在精密製造工業中，CNC工具機切削過程加工精密度扮演著重要的角色。傳統CNC工具機加工方式，通常是將CAD/CAM所規劃設計出的輪廓與刀具路徑，利用直線或圓弧近似的方式產生NC加工碼。但此方式的加工容易造成工件表面的不平整。因此，近幾年來利用參數式曲線於CNC工具機的加工方式已日趨成型。
參數式曲線的加工方式最主要是利用曲線參數的迭代，以找出下一個加工點的路徑位置，而曲線參數迭代的方式將是影響加工精度的關鍵因素之一。因此，本文提出利用預測-修正法的概念，藉以求出最佳的曲線參數，並針對加工路徑補間計算，推導出各軸控制系統之相對取樣時間的進給數。最後利用電腦模擬的方式，驗證理論的可行性。

This paper presents an efficient approach to the cutting path interpolation for CNC machine tools. On the basis of Hamming method for error analysis, the optimized curve parameters, the correlative interpolating calculation of parameter, and the relative sampling time of feed rate for controlling path of cutter location are developed. It begins the solution with a fourth order Runge-Kutta, and then continues with a predictor-corrector. Moreover, computer-aided simulation is also proposed to identify the feasibility of the presented methodology. With the identification results, the cutter path trajectory can be previewed before the real run.

參考文獻：
[1] Bedi S., Ali I., Quan N., “Advanced interpolation techniques for N.C. machine,” Transactions ASME Journal of Engineering for Industry, Vol. 115, pp. 329-336, 1993.
[2] Chou J.J., Yang D.C.H., “Command generation for three-axis CNC machining,” Transactions ASME Journal of Engineering for Industry, Vol. 113, pp. 305-310, 1991.
[3] Chou J.J., Yang D.C.H., “On the generation of coordinated motion of five-axis CNC/CMM machining,” Transactions ASME Journal of Engineering for Industry, Vol. 114, pp. 15-22, 1992.
[4] Kim D.I., “Study on interpolation algorithms of CNC machine tools,” IEEE Industry Applications Conference, Vol. 3, pp. 1930-1937, 1995.
[5] Koren Y., “Computer control of manufacturing systems,” New York: McGraw-Hill, 1982.
[6] Koren Y., “Interpolator for a computer numerical control system,” IEEE Transactions on Computer, Vol. 1, pp. 32-37, 1976.
[7] Koren Y., “Control of Machine tools,” Transactions ASME Journal of Manufacturing Science and Engineering, Vol. 119, pp. 749-753, 1997.
[8] Koren Y., Lo C.C., Shpitanlni M., “CNC interpolators: Algorithms and Analysis,” Manufacturing Science and Engineering ASME, PED-Vol. 64, pp. 83-92, 1993.
[9] Koren Y., Massory, O., “Reference-Word Circular interpolators for CNC systems,” Transactions ASME Journal of Engineering for Industry, Vol. 104, pp. 400-405, 1982.
[10] Koren Y., O., “Reference-Pulse Circular interpolators for CNC systems,” Transactions ASME Journal of Engineering for Industry, Vol. 103, pp.131-136, 1981.
[11] Lin R.S., Koren Y., “Efficient tool-path planning for machining free-form surfaces,” Transactions ASME Journal of Engineering for Industry, Vol. 118, pp. 20-28, 1996.
[12] Lin R.S., “Real time surface interpolator for 3-D parametric surface machining on 3-axis machine tools,” International Journal of Mechine Tools & Manufacture, Vol. 40, pp. 1513-1526, 2000.
[13] Lo C.C., “Feedback interpolators for CNC machine tools,” Transactions ASME Journal of Manufacturing Science and Engineering, Vol. 119, pp. 587-592, 1997.
[14] Lo C.C., Hsiao C.Y., “CNC machine tool interpolator with path compensation for repeated contour machining,” Computer Aided Design, Vol. 30, pp. 55-62, 1998.
[15] Lo C.C., “A new approach to CNC tool path generation,” Computer Aided Design, Vol. 30, pp. 649-655, 1998.
[16] Piegl L., “On NURBS: A Survey,” IEEE Computer Graphics & Application, Vol. 1, pp. 55-71, 1991.
[17] Piegl L., Tiller W., “The NURBS Book,” Springer-Verlag, New York, 1995.
[18] Qiyi G., Zhang, R. B. G., “Development and implementation of a NURBS curve motion interpolator,” Robotics and Computer-Integrated Manufacturing, Vol. 14, pp. 27-36, 1998.
[19] Rida T. F., Y. F. Tsai, “Exact Taylor coefficients for variable-feedrate CNC curve interpolator,” Computer Aided Design, Vol. 33, pp. 155-165, 2001.
[20] Shpitanlni M., Koren Y., Lo C.C., “Real time curve interpolator,” Computer Aided Design, Vol. 26, pp. 832-838, 1994.
[21] Yang D.C.H., Kong T., “Parametric interpolator versus linear interpolator for precision CNC machining,” Computer Aided Design, Vol. 26, pp. 225-234, 1994.
[22] Yeh S.S., Hsu P.L., “The speed-controlled interpolator for machining parametric curves,” Computer Aided Design, Vol. 31, pp. 349-357, 1999.
[23] Yeh S.S., Hsu P.L., “Adaptive-feedrate interpolator for parametric curves with a confined chord error,” Computer Aided Design, Vol. 34, pp. 229-237, 2002.
[24] 李宜達, “控制系統設計與模擬,” 全華科技圖書, 民國八十六年。
[25] 林榮信, 胡景文, “五軸工具機動態輪廓誤差分析,” 機械工業雜誌, pp. 172-181, 民國八十九年三月。
[26] 姚宏宗, 林榮信, ”CNC工具機電腦輔助加工新趨勢,” 機械月刊, 第二十七卷第三期, pp. 490-499, 民國九十年三月。
[27] 袁帝文, ”應用數值方法,” 儒林圖書, 民國八十六年。
[28] 徐永源, ”數控工具機,” 高立圖書, 民國八十七年。
[29] 許文通, ”數控工具機路徑誤差之控制,” 碩士論文, 國立台灣科技大學機械工程研究所, 民國八十三年。
[30] 陳明亮, ”控制器路徑產生與插值設計,” 機械月刊, 第二十五卷第三期, pp. 482-489, 民國八十八年三月。
[31] 郭洲成, ”CNC伺服控制器之NURBS即時插值器設計與實現,” 碩士論文, 國立成功大學機械工程研究所, 民國八十九年。
[32] 康兆安, ”TRR-XY混合式虛軸工具機之曲面插補原理及其電腦輔助製造系統研究,” 碩士論文, 國立成功大學製造工程研究所, 民國八十九年。
[33] 梁世璋, 曾文鵬, “高速控制器插值器NURBS技術,” 機械工業雜誌, pp. 139-145, 民國九十一年三月。
[34] 黃淳權譯, ”數值分析,” 全威圖書, 民國八十九年。
[35] 黃俊銘譯, ”數值方法-使用MATLAB程式語言,” 全華科技圖書, 民國九十年。
[36] 楊憲東, ”精密機械控制原理與模擬,” 全華科技圖書, 民國八十七年。
[37] 蔡明祺, 李榮顯, 姚武松, 梁碩芃, ”線性馬達驅動之工具機系統簡介,” 機械月刊, 第二十六卷第三期, pp. 367-381, 民國八十九年三月。