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Trajectory optimization of a walking mechanism having revolute joints with clearance using ANFIS approach

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Abstract

Clearance as a real joint characteristic leads to deviation from desired trajectory in articulated mechanisms. This phenomenon makes the kinematic and dynamic performances of the mechanism worse. In this study, kinematic analysis of a Jansen’s mechanism used in a walking machine is performed. The model mechanism having two revolute joints with clearance is investigated for the trajectory analysis of the output link. It is clear that the mechanism’s trajectory is very sensitive to the clearance joint characteristics even if the clearance size is small. The adaptive network-based fuzzy inference system (ANFIS) is used to model the characteristics of joints with clearance. By using the suitable design variables and constraints, minimization of the trajectory errors arising from clearance is considered as an optimization problem. Optimization techniques are used to solve this problem for adjusting the optimum values of design variables. The obtained link dimensions show the success of the proposed modeling and optimization approach.

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References

  1. Laribi, M.A., Mlika, A., Romdhane, L., Zeghloul, S.: A combined genetic algorithm-fuzzy logic method (GA-FL) in mechanisms synthesis. Mech. Mach. Theory 39, 717–735 (2004)

    Article  MATH  Google Scholar 

  2. Zhou, H., Cheung, E.H.M.: Optimal synthesis of crank-rocker linkages for path generation using the orientation structural error of the fixed link. Mech. Mach. Theory 36, 973–982 (2001)

    Article  MATH  Google Scholar 

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

    Google Scholar 

  4. Smaili, A., Diab, N.: Optimum synthesis of hybrid-task mechanism using ant gradient search method. Mech. Mach. Theory 42, 115–130 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Shi, Z., Yang, X., Yang, W., Cheng, Q.: Robust synthesis of path generating linkages. Mech. Mach. Theory 40, 45–54 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cabrera, J.A., Simon, A., Prado, M.: Optimal synthesis of mechanisms with genetic algorithms. Mech. Mach. Theory 37, 1165–1177 (2002)

    Article  MATH  Google Scholar 

  7. Ting, K.W., Zhu, J., Watkins, D.: The effects of joint clearance on position and orientation deviation of linkages and manipulators. Mech. Mach. Theory 35, 391–401 (2000)

    Article  MATH  Google Scholar 

  8. Tsai, M.J., Lai, T.H.: Kinematic sensitivity analysis of linkage with joint clearance based on transmission quality. Mech. Mach. Theory 39, 1189–1206 (2004)

    Article  MATH  Google Scholar 

  9. Choi, J.H., Lee, S.J., Choi, D.H.: Tolerance optimization for mechanisms with lubricated joints. Multibody Syst. Dyn. 2, 145–168 (1998)

    Article  MATH  Google Scholar 

  10. Flores, P., Ambrosio, J., Claro, H.C.P., Lankarani, H.M., Koshy, C.S.: A study on dynamics of mechanical systems including joints with clearance and lubrication. Mech. Mach. Theory 41, 247–261 (2006)

    Article  MATH  Google Scholar 

  11. Flores, P.: Modeling and simulation of wear in revolute clearance joints in multibody systems. Mech. Mach. Theory 44, 1211–1222 (2009)

    Article  MATH  Google Scholar 

  12. Flores, P., Ambrosio, J., Claro, J.C.P., Lankarani, H.M.: Influence of the contact–impact force model on the dynamic response of multi-body systems. Proc. Inst. Mech. Eng. Part K. J. Multib. Dyn. 220, 21–34 (2006)

    Google Scholar 

  13. Tian, Q., Liu, C., Machado, M., Flores, P.: A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems. Nonlinear Dyn. 64, 25–47 (2011)

    Article  Google Scholar 

  14. Flores, P., Koshy, C.S., Lankarani, N.M., Ambrosio, J., Claro, J.C.P.: Numerical and experimental investigation on multibody systems with revolute clearance joints. Nonlinear Dyn. 65, 383–398 (2011)

    Article  Google Scholar 

  15. Flores, P.: A parametric study on the dynamic response of planar multibody systems with multiple clearance joints. Nonlinear Dyn. 61, 633–653 (2010)

    Article  MATH  Google Scholar 

  16. Flores, P., Ambrósio, J.: On the contact detection for contact-impact analysis in multibody systems. Multibody Syst. Dyn. 24, 103–122 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Erkaya, S., Uzmay, İ.: Determining link parameters using genetic algorithm in mechanisms with joint clearance. Mech. Mach. Theory 44, 222–234 (2009)

