在機構的變轉速輸入相關研究上，對於轉速函數的設計上曾選用多項式函數、貝茲曲線及傅立葉級數，在最佳化方法上則皆使用以數學優化為基礎的方法，其具有計算速度快的優點，但較容易落入區域最小值。在選用輸入轉速函數上，還沒有明確建議使用何種函數會比較適當。因此，本研究以利用等導程滾珠螺桿搭配變轉速輸入理論應用於劍桅式無梭織布機的引緯機構作為設計實例，分別以貝茲曲線及傅立葉級數作為輸入轉速曲線，以及選擇以數學優化與啟發式演算法兩種類型的最佳化算法進行設計。
首先介紹引緯機構與其設計需求與限制，並推導滾珠螺桿複合機構的運動方程式及輸入扭矩方程式。接著，提出可供變轉速函數設計的輸入轉速函數與最佳化方法，針對不同的目標函數設計出一系列的轉速曲線，並利用商用軟體ADAMS驗證了理論設計的正確性。其後，討論造成不同轉速函數間結果優劣的原因。最後由最佳化結果，歸納出貝茲曲線與傅立葉級數於最佳化過程所適用的最佳化方法，以及改善最佳化成果的方式。

In the research of mechanism with variable input-speeds, the polynomial function, Bezier curve, and Fourier series are used in the design of the speed function. The optimization methods are based on mathematical programming, with the advantage of fast calculation speed, but easier to fall into the regional minimum. Since it is not suggested which function will be more appropriate in selecting the input speed function, this work targets on the variable input-speed functions of variable input-speed ball-screw compound mechanism on a rapier type shuttleless loom by using Bezier curve and Fourier series as the basis of input speed function, along with mathematical programing and heuristic algorithm as the basis of optimization method.
This work introduces the design requirements and constraints of the weft insertion mechanism . The kinematic equations and input torque equation of the ball screw compound mechanism are derived, and the input speed function and optimization method for the variable speed function design are proposed. According to the design requirements and constraints, a series of speed curves of different objective functions are designed, and the correctness of the theoretical design is verified by using commercial software ADAMS. Furthermore, the reasons for the relative merits between different speed functions are discussed. Finally, the applicable optimization methods to Bezier curve and the Fourier series and ways to improve optimization are summarized from the optimization results.

[1] H. A. Rothbart, 1956, Cams: Design, Dynamics and Accuracy, John Wiley & Sons, New York.
[2] D. Tesar and G. K. Matthew, 1976, The Dynamics Synthesis, Analysis, and Design of Modeled Cam Systems, Lexington Books, Maryland.
[3] H. S. Yan and M. K. Fong, 1994, “An approach for reducing the peak acceleration of cam-follower systems using a B-spline representation,” Journal of the Chinese Society of Mechanical Engineers, Taipei, 15(2), pp. 48-55.
[4] H. S. Yan, M. H. Hsu, M. K. Fong and W. H. Hsieh, 1994, “A kinematic approach for eliminating the discontinuity of motion characteristics of cam-follower systems,” Journal of Applied Mechanisms & Robotics, 1(2), pp. 1-6.
[5] H. S. Yan, M. C. Tsai and M. H. Hsu, 1996.05, “An experimental study of the effects of cam speeds on cam-follower systems,” Mechanism and Machine Theory, Vol.31, No.4, pp.397-412.
[6] H. S. Yan, M. C. Tsai and M. H. Hsu, 1996.06, “A variable-speed method for improving motion characteristics of cam-follower systems,” ASME Transactions, Journal of Mechanical Design, Vol.118, No.2, pp.250-258.
[7] 白友中，1995年，凸輪機構之週期性轉速追蹤控制，碩士論文，國立成功大學機械工程學系，臺南。
[8] Van de Straete and H. J. De Schutter, 1996, “Hybrid cam mechanisms,” IEEE/ASME Transactions on Mechatronics, 1(4), pp. 284-289.
[9] M. H. Hsu and W. R. Chen, 1999, “On the design of speed function for improving torque characteristics of cam-follower systems,” Proceedings of the Tenth World Congress on the Theory of Machines and Mechanisms, Oulu, 1, pp. 272-277.
[10] Y. A. Yao, C. Zhang and H. S. Yan, 2000.04, “Motion control of cam mechanisms,” Mechanism and Machine Theory, Vol.35, No.4, pp.593-607.
[11] Y. A. Yao, H. S. Yan, C. Zhang and H. J. Zou, 2000.10, “Integrated design of cam mechanisms and servo-control systems,” Science in China (Series E), Vol.43, No.5, pp.511-518.
