五軸加工近年來受到工業界的高度重視，被廣泛的運用在複雜零件的加工。五軸工具機主要使用於複雜曲面之加工，尤其是曲率變化大、加工精度要求高的情況。本文以可視錐理論與工作空間，分析複雜曲面的可製造性。在可製造性評估中，加入工具機構型判斷及刀具尺寸限制的演算法則。本文將針對各種工具機構型的不可加工點數、最小旋轉角度範圍及法向量分量分析，提出一套工具機構型建議。以往可視性與可視錐分析將刀具忽略為一無窮遠的直線，而造成加工時真實存在的刀具可能對曲面造成過切。為了避免發生此情形，本文根據曲面幾何推算出不同種類的刀具限制尺寸，再以該刀具尺寸計算出不發生干涉的刀軸方位並結合可視錐作分析。
本文以視窗程式為架構，發展ㄧ使用者操作介面，提供工具機構型及刀具尺寸建議。本文最後以馬鞍型曲面實例，透過本文所提出之演算法則完成工具機構型、刀具尺寸、旋轉角度範圍的建議，再透過VERICUT模擬軟體進行工具機構型建議的驗證。

Machining of complex parts has been paid great attention in industry recently. Five-axis machine tool is used to machine complex surface, especially for the surface with large change of curvature and high accuracy requirement. Theories of visibility cone and working space are used to analyze the manufacturability of complex surface in this paper. The algorithm of configurations determination of machine tools and cutter size are added to manufacturability evaluation. The determination of machine tool configurations is based on the unmachining points, the minimum rotation angle scope and normal vector analysis. In previous visibility analysis, the cutter geometry and its effect on the manufacturability are often ignored and only a vector with infinite length is considered. In order to avoid tool interference, this paper calculates the cutter size without interference and adapting with original visibility cone analysis according to geometric parameters of different cutters. This result was used to obtain the tool orientation without interference.
In this paper, an user interface is developed. The interface provide for the machine tool configuration and cutter size suggestions.
Finally, a composite surface was taken as the example to demonstrate the new algorithm and to obtain manufacturability suggestions. The machine tool configuration suggested by the proposed system was verified by VERICUT software.

1. Balasubramaniam, M., P. Laxmiprasad, S. Sa and Z. Shaikh, “Generating 5-axis NC Roughing Paths Directly from a Tessellated Representation”, Computer-Aided Design, Vol.32, pp.261-277 (2000).
2. Balasubramaniam, M., S. E. Sarma and K. Marciniak, “Collision-Free Finishing Toolpaths from Visibility Data”, Computer-Aided Design, Vol.35, pp.359-374 (2003).
3. Bedi, S., S. Gravelle and Y. H. Chen,“Principal Curvature Alignment Technique for Machining Complex Surfaces”,ASME Trans. Journal of Manufacturing Science and Engineering,Vol.119,pp.756-765(1997).
4. Chen, L. L. and T. C. Woo, “Computational Geometry on the Sphere With Application to Automated Machining”, ASME Trans. Journal of Mechanical Design, Vol.114, pp.228-295 (1992).
5. Chen, L. L., S. Y. Chou and T. C. Woo, “Separating and Intersecting Spherical Polygons: Computing Machinability on Three-, Four-, and Five-Axis Numerically Controlled Machines”, ACM Trans. on Graphics, Vol.12, No.4,pp.305-326 (1993).
6. Chen, L. L., S. Y. Chou and T. C. Woo, “Partial Visibility for Selecting a Parting Direction in Mold and Die Design”, Journal of Manufacturing System, Vol.14, No.5, pp.319-330 (1995).
7. Choi, B. K. and C. S. Jun, “Ball-End Cutter Interference Avoidance in NC Machining of Sculptured Surface”, Computer-Aided Design, Vol.21, No.6, pp.371-378 (1989).
8. Elber, G. and E. Zussman, “Cone Visibility Decomposition of Freeform Surfaces”, Computer-Aided Design, Vol.30, No.4, pp.315-320 (1998).
9. Gupta, P., R. Janardan, J. Majhi and T. Woo, “Efficient Geometric Algorithms for Workpiece Orientation in 4- and 5-Axis NC Machining”, Computer-Aided Design, Vol.28, No.8, pp.577-587 (1996).
10. Jensen, C. G., W. E. Red and J. Pi, “Tool Selection for Five-Axis Curvature Matched Machining”, Computer-Aided Design, Vol.34, pp.251-266 (2002).
11. Kang, J. K. and S. H. Suh, “Machinability and Set-up Orientation for Five-Axis Numerically Controlled Machining of Free Surfaces”, The International Journal of Advanced Manufacturing Technology, Vol.13, pp.311-325 (1997).

