隨著科技的進步，工業產品開始朝向外形複雜而多變發展，因此，製造業對刀具的需求日益多樣化。為能有效應用多軸刀具研磨機於刀具研磨。本研究針對瑞士Ewag公司的六軸CNC工具磨床提出正、逆向運動學分析及誤差分析，以供業界參考。
本研究是用齊次座標轉換矩陣，描述ewag六軸數控工具磨床的空間方位關係，推導其正、逆向運動學。並對其逆向運動方程式作全微分，探討位姿矩陣的微變量與各桿件變數微變量關係。同時，以數值方法驗證數學模型的正確性。最後考慮各桿件的幾何誤差及運動誤差源，求得工
具磨床一階誤差模型。而此正、逆向運動學是研磨刀具時的NC程式製作基礎，誤差分析結果可供業者對Ewag工具磨床的精度有深入了解。

With the swift progress of the new manufacturing technology, the geometry of industry product is increasingly complicated and changeable. Hence, the demand from manufacturing for various types of tools is escalated. In order to make the best use of multi-axis tool-grinding machine for tool grinding, this thesis will investigate the forward and inverse kinematics and error analysis of a 6-axis CNC tool-grinding machine from Ewag, Swissland.
In this thesis the forward and inverse kinematics of Ewag CNC 6-axis tool-grinding machine are presented by using homogeneous transformation matrices. The inverse kinematics equations are then differentiated to obtain the differential changes of its pose matrix. Numerical method is employed to verify the validity of the developed model. Finally, the first order error of that machine due to links’ geometrical and kinematic errors are studied. The forward and inverse kinematics will be the foundation of NC programming for tool grinding processes. Error analysis can offer users more understanding of that machine’s capabilities.

[1] Denavit ，J. and Hartenberg，R.S.”A Kinematic Notation for Lower Pair Mechanism Based on Matrices ”，ASME J. of applied mechanics Vol22 Vol.77，pp.215-221，1995.
[2] 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.
[3] Dhande，S.G.and Chakraborty，J. “Mechanical Error Analysis of spatial Linkages”，ASME J. Engng. Ind.，Vol.95，No.3，pp.672-676，1973.
[4] Rao S.S. and Ambekar，A.G.”Mechanical Error Analysis of Apherical Function Generating Mechanism ：Aprobabilistic Approach”，ASME Paper no.74-DET-15，1974.
[5] Schultschik，R.”The Components of Volumetric Accuracy”，Annals of CIRP Vol.26，1977.
[6] TavKhelidze，D.S.、Davitashvili and Demurishvili，N.V.”The Determination of Technological Error in Spherical 4-linkaged Mechanism”，Mechanism and machine theory，Vol.14，No.1，pp.43-59，1979.
[7] 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.
[8] 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，pp.l51-63，1986.
[9] Benhaib 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：pp.317-322，1977.
[10] Eman K.F. and Wu B.T. “A Generalized Geometric Error Model for Multi-axis Machine”，Annals of the CIRP 36，No.1，pp.253-256，1987.
[11] 謝榮發 “多槽鑽頭設計與研磨”博士論文，2003
[12] 王世明、劉源良、游涵任、康淵“六自由度史都華平台工具機之誤差分析研究“中國機械工程學會第十八屆學術研討會論文集，333-340頁，2001
[13] Richard P. Paul“ ROBOT MANIPULATORS : MATHEMATICS. PROGRAMMING，AND CONTROL“，1981