Calibration Method for a Parallel Mechanism Type Machine Tool by Response Surface Methodology –Consideration via Simulation on a Stewart Platform Mechanism–
Hiroshi Yachi and Hiroshi Tachiya
Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa-shi, Ishikawa 920-1192, Japan
This paper proposes a calibration method for parallel mechanisms using Response Surface Methodology. This method is a statistical approach to estimating an unknown input-output relationship using a small set of efficient data collected on an intended system. Although identifying locations causing positional errors in a parallel mechanism and precisely measuring the position and posture of the output point are difficult, the proposed calibration method based on Response Surface Methodology aims to compensate for positional and postural errors, without indentifying the locations causing these errors, by using a small yet efficient measurement data set. This study analyzes the effectiveness of the method we propose by applying it to a Stewart platform, which is a typical spatial 6-DOF parallel mechanism.
-  T. Oiwa and K. Shutoh, “Acalibrationj Method for Coordinate Measuring Machine using Parallel Mechanism –Calibration with Redundant Passive Prismatic Joint–,” Trans. of the Japan Society for precision Engineering, Vol.71, No.4, pp. 512-516, 2005 (in Japanese).
-  H. Ota, et al., “Study of Kinematic Calibration Method for Parallel Mechanism (2nd Report) –Kinematic Calibration Using Forward Kinematics–,” Trans. of the Japan Society for precision Engineering, Vol.66, No.10, pp. 1568-1572, 2000 (in Japanese).
-  Y. Takeda, “Kinematic Calibration of In-Parallel Actuated Mechanisms Using Fourier Series (1st Report, Calibration Method and Selection Method of the Set of Measurement Paths),” Trans. of the Japan Society of Mechanical Engineers, Series C, Vol.68, No.673, pp. 246-253, 2002 (in Japanese).
-  R. H. Myers and D. C. Montgomery, “Response Surface Methodology-Process and Product Optimization Using Designed Experiments,” John Wiley & Sons, New York, 1995.
-  S. Yamada, “Design of Experiment,” The method volume. Japan: JUSE Press, Ltd., pp. 247-260, 2004.
-  T. Kashimura, et al., “Optimization of Nonlinear Problem by Designed of Experiments-Statistical Design Support System,” Asakura, Tokyo, 1998 (in Japanese).
-  D. Stewart, “A Platform with Six Degrees of Freedom,” Instn. Mechs. Engrs. 1965-66(I), 180-15(1965-66), pp. 371-386.
-  A. Todoroki, “Response surface methodology,” Trans. of the Japan Society of Mechanical Engineers, No.99-73, pp. 11-23, 1999.
-  OKUMA Inc. web site:
-  S. Yamada, “Design of Experiment,” The method volume. Japan: JUSE Press, Ltd., pp. 121-138, 2004.
-  H. Kitano, “Genetic Algorithms,” J. of Japanese Society for Artificial Intelligence, Vol.7, No.1, pp. 26-37, 1992.
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