高階NC工具機是我國急欲發展的關鍵產品之一，但目前我國的高階工具機大都自德、日進口，無法自製，在高階工具機中，五軸NC工具機是技術困難度最高、利潤最高，也是需求最殷切的項目，而五軸加工路徑後處理法則的探討與控制器的水準提高息息相關，是五軸加工領域中一個非常重要的研究議題。後處理的任務是將CAM軟體所產生的Cutter location data（簡稱CL data）轉換成特定的五軸工具機進行加工時所需的Numerical control data（簡稱NC data）。由於五軸加工機比三軸加工機多了兩個旋轉軸，因此複雜度大幅增加，就像一個神秘的領域，常人不易瞭解，而探討不同五軸工具機機型的後處理器的轉換法則，以開發國人自製的泛用型後處理器，將有助於高階NC工具機之技術層次的大幅提升。
本論文的研究目的是探討五軸加工後處理的通用法則，並進行公式推導，此法則適用於各種不同型式的五軸加工機。由於五軸加工機之旋轉機構的多樣性，因此傳統的五軸NC加工程式之求解方式皆針對特定的機構提出特殊的方法，如此將形成高度複雜的計算公式。為了解決此問題，本研究提出球面雙圓法（Spherical two-circle method，簡稱STC法）以利推導適用於任意旋轉機構的五軸加工機的通用型計算法則，此方法針對五軸加工機的旋轉角賦予明確的幾何意義，可用來驗證CL data轉換為NC data的正確性。STC法的特點是先擱置五軸運動中的線性運動，而著重於兩個旋轉軸的運動，並將此兩個旋轉運動分解成主軸向量或刀軸向量依序繞次旋轉軸及主旋轉軸進行旋轉，如此可輕易地經由刀軸向量求得兩個旋轉軸的旋轉角，再利用求得的旋轉角以正向運動學的方法求出NC data的點座標，並推導後處理器的座標轉換公式。STC法的觀念不僅可應用於主軸型五軸加工機，也可應用於床台型及混合型，不但可用於旋轉軸正交型，也可應用於旋轉軸非正交型。STC法的概念是以圖形作幾何分析，因此利用兩個旋轉圓相交與否的關係，可快速推導出刀軸向量的有效範圍及判別旋轉軸的方向是否恰當。

High-end NC tooling machinery is one of the key products that Taiwan is eager to develop. However, as Taiwan lacks the capability of manufacturing these high-end machine tools, a majority of them are imported from Germany or Japan. Of the high-end machine tools, 5-axis NC machine tools are the most technically difficult, most profitable, and the most sought-after product item. While the exploration of post process of the 5-axis tool path is closely relevant to enhancing the level of controller, it is also a very important research issue in the 5-axis machining fields. The task of post processing consists of converting the Cutter Location data (CL data) generated by the CAM software into the Numerical Control data (NC data) required for 5-axis machining. Because the 5-axis machine tool has two additional rotary axes added to the 3-axis machine tool, the increased complexity is compared to a mysterious realm, and is difficult to understand by a majority of people. Therefore, exploring the post processing conversion algorithms of various 5-axis machine tools, in order to develop a Taiwan-made general-purpose post processor, should be helpful in significantly enhancing the understanding of the technology levels required for making high-end machine tools.
The purpose of this paper is to explore general post processing algorithms of 5-axis machining which are applicable to various types of 5-axis machine tools. Since different 5-axis milling machines typically feature unique rotation mechanisms, the solutions developed to generate NC data are traditionally targeted toward specific mechanisms and obtained via specific methods, normally resulting in complex algorithms. In order to resolve this problem, this paper proposes a spherical two-circle (STC) method. This method provides intuitive physical meanings for rotation angles of 5-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC data. The STC method disregards linear movements, and instead focuses on the movements of the two rotational axes. These rotational movements are decomposed into the spindle vector or tool orientation vector rotating about the secondary rotation axis and the primary rotation vector. The two rotation angles can be derived easily using the tool orientation vector. The point coordinates for the NC data can then be obtained according to the derived rotation angles, and the coordinate transformation equations for the post-processor can be derived. The concept of the spherical two-circle method can be applied not only to spindle type 5-axis milling machines but also to the table and hybrid type, not only to orthogonal type 5-axis milling machines but also to non-orthogonal type machines. The concept of the proposed STC method stems from the use of geometry to analyze the features of two rotation mechanism, therefore, using the intersection relationship of two rotation circles can lead to find the range of feasible tool orientations and select a suitable direction of rotation axis.

