Advertisement

Mathematical Model and Experimental Validation for a Four Bar Mechanism with a Flexible Coupler Link

  • Daniel Rodríguez Flores
  • Héctor Cervantes CulebroEmail author
  • Carlos-Alberto Cruz-Villar
Conference paper
  • 56 Downloads
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 84)

Abstract

A mathematical model for a four bar mechanism with a flexible coupler link is presented in this paper. Modeling equations are obtained using a constrained Lagrangian Formulation, resulting in a nonlinear integro-differential system of equations with a fourth order Partial Differential Equation (PDE). This system of equations is subject to boundary, initial and consistent conditions in order to obtain the system response and observe the elastic deformation of the flexible link. Measurements of the elastic deformation at the coupler link are presented, and the proposed model is experimentally validated.

Keywords

Flexible link Partial differential equation Four-bar mechanism Timochenko’s beam 

References

  1. 1.
    Dogan, M., Morgul, O.: Nonlinear PDE control of two-link flexible arm with nonuniform cross section. In: American Control Conference Minneapolis, Minnesota, USA, pp. 400–405 (2006)Google Scholar
  2. 2.
    Low, K.H., Vidyasagar, M.: A lagrangian formulation of the dynamic model for flexible manipulator systems. J. Dyn. Syst. Meas. Control 110(2), 175–181 (1988)CrossRefGoogle Scholar
  3. 3.
    Wenhuan, Y.: Mathematical modelling for a class of flexible robot. Appl. Math. Model. 19(9), 537–542 (1995)CrossRefGoogle Scholar
  4. 4.
    Bayo, E.: Timoshenko versus Bernoulli beam theories for the control of flexible robots. In: Proceeding of IASTED International Symposium on Applied Control and Identification, pp. 178–182 (1986)Google Scholar
  5. 5.
    Theodore, R.J., Ghosal, A.: Modeling of flexible-link manipulators with prismatic joints. IEEE Trans. Syst. Man Cybern. B Cybern. 27(2), 296–305 (1997)CrossRefGoogle Scholar
  6. 6.
    Zhu, G., Ge, S.S., Lee, T.H.: Simulation studies of tip tracking control of a single-link flexible robot based on a lumped model. Robotica 17(01), 71–78 (1999)CrossRefGoogle Scholar
  7. 7.
    Megahed, S.M., Hamza, K.T.: Modeling and simulation of planar flexible link manipulators with rigid tip connections to revolute joints. Robotica 22(03), 285–300 (2004)CrossRefGoogle Scholar
  8. 8.
    Martins, J.M., Mohamed, Z., Tokhi, M.O., Da Costa, J.S., Botto, M.A.: Approaches for dynamic modelling of flexible manipulator systems. IEEE Proc. Control Theory Appl. 150(4), 401–411 (2003)CrossRefGoogle Scholar
  9. 9.
    Mohamed, Z., Tokhi, M.O.: Command shaping techniques for vibration control of a flexible robot manipulator. Mechatronics 14(1), 69–90 (2004)CrossRefGoogle Scholar
  10. 10.
    Karkoub, M., Yigit, A.S.: Vibration control of a four-bar mechanism with a flexible coupler link. J. Sound Vib. 222(2), 171–189 (1999)CrossRefGoogle Scholar
  11. 11.
    Yang, K.-H., Park, Y.-S.: Dynamic stability analysis of a flexible four-bar mechanism and its experimental investigation. Mech. Mach. Theory 33(3), 307–320 (1998)CrossRefGoogle Scholar
  12. 12.
    Hać, M.: Dynamics of planar flexible mechanisms by finite element method with truss-type elements. Comput. Struct. 39(1), 135–140 (1991)CrossRefGoogle Scholar
  13. 13.
    Madenci, E., Guven, I.: The finite element method and applications in engineering using ANSYS®. Springer, Boston (2015)CrossRefGoogle Scholar
  14. 14.
    Ülker, H.: Dynamic analysis of flexible mechanisms by finite element method. PhD thesis, İzmir Institute of Technology (2010)Google Scholar
  15. 15.
    Rao, S.S., Fook Fah, Y.: Mechanical Vibrations. Prentice Hall, Indianapolis (2011)Google Scholar
  16. 16.
    Tokhi, M.O., Azad, A.K.: Flexible Robot Manipulators: Modelling, SImulation and Control, vol. 68. IET, London (2008)CrossRefGoogle Scholar
  17. 17.
    Wang, J., Gosselin, C.M., Cheng, L.: Modeling and simulation of robotic systems with closed kinematic chains using the virtual spring approach. Multibody Sys. Dyn. 7(2), 145–170 (2002)CrossRefGoogle Scholar
  18. 18.
    Brasey, V.: A half-explicit runge-kutta method of order 5 for solving constrained mechanical systems. Computing 48(2), 191–201 (1992)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Kumpanya, D., Thaiparnat, S., Puangdownreong, D.: Parameter identification of bldc motor model via metaheuristic optimization techniques. Proc. Manuf. 4, 322–327 (2015)Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Daniel Rodríguez Flores
    • 1
  • Héctor Cervantes Culebro
    • 2
    Email author
  • Carlos-Alberto Cruz-Villar
    • 1
  1. 1.CINVESTAVMexico CityMexico
  2. 2.Tecnológico de MonterreyCiudad de MexicoMexico

Personalised recommendations