臺灣博碩士論文加值系統

本文應用五種演化型演算法，即遺傳演算法(GA)、粒子群演算法(PSO)、混合粒子群演算法(HPSO)、差分演算法(DE)及自適應差分演算法(SaDE)等，以求解四連桿與瓦特II型六連桿路徑產生機構之最佳化尺寸合成問題。最小化目標函數為機構所產生耦點與設計點距離誤差之平方和。經執行四連桿路徑產生機構之八種不同類型耦點軌跡之尺寸合成範例，並比較各最佳化方法的收斂速率與合成機構之耦點軌跡誤差，得知首次應用於機構最佳化尺寸合成之自適應差分演算法(SaDE)較優於其他四種演算法及其他文獻結果。故可合理預期，此SaDE法應用於複雜多迴路之路徑產生機構的尺寸合成問題，應具有潛在優勢。瓦特II型六連桿機構已見應用於人類義肢或機器人足部機構，本研究先以向量迴路法推導出瓦特II型六連桿機構之運動特性(角位置、角速度、角加速度、傳力角及機械利益等)關係式，再應用運動靜力分析(Kinetostatic analysis)，導出機構運動之動力矩陣式，以用來求解各接頭作用力。之後選取人類理想步行軌跡上的11個點當作設計點，並在機構運動與幾何拘束條件限制下，採用前述五種不同演化型演算法來做瓦特II型六連桿腿部機構之最佳化尺寸合成，並分析比較所得結果，結果亦以SaDE法所得為最佳化機構。而後，依據SaDE法所得之最佳化機構尺寸，自行撰寫MATLAB程式以分析其運動特性與各接頭作用力。此外，再以ADAMS 軟體進行動力分析與耦點軌跡分析，驗證MATLAB程式所得結果為正確。最後，將四組相同之瓦特II型六連桿機構，以左右對稱、前後相反方式組成四足步行機器人之四條腿機構，並以ADAMS 模擬其步行運動之足步軌跡與動力分析。本文研究，成功以SaDE法完成瓦特II型六連桿機構之最佳化尺寸合成，證實其具有較優秀的收斂效率與結果，亦可供其他複雜多迴路機構之最佳化設計參考。

In this study, five evolutionary algorithms-a genetic algorithm (GA), particle swarm optimization (PSO), hybrid particle swarm optimization (HPSO), differential evolution (DE), and self-adaptive differential evolution (SaDE)-were used to optimize dimensional synthesis for the path generation mechanisms of four-bar linkages and Watt-II six-bar linkages. The dimensional synthesis was optimized by minimizing the objective function, which was defined as the sum of squares of the distance error between design points and trajectories of coupler-point of generated mechanisms. Through dimensional synthesis performed on eight different coupler-point trajectories for the path generation of four-bar linkages, the comparisons were made for the rate of convergence of all optimization methods, as well as the errors between coupler-point trajectories of synthesized mechanisms. The results indicated that the SaDE algorithm outperformed the other four evolutionary algorithms, as well as the algorithms adopted in previous studies. Accordingly, the SaDE algorithm may be applicable to the dimensional synthesis problem of multi-loop path generation mechanisms. Because Watt-II six-bar linkages have applications in prosthetics and robot feet, this study employed the vector loop method to derive the kinematic relation of the parameters of the mechanism and performed a kinetostatic analysis to yield a dynamic matrix for solving all joint forces. Subsequently, 11 points on the ideal human walking trajectory were used as design points; the five aforementioned evolutionary algorithms were adopted under kinematic and geometric restrictions to perform optimal dimensional synthesis of Watt-II six-bar leg mechanisms. The results of this synthesis suggested that the SaDE algorithm outperformed the other algorithms in determining the optimal dimensions of the mechanisms. Afterwards, a MATLAB program was written to analyze the kinematic properties and all joint forces of the SaDE-derived optimal Watt-II six-bar leg mechanism. Furthermore, ADAMS was used to perform coupler-point trajectories and dynamic analyses, thereby validating the results obtained through the MATLAB program. Finally, the walking mechanism of a four-leg robot was constructed by assembling four identical Watt-II six-bar linkages symmetrically between the left and right sides but in reverse order between the front and back; ADAMS was then used to simulate the trajectory of the robot’s walking motion and perform a dynamic analysis. In summary, this study used a SaDE algorithm for the optimal dimensional synthesis of Watt-II six-bar linkages and confirmed that the SaDE algorithm had a higher rate of convergence and more satisfactory results than the other evolutionary algorithms. The findings are expected to improve the optimization and design of other complex multi-loop linkages.

