產品的一致性是製造業所追求的目標，因此工作母機的精度要求是相當重要的，所以其在出廠前必須進行誤差檢驗並進行補償以提高精度。如何作誤差分析與補償成為不容忽視的課題。
工具機的硬體誤差分為桿件幾何誤差及接頭間的運動誤差。因此本論文旨在利用齊次變換矩陣，將三軸高速切削CNC雕刻機之刀尖實際位置以矩陣參數形式表示，而誤差即是實際的幾何參數與理想狀況的幾何參數之差值。
本論文內容尚包括利用雷射干涉儀作定位誤差量測與Ball Bar循圓量測，並且進行單軸定位誤差的軟體補償。誤差分析則是針對循圓檢測圖形變化，進行數學模擬，並比較所推導的三軸工具機誤差參數模式，找出誤差參數與圖形變化之關聯性。

The product consistency is one of the prime goals for the manufacturing industry. In order to achieve this goal, precision of the machining center become more and more important, thus the error test and error compensation must be applied to improve the precision of machining center. The error components considered in this thesis are errors in link dimensions and error motions caused by joint clearances.
Homogeneous transformation matrix has provided a generalized analytical basis for numerical analysis of the kinematical, the static, and the dynamic behavior of complex mechanisms. The purposes of this thesis are to utilize the homogenous transformation matrix to describe the cutting edges position of three axis machining center and to build an error model of it. Besides, this thesis also contains the examination of positioning error and the contouring error of this machining center.

【1】 Denavit, J. and Hartenberg, R. S. “A Kinematic Notation for Lower Pair Mechanisms Based on Matrices”, ASME,, J. of applied mechanics, Vol.22, Vol. 77, pp. 215-221, 1955.
【2】 Hartenberg, R. S. and Denavit, J. “ Kinematic Synthesis of Linkages”, McGraw-Hill, New York, 1964.
【3】 Suh, C. H. and Radcliffe, C. W. “Kinematics and Mechanism Design”, John Wiley and Sons, New York, Chapter 3, 4, 7,and 9; 1978.
【4】 Dhall, S. and Kramer, S. N. “Computer-Aided Design of the RSSR Function Generating Spatial Mechanism Using the Selective Precision Synthesis Method”, ASME, J. of Mechanisms, Transmission, and Automation in Design, Vol. 110, pp. 378-382, 1988.
【5】 Austin, T. C., Denavit, J. and Hartenberg, R. S. “Analysis of Errors in the Double Hooke Joint”, ASME, J. Engng. Ind., Series B, Vol. 87, No.2, pp. 251-257, 1965.
【6】 Dhande, S. G. and Chakraborty, J. “Mechanical Error Analysis of Spatial Linkages", ASME, J. Engng. Ind., Vol. 95, No. 3, pp. 672- 676, 1973.
【7】 Rao, S. S. and Ambekar, A. G. “Mechanical Error Analysis of Spherical Function Generating Mechanism: A Probabilistic Approach", ASME Paper no. 74-DET-15, 1974.
【8】 Schultschik, R. “The Components of Volumetric Accuracy”, Annals of CIRP Vol.26, 1977.
【9】 Tavkhelidze, D. S., Davitashvili, N. S. and Demurishvili, N. V. “The Determination of Technological Error in Spherical 4-linkaged Mechanism”, Mechanism and machine theory, Vol. 14, No.l pp. 43-59, 1979.
【10】 Chen, J., Wang, C. B. and Yang, J.C.S. “Robot Position Accuracy Improvement through Kinematic Parameter Identification”, Third Canadian CAD/CAM Robot Conference. Toronto, Canada, pp.4.7-4.12, 1985.
【11】 Ferreira, P. M. and Liu, R. C. “An Analytical Quadratic Model for The Geometric Error of a Machine Tool”, Journal of Manufacturing Systems 5, No.1: 51-63, 1986.
【12】 Benhabib, B., Fenton, R. G. and Goldenberg, A. A. “Computer- Aided Joint Error Analysis of Robots”, IEEE Journal of Robotics and Automation Vol. RA-3, No.4: 317-322, 1977.
【13】 Ehmann, K. F. and Wu, B. T. “A Generalized Geometric Error Model for Multi-axis Machine”, Annals of the CIRP 36 ,No.1: 253- 256, 1987.
【14】 Lin, P. D. and Ehmann, K. F. “Error Analysis, Measurement and Compensation for Multi-axis Machines”, Ph.D. Thesis, Northwestern University. Evanston, Illinois, 1989.