[12] H. S. Yan, Y. A. Yao and H. J. Zou, 2001, “Polydyne servo-cam design,” Journal of the Chinese Society of Mechanical Engineers, Taipei, Vol.22, No.2, pp.90-104.
[13] Y. A. Yao, H. S. Yan and C. Zhang, 2003.09, “A variable-speed method for reducing residual vibrations in elastic cam-follower systems,” ASME Transactions, Journal of Dynamic Systems, Measurement, and Control, Vol.125, No.3, pp.480-482.
[14] Y. A. Yao and H. S. Yan, 2003, “A novel concept for minimizing speed fluctuations in motor driven mechanisms,” Journal of the Chinese Society of Mechanical Engineers, Taipei, Vol.24, No.4, pp.565-570.
[15] Y. A. Yao, J. Z. Cha and H. S. Yan, 2004.10, “Co-design of mechanism and control,” Chinese Journal of Mechanical Engineering, Beijing, Vol.40, No.10, pp.1-5.
[16] H. S. Yan and W. J. Tsai, 2008.02, “A variable-speech approach for preventing cam-follower separation,” Journal of Mechanical Design, Systems, and Manufacturing, JSME International Journal, Vol.2, No.1, pp.12-23.
[17] H. S. Yan and W. J. Tsai, 2008, “Motion adaptation of cam-follower systems by variable input speeds,” Proceedings of the Institute of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science., Vol.222(C3), pp.459-472.
[18] H. S. Yan and C.C. Yeh, 2010, “Integrated kinematic and dynamic design for variable-speed plate cam mechanisms,” Proceedings of the Institute of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, Vol.225(C3), pp.194-203.
[19] R. L. Kaplan and S. S. Rao, 1987, "Goal programming approach for the balancing of variable input speed mechanisms," Proceedings of the 1987ASME Design Technology Conferences, Publication DE, Vol. 10-1, pp.163-172.
[20] I. S. Kochev, 1990, "Full shaking moment balancing of planar linkagesby a prescribed input speed fluctuations," Mechanism and MachineTheory, Vol. 25, No. 4, pp. 459-466.
[21] H. S. Yan and R. C. Soong, “Kinematic and dynamic design of four-bar linkages by links counterweighing with variable input speed,” Mechanism and Machine Theory, Vol. 36, No. 4, pp. 1051-1071, 2001.
[22] H. S. Yan and R. C. Soong, 2002, “Kinematic and dynamic design of four-bar linkages by mass retribution with variable input speed,” Journal of the Chinese Society of Mechanical Engineers, Taipei, Vol. 23, No. 4, pp.321-332.
[23] H. S. Yan and R. C. Soong, 2002, “Kinematic and dynamic design of four-bar linkages with variable input speed and external applied loads,” Transactions of the Canadian Society for Mechanical Engineering, Vol. 26, No. 3, pp. 281-310.
[24] H. S. Yan and R. C. Soong, “An integrated design approach of four-bar linkages with variable input speed,” JSME International Journal, Mechanical Systems, Machine Elements and Manufacturing, Series C, Vol. 47, No. 1, pp. 350-362.
[25] Y. A. Yao, H. S. Yan, H. J. Zou, 2002, “Output motion control of variable-input- speed linkage mechanisms,” Transactions of the Canadian Society for Mechanical Engineering, Vol.26, No.1, pp.1-14.
[26] Y. A. Yao, H. S. Yan and H. L. Zou, 2005, "Dynamic design of variable speed planar linkages," Chinese Journal of Mechanical Engineering(Beijing), Vol. 18, No. 1, pp. 51-54.
[27] 陳誌峰，邱顯堂，2005，"用傅立葉級數決定輸入轉速之四連桿機構最佳平衡設計"，中華民國機構與機器原理學會第八屆全國機構與機器設計學術研討會，臺北，pp. 498-505。
[28] H. S. Yan and G. J. Yan, 2009, “Integrated control and mechanism design for variable input-speed servo four-bar linkages,” Journal of Mechatronics, Vol.19, pp.274-285.
[29] H. S. Yan and W. R. Chen, 2000.04, “On the output motion characteristics of variable input speed servo-controlled slider-crank mechanisms,” Mechanism and Machine Theory, Vol.35, No.4, pp.541-561.
[30] H. S. Yan and W. R. Chen, 2000.04, “A variable input speed approach for improving the output motion characteristics of Watt-type pressed,” International Journal of Machine Tools & Manufacture, Vol.40, No.5, pp.675-690.
