Skip to main content
Log in

Dynamic synthesis of a planar slider–crank mechanism with clearances

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In practice, clearances in the joints are inevitable due to tolerances, and defects arising from design and manufacturing. It is noteworthy that in the presence of clearance at a joint, a mechanism gains some additional, uncontrollable degrees of freedom which are the source of error. Moreover, joints undergo wear and backlashes and so cannot be used in precision mechanisms. In this paper, an optimization method is proposed to alleviate the undesirable effects of joint clearances. The main consideration here is to optimize the mass distribution of links of a mechanism to reduce or eliminate the impact forces in the clearance joints. An algorithm based on PSO solves this highly nonlinear optimization problem for a slider–crank mechanism with revolute clearance joints. Finally, an example is included to demonstrate the efficiency of the algorithm. The results clearly reveal that the linear and angular accelerations of the links and the contact forces in the optimal design are very smooth and bounded.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Bai, Z.F., Zhao, Y.: Dynamic behaviour analysis of planar mechanical systems with clearance in revolute joints using a new hybrid contact force model. Int. J. Mech. Sci. 54, 190–205 (2012)

    Article  Google Scholar 

  2. Olyaei, A.A., Ghazavi, M.R.: Stabilizing slider–crank mechanism with clearance joints. Mech. Mach. Theory 53, 17–29 (2012)

    Article  Google Scholar 

  3. 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 

  4. Koshy, C.S., Flores, P., Lankarani, H.M.: Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints: computational and experimental approaches. Nonlinear Dyn. 73(1–2), 325–338 (2013)

    Article  Google Scholar 

  5. Lopes, D.S., Silva, M.T., Ambrósio, J.A., Flores, P.: A mathematical framework for contact detection between quadric and superquadric surfaces. Multibody Syst. Dyn. 24(3), 255–280 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  7. Flores, P., Lankarani, H.M.: Dynamic response of multibody systems with multiple clearance joints. ASME J. Comput. Nonlinear Dyn. 7(3), 031003–031013 (2012)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  9. Innocenti, C.: Kinematic clearance sensitivity analysis of spatial structures with revolute joints. J. Mech. Des. Trans. ASME 124(1), 52–57 (2002)

    Article  Google Scholar 

  10. Sardashti, A., Daniali, H.M., Varedi, S.M.: Optimal free-defect synthesis of four-bar mechanism with joint clearance using PSO algorithm. Meccanica 48, 1681–1693 (2013)

    Article  MATH  Google Scholar 

  11. Dubowsky, S., Freudenstein, F.: Dynamic analysis of mechanical systems with clearances. Part 1: Formulation of dynamic model. J. Eng. Ind. 93(1), 305–309 (1971)

    Article  Google Scholar 

  12. Dubowsky, S., Freudenstein, F.: Dynamic analysis of mechanical systems with clearances. Part 2: Dynamic response. J. Eng. Ind. 93(1), 310–316 (1971)

    Article  Google Scholar 

  13. Earles, S.W.E., Wu, C.L.S.: Motion analysis of a rigid link mechanism with clearance at a bearing using Lagrangian mechanics and digital computation. Mechanisms 83–89 (1973)

  14. Grant, S.J., Fawcett, J.N.: Effects of clearance at the coupler-rocker bearing of a 4-bar linkage. Mech. Mach. Theory 14, 99–110 (1979)

    Article  Google Scholar 

  15. Bengisu, M.T., Hidayetoglu, T., Akay, A.: A theoretical and experimental investigation of contact loss in the clearances of a four-bar mechanism. J. Mech. Transm. Autom. Des. 108, 237–244 (1986)

    Article  Google Scholar 

  16. 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 

  17. Flores, P., Ambrosio, J.: Revolute joints with clearance in multibody systems. J. Comput. Struct. 82, 1359–1369 (2004)

    Article  Google Scholar 

  18. Flores, P., Ambrosio, J., Claro, J.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 

  19. Flores, P., Lankarani, H.M.: Spatial rigid-multi-body systems with lubricated spherical clearance joints: modeling and simulation. Nonlinear Dyn. 60(1–2), 99–114 (2010)

    Article  MATH  Google Scholar 

  20. 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(3), 357–375 (2011)

    Article  MATH  Google Scholar 

  21. Flores, P., Koshy, C.S., Lankarani, H.M., Ambrósio, J., Claro, J.C.P.: Numerical and experimental investigation on multibody systems with revolute clearance joints. Nonlinear Dyn. 65(4), 383–398 (2011)

    Article  Google Scholar 

  22. Flores, P., Lankarani, H.M., Ambrósio, J., Claro, J.C.P.: Modelling lubricated revolute joints in multibody mechanical systems. Proc. Inst. Mech. Eng. K J. Multi-body Dyn. 218(4), 183–190 (2004)

    Google Scholar 

  23. Schwab, A.L., Meijaard, J.P., Meijers, P.: A comparison of revolute joint clearance models in the dynamic analysis of rigid and elastic mechanical systems. Mech. Mach. Theory 37, 895–913 (2002)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  25. Zhu, J., Ting, K.L.: Uncertainty analysis of planar and spatial robots with joint clearances. Mech. Mach. Theory 35, 1239–1256 (2000)

    Article  Google Scholar 

  26. Feng, B., Morita, N., Torii, T.: A new optimization method for dynamic design of planar mechanism with clearances at joints. ASME 124, 68–73 (2002)

    Article  Google Scholar 

  27. Zhang, Y., Huang, X.: Robust tolerance design for function generation mechanism with joint clearances. Mech. Mach. Theory 45, 1286–1297 (2010)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  30. Erkaya, S.: Trajectory optimization of a walking mechanism having revolute joints with clearance using ANFIS approach. Nonlinear Dyn. 71, 75–91 (2013)

  31. Ambrósio, J.: Impact of rigid and flexible multibody systems: deformation description and contact models. In: Schiehlen, W., Valásek, M. (eds.) Virtual Non-linear Multi-body Systems, vol. 2, pp. 15–33. NATO Advanced Study Institute, Prague (2002)

  32. Rao, S.S.: Engineering Optimization Theory and Practice, 4th edn. Wiley, New Jersey (2009)

    Google Scholar 

  33. Tian, Qiang, Zhang, Yunqing, Chen, Liping, Flores, Paulo: Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Comput. Struct. 87, 913–929 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to H. M. Daniali.

Appendix

Appendix

Here, the model of the connecting rod is given in Fig. 12. The inertial properties of this model is used in our algorithm which leads to the optimal design.

Fig. 12
figure 12

The model of the connecting rod

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Varedi, S.M., Daniali, H.M. & Dardel, M. Dynamic synthesis of a planar slider–crank mechanism with clearances. Nonlinear Dyn 79, 1587–1600 (2015). https://doi.org/10.1007/s11071-014-1762-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1762-x

Keywords

Navigation