臺灣博碩士論文加值系統

摘 要
針對日內瓦機構，本文提出一套增進其特性的方法。不同於傳統以等速驅動主動輪的方式，此方法利用最佳控制理論來合成主動輪的運動軌跡。在本文中，將先建立起轉速設計的準則，以消除日內瓦機構在起點與終點時的抖震負載，並由三方面的特性來規劃主動輪轉速。第一，以最小化輸出加速度為目的來設計主動輪轉速，第二，以最小化輸入馬達扭力為目標來設計主動輪轉速，第三，以主動輪與從動輪間的機構磨耗程度，作為轉速設計的考量。而每個轉速設計方案都將表示成參數化的最佳設計問題，且利用有效率的數值方法加以求解。最後本研究考量這些設計方案間的抵觸性，把原本的轉速設計問題擴展到多目標最佳轉速設計問題，並以三個設計實例來說明整個設計的過程。

Optimal Speed Programming of the Geneva Mechanism
Chih-Chong Cho
Abstract
A method is proposed to improve the performance of the traditional Geneva mechanism. Rather than driving the input crank at a uniform speed, this method uses optimal control theory to synthesize the motion of the crank. In this thesis, design criteria are first developed based upon the elimination of the impact loading at the beginning and end of the motion cycle. In addition, three approaches to program the crank speed are introduced. First, the crank speed is designed to be optimal so as to minimize the output acceleration. In the second approach, the crank speed is determined by minimizing the input motor torque. The third approach uses the degree of wear between the crank pin and wheel slot as the index to program the crank speed. All design methods are formulated as the parameterized optimization problem and solved via an efficient numerical method. Furthermore, trade-offs among the desired characteristics is taken into account by formulating the problem into a multi-objective optimization problem. Three design examples are given to illustrate the design procedure.

目 錄
誌謝….……………………………………………………….………………. I
中文摘要….………………………………………………………..……….. II
英文摘要………………………………………………….………………… III
目錄………………………………………………………………….…….... IV
圖目錄………….…………………………………………….…………… VII
表目錄……………………………………………………………………….. X
符號說明….…………………………………………………….…..…....…. XI
第一章緒論
1.1 前言……..…………………………………………….…………..… 1
1.2 文獻回顧………………………………………………………...….. 2
1.3 研究目的及方法………………………………………………...….. 5
1.4 本文架構………………………………………………………...….. 5
第二章運動分析
2.1 動作原理……………………………………..…………………..…. 7
2.2 系統模型之建立………………………………………………….… 9
2.3 運動方程式…..………….………………………………………… 10
2.3.1 位置分析…..………………………………….……………… 11
2.3.2 速度分析…..…………………………………….…………… 12
2.3.3 加速度分析…..………………………………….…………… 12
2.4 運動特性正規化…..……………………….……………………… 13
2.4.1 無因次運動方程式…..…….………………………………… 13
2.4.2 等速驅動下之日內瓦輪運動特性…..………….…………… 15
2.5 變轉速日內瓦機構…..…………………….……………………… 19
第三章轉速規劃之目標與方法
3.1 目標函數之建立…..……………………….……………………… 24
3.1.1 輸出性能指標…..…………………………………….……… 24
3.1.2 輸入性能指標…..…………………………………….……… 26
3.1.3 結構性能指標…..…………………………………….……… 27
3.1.4 單目標轉速規劃問題…..…………………………….……… 30
3.2 最佳控制問題………………………..……………………….…… 31
3.2.1 最佳控制問題的表示式…..………………………….……… 31
3.2.2 最佳控制問題的處理方式…..……………………….……… 34
3.2.3 Pseudospectral Chebyshev Method…..………………….…… 36
3.3 單目標轉速規劃之結果與討論…………………………...……… 41
3.3.1 最佳化輸出性能指標 J1…..………………...……….……… 42
3.3.2 最佳化輸入性能指標 J2…..………………………………… 46
3.3.3 最佳化結構性能指標 J3…..…………………...……….....… 49
3.4 單目標轉速規劃之修正與討論…………………………...……… 53
3.4.1 修正最佳化輸出性能指標 J1…..………..…………..……… 53
3.4.2 修正最佳化輸入性能指標 J2…..…...…………….………… 56
3.4.3 修正最佳化結構性能指標 J3…..…………………...….....… 58
第四章多目標轉速規劃
4.1 多目標最佳化原理………………………………………………... 62
4.1.1 Pareto 最佳解…..………………………………………...….. 63
4.1.2 折衷規劃法…..…………………………………………..…... 64
4.1.3 分析層級程序法…..………………………………………..... 67
4.2 多目標轉速規劃實例…..…………..……………………………... 70
4.2.1 設計需求…..…………………………………...…………….. 70
4.2.2 結果與討論…..……………………………...……………….. 72
第五章結論及未來研究方向
5.1 結論…..………………………………..…………………………... 80
5.2 未來研究方向…..……………………………………………..…... 81
參考文獻…..……………………………………………………………...… 83
附錄 A ..…..……………………………………………………………...… 88

參考文獻
1.牧野 洋，自動機械機構學，復漢出版社印行，1994.
