustrate the effectiveness of this approach.


parallel kinematic machine tool nonlinearity measure curvature interpolation accuracy analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Carlo, I., Direct Position Analysis of The Stewart Platform Mechanism, Mech. Mach. Theory, 1990, 25(6): 611–621.CrossRefGoogle Scholar
  2. 2.
    Fitehter, E. F., A Stewart platform based manipulator general theory and practical construction, Inter. Journal of Robtics Research, 1986, (2): 157–182.CrossRefGoogle Scholar
  3. 3.
    Raghavan, M., The Stewart platform of general geometry has 40 configurations, ASME J. Mechanical Design, 1993, 115 (2): 277–281.CrossRefGoogle Scholar
  4. 4.
    Wampler, C. W., Forward displacement analysis of general six-in-parallel SPS (Stewart) platform manipulators using SOMA Coordinates, Mech. Mach. Theory, 1995, 31(3): 331–337.CrossRefGoogle Scholar
  5. 5.
    Wen, F. A., Liang, C. C., Displacement analysis of the 6-6 stewart platform mechanisms, Mech. Mach. Theory, 1994, 29(4): 547–557.CrossRefGoogle Scholar
  6. 6.
    Liang, C. G., Rong, H., The forward displacement solution to a Stewart platform type maniputator, China Journal of Mechanical Engineering, 1991, 27(2): 26–30.Google Scholar
  7. 7.
    Huang, Z., Spatial Mechanisms, Beijing: China Machine Press, 1991.Google Scholar
  8. 8.
    Liu, K. et al., The singularities and dynamics of a stewart platform manipulator, J. of Intelligent and Robotic Systems, 1993, 8: 287–308.CrossRefGoogle Scholar
  9. 9.
    Bates, D. M., Watts, D. G., Relative curvature measures of nonlinearity, Journal of the Royal Statistical Society, 1980, (B42): 1–25.MATHMathSciNetGoogle Scholar
  10. 10.
    Huang Tian, Wang Jinsong, Whitehouse, D. J., Theory and methodology for kinematic design of Gough-Stewart platforms, Science in China, Series E, 1999, 42(4): 425–436.MATHGoogle Scholar
  11. 11.
    Wang, Z. H., Wang, J. S., Yang, X. D., Wei, Y. M., Interpolation scheme and simulation study on its accuracy for a Stewart platform based CNC machine Tool VAMTIY, China Mechanical Engineering, 1999, 10(10): 1121–1123.Google Scholar
  12. 12.
    Wang Zhonghua, Wang Jinsong, Study on interpolation and its error distribution in workspace for a Stewart platform based CNC machine tool, in Proceedings of International Conference on Advanced Manufacturing Systems and Manufacturing Automation (AMSMA’ 2000), 19th-2st, June, 2000, Guangzhou, China.Google Scholar

Copyright information

© Science in China Press 2002

Authors and Affiliations

  • Jinsong Wang
    • 1
  • Zhonghua Wang
    • 1
  • Tian Huang
    • 2
  • D. J. Whitehouse
    • 3
  1. 1.Department of Precision Instruments & MechanologyTsinghua UniversityBeijingChina
  2. 2.Department of Mechanical EngineeringTianjin UniversityTianjinChina
  3. 3.Department of EngineeringUniversity of WarwickCoventryUK

Personalised recommendations