多軸工具機對於複雜曲面加工，不僅能達到快速、精密切削方式，且可降低工件定位之誤差，進而提高製造效率。然而，工程師往往憑經驗判斷工件夾持方位，因此常無法順利加工完外型複雜的曲面。若刀具路徑未規劃前，能有個客觀評估工件夾持方位及適合工具機構型，則可達到產品快速開發之成效。
本論文利用可視錐理論並配合工具機工作空間分析，建構出可判斷最佳工件夾持方位及適合之工具機之模組。首先，針對三軸、四軸及五軸工具機合成出其構造構型，利用形狀創成函數分析其工作空間。接著，沿著u、v方向擷取欲加工曲面之點位置及法向量，並計算出曲面上每個點在u、v方向之可視範圍，即為此點之可視錐。於三軸加工中，將曲面法向量投影至單位球上，利用工件夾持方位之改變，使法向量能在球銑刀之可視範圍內。在四軸加工中，將曲面各點之可視錐與刀軸可行方位交集，由工件夾持方位之改變，找出最多交集時的最佳夾持方位。於五軸加工中，依據不同構型工具機之工作空間，判斷欲加工曲面的可視範圍，使工具機工作空間能由工件夾持方位之改變，與曲面上每點之可視錐有最多交集。
本論文提出可製造性評估方法可避免傳統經驗上誤判工件夾持方位及工具機構型，並避免刀具與曲面發生干涉，以利後來之刀具路徑規劃。且對於產品加工，經由工件夾持方位改變，可節省時間及成本浪費；於選擇工具機方面，亦可避免使用不適之之工具機構型。

The multi-axis machining of complex surface is not only a fast and accurate method but also reduces errors of workpiece set-up. However, engineers usually determine set-up orientation by experiences and often they cannot finish complex surfaces at one set-up. If there is a rational evaluation for the workpiece orientation and the configuration of machine tool before planning of toolpath, it would increase the efficiency of process development.
Adapting the visibility cone together with workspace analysis, the selection module for the optimum workpiece orientation and the suitable configuration of machine tool was constructed in the thesis. First, the configurations of 3,4 and 5-axis machine tools were synthesized and then, the workspace was analyzed using form-shaping function. The position and normal vector of each point along u, v directions in the machining surface were got to calculate the visibility range as the point of the visibility cone. In 3-axis machining, all normal vectors of surface were projected on a unit sphere. All normal vectors had to be in the visibility range of the ball mill cutter as the workpiece set-up orientation changed. In 4-axis machining, the most intersection between the visibility cone of each point and the workspace was found by changing the set-up orientation. In 5-axis machining, according to different workspaces of 5-axis machine tools, the visibility range of machining surface was determined to find the most intersection between the visibility cone and the workspace by changing the workpiece orientation.
This thesis proposed a method of manufacturability evaluation to obtain the optimum workpiece set-up orientation and the suitable configuration of machine tools. The tool interference with surface can be avoided to improve the planning of toolpath. For manufacturing, it can reduce cost by changing to optimum set-up orientation. For selection machine tool, it can also avoid the use of unsuitable configuration of machine tool.

1. Balasubramanian, M., P. Laxmiprasad, S. Sarma, and Z. Shaikh, “Generation 5-Axis NC Roughing Paths Directly from A Tessellated Pepresentation”, Computer-Aided Design, Vol. 32, pp. 261-277(2000).
2. 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. 305-326 (1992).
3. Chen, L.L., and S. H. Suh and T.C. Woo, “Parting Directions for Mould and Die Design”, Computer-Aided Design, Vol. 25,No. 12,pp. 762-768(1993).
4. Choi, B. K., D. H. Kim and R. B. Jerard, “C-Space Approach to Tool-Path Generation for Die and Mould Machining”, Computer-Aided Design, Vol. 29, No. 9,pp. 657-669(1997).
5. 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).
6. Gupta, K. C., B. Roth, “Design Considerations for Manipulators Workspace”, ASME Journal of Mechanical Design, Vol. 104, pp. 704-771(1982).
7. Gershon, E. and E. Zussman, “Cone Visibility Decomposition of Freeform Surfaces”, Computer-Aided Design, Vol.30, No.4, pp. 315-320(1998).
8. Idemura, T. and Y. Takeuchi, “Machining and Grinding by 5-Axis Control Machining Center –For the Workpiece with Convex Sculptured Surface” Journal of the Japan Society for Precision Engineering(in Japanese), Vol. 57,No. 11, pp. 1989-1994(1991).