1.Yoshimi Takeuchia and Takahiro Watanabe, “Generation of 5-Axis control collision-free tool path and post-processing for NC data”, 1992, Annals of the CIRP, Vol. 41, No. 1, pp. 539-542.
2.Ling-Wen Tsai, Robot Analysis, John Wiley & Sons, Inc., 1999, New York, pp. 66.
3.A. Rüegg and P. Gygax, “A generalized kinematics model for three to five axis milling machines and their implementation in a CNC” , 1992, Annals of the CIRP, Vol. 41, No. 1, pp. 547-550.
4.Sakamoto Shiquhiko and Inasaki Ichiro, “Analysis of generating motion for five-axis machining centers”, 1993, The Japan Society of Mechanical Engineers, Vol. 59, No. 561, pp. 1553-1559.
5.R. S. Lee and C. H. She, “Developing a postprocessor for three types of five-axis machine tools”, 1997, International Journal of Advanced Manufacturing Technology, Vol. 13, pp. 658-665.
6.R. MD. Mahbubur, J. Heikkala, K. Lappalainen and J. A. Karjalainen, “Positioning accuracy improvement in five axis milling by post processing”, 1997, International Journal of Machine Tools and Manufacture, Vol. 37, No. 2, pp. 223-236.
7.Y. H. Jung, D. W. Lee, J. S. Kim and H. S. Mok, “NC post-processor for 5-axis milling machine of table-rotating or tilting type”, 2002, Journal of Materials Processing Technology, Vol. 103-131, pp. 641-646.
8.Chen-Hua She and Chun-Cheng Chang, “Development of a five-axis postprocessor system with a nutating head”, 2007, Journal of Materials Processing Technology, Vol. 187-188, pp. 60-64.
9.Chen-Hua She and Zhao-Tang Huang, “Postprocessor development of a five-axis machine tool with nutating head and table configuration”, 2008, International Journal of Advanced Manufacturing Technology, Vol. 38, pp.728-740.
10.Mahbubur Rahman, Jouko Heikkala and Kauko Lappalainen, “Modeling, measurement and error compensation of multi-axis machine tools. Part I: theory”, 2000, International Journal of Machine Tools and Manufacture, Vol. 40, pp. 1535-1546.
11.Y. Kakino, Y. Ihara and A. Shinohara, Accuracy inspection of NC machine tools by double ball bar method, Carl Hanser GmbH, 1993.
12.K. Kim and M. K. Kim, “Volumetric accuracy analysis based on generalized geometric error model in multi-axis machine tools”, 1991, Mechanism and Machine Theory, Vol. 26, pp 207-219.
13.L. M. Zheng, H. Lin and R. L. Gai, “Postprocessor based on generalized kinematics model of five-axis machine tools”, 2010, International Journal of Computer Integrated Manufacturing Systems, Vol. 16, No. 5, pp. 1006-1011.
14.J. Andres, L. Gracia and J. Tornero, “Inverse kinematics of a redundant manipulator for cam integration an industrial perspective of implementation”, 2009, International Conference on Mechatronics, April 14-17, Malaga, Spain.
15.Fusaomi Nagata, Yukihiro Kusumotob and Keigo Watanabe, “Intelligent machining system for the artistic design of wooden paint rollers”, 2009, Robotics and Computer-Integrated Manufacturing, Vol. 25, No. 3, pp. 680-688.
16.Chen-Hua She and Rong-Shean Lee, “A postprocessor based on the kinematics model for general five-axis machine tools”, 2000, Journal of Manufacturing Processes, Vol. 2, No. 2, pp. 131-141.
17.S. Ashmall, “Post-processors for general purpose N.C. processor”, 1972, Proceedings of the Institution of Mechanical Engineers, Vol. 186, No. 25, pp. 551-556.
18.Chen-Hua She and Chun-Cheng Chang, “Design of a generic five-axis postprocessor based on generalized kinematics model of machine tool”, 2007, International Journal of Machine Tools and Manufacture, Vol. 47, pp. 537-545.
19.M. Nagasaka and Y. Takeuchi, “Generalized post-processor for 5-axis control machining based on form shape function”, 1996, Journal of the Japan Society for Precision Engineering, Vol. 62, No. 11, pp. 1607-1611.
20.Knut Srby, “Inverse kinematics of five-axis machines near singular configurations”, 2007, Machine Tools and Manufacture, Vol. 47, pp. 299-306.
21.胡修華, “泛用型五軸後處理器設計”, 1997, 碩士論文, 國立台灣大學機械工程學研究所。
22.I. D. Faux and M. J. Pratt, Computational Geometry for Design and Manufacture, 1979, Ellis Horwood Ltd., New York, pp. 73.