【15】 Dőnmez, M. A. “A general Methodology for Machine Tool Accuracy Enhancement by Error Compensation”, Precision Engineering, Vol. 8(4), 1986.
【16】 Fan, K. C. “Generated Study of Volumetric Error Analysis for NC Machine and CMMs, Part I. Applications”, Journal of the Chinese Society of Mechanical Engineers, Vol. 10,No. 2, pp.135-144, 1989.
【17】 Fan, K. C. “Generated Study of Volumetric Error Analysis for NC Machine and CMMs, Part II. Applications”, Journal of the Chinese Society of Mechanical Engineers, Vol. 10,No. 2, pp.135-144, 1989.
【18】 Bryan, J. B. “A Simple Method For Testing Measuring Machines and Machine Tools”, Precision Engineering Vol. 4 No. 2 pp.61-69, 1982.
【19】 Knapp, W. “Test of the three-dimensional Uncertainty of Machine Tools and Measuring Machines and its Relation to Machine Errors”, Annals of CIRP Vol. 32 No.1: pp.459-464, 1983.
【20】 Knapp, W. “Circular Test for Three Coordinate Measuring Machine Tools”, Precision Engineering Vol. 5 No. 3: pp. 115-124, 1983.
【21】 Kakino, Y. “Compensation of 3-Dimensional Coordinate Measuring Machine and Evaluation of Double Ball Bar Test by Error Vector Analysis”, Journal of JSPE Vol.51 No.6: pp.1224-1250, 1985.
【22】 Kakino, Y., Ihara, Y. and Nakatsu, Y. “The Measurement of Motion Errors of NC Machine Tools and Diagnosis of Their Origins by Using Telescoping Magnetic Ball Bar Method”, Annals of CIRP Vol. 36 No. 1 pp.337-380, 1987.
【23】 Kakino, Y., Ihara, Y., Kamei, A. and Ise, T. “Study on the Motion Accuracy of NC Machine Tools (1st Report) - The Measurement and Evaluation of Motion Errors by Double Ball Bar Test”, Journal of JSPE Vol.7 pp. 1193 –1198, 1986.
【24】 Kakino, Y., Ihara, Y. and Nakatsu, Y. “A Study on the Motion Accuracy of NC Machine Tools (2nd Report) - Diagnosis of Motion Error Origins by Using Double Ball Bar Test”, Journal of JSPE Vol. 52 No.10: pp.l739-1745, 1986.
【25】 Knapp, W. “Circular Test on NC Machine Tools in Industrial Application”, Journal of Industrial an Production Engineering Vol. 10 No. 3: pp.99-100, 1986.
【26】 Knapp, W. “Accuracy of Length Measurement and Positioning : Statical Measurement and Contouring”, Annals of CIRP Vol.37 No.1: pp.511-514.24, 1988.
【27】 Burdekin, M. and Park, J. “CONTISURE-A Computer-Aided System for Assessing the Contouring Accuracy of NC Machine Tools”, 27th Int’l MATADOR Conference pp.197-203, 1988.
【28】 Burdekinand, M. and Jywe, W. “Optimizing the Contouring Accuracy of CNC Machines Using the Contisure System”, 29th Int'l MATADOR Conference, 1992.
【29】 Wang, S. M. and Ehmann, K. F. “Measurement Method for the Position Errors of a Multi-axis Machine. Part I: Principles and Sensitivity Analysis”, International Journal of Machine Tools & Manufacture, Vol. 39(6), 1999.
【30】 Wang, S. M. and Ehmann, K. F. “Measurement Method for the Position Errors of a Multi-axis Machine. Part II: Applications and Experimental Results”, International Journal of Machine Tools & Manufacture, Vol. 39(9), 1999.
【31】 范光照、張郭益，”精密量具及機件檢驗”，高立出版社 1998.
【32】 姜俊賢，”精密量具及機件檢驗”，文京出版社 1993.
【33】 BSI 4656, “British Standard Method of Determination of Accuracy and Repeatability of Positioning of NC Machine Tools,” Part 16,1985.
【34】 VDI/DGQ 3441, ”Testing of the Operational and Positional Accuracy of Machine Tool”, March 1977.
【35】 「循軌量測軌跡判讀實例研討會」, 中華民國精密機械發展協會, 民國81年10月.
【36】 Whitehouse, “A Best Fit Reference Line for Use in Partial Arcs”, Journal of Physics E: Scientific Instruments, Vol. 6, 1973.
【37】 「工具機動態、迴轉軸定位測試與標準研習會」, 經濟部工業局, 45-47頁.