中文摘要 I
ABSTRACT III
誌謝 V
目錄 VI
圖目錄 IX
表目錄 XV
符號說明 XVII
第一章 緒論 1
1.1前言 1
1.2文獻回顧 2
1.3研究目的及方法 13
1.4論文架構 14
第二章 平面連桿與機器人足部機構運動分析 16
2.1平面四連桿機構之運動分析 17
2.2瓦特II型平面六連桿機構之運動分析 21
2.2.1位置分析 22
2.2.2速度分析 27
2.2.3加速度分析 28
2.2.4傳力角分析 29
2.2.5機械利益分析 29
2.3瓦特II型平面六連桿機構之運動靜力分析 30
第三章 演化型最佳化算法 37
3.1最佳化方法 37
3.2遺傳演算法 40
3.3粒子群最佳化演算法 47
3.4混合粒子群最佳化演算法 56
3.5差分演算法 60
3.6自適應差分演算法 66
第四章 四連桿與瓦特II型六連桿機構之最佳化尺寸合成設計 71
4.1最佳化設計 71
4.2平面四連桿機構最佳化結果 73
4.2.1範例1 - 五設計點弧形軌跡 74
4.2.2範例2 - 十八設計點不規則封閉環型軌跡 78
4.2.3範例3 - 十二設計點類八字軌跡 82
4.2.4範例4 - 十二設計點雙尖點軌跡 86
4.2.5範例5 - 六設計點直線軌跡 90
4.2.6範例6 - 二十五設計點不規則封閉環型軌跡 96
4.2.7範例7 - 六設計點半月型軌跡 101
4.2.8範例8 - 十設計點類圓形軌跡 105
4.3理想足部軌跡曲線 111
4.4瓦特II型平面六連桿機構最佳化結果 114
第五章 MATLAB與ADAMS運動模擬分析 119
5.1位置分析 120
5.2角速度分析 120
5.3角加速度分析 121
5.4質心速度分析 121
5.5質心加速度分析 122
5.6傳力角分析 122
5.7機械利益分析 123
5.8接頭作用力分析 123
5.9四足步行機構之分析 126
5.9.1耦點與地面作用力分析 126
5.9.1接頭作用力分析 129
第六章 結論與建議 131
參考文獻 134
自述 142

1.顏鴻森，吳隆庸，機構學(第四版)，東華書局出版，台灣，2013.
2.G.N. Sandor and A.G. Erdman, “Advanced Mechanism Design: Analysis and Synthesis,” Vol. 2, Prentice-Hall, Englewood Cliffs, NJ, 1984.
3.A.S. Fraser, “Simulation of genetic systems by automatic digital computers I: Introduction,” Australian Journal of Biological Sciences, Vol.10, pp.484-499, 1957.
4.J.H. Holland, “Adaptation in natural and artificial systems,” The University of Michigan Press, USA, 1975.
5.J. Kennedy and R.C. Eberhart, “Particle swarm optimization,” Proc. IEEE International Conference on Neural Network, Vol.4, pp.1942-1948, 1995.
6.R. Storn and K. Price, “Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces,” Technical Report TR-95-012, ICSI, 1995.
7.Y.H. Shi and R.C. Eberhart, “A modified particle swarm optimizer,” Evolutionary Computation Proceedings, pp.69-73, 1998.
8.C.N. Ko, Y.P. Chang, and C.J. Wu, “An orthogonal-array-based particle swarm optimizer with nonlinear time-varying evolution,” Applied Mathematics and Computation, Vol. 191, pp.272-279, 2007.
9.M. Clerc, “The swarm and the queen: towards a deterministic and adaptive particle swarm optimization,” Evolutionary Computation, Vol. 3, pp. 1951-1957, 1999.
