車削為最常見且重要的加工方法之一。車刀為車削所用的刀具，車刀為單刃刀具，刀刃形狀為楔形，其影響切削性能之特徵角度有斜角、楔角與隙角。
首先本文將介紹車刀外型的設計，利用齊次座標轉換為工具，建立車刀外型與研磨輪外型的數學模型。接下來介紹兩種ISO標準的特徵角度的計算系統：刀具手持系統與刀具工作系統。因刀具工作系統較能反映出實際加工的狀況，故本文會進行刀具工作特徵角的分析，利用fortran計算刀刃上各個位置其特徵角度的變化。
為了研磨加工出當初所設計的車刀的外型，必須推導出研磨輪相對於車刀的位姿矩陣。這裡同樣使用齊次作標轉換為工具，配合曲面運動法來解囓合條件，即可推導出研磨輪相對於車刀的位姿。這裡同樣使用fortran分別來計算研磨輪研磨刀面與刀腹時研磨輪相對於車刀的位姿。
本文最後將針對六軸工具機作介紹，利用修正型D-H座標設定法則與齊次座標轉換為工具，即可對六軸工具機建模並推導其功能函數矩陣。

Turning is one of the most popular and important machining processes. Turning tools are tools which are used for turning. Turning tools are single-edge tools, and their shapes of edge are wedges. The characteristic angles which will effect cutting performance are rake angle, wedge angle and clearance angle.

First we will introduce the design of turning tools. We can built the math models of turning tools and grinding wheels by homogeneous coordinate transformation matrix. Then we’ll introduce two kinds of characteristic angles of International Standards Organization (ISO). They are tool-in-hand system and tool-in-use system. Because that tool-in-use system can reflect the condition of real process, we will analyze the characteristic angles of tool-in-use system by Fortran.

In order to grind the turning tool we have designed, we must derive the pose of grinding wheel relative to turning tool. We can derive the pose of grinding wheel relative to turning tool by homogeneous coordinate transformation matrix and surface movement law. We also use Fortran to calculate the pose of grinding wheel while grinding the face and the flank.

At last we’ll introduce the six-axis machine tool. By using modified Denavit-Hartenberg (D-H) notation and homogeneous coordinate transformation matrix, we can model the multi-axis machine tool.

[1] G. Boothroyd, Fundamentals of Metal Machining and Machine Tools,McGraw-Hill Book Company, 1975
[2] A.R. Watson, and R.A. Williams “Specification of the Cutting Geometry of Single Point Tools and Twist Drills Using the ISO System,” International Journal Machine Tools Design& Research Vol.17, pp.103-116, 1977
[3] E. Budak, and Y. Altintas, “Prediction of Milling Force Coefficients from Orthogonal Cutting Data,” Manufacturing Science and Engineering ASME PED 1993, 64 453-459
[4] G. Yucesan, Q. Xie and A. E. Bayoumi, “ Deteermination of Process Parameter Through a Mechanistic Force Model of Milling Operations,” Int. J. Mach. Tool Manu. 33, 627. 1993
[5] L. Dobrjanskyi and F. Freudenstein, “Some Applications of Graph Theory to the Structural Analysis of Mechanisms,” Trans. ASME J. Eng. Ind. Pp.153-158, 1967
[6] Mruthyunjaya, T.S., and Raghavan, M.R., “Structural Analysis of Kinematic Chains and Mechanisms Based on Matrix Representation,“ ASME Journal of Mechanical Design, Vol.101, No.3, pp.488-494, 1979
[7] 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.215-551,1955
[8] P. D. Lin, and K. F. Ehmann, “Direct Volumetric Error Evaluation for Multi-Axis Machines, “ Int J. Mach. Tools Manufact, Vol. 33, No. 3, pp. 6675-6693, 1993
[9] J. Wang, and O. Masory, “ On the Accuracy of a Stewart Platform-Part I The Effect of Manufacturing Tolerances,” Proceedings of the 1993 IEEE, International Conference on Robotics and Automation, pp.114-120, 1993
[10] Lin, Psang Dain, and Chu, Min Ben, “ Machine Tools Setting for Cams with Flat-Face Followers,” International Journal Machine Tools & Manufacture Vol.34,pp.1119-1131,1994
[11] 謝榮發，”多槽鑽頭設計與研磨”，博士論文，國立成功大學機械研究所，2003
[12] 林銘福，"橢圓刃球端銑刀與階梯銑刀之設與分析"，博士論文國立成功大學機械研究所，2006
[13] 林志雄，切削工具學，興業圖書股份有限公司，1980
[14] 洪良德，切削刀具學，全華科技圖書股份有限公司，1985
[15] 唐文聰，切削加工技術，全華科技圖書股份有限公司，1986
[16] 傅光華，切削刀具學，高立出版社，1986
[17] 艾興，薛秉源，金屬切削刀具，科技圖書股份有限公司，1989
[18] 劉偉均，切削加工學，台灣東華書局股份有限公司，1989
[19] 徐明堅，最新切削加工技術，復漢出版社，1992
[20] 金屬中心，金屬切削刀具專題研究，金屬中心，1995
[21] 李阿卻，切削刀具學，全華科技圖書股份有限公司，1999