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Optimization of dynamic quantities of a four-bar mechanism using the Hybrid Cuckoo Search and Firefly Algorithm (H-CS-FA)

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Abstract

This paper presents an optimization technique for dynamic balancing of a four-bar mechanism for the purpose of minimization of joint reactions, shaking forces and shaking moment. Joint reaction forces were determined by using a new method which can be applied in rigid planar closed-loop kinematic chains with revolute joints, and it is based on the use of absolute angles of rotation. The problem of balancing the obtained joint reaction forces was then solved as a multi-objective optimization problem. Kinematic and dynamic parameters of the four-bar linkage were taken as design variables. Three cases with simultaneous minimization of several objective functions were considered. The new hybrid algorithm named Hybrid Cuckoo Search and Firefly Algorithm (H-CS-FA) was used for solving the defined optimization problem in accordance with the given constraints. The appropriate selection of objective functions (three cases) and the application of the proposed algorithm resulted in a significant reduction of the values of joint reactions, shaking forces, shaking moment and driving torque. A concrete numerical example was used to show the efficiency of the new hybrid algorithm. The results obtained by H-CS-FA are compared with those obtained by using basic algorithms in the hybridization process (CS and FA) which proved the superiority of the newly proposed optimization procedure.

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Acknowledgements

Authors wish to acknowledge the support of the Ministry of Education and Science of the Republic of Serbia for support through research projects TR-35038, TR-35006 and TR-33015.

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Authors and Affiliations

  1. Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, Dositejeva 19, 36000, Kraljevo, Serbia

    Marina Bošković, Radovan R. Bulatović & Slaviša Šalinić

  2. School of Mechanical Engineering of Applied Study Trstenik, Radoja Krstića 19, 37240, Trstenik, Serbia

    Goran R. Miodragović

  3. Faculty of Engineering University of Kragujevac, University of Kragujevac, Sestre Janjić 6, 34000, Kragujevac, Serbia

    Gordana M. Bogdanović

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  1. Marina Bošković
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  2. Radovan R. Bulatović
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  3. Slaviša Šalinić
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  4. Goran R. Miodragović
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  5. Gordana M. Bogdanović
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Correspondence to Radovan R. Bulatović.

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Appendix

Appendix

The Cartesian coordinates of mass centers \(C_p \left( {p=1, 2, 3} \right) \) of the mechanisms \(\left( {V_p } \right) \left( {p=1, 2, 3} \right) \) of the mechanism shown in Fig. 3 are:

$$\begin{aligned} x_{C_1 }= & {} s_1 +d_1 \cos \left( {\theta _1 +\alpha _1 } \right) ,\\ y_{C_1 }= & {} s_2 +d_1 \sin \left( {\theta _1 +\alpha _1 } \right) ,\\ x_{C_2 }= & {} s_1 +L_1 \cos \theta _1 +s_3 +d_2 \cos \left( {\theta _2 +\alpha _2 } \right) ,\\ y_{C_2 }= & {} s_2 +L_1 \sin \theta _1 +s_4 +d_2 \sin \left( {\theta _2 +\alpha _2 } \right) ,\\ x_{C_3 }= & {} L_4 +s_5 +d_3 \cos \left( {\theta _3 +\alpha _3 } \right) ,\\ y_{C_3 }= & {} s_6 +d_3 \sin \left( {\theta _3 +\alpha _3 } \right) . \end{aligned}$$

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Bošković, M., Bulatović, R.R., Šalinić, S. et al. Optimization of dynamic quantities of a four-bar mechanism using the Hybrid Cuckoo Search and Firefly Algorithm (H-CS-FA). Arch Appl Mech 88, 2317–2338 (2018). https://doi.org/10.1007/s00419-018-1457-8

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