10.R. Storn, “On the usage of differential evolution for function optimization,” Biennial Conference of the North American, pp.519-523, 1996.
11.J. Lampinen and I. Zelinka, “Mechanical engineering design optimization by differential evolution,” New Ideas in Optimization, pp.127-146, 1999.
12.A.K. Qin and P.N. Suganthan, “Self-adaptive differential evolution algorithm for numerical optimization,” Evolutionary Computation, Vol. 2, pp.1785-1791, 2005.
13.K.V. Price, R.M. Storn and J.A. Lampinen, “Differential evolution: a practical approach to global optimization,” Natural Computing, 2005.
14.V.L. Huang, A.K. Qin and P.N. Suganthan, “Self-adaptive differential evolution algorithm for constrained real-parameter optimization,” Congress on Evolutionary Computation, pp.17-24, 2006.
15.Y.H. Kang and C.T. Lee, “The synthesis of four-bar linkages for path generation using hybrid particle swarm optimization,” The First IFToMM Asian Conference on Mechanism and Machine Science, Oct. 21-25, 2010, Taipei, Taiwan.
16.A. Kunjur and S. Krishnamurty, “Genetic algorithms in mechanism synthesis,” Journal of Applied Mechanism and Robotics, Vol.4, No.2, pp.18-24, 1997.
17.J.A. Cabrera, A. Simon and M. Prado, “Optimal synthesis of mechanisms with genetic algorithms,” Mechanism and Machine Theory, Vol.37, pp.1165-1177, 2002.
18.M.A. Laribi, A. Mlika, L. Romdhane and S. Zegloul, “A combined genetic algorithm-fuzzy logic method (GA-FL) in mechanism synthesis,” Mechanism and Machine Theory, Vol.39, pp.717-735, 2004.
19.A. Smaili and N. Diab, “Optimum synthesis of mechanism using tabu-gradient search algorithms,” ASME Journal of Mechanical Design, Vol.127, pp.917-923, 2005.
20.A. Smaili and N. Diab, “Optimum synthesis of hybrid-task mechanisms using ant-gradient search method,” Mechanism and Machine Theory, Vol.42, pp.115-130, 2007.
21.S.K. Acharyya and M. Mandal, “Performance of EAs for four-bar linkage synthesis,” Mechanism and Machine Theory, Vol.44, pp.1784-1794, 2009.
22.J. Buskiewicz, R. Starosta and T. Walczak, “On the application of curve curvature in path synthesis,” Mechanism and Machine Theory, Vol. 44, pp.1223-1239, 2009.
23.N. Nariman-Zadeh, M. Felezi, A. Jamali and M. Ganji, “Pareto optimal synthesis of four-bar mechanisms for path generation,” Mechanism and Machine Theory, Vol. 44, pp.180-191, 2009.
24.許剛錦，平面連桿組路徑產生機構之混合粒子群最佳化尺寸合成，碩士論文，國立高雄應用科技大學機械工程系，高雄，台灣，2010.
25.W.Y. Lin, “A GA-DE hybrid evolutionary algorithm for path synthesis of four-bar linkage,” Mechanism and Machine Theory, Vol.45, pp.1096-1107, 2010.
26.J.A. Cabrera, A. Ortiz, F. Nadal and J.J. Castillo, “An evolutionary algorithm for path synthesis of mechanisms,” Mechanism and Machine Theory, Vol.46, pp.127-141, 2011.
27.謝東霖，演化型演算法應用於四連桿路徑產生機構與六連桿義肢膝關節機構之最佳化尺寸合成，碩士論文，國立高雄應用科技大學機械工程系，高雄，台灣， 2012.
28.H. Zhou and E.H.M. Cheung, “Optimal synthesis of crank-rocker linkages for path generation using the orientation structural error of the fixed link,” Mechanism and Machine Theory, Vol.36, pp.973-982, 2001.
29.H. Cochrane, K. Orsi and P. Reilly, “Lower limb amputation Part 3: Prosthetics‐a 10 year literature review,” Prosthetics and Orthotics International, Vol. 25, pp.21-28, 2001.
30.J. Andrysek, “Lower-limb prosthetic technologies in the developing world: a review of literature from 1994-2010,” Prosthetics and Orthotics International, Vol.34, pp.378-398, 2010.
