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Minimization of Shaking Force and Moment on a Four-Bar Mechanism Using Genetic Algorithm

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Dynamic Balancing of Mechanisms and Synthesizing of Parallel Robots

Abstract

In this study, optimal balancing of a 2D articulated mechanism is investigated to minimize the shaking force and moment fluctuations. Balancing of a four-bar mechanism is formulated as an optimization problem. On the other hand, an objective function based on the subcomponents of shaking force and moment is constituted, and design variables consisting of kinematic and dynamic parameters are defined. Genetic algorithm is used to solve the optimization problem under the appropriate constraints. By using commercial simulation software, optimized values of design variables are also tested to evaluate the effectiveness of the proposed optimization process. This work provides a practical method for reducing the shaking force and moment fluctuations. The results show that both the structure of objective function and particularly the selection of weighting factors have a crucial role to obtain the optimum values of design parameters. By adjusting the value of weighting factor according to the relative sensitivity of the related term, there is a certain decrease at the shaking force and moment fluctuations. Moreover, these arrangements also decrease the initiative of mechanism designer on choosing the values of weighting factors.

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References

  1. Feng, G.: Complete shaking force and shaking moment balancing of 17 types of eight-bar linkages only with revolute pairs. Mech. Mach. Theory 26(2), 197–206 (1991)

    Article  Google Scholar 

  2. Ye, Z., Smith, M.R.: Complete balancing of planar linkages by an equivalence method. Mech. Mach. Theory 29(5), 701–712 (1994)

    Article  Google Scholar 

  3. Li, Z.: Sensitivity and robustness of mechanism balancing. Mech. Mach. Theory 33(7),1045–1054 (1998)

    Article  MATH  Google Scholar 

  4. Chiou, S.T., Bai, G.J., Chang, W.K.: Optimum balancing designs of the drag-link drive of mechanical presses for precision cutting. Int. J. Mach. Tools Manuf. 38(3), 131–141 (1998)

    Article  Google Scholar 

  5. Arakelian, V.H., Smith, M.R.: Complete shaking force and shaking moment balancing of linkages. Mech. Mach. Theory 34, 1141–1153 (1999)

    Article  MATH  Google Scholar 

  6. Tepper, F.R., Lowen, G.G.: General theorems concerning full force balancing of planar linkage by internal mass redistribution. J. Manuf. Sci. Eng. 94, 789–796 (1972)

    Google Scholar 

  7. Esat, I., Bahai, H.: A theory of complete force and moment balancing of planer linkage mechanisms. Mech. Mach. Theory 34, 903–922 (1999)

    Article  MATH  Google Scholar 

  8. Feng, B., Morita, N., Torii, T.: A new optimization method for dynamic design of planar linkage with clearances at joints-optimizing the mass distribution of links to reduce the change of joint forces. J. Mech. Des. 124, 68–73 (2002)

    Article  Google Scholar 

  9. Kochev, I.S.: General theory of complete shaking moment balancing of planar linkages: a critical review. Mech. Mach. Theory 35, 1501–1514 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  10. Guo, G., Morita, N., Torii, T.: Optimum dynamic design of planar linkage using genetic algorithms. JSME Int. J. C 43(2), 372–377 (2000)

    Article  Google Scholar 

  11. Arakelian, V., Dahan, M.: Partial shaking moment balancing of fully force balanced linkages. Mech. Mach. Theory 36, 1241–1252 (2001)

    Article  MATH  Google Scholar 

  12. Arakelian, V.H., Smith, M.R.: Shaking force and shaking moment balancing of mechanisms: a historical review with new examples. J. Mech. Des. 127(2), 334–339 (2005)

    Article  Google Scholar 

  13. Arakelian, V.H.: Shaking moment cancellation of self-balanced slider-crank mechanical systems by means of optimum mass redistribution. Mech. Res. Commun. 33, 846–850 (2006)