9. Ishizawa, H., Yamada, M., Tanaka, D., and Kishinami, T., “Form Shaping Function Model of 5-Axis Machine Tools-Classification of 5-Axis Machine Tools Based on Form Shaping Function” 5th Sapporo International Computer Graphics Symposium(in Japanese), No. 26-27, pp. 1-6(1991).
10. Kim, D. S., P. Y. Papalambros, and T. C. Woo, “Tangent, Normal, and Visibility Cones on Bezier Surfaces”, Computer Aided Geometric Design, Vol. 12, pp. 305-320 (1995).
11. Kumar, A. and M. S. Patel, “Mapping the Manipulator Workspace Using Interactive Computer Graphic”, The International Journal of Robotics Research, Vol. 5, No. 2, pp. 122-130(1986).
12. Kumar, A. and K. J. Waldron, “The Workspaces of a Mechanical Manipulator ”, ASME Journal of Mechanical Design, Vol.103, pp. 665-672(1981).
13. Kang, J. K. and S. H. Suh, “Machinability and Set-Up Orientation for Five-Axis Numerically Controlled Machining of Free Surfaces”, International Journal of Advanced Manufacturing Technology, Vol. 13,pp. 311-325(1997).
14. Kweoon, S. and D. J. Medeiros, “Part Orientation for CMM Inspection Using Dimensioned Visibility Map”, Computer-Aided Design, Vol.30, No. 9, pp.741-749(1998).
15. Kumar, A. and M. S. Patel, “Mapping the Manipulator Workspace Using Interactive Computer Graphic”, The International Journal of Robotics Research, Vol. 5, No. 2, pp. 122-130(1986).
16. Lin, 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).
17. Litvin, F. L., “Gear Geometry and Applied Theory” , PTR Prentice Hall, Englewood Cliffs, New Jersy (1994).
18. Lee, Y. S. and T. C. Chang, “Automatic Cutter Selection for 5-axis Sculptured Surface Machining”, The International Journal of Production Research, Vol. 34, No. 4, pp.977-998 (1996).
19. Morishige, K., K. Kase and Y. Takeuchi, “Collision-Free Tool Path Generation Using 2-Dimensional C-Space for 5-Axis Control Machining”, International Journal of Advanced Manufacturing Technology, Vol. 13, pp. 393-400(1997).
20. Paul, R. P., “Robot Manipulators: Mathematics”, Programming and Control, MIT Press, Cambridge, Mass (1981).
21. Reshetov, D. N. and V. T. Portman, “Accuracy of Machine Tool”, ASME Press, pp.25-60(1988).
22. Rogers, D. F. and J. A. Adams, “Mathematical Elements for Computer Graphics”, 2nd, McGraw-Hill Publishing Co. (1990).
23. Sakamoto, S. and I. Inasaki, “Analysis of Generating Motion for Five Axis Machining Centers ”, Japanese Society of Mechanical Engineers. Vol. 59, No. 561, pp. 1553-1559(1993).
24. Tang, K., T. Woo and J. Gan, “Maximum Intersection of Spherical Polygons and Workpiece Orientation for 4- and 5-axis NC Machining”, ASME Trans. Journal of Mechanical Design, Vol. 114, pp. 477-485 (1992).
25. Takeuchi, Y., H. Shi Izu, T. Idemura, T. Watanabe, and T. Ito, , “5-Axis Control Machining Based on Dolid Model” Journal of the Japan Society for Precision Engineering(in Japanese), Vol. 56, No. 11, pp.2063-2068(1990).
26. Takeuchi, Y., K. Wada, T., Hisaki, and M. Yokoyama, “Computer-Controlled 5-Axis Machine Tool Based on Trochoidal Interpolation”, Journal of Japan Society for Precision Engineering(in Japanese), Vol. 60, No. 1, pp.75-79(1994).
27. 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).
28. Woo, T. C. and B. F. von Turkovich, “Visibility Map and Its Application to Numerical Control”, Annals of the CIRP, Vol.39, pp. 451-454 (1990).
29. Woo, T. C., ”Visibility Maps and Spherical Algorithms”, Computer-Aided Design, Vol.26, No.1, pp. 6-16 (1994).
30. Yin, Z. P., H. Ding and Y. L. Xiong, “Visibility Theory and Algorithms with Application to Manufacturing Processes”, International Journal of Production Research, Vol. 38,No. 13,pp. 2891-2909(2000).
31. 位元文化研究室 著， “精通視窗程式設計-適用Visual C++6.0”, 文魁資訊股份有限公司， 2000年3月 ，Section1-15。
32. 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。
33. 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。
34. 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。
35. 陳嘉仁， “多軸曲面加工利用可視性映射做工具機構型選擇之研究”， 碩士論文， 國立成功大學機械工程研究所， 90年7月。
36. 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。
37. 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。