31.B.Y. Tsuge, “Kinematics synthesis of lower limb supporting linkages,” Prosthetics and Orthotics International, University of California, Irvine, 2015.
32.H. Funabashi, K. Ogawa, Y. Gotoh and F. Kojima, “Synthesis of leg-mechanisms of biped walking machines (Part I, Synthesis of ankle-path-generator),” Bulletin of the Japan Society of Mechanical Engineers, Vol.28, No.237, pp.537-543, 1985.
33.H. Funabashi, K. Ogawa, I. Honda and N. Iwatsuki, “Synthesis of leg-mechanisms of biped walking machines (Part II, Synthesis of foot-driving mechanism),” Bulletin of the Japan Society of Mechanical Engineers, Vol.28, No.237, pp.544-549, 1985.
34.T. Jansen, https://www.ted.com/speakers/theo_jansen, 2016.
35.D.J. Todd, “Evaluation of mechanically co-ordinated legged locomotion (the Iron Mule Train revisited),” Robotica, Vol. 9, No. 4, pp.417-420, 1991.
36.R.P. Williams, L.W. Tsai and S. Azarm, “Design of a crank-and-rocker driven pantograph: A leg mechanism for the University of Maryland’s 1991 Walking Robot,” Proceedings of 2nd National Conference on Applied Mechanisms and Robotics, Paper No. VIB.2, Cincinnati, OH, USA, 1991.
37.W.B. Shieh, L.W. Tsai, S. Azarm and A.L. Tits, “A new class of six-bar mechanisms with symmetrical coupler curves,” Journal of Mechanical Design, Vol. 120, No. 1, pp.150-153, 1996.
38.D. Jin, R. Zhang, H.O. Dimo, R. Wang and J.Zhang, “Kinematic and dynamic performance of prosthetic knee joint using six-bar mechanism,” Journal of Rehabilitation Research and Development, Vol.40, No.1, pp.39-48, 2003.
39.F. Iida, G. Gómez and R. Pfeifer, “Exploiting body dynamics for controlling a running quadruped robot,” Advanced Robotics, ICAR'05. Proceedings., 12th International Conference on. IEEE, pp.229-235, 2005.
40.C. Liang, M. Ceccarelli and Y. Takeda, “Operation analysis of a one-DOF pantograph leg mechanisms,” Proceedings of 17th International Workshop on Robotics in Alpe-Adria-Danube Region, 2008.
41.H. Mehdigholi and S. Akbarnejad, “Optimization of Watt's Six-Bar Linkage to Generate Straight and Parallel Leg Motion,” Journal of Humanoids, Vol.1, No.1, pp.11-16, 2008.
42.C. Liang, M. Ceccarelli and G. Carbone, “A novel biologically inspired tripod walking robot,” Environments, Vol.1, No.2, pp.83-91, 2009.
43.H.S. Yan and C.Y. Huang, “On the design of a self-balanced quadruped walking machine with ten-bar leg mechanisms,” American Society of Mechanical Engineers, pp.663-673, 2009.
44.O. Al-Araidah, W. Batayneh, T. Darabseh and S.M. BaniHani, “Conceptual design of a single DoF human-like eight-bar leg mechanism,” Jordan Journal of Mechanical and Industrial Engineering, Vol.5, No.4, pp.285-289, 2011.
45.S.M. Behrens, R. Unal, E.E.G. Hekman, R. Carloni, S. Stramigioli and H.F.J.M. Koopman, “Design of a fully-passive transfemoral prosthesis prototype,” Annual International Conference of the IEEE, pp.591-594, 2011.
46.S. Erkaya, “Trajectory optimization of a walking mechanism having revolute joints with clearance using ANFIS approach,” Nonlinear Dynamics, Vol.1, No.17, pp.75-91, 2012.
47.N. Ghaemi, M. Dardel M.H. Ghasemi and H. Zohoor, “Optimization of six bar knee linkage for stability of knee prosthesis,” Majlesi Journal of Mechatronic Systems, Vol.1, No.4, pp.38-45, 2012.