    Article  MATH  Google Scholar 

  14. Alici, G., Shirinzadeh, B.: Optimum dynamic balancing of planar parallel manipulators based on sensitivity analysis. Mech. Mach. Theory 41(12), 1520–1532 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  15. Chaudhary, H., Saha, S.K.: Balancing of four-bar linkages using maximum recursive dynamic algorithm. Mech. Mach. Theory 42, 216–232 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Chaudhary, H., Saha, S.K.: Balancing of shaking forces and shaking moments for planar mechanisms using the equimomental systems. Mech. Mach. Theory 43, 310–334 (2008)

    Article  MATH  Google Scholar 

  17. Erkaya, S., Uzmay, İ.: Investigation on effect of joint clearance on dynamics of four-bar mechanism. Nonlinear Dyn. 58, 179–198 (2009)

    Article  MATH  Google Scholar 

  18. Ilia, D., Sinatra, R.: A novel formulation of the dynamic balancing of five-bar linkages with applications to link optimization. Multibody Syst. Dyn. 21, 193–211 (2009)

    Article  MATH  Google Scholar 

  19. Park, J.G., Jeong, W.B., Seo, Y.S., Yoo, W.S.: Optimization of crank angles to reduce excitation forces and moments in engines. J. Mech. Sci. Technol. 21(2), 272–281 (2007)

    Article  Google Scholar 

  20. MATLAB (Symbolic Math Toolbox and Optimization Toolbox). The MathWorks Inc, 3 Apple Hill Drive, Natick, MA 01760-2098

    Google Scholar 

  21. Kunjur, A., Krishnamurty, S.: Genetic algorithms in mechanism synthesis. J. Appl. Mech. Rob. 4, 18–24 (1997)

    Google Scholar 

  22. Yang, B.S., Choi, S.P., Kim, Y.C.: Vibration reduction optimum design of a steam-turbine rotor-bearing system using a hybrid genetic algorithm. Struct. Multidiscip. Optim. 30, 43–53 (2005)

    Article  Google Scholar 

  23. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Boston, MA (1989)

    MATH  Google Scholar 

  24. Chaudhary, H., Saha, S.K.: Dynamics and Balancing of Multibody Systems. Lecture Notes in Applied and Computational Mechanics, vol. 37. Springer, Berlin (2009)

    MATH  Google Scholar 

  25. Erkaya, S., Uzmay, İ.: A neural-genetic (NN-GA) approach for optimising mechanisms having joints with clearance. Multibody Syst. Dyn. 20, 69–83 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  26. MSC.ADAMS 2005 r2: Automatic dynamic analysis of mechanical systems. MSC Software Corporation

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mechatronics Engineering, Engineering Faculty, Erciyes University, 38039, Kayseri, Turkey

    Selçuk Erkaya

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  1. Selçuk Erkaya
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Correspondence to Selçuk Erkaya .

Editor information

Editors and Affiliations

  1. University of Ontario Institute of Technology, Oshawa, ON, Canada

    Dan Zhang

  2. University of Ontario Institute of Technology, Oshawa, ON, Canada

    Bin Wei

Appendix

Appendix

Simulation results of force and moment characteristics for Case I are given in Figs. 13.8 and 13.9.

Fig. 13.8
figure 8

Simulation results for Case I; (a) and (b) Crank–frame joint force, (c) and (d) Follower– frame joint force

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Fig. 13.9
figure 9

Simulation results for Case I; (a) and (b) Shaking force components, (c) Shaking moment, (d) Driving torque

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Simulation result of bearing vibrations for Case I is outlined in Fig. 13.10.

Fig. 13.10
figure 10

Bearing vibrations in vertical direction of original and optimized mechanisms for Case I; (a) Left bearing, (b) Right bearing

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Erkaya, S. (2016). Minimization of Shaking Force and Moment on a Four-Bar Mechanism Using Genetic Algorithm. In: Zhang, D., Wei, B. (eds) Dynamic Balancing of Mechanisms and Synthesizing of Parallel Robots. Springer, Cham. https://doi.org/10.1007/978-3-319-17683-3_13

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  • DOI: https://doi.org/10.1007/978-3-319-17683-3_13

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17682-6

  • Online ISBN: 978-3-319-17683-3

  • eBook Packages: EngineeringEngineering (R0)

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