Journal of Mechanical Science and Technology

, Volume 32, Issue 2, pp 559–565 | Cite as

Reducing undesirable vibrations of planar linkage mechanism with joint clearance

  • Zheng Feng BaiEmail author
  • Xin Jiang
  • Fei Li
  • Ji Jun Zhao
  • Yang Zhao


An optimization design method is presented to reduce the undesirable vibrations caused by clearance for planar linkage mechanism. A clearance joint is defined and considered a contact/impact force constraint. Contact and impact force models for the clearance joint are established using a normal contact force model based on Hertz model with energy loss and a tangential friction model based on modified Coulomb model with dynamic friction coefficient, respectively. In view of the clearance joint, dynamic equations and optimization method for a planar four-bar mechanism are then presented as an application example. The optimization aims to minimize the maximum absolute acceleration peaks of the mechanism by determining the link lengths of the planar linkage mechanism. Finally, the optimization design is solved by a generalized reduced gradient algorithm. Results show evident decrease in vibration peaks of the mechanism and obvious reduction in the contact forces in the clearance joint, which contribute to a good performance of planar linkage mechanism systems.


Clearance joint Planar linkage mechanism Dynamic responses Optimization method 


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  1. [1]
    P. Flores, J. Ambrosio, J. C. P. Claro, H. M. Lankarani and C. S. Koshy, A study on dynamics of mechanical systems including joints with clearance and lubrication, Mech. Mach. Theory, 41 (2006) 247–261.CrossRefzbMATHGoogle Scholar
  2. [2]
    P. Flores, Modeling and simulation of wear in revolute clearance joints in multibody systems, Mech. Mach. Theory, 44 (6) (2009) 1211–1222.CrossRefzbMATHGoogle Scholar
  3. [3]
    S. Mukras, N. H. Kim, N. A. Mauntler, T. L. Schmitz and W. G. Sawyer, Analysis of planar multibody systems with revo-lute joint wear, Wear, 268 (2010) 643–652.CrossRefGoogle Scholar
  4. [4]
    X. Wang and G. Liu, Modeling and simulation of revolute joint with clearance in planar multi-body systems, J. Mech Sci. Technol., 29 (10) (2015) 4105–4111.CrossRefGoogle Scholar
  5. [5]
    Z. F. Bai and Y. Zhao, Dynamics modeling and quantitative analysis of multibody systems including revolute clearance joint, Precision Engineering, 36 (2012) 554–567.CrossRefGoogle Scholar
  6. [6]
    J. Li, H. Huang, S. Yan and Y. Yang, Kinematic accuracy and dynamic performance of a simple planar space deployable mechanism with joint clearance considering parameter uncertainty, Acta Astronaut, 136 (2017) 34–45.CrossRefGoogle Scholar
  7. [7]
    E. D. Stoenecu and D. B. Marghitu, Dynamic analysis of a planar rigid-link mechanism with rotating slider joint and clearance, J. Sound Vib., 266 (2003) 394–404.CrossRefGoogle Scholar
  8. [8]
    Z. F. Bai, Y. Q. Liu and Y. Sun, Investigation on dynamic responses of dual-axis positioning mechanism for satellite antenna considering joint clearance, J. Mech Sci. Technol., 29 (2) (2015) 453–460.CrossRefGoogle Scholar
  9. [9]
    I. Khemili and L. Romdhane, Dynamic analysis of a flexible slider-crank mechanism with clearance, Eur. J. Mech. ASolid., 27 (2008) 882–898.CrossRefzbMATHGoogle Scholar
  10. [10]
    Y. Chen, Y. Sun and D. Yang, Investigations on the dynamic characteristics of a planar slider-crank mechanism for a high-speed press system that considers joint clearance, J. Mech Sci. Technol., 31 (1) (2017) 75–485.CrossRefGoogle Scholar
  11. [11]
    S. Erkaya, Investigation of joint clearance effects on welding robot manipulators, Robot. CIM-Int. Manuf., 28 (4) (2012) 449–457.CrossRefGoogle Scholar
  12. [12]
    S. Erkaya and I. Uzmay, Optimization of transmission angle for slider-crank mechanism with joint clearances, Struct Multidisc Optim., 37 (2009) 493–508.CrossRefGoogle Scholar
  13. [13]
    S. Erkaya and I. Uzmay, Determining link parameters using genetic algorithm in mechanisms with joint clearance, Mech. Mach. Theory, 44 (2009) 222–234.CrossRefzbMATHGoogle Scholar
  14. [14]
    S. M. Varedi, H. M. Daniali and M. Darde, Dynamic synthesis of a planar slider–crank mechanism with clearances Optimal dynamic design of a planar slider-crank mechanism with a joint clearance, Nonlinear Dyn., 79 (2015) 1587–1600.CrossRefGoogle Scholar
  15. [15]
    S. M. Varedi, H. M. Daniali, M. Dardel and A. Fathi, Optimal dynamic design of a planar slider-crank mechanism with a joint clearance, Mech. Mach. Theory, 86 (2015) 191–200.CrossRefGoogle Scholar
  16. [16]
    Z. F. Bai and Y. Zhao, A hybrid contact force model of revolute joint with clearance for planar mechanical systems, Int. J. Nonlin. Mech., 48 (2013) 15–36.CrossRefGoogle Scholar
  17. [17]
    C. S. Koshy, P. Flores and H. M. Lankarani, 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 (2013) 325–338.CrossRefGoogle Scholar
  18. [18]
    H. M. Lankarani and P. E. Nikravesh, A contact force model with hysteresis damping for impact analysis of multibody systems, ASME J. Mech. Design, 112 (1990) 369–376.CrossRefGoogle Scholar
  19. [19]
    L. S. Lasdon, R. L. Fox and M. W. Ratner, Nonlinear optimization using the generalized reduced gradient method, RAIRO, 3 (1974) 73–104.MathSciNetzbMATHGoogle Scholar
  20. [20]
    S. S. Rao, Engineering optimization: Theory and practice, John Wiley & Sons, New York (1996).Google Scholar
  21. [21]
    G. A. Gabriele and K. M. Ragsdell, The generalized reduced gradient method: A reliable tool for optimal design, ASME-J. Eng. Industry, 99 (2) (1977) 394–400.CrossRefGoogle Scholar
  22. [22]
    Y. Smeers, Generalized reduced gradient method as an extension of feasible direction methods, J. Optimiz. Theory App., 22 (2) (1977) 209–226.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Zheng Feng Bai
    • 1
    Email author
  • Xin Jiang
    • 1
  • Fei Li
    • 1
  • Ji Jun Zhao
    • 1
  • Yang Zhao
    • 1
  1. 1.Harbin Institute of TechnologyWeihaiChina

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