    Article  MATH  Google Scholar 

  18. Erkaya, S., Uzmay, İ.: Optimization of transmission angle for slider-crank mechanism with joint clearances. Struct. Multidiscip. Optim. 37, 493–508 (2009)

    Article  Google Scholar 

  19. 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 

  20. 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  MathSciNet  MATH  Google Scholar 

  21. Erkaya, S., Uzmay, İ.: Experimental investigation of joint clearance effects on the dynamics of a slider-crank mechanism. Multibody Syst. Dyn. 24, 81–102 (2010)

    Article  MATH  Google Scholar 

  22. Erkaya, S., Uzmay, İ.: Effects of balancing and link flexibility on dynamics of a planar mechanism having joint clearance. Sci. Iranica, Trans. B Mech. Eng. 19(3), 483–490 (2012)

    Google Scholar 

  23. Erkaya, S.: Investigation of joint clearance effects on welding robot manipulators. Robot. Comput.-Integr. Manuf. 28, 449–457 (2012)

    Article  Google Scholar 

  24. Khemili, I., Romdhane, L.: Dynamic analysis of a flexible slider–crank mechanism with clearance. Eur. J. Mech. A, Solids 27(5), 882–898 (2008)

    Article  MATH  Google Scholar 

  25. Bauchau, O.A., Rodrigez, J.: Modelling of joints with clearance in flexible multibody systems. Int. J. Solids Struct. 39, 41–63 (2002)

    Article  MATH  Google Scholar 

  26. Flores, P., Ambrosioi, J., Claro, J.P.: Dynamic analysis for planar multibody mechanical systems with lubricated joints. Multibody Syst. Dyn. 12, 47–74 (2004)

    Article  MATH  Google Scholar 

  27. Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. J. Mech. Des. 112, 369–376 (1990)

    Article  Google Scholar 

  28. Lankarani, H.M., Nikravesh, P.E.: Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn. 5, 193–207 (1994)

    Google Scholar 

  29. Flores, P., Machado, M., Silva, M.T., Martins, J.M.: On the continuous contact force models for soft materials in multibody dynamics. Multibody Syst. Dyn. 25, 357–375 (2011)

    Article  MATH  Google Scholar 

  30. Machado, M., Moreira, P., Flores, P., Lankarani, H.: Compliant contact force models in multibody dynamics: evolution of the hertz contact theory. Mech. Mach. Theory 53, 99–121 (2012)

    Article  Google Scholar 

  31. Erkaya, S.: Prediction of vibration characteristics of a planar mechanism having imperfect joints using neural network. J. Mech. Sci. Technol. 26(5), 1419–1430 (2012)

    Article  Google Scholar 

  32. Jansen, T., Jansen, T.: The Great Pretender, Netherlands: 010 Uitgeverij (2007)

  33. Jang, J.: ANFIS adaptive-network-based fuzzy inference systems. IEEE Trans. Syst. Man Cybern. 23(3), 665–685 (1993)

    Article  Google Scholar 

  34. Geethanjali, M., Slochanal, S.M.R.: A combined adaptive network and fuzzy inference system (ANFIS) approach for overcurrent relay system. Neurocomputing 71, 895–903 (2008)

    Article  Google Scholar 

  35. Rao, S.S.: Engineering Optimization-Theory and Practice, 3rd edn. Wiley, New York (1996)

    Google Scholar 

  36. MATLAB (ver 7.0). The MathWorks Inc, 3 Apple Hill Drive, Natick, MA 01760-2098

  37. ANSY, Y14.5M-1994, Dimensional and Tolerancing, ASME, New York (1994)

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Authors and Affiliations

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

    Selçuk Erkaya

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  1. Selçuk Erkaya
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Correspondence to Selçuk Erkaya.

Appendix

Appendix

K 1, K 2, and K 3 used in Eq. (15) are defined as

K 4, K 5, and K 6 in Eq. (17) are also given as

By using the system parameters, K 7, K 8, and K 9 in Eq. (19) are defined as

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Erkaya, S. Trajectory optimization of a walking mechanism having revolute joints with clearance using ANFIS approach. Nonlinear Dyn 71, 75–91 (2013). https://doi.org/10.1007/s11071-012-0642-5

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  • DOI: https://doi.org/10.1007/s11071-012-0642-5

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