由於刀具是製造工業非常重要的切削工具，因此刀具的功能與品質對於切削加工的品質、精度、效率有很直接的影響，有鑒於此，刀具產業的興盛，必須仰賴基礎知識的加強與研發能力的提升和技術創新。
刀具的幾何形狀對切削的品質有很大的影響，尤其是曲面加工部份，必須使用複雜外型的銑刀運用到高精度的工具機上才能完成，因此本研究將以機械製造業廣泛使用的端銑刀為例，透過數學建模來探討銑刀的設計與製造並確認可行性。
本研究在刀具設計與製造上結合基礎數學理論與電腦輔助設計的應用技術，並依據國際標準(ISO)定義刀具角度，運用齊次轉換矩陣建立刀具的刀刃曲線，並藉由微分幾何、共軛嚙合理論、數值方法等理論基礎來探討銑刀的設計製造，利用RPY矩陣以使得在空間中的研磨輪可適應各種研磨方位，建構研磨端銑刀的位姿矩陣。

The cutter is a fundamental machine tool in manufacturing industries. Therefore the performance and quality of a cutter affects the cutting precision, product quality, and the efficiency of manufacturing directly. Thus the enhancement of the cutter knowledge and new technology are most important to the manufacturing industry developement.

Its geometry of cutting edge has serious effect on milling process and product quality, especially for the curve surface manufacturing. To address the problem, it is necessary to utilize the complicated end-mill on the high precision machine.End mills are widely used in manufacturing industries.. Thus we illustrate the developed mathematical models for the design and manufacture with an end mill.

Current cutter design and manufacturing technologies combine the fundamental mathematical theory with computer-aided design technology. The cutting edge refers to the International Standard Organization (ISO) by using homogeneous transformation matrix. In the study, the design and manufacturing of an end mill are based on differential geometry, conjugate theory, coordinate transfer and numerical methods. In addition, we utilize the transformation of RPY matrix to obtain the required degrees of the position, posture and the matrix of the grinding wheel.

1. G. Boothroyd, Fundamentals of Metal Machining and Machine Tool, McGraw-Hill Book Company(1975)
2. J. Agullo-Batlle, S. Cardona-Foix and C. Vinas-sanz, "On the Design of Milling Cutters or Grinding Wheel For Twist Drill Manufacture. A CAD Approach”, Mechanical Design & Research Vol. 17, pp315-318.
3. Kataev, A. V., “CAD of Tool with Complex Forming Face,” SovietEngineering, 1989,9(7):22-28.
4. Sheth, D. S. and Malkin, S., “CAD/CAM for Geometry and ProcessAnalysis of Helical Flute Machining,” Ann. CIRP Vol.39, 1990,pp.129-132.
5. S. Kaldor , Ada Mod Rafale and D. Messinger, "On the CAD of Profiles for Cutters and Helical Flutes - Geometrical Aspects”, Annals of the CIRP Vol.37/1/1988 , pp53-56.
6. S. Engin 1, Y. Altintas,“Mechanics and Dynamics of General Millingcutters.Part I: Helical End Mills”Received 9 February 2001; Accepted 2 April 2001
7. Nemes J.A., Asamoah A.S. and Budak E., “Cutting Load Capacity of End Mills with Complex Geometry,” Annals of the CIRP, 50, pp.65-68, 2001.
8.Merdol S.D.and Altintas Y., “Mechanics and Dynamics of SerratedEndMills,” ASME IMECE2002-39114, New Orleans, LA, 2002.
9.Campomanes M.L., “Kinematics and Dynamics of Milling with RoughingEnd Mill,” Metal Cutting and High Speed Machining, Kluwer Academic/Lpenum Publishers, 2002.
10. Barsov, A., Cutting Tool Production, Moscow, Mir Publisher, pp. 179-194,
1978
11 .Hidehj, A. Y., “Development of Elliptic Ball-End Mill,” Bulls. Jap.Soc. of
Prec. Eng., Vol. 20, N0. 4, pp. 59-66, 1986.
12.曾乾生，”Ewag六軸CNC工具磨床之研究”，碩士論文，國立成功大學機械研究所，2003
13.林銘福，”橢圓刃球端銑刀與階梯端銑刀之設計與分析”，博士論文，國立成功大學機械研究所，2000
14.謝榮發，〝多槽鑽頭設計與研磨〞，國立成功大學機械工程學系博士論文，2002
15.洪良德，切削刀具學，全華科技圖書股份有限公司，1985
16.李阿卻，切削刀具學，全華科技圖書股份有限公司，1999
17.林志雄，切削工具學，興業圖書股份有限公司，1980
18.唐文聰，切削加工技術，全華科技圖書股份有限公司，1986
19.艾興，薛秉源，金屬切削刀具，科技圖書股份有限公司，1989
20.劉偉均，切削加工學，台灣東華書局股份有限公司，1989
21.傅光華，切削刀具學，高立出版社，1986
22.蕭奧，林維新，紀松水，Shaw, Milton C.，切削理論，全華出版社，1987