48.D. Giesbrecht, C.Q. Wu and N. Sepehri, “Design and optimization of an eight-bar legged walking mechanism imitating a kinetic sculpture, "WIND BEAST",” Transactions of the Canadian Society for Mechanical Engineering, Vol.34, No.4, pp.343-355, 2012.
49.E.C. Lovasz, C. Pop and V. Dolga, “Novel solution for leg motion with 5-link belt mechanism,” International Journal of Applied Mechanics and Engineering, Vol.19, No.4, pp.699-708, 2014.
50.C. Adriana, C. Dinu, D. Ileana, U.L. Marian and G.C. Alionte, “Passive Modular Groups for Inverse Structural Modelling of Bimobile Systems,” Procedia Engineering, Vol.100, pp.918-927, 2015.
51.G. Singh, A. Singla and G.S. Virk, “Modeling and simulation of a passive lower-body mechanism for rehabilitation,” Conference on Mechanical Engineering and Technology, Varanasi, India, 2016.
52.T. Murali, S. Perumal, R. Mohan and P. Palanisamy, “Design and synthesis of six legged walking robot using single degree of freedom linkage,” Imperial Journal of Interdisciplinary Research, Vol. 2, No.3, pp.476-483, 2016.
53.D.W. Haldane, M. Plecnik, J.K. Yim and R.S. Fearing, “A power modulating leg mechanism for monopedal hopping,” in IEEE/RSJ International Conference on Intelligent Robotics and Systems, pp.4757-4764, 2016.
54.M.M. Plecnik and J.M. McCarthy, “Design of Stephenson linkages that guide a point along a specified trajectory,” Mechanism and Machine Theory, Vol.96, pp.38-51, 2016.
55.A.G. Erdman, G.N. Sandor and S. Kota, “Mechanism Design Analysis and Synthesis,” 4th ed., Prentice Hall, New York, USA, pp.176-181,2001.
56.周至宏，最佳化方法課程講義，國立高雄應用科技大學電機工程系，高雄，台灣，2015.
57.L.J. Fogel, “Autonomous automata,” Industrial Research, Vol.4, pp.14-19, 1962.
58.J.R. Koza, “Genetic programming: on the programming of computers by means of natural selection,” MIT press, Vol.1, 1992.
59.M. Dorigo, Optimization, Learning and Natural Algorithms, Ph.D. Thesis, Politecnico di Milano, 1992.
60.Z. Michalewicz, “Genetic Algorithms+ Data Structures= Evolution Programs,” Mathematical Intelligencer, 1994.
61.L.D. Whitley, “The GENITOR Algorithm and Selection Pressure: Why Rank-Based Allocation of Reproductive Trials is Best,” ICGA, Vol.89, 1989.
62.S.J. Wu and P.T. Chow, “Integrated discrete and configuration optimization of trusses using genetic algorithms,” Computers & Structures, Vol.55, pp.695-702, 1995.
63.K.D. Jong, An Analysis of The Behavior of A Class of Genetic Adaptive Systems, Ph. D. Thesis, University of Michigan, Dissertation Abstracts International, Vol.36, 1975.
64.A. Popov, “Genetic algorithms for optimization,” Programs for MATLAB ® Version 1.0, User Manual, 2005.
65.Y.H. Shi and R.C. Eberhart, “Parameter selection in particle swarm optimization,” Evolutionary Programming VII, pp.591-600, 1998.
66.耿春亞，馬軍，郭忠武，丁輝，丁海曙，關於正常青年人步態豎直方向力的檢測與統計分析，航太醫學與醫學工程，Vol. 16，No. 5，pp. 364-367，2003.
67.錢竟光，宋雅傳，李勇強，唐瀟，步行動作的生物力學原理及其步態分析，南京體育學院學報:自然科學版，Vol. 5，No. 4，pp. 1-7，2006.
68.韓亞麗，王興松，羅翔，雙足機器人穩定行走步行模式的研究，東南大學學報:自然科學版，Vol. 39 N o. 2，pp. 238-244，2009.
69.黃琳元，蔣祥第，蔣志德，雙足機器人運動學分析與步態規劃，建國科技大學機械工程系暨製造科技研究所，彰化，台灣，2013.