2.徐業良，工程最佳化設計，宏明印行，1995.
3.陳貽安，碩士學位論文，硬碟機磁頭懸臂之多目標結構與控制最佳化設計，國立台灣大學機械工程研究所，1994.
4.謝和興，碩士學位論文，使用日內瓦機構之系統研究，國立台灣大學機械工程研究所，1998.
5.Al-Sabeeh, A. K., 1993, “ Double Crank External Geneva Mechanism,” ASME Journal of Mechanical Design, Vol. 115, pp. 666-670.
6.Ambardekar, M. N., and Gupta, K. N., 1990, “Stochastic Optimal Control of Vibrations of a High-Speed Cam-Driven Mechanism,” Mechanism and Machine Theory, Vol. 25, pp. 59-68.
7.Ambrose, G., Don, R. H., and Lucien, D., Multiobjective decision analysis with engineering and business applications, New York : Wiley, 1982.
8.Bagic, C., 1977, “Synthesis of Double-Crank Driven Mechanisms with Adjustable Motion and Dwell Time Ration,” Mechanism and Machine Theory, Vol. 12, No. 6, pp. 619-638.
9.Biegler, L. T., 1984, “Short Note Solution of Dynamic Optimization Problems by Successive Quadratic Programming and Orthogonal Collocations,” Computers and Chemical Engineering, Vol. 8, pp. 243-248.
10.Bryson, J. A. E., Ho, Y. C., Applied Optimal Control, Hemisphere Publishing Corp., 1975.
11.Cheng, C. Y., and Lin, Y., 1995, “Improving Dynamic Performance of the Geneva Mechanism Using Non-Linear Spring Elements,” Mechanism and Machine Theory, Vol. 30, pp. 119-129.
12.Chew, M., Freudenstein, F., and Longman, R. W., 1983, “Application of Optimal Control Theory to the Synthesis of High-Speed Cam-Follower Systems. Part 1: Optimality Criterion,” ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN, Vol. 105, pp. 577-584.
13.Chew, M., Freudenstein, F., and Longman, R. W., 1983, “Application of Optimal Control Theory to the Synthesis of High-Speed Cam-Follower Systems. Part 2: System Optimization.” ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN, Vol. 105, pp. 585-591.
14.Cuthrell, J. E., and Biegler, L. T., 1987, “On the Optimization of Differential-Algebraic Process Systems,” AIChE Journal, Vol. 33, pp. 1257-1270.
15.Dijksman, E. A., 1966, “Jerk-Free Geneva Wheel Driving,” J. Mechanisms, Vol. 1, pp. 235-283, Pergamon Press, Printed in Great Britain.
16.Dijksman, E. A., 1976, “Gear-Wheel Drive Geneva Wheels,” Rev. Roum. Sci. Techn.-Me’c. Appl., Tome 21, No. 4, pp. 581-606
17.Elnagar, G. N., and Razzaghi, M., 1996, “An Alternative Method for a Classical Problem in the Calculus of Variations,” Mathematical Methods in the Applied Sciences, Vol. 19, pp. 1091-1097.
18.Elnagar, G. N., and Mohammad, A., K., 1998, “Pseudospectral Chebyshev Optimal Control of Constrained Nonlinear Dynamical Systems,” Computational Optimization and Applications, Vol. 11, pp. 190-217.
19.Fabien, B. C., Longman, R. W., and Freudenstein, F., 1994, “The Design of High-Speed Dwell-Rise-Dwell Cams Using Linear Quadratic Optimal Control Theory,” Journal of Mechanical Design, Vol. 116, pp. 867-874.