[31] H. S. Yan and W. R. Chen, 2002.06, “Optimized kinematic properties for Stevenson-type presses with variable input speed approach,” ASME Transactions, Journal of Mechanical Design, Vol.124, No.2, pp.350-354.
[32] Ali. Kirecci and L. C. Dulger, 2000, “A study on a hybrid actuator,” Mechanism and Machine Theory, Vol. 35, No. 4, pp. 1141-1149.
[33] J. Y. Liu, M. H. Hsu and F. C. Chen, 2001, “On the design of rotating speed functions to improve the acceleration peak value of ball-screw transmission mechanism, ” Mechanism and Machine Theory, Vol. 39, No. 4, pp. 1035-1049.
[34] 陳仁智，顏鴻森，2004.11.26-27，“具負載變轉速滾珠螺桿機構於伺服沖床之研究”，第二十一屆學術研討會，中國機械工程學會，2025-2030頁，高雄市。
[35] 顏鴻森，林志明，劉俊佑，2005.08，“一種具變轉速滾珠螺桿機構之伺服沖床設計”，機械設計與研究，上海市，21卷，4期，6-8&12頁。
[36] H. S. Yan and M. S. Kuo, 2011, “Using the Fourier series function to improve the kinematic characteristic of ball-screw servo press mechanism,” Machine Design and Research, 2011 Special issue, pp.40-42, Shanghai.
[37] 徐翊清，2013年6月，一種變轉速複合螺桿機構之運動與動力特性設計，碩士論文，國立成功大學機械工程學系，臺南。
[38] J. H. Yang, M. H. Hsu, H.S. Yan, 2016.02, “Kinematic and dynamic characteristics design of a variable-speed machine with slider-crank and screw mechanisms,” ASME Transactions, Journal of Mechanisms and Robotics, Technical brief, Vol. 8, pp. 014502-1~6.
[39] J. J. Lee and C. C. Cho, 2002, “Improving kinematic and structural performance of Geneva mechanisms using the optimal control method,” Proceedings of the Institution of Mechanical engnineers, Part C: Journal of Mechanical Engineering Science, 216, pp. 761-774.
[40] 葉東龍，2017年5月，應用變轉速滾珠螺桿複合機構於劍桅式無梭織布機之研究，碩士論文，國立成功大學機械工程學系，臺南。
[41] 顏鴻森、李榮顯、黃文敏、蔡明俊、邱顯堂、陳家豪、陳元方、陳朝光、王俊志、蘇演良、林昌進，1995年10月，劍桅式無梭織布機變導程螺桿傳動機構之電腦整合設計與製造 No.5載具技術報告，國科會專題研究計畫(NSC 83-0422-E-006)，國立成功大學機械工程學系，臺南。
[42] 黃文敏，1995年9月，劍桅式無梭織布機變導程螺桿傳動機構之電腦整合設計與製造總技術報告-A.構想設計，國科會專題研究計畫(NSC 83-0422-E-006)，國立成功大學機械工程學系，臺南。
[43] 蔡明俊，1995年9月，劍桅式無梭織布機變導程螺桿傳動機構之電腦整合設計與製造總技術報告-B.運動分析，國科會專題研究計畫(NSC 83-0422-E-006)，國立成功大學機械工程學系，臺南。
[44] 邱顯堂，1995年9月，劍桅式無梭織布機變導程螺桿傳動機構之電腦整合設計與製造總技術報告-C.動力分析，國科會專題研究計畫(NSC 83-0422-E-006)，國立成功大學機械工程學系，臺南。
[45] 顏鴻森，1995年9月，劍桅式無梭織布機變導程螺桿傳動機構之電腦整合設計與製造總技術報告-F.幾何設計，國科會專題研究計畫(NSC 83-0422-E-006)，國立成功大學機械工程學系，臺南。
[46] 范揚昇，1992年6月，無梭織布機韌性劍帶驅動機構之構造設計，碩士論文，國立成功大學機械工程學系，臺南。
[47] A. S. Hall, Jr., 1981, Notes on Mechanism Analysis, BALT Publishers, Lafayette, Indiana.
[48] R. L. Norton, 2013, Kinematics and Dynamics of Machinery, McGraw-Hill, New York.
[49] P. Bezier, 1986, The Mathematical Basis of the UNISURF CAD System, Butterworths, London.
[50] K. Erwin, 1999, Advanced Engineering Mathematics, 8th edition, John Wiley & Sons.