A Fast Forward Kinematic Analysis of Stewart Platform

스튜어트 플랫폼의 빠른 순기구학 해석

  • Published : 2001.03.01


The inverse kinematics problem of Stewart platform is straightforward, but no closed form solution of the forward kinematic problem has been presented. Since we need the real-time forward kinematic solution in MIMO control and the motion monitoring of the platform, it is important to acquire the 6 DOF displacements of the platform from measured lengths of six cylinders in small sampling period. Newton-Raphson method a simple algorithm and good convergence, but it takes too long calculation time. So we reduce 6 nonlinear kinematic equations to 3 polynomials using Nairs method and 3 polynomials to 2 polynomials. Then Newton-Raphson method is used to solve 3 polynomials and 2 polynomials respectively. We investigate operation counts and performance of three methods which come from the equation reduction and Newton-Raphson method, and choose the best method.


Stewart Platform;Forward Kinematics;Newton-Raphson Method


  1. Steven J. Leon, 1994, Linear Algebra with Applications, Prentice Hall
  2. Raghvan, M., 1993, 'The Platform of General Geometry has 40 Configurations,' ASME Journal of Mechanical Design, Vol. 115, pp. 277-282
  3. 이형상, 한명철, 1998, '신경망을 이용한 스튜어트 플랫폼의 순기구학 추정기 설계,' Proceedings of the 13th KACC, October 1998, pp. 1280-1284
  4. Ma, O. and Angeles, J., 1991, 'Architecture Singularities of Platform Manipulators,' Proceedings of the 1991 IEEE International Conference on Robotics and Automation, Sacramento, Califonia, pp. 1542-1547
  5. John, J. Craig, 1989, Introduction to Robotics, Addison Wesley
  6. 정규홍, 이교일, 1994, '스튜어트 플랫폼 순기구학 해의 실시간 추정기법,' 대한기계학회논문집, 제18권, 제7호, pp. 1632-1642
  7. 강지윤, 김동환, 이교일, 1996, '스튜어트 플랫폼의 견실한 순기구학 추정기 설계,' Proceedings of the 11th KACC, October 1996, pp. 28-31
  8. Dasgupta, B. and Mruthyunjaya, T. S., 1994, 'A Canonical Formulation of the Direct Position Kinematics Problem For a General 6-6 Stewart Platform,' Mechanism and Machine Theory, Vol. 29, No. 6, pp. 819-827
  9. Nair, R. and Maddocks, J. H., 1994, 'On the Forward Kinematics of Parallel Manipulators,' The International Journal of Robotics Research, Vol. 13, No. 2, pp. 171-188
  10. Innocenti, C. and Parenti-Castelli, V., 1990, 'Direct Position Analysis of the Stewart Platform Mechanism,' Mechanism and Machine Theory, Vol. 25, No. 6, pp. 611-621
  11. Geng, Z., Haynes, L., Lee, J. and Carroll, R., 1992, 'On the Dynamic Model and Linematic Analysis of a Class of Stewart Platforms,' Journal of Robotics Automation Systems, Vol. 9, pp. 237-254
  12. Ku, Der-Ming, 1999, 'Direct Displacement Analysis of a Stewart Platform Mechanism,' Mechanism and Machine Theory, Vol. 34, pp. 453-465
  13. Nanua, P., Waldron, K. J. and Murthy, V., 1990, 'Direct Kinematic Solution of a Stewart Platform,' IEEE Transactins on Robotics and Automations, Vol. 6, No. 4, pp. 438-444
  14. Dieudonne, J. E. and Perish, R. V., 1972, 'An Actuator Extension Transfor-mation for a Motion Simulator and Inverse Transformation Applying Newton-Raphson Method,' NASA Tech. Note, NASA TND-7607
  15. McCallion, H. and Truong, P. D., 1979, 'The Analysis of a Six-Degree-of-Freedom Work Station for Mechanised Assembly,' Proceedings of the Fifth World Congress for the Theory of Machines and Mechanisms, an ASME Publication, pp. 603-616