20.Fenton, R. G., 1965, “Charts Provide Quick Simple Method for Dynamic Analysis of Geneva Mechanisms,” Machine Design, Vol. 37, pp. 177-182.
21.Fenton, R. G., 1975, “Geneva Mechanisms Connected in Series,” ASME Journal of Engineering for Industry, Vol. 97, pp. 603-608.
22.Fenton, R. G., Zhang, Y., and Xu, J., 1991, “Development of a New Geneva Mechanism With Improved Kinematic Characteristics,” ASME Journal of Mechanical Design, Vol. 113, pp. 40-45.
23.Hunt, K. H., 1973, “Profiled-Follower Mechanisms,” Mechanism and Machine Theory, Vol. 8, pp. 371-395.
24.Hunt, K. H., Fink, N., and Mayar, J., 1960, “Linkage Geneva Mechanisms—A Study in Mechanism Geometry,” Proc. Mech. Inst. Engrs., 174, 643.
25.Johnson, R. C., 1956, “How to Design Geneva Mechanisms to Minimize Contact Stresses and Torsional Vibrations,” Machine Design, Vol. 28, No. 6, pp. 107-111.
26.Kanzaki, K., and Itao, K., 1972, “Polydyne Cam Mechanisms for Typehead Positioning,” ASME Journal of Engineering for Industry, Vol. 94, pp. 250-254.
27.Kirk, D. E., Optimal Control Theory, Prentice-Hall Inc., 1970.
28.Lichwitz, O., “Mechanism of Intermittent Motion,” Machine Design, Vol. 23, No. 12, Dec. 1951, pp. 134-148; Vol. 24, No. 1, Dec. 1952, pp. 127-182
29.Lee, T. W., 1981, “Optimization of High Speed Geneva Mechanisms,” ASME Journal of Mechanical Design, Vol. 103, pp. 621-630.
30.Rothbart, H. A., 1956, Cams: Design, Dynamics and Accuracy, John Wiley & Sons, New York.
31.Sadek, K. S. H., Lloyd, J. L., and Smith, M. R., 1990, “A New Design of Geneva Drive to Reduce Shock Loading,” Mechanism and Machine Theory, Vol. 25, pp. 589-595.
32.Saaty, T. L, 1990, Multicriteria Decision Making: The Analytic Hierarchy Process, RWS publication 2nd edition, Pittsburgh.
33.Sun, J. G., Longman, R. W., and Freudenstein, F., 1984, “Objective Function for Optimal Control in Cam-Follower Synthesis,” Proceedings of the American Control Conference, San Diego, California.
34.Tesar, D. and Matthew, G. K., 1976, The Dynamic Synthesis, Analysis and Design of Modeled Cam System, Lexington Books, New York.
35.Wang, A. C., and Lee, T. W., 1983, “On the Dynamics of Intermittent-Motion Mechanisms. Part 2: Geneva Mechanisms, Ratchets, and Escapements,” ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN, Vol. 105, pp. 541-551.
36.Yan, H. S., Hsu, M. H., Fong, M. K., and Hsieh, W. H., 1994, “A kinematic approach for eliminating the discontinuity of motion characteristics of cam-follower systems,” Journal of Applied Mechanisms & Robotics, Vol. 1, No. 2., pp. 1-6.
37.Yan, H. S., Tsai, M. C., and Hsu, M. H., 1996, “A variable-speed method for improving motion characteristics of cam-follower systems,” ASME Transactions, Journal of Mechanical Design, Vol. 118, No. 1, pp. 250-258.
38.Yan, H. S., and Chen, W. R., 2000, “On the Output Motion Characteristics of Variable Input Speed Servo-Controlled Slider-Crank Mechanisms,” Mechanism and Machine Theory, Vol. 35, pp. 541-561.
39.Yang, A. T., and Hsia, L. M., 1979, “Multistage Geared Geneva Mechanism,” ASME Journal of Mechanical Design, Vol. 101, pp. 41-46.
40.Yao, Y. A., Zhand, C., and Yan, H. S., 2000, “ Motion Control of Cam Mechanisms,” Mechanism and Machine Theory, Vol. 35, pp. 593-607.
41.Yoshitsugu, K., and Masaharu, T., 1979, “A Study on High-Speed Intermittent Motion Mechanism* — Reducing a Residual Vibration by Use of a Dynamic Vibration Absorber —,” Bull. Japan Soc. Of Prec. Engg., Vol. 13, pp. 27-32.