Optimization with Genetic Algorithm (GA): Planar mechanism synthesis

Document Type : Research Note


1 Department of Mechanical Engineering, Faculty of Engineering, Gaziantep University, Gaziantep, Turkey

2 Department of Mechanical Engineering, Faculty of Engineering, _Izmir University of Economics, _Izmir, Turkey


Dimensional synthesis of mechanisms to trace given points is an important issue in mechanism and machine science. Having no exact solution makes this issue an optimization problem. This study offers an optimization approach for the dimensional synthesis of planar mechanisms. Four-bar mechanisms having one degree of freedom (DOF) are chosen as the configurations. The proposed method is implemented by establishing the objective functions with specified constraints and searching for the results by using an optimization algorithm. Genetic Algorithm (GA) in Optimization Toolbox-Matlab® is selected as a solver. Different types of four-bar mechanisms like crank-rocker and double-crank including different target points are performed. Mechanisms are depicted by resulted parameters and a Matlab® script prepared plays their animations. As a result, it is proved that the mechanisms whose dimensional properties are obtained by the GA solver have a good tracing capability for the desired paths. This study has the property of being a design guide. Its application is not limited to four bar mechanism. Planar mechanisms with different configurations can be easily synthesized by using this technique.


1. Blackett, R.C. "Optimal synthesis of planar five link mechanisms for the production of nonlinear mechanical advantage", MSc. Science, Virginia Polytechnic Inst. and State University (2001).
2. Cabrera, J.A., Simon, A., and Prado, M. "Optimal synthesis of mechanisms with genetic algorithms", Mechanism and Machine Theory, 37, pp. 1165-1177 (2002). http://dx.doi.org/10.1016/S0094-114X(02)00051-4.
3. Zahoor, H. and Nia, H.T. "Optimal synthesis of planar and spatial mechanism for path generation using regression deviation", Scientia Iranica, 12, pp. 190- 198 (2005).
4. Geletu, A. "Solving Optimization Problems using MATLAB Optimization Toolbox", (2007). https://www.researchgate.net/publication/255586170. Solving O ptimization Problems using the Matlab Optimization Toolbox - a Tutorial.
5. Nariman-Zadeh, N., Felezi, M., Jamali, A., et al. "Pareto optimal synthesis for four bar mechanisms for path generation", Mech. And Machine Theory, 44, pp. 180-191 (2009). http://dx.doi.org/10.1016/j.mechmachtheor y.2008.02.006.
6. Acharyya, S.K. and Mandal, M. "Performance of EAs for four bar linkage synthesis", Mechanism and Machine Theory, 44, pp. 1784-1794 (2009).DOI: http://dx.doi.org/10.1016/j.mechmachtheory 2009.03.003.
7. Erdogan, H. "Synthesis of Planar Mechanisms using Evolutionary Algorithms", MSc. Thesis, Gaziantep University (2011).
8. Shete, S.S. and Kulkarni, S.A. "Dimensional synthesis of four bar mechanism using genetic algorithm", Int. J. of Engineering Research, 4, pp. 123-126 (2015).
9. Sleesongsom, S. and Bureerat, S. "Optimal synthesis of four bar linkage path generation through evolutionary computation with a novel constraint handling technique", Computational Intelligence and Neuroscience, 22018 (2018). DOI: 10.1155/2018/5462563.
10. Chaphet, P., Santichatsak, S., Na Thalong, T., et al. "High-lift mechanism motion generation synthesis using a metaheuristic", Proceedings, 39, pp. 2-6 (2019).
11. Pavlovic, J., Janosevic, D., and Jovanovic, V. "Optimization of manipulator drive mechanisms in hydraulic excavators on the basis of the tribological criterion", Scientia Iranica, 27(5), pp. 2372-2381 (2020).
12. Sardashti, A, Daniali, H, and Varedi-Koulaei S. "Geometrical similarity error function-innovative adaptive algorithm methodology in path generation synthesis of the four-bar mechanism using metaheuristic algorithms", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 236(3), pp. 1550-1570 (2022). DOI: 10.1177/09544062211015787.
13. Kang, Y.-H., Lin, J.-W., and You, W.-C. "Comparative study on the synthesis of path-generating four-bar linkages using metaheuristic optimization algorithms", Appl. Sci., 12, 7368 (2022).https://doi.org/10.3390/ app12157368.
14. Holland, J.H. "Genetic algorithms", Scientific American, 267(1), pp. 66-72 (1992).
15. Nobakhti, A. "On natural based optimization", Cognitive Computation, 2, pp. 97-119 (2010). DOI: 10.1007/s12559-010-9039-2.
16. Khan, M.Z.R. and Bajpai, A.K. "Genetic algorithm and its application in mechanical engineering", IJERT, 2, pp. 677-683 (2013).
17. Bhoskar, T., Kulkarni, O.K., Kulkarni, N.K., et al. "Genetic algorithm and its applications to mechanical engineering: A review", 2, pp. 2624-2630 (2015). DOI: https://doi.org/10.1016/j.matpr.2015.07.219.
18. Al-Smadi, Y.M., Aburmaileh, Y., Russel, K., et al. "Genetic algorithm for sensitivity analysis of automobile hood four-bar mechanism synthesis using motion generation", Int. J. of Automotive and Mechanical Eng. (IJAME), 19(1), pp. 9362-9378
(2022). DOI: https://doi.org/10.15282/ijame.19.1.2022.01.0720.
19. Sandor, G.N. and Erdman, A.G., Advanced Mechanism Design, Analysis and Synthesis, Prentice-Hall, New Jersey (1984).
20. Soylemez, E., Mechanisms, 4th Edition, METU, Publication 64, ISBN 978-975-429-276-3 (2009).
21. Optimization Toolbox Documentation, https://www.mathworks.com/help/pdf doc/optim/ index.html?s tid=mwa osa a, 2023.
22. Messac, A., Optimization in Practice with MATLAB for Engineering Students and Professionals, Cambridge University Press (2015).