Matlab’s GA and Optimization Toolbox: A Fourbar Mechanism Application

Abstract

This study presents an optimization approach for synthesis of planar mechanisms. A four bar mechanism is chosen for an application example. This mechanism is studied with the constraints assigned. Genetic Algorithm (GA) is applied during optimization study. GA in Optimization Toolbox is then compared with nonlinear constrained numerical optimization command; fmincon in Matl ab©. Different case studies are performed by considering different target points. These mechanisms are drawn using Excel© spread sheet to see their animations. An optimization example is presented here. Performances of both algorithms are then compared in terms of coupler curves precision points. Their use in designing a four bar mechanism is explored for its further use.

Keywords

• Four bar mechanism; Mechanism synthesis; Optimization; Genetic algorithm

References

1. H. Lipson, ‘Evolutionary Synthesis of Kinematic Mechanisms.’, Comp. Synt. Lab., Sibley School of Mech. and Aerospace Eng., and Fac. of Computing and Inf. Science, Comell University, Ithaca, NY-USA,2000.
2. J.H.Bickford ‘Mechanisms for Intermittent Motion.’, Director of production planning, Veeder-Root Company. ‘Int. Press Inc., 200 Medison Avenue, N.Y. 10016, 1972.
3. E.Söylemez, ‘Mechanisms’, M.E.T.U Mechanical Engineering Department, Publication Number: 64, Ankara.
4. A.H.Soni, ‘Mechanism Synthesis and Analysis.’, School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, Oklahoma,
5. R.N.Norton, ‘Design of Machinery-An Introduction to the Synthesis and Analysis of Mechanisms and Machines’,McGraw Hill–1992.
6. R.S.Hartenberg, D.J., ‘Kinematic Synthesis of Linkages, McGraw Hill-1964.
7. Y.Lui & J. McPhee, ‘Automated Kinematik Synthesis of Planar Mechanisms with Revolute Joints.’, System Design Engineering, University of Waterloo, Ontario, Canada.
8. Ting-Yu Chen, Chen-Ming Yang, ‘Multidisciplinary design optimization of Mechanisms.’, Dept. of Mech. Eng., National Chung Hsing Unv. Taiwan, 25 Oct.2004.

9. T.Back, D.B.Fogel, T. Michalewicz, ‘Evolutionary Computation 1- Basic Algorithms and Operators’, Taylor and Francis, 2000.
10. A.E.Eiben, J.E.Smith, ‘Introduction to Evolutionary Computing’, Springer-Berlin 2003.
11. R.L. Haupt, S.E. Haupt, ‘Practical Genetic Algorithms’, 2nd Edition, Wiley-2004.
12. J.C.Hoskins, Glenn A. Kramer, ‘Synthesis of Mechanical Linkages using Artificial Neural Networks and Optimization’, IEEE, 1993, 822J-822N.
13. M.H.F. Dado, ‘An automated procedure for dimensional synthesis of planar mechanisms’, J.King Saud Unv., Vol.8, Eng. Sci(1), p.17-41, 1996 .
14. R.C.Blackett, ’Optimal Synthesis of Planar Five Link Mechanisms for the Production of Nonlinear Mechanical Advantage’, MS Thesis, Virginia Polytechnic Institute, 2001.
15. P.S.Shiokolas, V. Chandra, J.Kebrle, D. Wilhite, ’Analysis and Simulation for Education using Matlab via the World Wide Web., II Representative Examples- System Simulation and Planar Mechanism Synthesis and Analysis, 109-121, Wiley Periodicals, 2002.[http:/zodhia.uta.edu/development/
16. J.A Cabrera, A Simon, M. Prado, ‘Optimal Synthesis of Mechanisms with Genetic Algorithms’, Mechanism and Machine theory, 37,2002, 1165-1177
17. R.R.Bulatovic, S.R. Djordjevic, ‘Optimal Synthesis of a Four Bar Linkage by Method of Controlled Deviation’, Theoretical Appl. Mech., Vol.31, No:3-4, pp.264-280, 2004.
18. M.A.Laribi, A.Mlika, L.Romdhane, S.Zeghloul, ‘A Combined Genetic Algorithm-Fuzzy Logic method (GA-FL) in Mechanisms Synthesis’, Mechanism and Machine Theory, 39, 2004, p.717-735.
19. K.G.Cheetancheri, Harry H. Cheng, ‘Computer-Aided Analysis of Mechanisms Using Ch Excel’, Department of Mech. And Aeronautical Engineering, 2005.
20. J.F. Collard, P.Fisette, P. Duysinx, ‘Optimal Synthesis of Mechanisms using time varying dimensions and natural coordinates’, 6th World Congress of Structured and Multidisiplinary Optimization, Rio de Janerio-Brazil, 2005, p.1-10
21. H.H.Cheng, Dung T. Trang,’ Web-Based Interactive Analysis and Animation of Mechanisms’, Transactions of the ASME, Journal of Computing and Information Science in Engineering, Vol.6, 2006, 84-90 [http://www.softintegration/webservices/mechanism/]
22. J.Xie, Y. Chen, ‘Application Back Propagation Neural Network to Synthesis of Whole Cycle Motion Generation Mechanism’, 12th IFToMM World Congress-Besancon-France, June 18-21, 2007.
23. Y.Liu, J.McPhee,’Automated Kinematic Synthesis of Planar Mechanisms with Revolute Joints’, Mechanics Based Design of Structures and Machines, 35, p.405-445, 2007.
24. S.Erkaya, İ.Uzmay, ‘A Neural-Genetic (NN-GA) approach for optimizing mechanisms having joints with clearance’, Multibody System Dynamics, 20, 2008, 69-83.
25. N.N. Zadeh, M. Felezi, A. Jamali, M. Ganji, ‘Pareto optimal Synthesis of four-bar mechanisms for path generation’, Mechanism and Machine Theory, 22, 2009, 180-191.
26. S.K. Archaryya, M. Mandal, ‘Performance of EAs for four-bar linkage synthesis’, Mechanism and Machine Theory, 44, 2009, 1784-1794.
27. A. Kentli, A.K. Kar, E.Taçgın, ‘Genetic Coding Application to Synthesis of Planar Mechanisms’, 5th. Int. Adv. Tech. Symp.(IATS’09), May 13-15, 2009, Karabük-Türkiye.
28. K. Sedlaczek, P.Eberhard, ‘Augmented Lagrangian Particle Swarm Optimization in Mechanism Design’, Journal of System Design and Dynamics, 410-421. [www.itm.uni-stuttgart.de{research/alpso]
29. F.Penunuri, R.P. Escalante, C. Villanueva, D. Pech-Oy, ‘Optimum Synthesis of Mechanism for single and hybrid tasks using differential evolution’, Mechanism and Machine theory, Vol.46, No.10, p. 1335-1349, 2011.
30. H.Erdoğan, ‘Synthesis of Planar Mechanisms using Evolutionary Algorithms’, Gaziantep University, Ms. Thesis, September 2011.