12. Kweon, S. and D. J. Medeiros, “Part Orientations for CMM Inspection Using Dimensioned Visibility Maps”, Computer-Aided Design, Vol.30, NO.9, pp.741-749 (1998).
13. Lee Y. S. and T. C. Chang, “2-Phase approach to global tool interference avoidance in 5-axis machining”, Computer-Aided Design, Vol. 27, No. 10, pp. 715-729, 1995.
14. Paul, R. P., “Robot Manipulators: Mathematics”, Programming and Control, MIT Press, Cambridge, Mass (1981).
15. Reshetov, D. N. and V. T. Portman, “Accuracy of Machine Tool”, ASME Press, pp.25-60 (1988).
16. Suh, S. H. and J. K. Kang, “Process Planning for Multi-Axis NC Machining of Free Surfaces”, International Journal of Production Research, Vol.33, No.10, pp.2723-2738 (1995).
17. Tang, K., T. Woo and J. Gan, “Maximum Intersection of Spherical Polygons and Workpiece Orientation for 4- and 5-Axis Machining”, Journal of Mechanical Design, Vol.114, pp.477-485 (1992).
18. Vafaeesefat, A. and H. A. Elemaraghy, “Automated Accessibility Analysis and Measurement Clustering for CMMs”, International Journal of Production Research, Vol.38, No.10, pp.2215-2231 (2000).
19. Woo, T. C. and B. F. von Turkovich, “Visibility Map and Its Application to Numerical Control”, Annals of the CIPP, Vol.39, pp.451-454 (1990).
20. Woo, T. C., “Visibility Maps and Spherical Algorithms”, Computer-Aided Design, Vol.26, No.1, pp.6-16 (1994).
21. Yin, Z. P., H. Ding and Y. L. Xiong, “Visibility Theory and Algorithms with Application to Manufacturing Processes”, Int. Journal of Production Research, Vol.38, No.13, pp.2891-2909 (2000).
22. You, C. F. and C. H. Chu, “Tool-Path Verification in Five-Axis Machining of Sculptured Surfaces”, Int. Journal of Advanced Manufacturing Technology, Vol.13, pp.248-255 (1997)
23. Zhu, C., “Avoiding Interference in Manufacturing a Free-Formed Surface with a Cylindrical End Mill Cutter”, Computer in Industry, Vol.14, pp.356-371 (1990).
24. 佘振華, “空間凸輪五軸加工數值控制程式設計系統之研究”, 博士論文, 國立成功大學機械工程研究所, 86年6月。
25. 李政男, “應用包絡元件於多軸加工數值控制程式設計系統之研究”, 博士論文, 國立成功大學機械工程研究所, 90年1月。
26. 葉煌成,“以具分度盤之三軸工具機對自由曲面加工之可製造性評估系統發展”,碩士論文,國立成功大學機械工程研究所, 89年6月。
27. 陳福成, “綜合加工機機構之構形合成”，博士論文，國立成功大學機械工程研究所，民國86年1月。
28. 陳耀乾, “以可視錐分析工件夾持方位及多軸工具機構型之研究”, 碩士論文, 國立成功大學機械工程研究所, 91年7月。
29. 黃世光, “多軸工具機之合成與分析”, 碩士論文, 國立成功大學機械工程研究所, 81年6月.
30. 張俊毅, “於多軸曲面加工時以可視錐分析工件做工具機及刀具尺寸限制之研究”, 碩士論文, 國立成功大學機械工程研究所, 92年7月。
31. 許家瑜, “於多軸曲面加工時刀軸方位與刀具限制之研究”, 碩士論文, 國立成功大學機械工程研究所, 93年7月。
32. 張純正, “可快速重組之曲面加工系統初步研究”, 碩士論文, 大葉大學機械工程研究所, 94年6月。
33. 蔡明志 譯, “C++ Primer Plus 4/e中文修訂版”, 碁峰資訊股份有限公司, 92年11月。
34. 位元文化 編著,“精通Visual C++ .NET 2003 視窗程式設計”,文魁資訊股份有限公司,92年12月。
35. 黃俊明,吳運明,詹永裕,“Unigraphics II模型設計-基礎篇”,全華科技圖書,90年2月。
36. VERICUT User Manual V5.3,CGTECH,2003.