曲面加工時，銑床的構型會影響到曲面的可加工性，因此選定正確的銑床構型來進行加工是很重要的工作。傳統上曲面加工時銑床構型的選擇是仰賴工程師的經驗，一旦遇到經驗法則無法處理的狀況時，經常會導致生產時程延誤，這是為了找出新的經驗法則來解決問題所必須付出的代價。為了彌補經驗法則的不足，本研究在發展一套製造可行性初步評估系統，來解決曲面加工時，銑床構型與加工行程判斷的問題。
本文利用可視錐配合單位球上之刀軸方位以評估出曲面在進行銑削加工時適合加工該曲面的銑床構型以及旋轉軸角度範圍限制。首先以曲面幾何配合刀具幾何進行刀具尺寸限制分析，再以曲面點資料配合旋轉軸角度範圍限制，進行銑床的加工行程分析，再將上述分析加以整合即為本論文的曲面製造可行性初步評估法則。最後利用鞋楦曲面來作為可製造性初步評估的實例並利用VERICUT軟體來進行評估結果驗證。
此製造可行性初步評估系統包含了構型與加工行程的評估，讓使用者能夠選用適當的銑床來進行曲面加工。

Milling machine configuration influences the manufacturability of surface; therefore, choosing correct milling machine configuration is an important task. Traditional methods of choosing milling machine configuration for multi-axis surface machining depend on the experiences of manufacturing engineers. If the experience rule cannot solve, it will cause the production delay. In this case, new experience rules should be generated to solve the problems. In order to remedy the deficiency of the experience rules, this study developed a manufacturability evaluation system to select the milling machine configuration and the traverse range for multi-axis surface machining.
In this research, configuration and minimal necessary angle for the rotary axis of milling machine are evaluated by visibility cone and tool orientation on unit-circle. First the cutter size is analyzed based on the cutter geometry and surface geometric parameters. Then the surface point data and the restriction of the angle of rotary axis are used to evaluate the traverse range of milling machine. These are the manufacturability preliminary evaluation rules proposed in this thesis. Finally, taking shoe last as an example, the manufacturability preliminary evaluation was verified by the simulation results generated from VERICUT.
This manufacturability preliminary evaluation system includes the configuration evaluation and traverse range evaluation of milling machine for a user to choose the suitable milling machine to machine the surface.

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., 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).
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. 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).
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. 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).
10. 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).
11. 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).
12. Paul, R. P., Robot Manipulators: Mathematics, Programming and Control, MIT Press, Cambridge, Mass (1981).
13. Reshetov, D. N. and V. T. Portman, “Accuracy of Machine Tool”, ASME Press, pp.25-60 (1988).
14. Suh, S. H. and J. J. Lee, “Five-Axis Part Machining With Three-Axis CNC Machine and Indexing Table”, ASME Trans. Journal of Manufacturing Science and Engineering, Vol.120, pp.120-128 (1998).
15. 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).
16. Tseng, Y. J. and S. Joshi, “Determining Feasible Tool-Approach Directions for Machining Bezier Curves and Surfaces”, Computer-Aided Design, Vol. 23, No.5, pp.367-379 (1991).
17. 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).
18. 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).
19. Woo, T. C., “Visibility Maps and Spherical Algorithms”, Computer-Aided Design, Vol.26, No.1, pp.6-16 (1994).
20. 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).
21. 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)
22. 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).
23. 吳維軒，“五軸曲面加工時工具機構型判斷之研究”，碩士論文，國立成功大學機械工程學研究所，民國95年。
24. 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，民國90年1月。
25. 林子寬，“鞋楦精加工4軸NC程式之產生”，碩士論文，國立台灣科技大學機械工程系，民國九十三年七月。
26. 許家瑜， “於多軸曲面加工時刀軸方位與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，民國92年。
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. 陳譽文，“五軸CNC曲面加工原理之研究”，碩士論文，國立中正大學機械工程研究所，民國88年。
29. 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，民國91年7月。
30. 張俊毅，”於多軸曲面加工時以可視錐分析做工具機及刀具尺寸限制分析”， 碩士論文，國立成功大學機械工程研究所，民國92年6月。
31. 黃正輝, “五軸工具機高速進給機構設計與改良”，碩士論文，國力清華大學動力機械工程學系，民國91年
32. 歐冠吟，”五軸工具機之夾具設計與改良”，碩士論文，國立清華大學動力機械工程學系，民國94年。