Nonlinear Dynamics

, Volume 73, Issue 1–2, pp 259–273 | Cite as

Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints

  • Onesmus Muvengei
  • John Kihiu
  • Bernard Ikua
Original Paper


In this paper, the behavior of planar rigid-body mechanical systems due to the dynamic interaction of multiple revolute clearance joints is numerically studied. One revolute clearance joint in a multibody mechanical system is characterized by three motions which are: the continuous contact, the free-flight, and the impact motion modes. Therefore, a mechanical system with n-number of revolute clearance joints will be characterized by 3 n motions. A slider-crank mechanism is used as a demonstrative example to study the nine simultaneous motion modes at two revolute clearance joints together with their effects on the dynamic performance of the system. The normal and the frictional forces in the revolute clearance joints are respectively modeled using the Lankarani–Nikravesh contact-force and LuGre friction models. The developed computational algorithm is implemented as a MATLAB code and is found to capture the dynamic behavior of the mechanism due to the motions in the revolute clearance joints. This study has shown that clearance joints in a multibody mechanical system have a strong dynamic interaction. The motion mode in one revolute clearance joint will determine the motion mode in the other clearance joints, and this will consequently affect the dynamic behavior of the system. Therefore, in order to capture accurately the dynamic behavior of a multi-body system, all the joints in it should be modeled as clearance joints.


Contact-impact forces Continuous-contact motion Free-flight motion Impact motion Lankarani–Nikravesh model LuGre friction model Multibody mechanical system Revolute clearance joint 



This work is part of the ongoing Ph.D. research titled, “Dynamic Analysis of Flexible Multi-Body Mechanical Systems with Multiple Imperfect Kinematic Joints.” The authors gratefully acknowledge the financial and logistical support of Jomo Kenyatta University of Agriculture and Technology (JKUAT) and the German Academic Exchange Service (DAAD) in carrying out this study.

The advice of Professor Parviz Nikravesh of the University of Arizona during the development of the MATLAB code for kinematic and dynamic analysis of a general planar multi-body mechanical system is highly appreciated.


  1. 1.
    Flores, P.: Dynamic Analysis of Mechanical Systems with Imperfect Kinematic Joints. Ph.D. Dissertation, University of Minho, Guimarães (2004) Google Scholar
  2. 2.
    Erkaya, S., Uzmay, I.: Experimental investigation of joint clearance effects on the dynamics of a slider-crank mechanism. Multibody Syst. Dyn. 24, 81–102 (2010) zbMATHCrossRefGoogle Scholar
  3. 3.
    Erkaya, S., Uzmay, I.: Investigation on effect of joint clearance on dynamics of four-bar mechanism. Nonlinear Dyn. 58, 179–198 (2009) zbMATHCrossRefGoogle Scholar
  4. 4.
    Megahed, S.M., Haroun, A.F.: Analysis of the dynamic behavioral performance of mechanical systems with multi-clearance joints. J. Comput. Nonlinear Dyn. 7, 1–11 (2011) Google Scholar
  5. 5.
    Flores, P.: A parametric study on the dynamic response of planar multibody systems with multiple clearance joints. Nonlinear Dyn. 4, 633–653 (2010) MathSciNetCrossRefGoogle Scholar
  6. 6.
    Canudas de Wit, C., Olsson, H., Astrom, K.J., Lischinsky, P.: A new model for control of systems with friction. IEEE Trans. Autom. Control 40(3), 419–425 (1995) zbMATHCrossRefGoogle Scholar
  7. 7.
    Muvengei, O., Kihiu, J., Ikua, B.: Dynamic analysis of planar multi-body systems with LuGre friction at differently located revolute clearance joints. Multibody Syst. Dyn. 28(4), 369–393 (2012) MathSciNetCrossRefGoogle Scholar
  8. 8.
    Lankarani, H.M., Nikravesh, P.E.: Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn. 194–207 (1994) Google Scholar
  9. 9.
    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) zbMATHCrossRefGoogle Scholar
  10. 10.
    Flores, P., Ambrosio, J.: On the contact detection for contact-impact analysis in multibody systems. Multibody Syst. Dyn. 24, 103–122 (2010) MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Muvengei, O., Kihiu, J., Ikua, B.: Dynamic analysis of multi-body mechanical systems with imperfect kinematic joints: a literature survey and review. Sustain. Res. Innov. Proc. 3, 61–76 (2011) Google Scholar
  12. 12.
    Flores, P., Ambrosio, J.: Revolute joints with clearance in multibody systems. Comput. Struct. 82, 1359–1369 (2004) CrossRefGoogle Scholar
  13. 13.
    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) zbMATHCrossRefGoogle Scholar
  14. 14.
    Flores, P., Ambrosio, J., Claro, J.C.P., Lankarani, H.M.: Influence of the contat-impact force model on the dynamic response of multi-body systems. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 220, 21–34 (2006) Google Scholar
  15. 15.
    Muvengei, O., Kihiu, J., Ikua, B.: Effects of input speed on the dynamic response of planar multi-body systems with differently located frictionless revolute clearance joints. JSME Int. J., Mech. Mater. Eng. 4, 234–243 (2010) Google Scholar
  16. 16.
    Muvengei, O., Kihiu, J., Ikua, B.: Numerical study of parametric effects on the dynamic response of planar multi-body systems with differently located frictionless revolute clearance joints. Mech. Mach. Theory 53, 30–49 (2012) CrossRefGoogle Scholar
  17. 17.
    Flores, P., Koshy, C., Lankarani, H., Ambrosio, J., Claro, J.: Numerical and experimental investigation on multibody systems with revolute clearance joints. Nonlinear Dyn. 65(4), 383–398 (2011) CrossRefGoogle Scholar
  18. 18.
    Cheriyan, S.K.: Chracterization of Mechanical Systems with Real Joints and Flexible Links. Ph.D. Dissertation, Wichita State University, Wichita (2006) Google Scholar
  19. 19.
    Khemili, I., Romdhane, L.: Dynamic analysis of a flexible slider-crank mechanism with clearance. Eur. J. Mech. A, Solids 27, 882–898 (2008) zbMATHCrossRefGoogle Scholar
  20. 20.
    Ravn, P.: A continuous analysis method for planar multibody systems with joint clearance. Multibody Syst. Dyn. 2, 1–24 (1998) zbMATHCrossRefGoogle Scholar
  21. 21.
    Ravn, P., Shivaswamy, S., Alshaer, B.J., Lankarani, H.M.: Joint clearances with lubricated long bearings in multibody mechanical systems. J. Mech. Des. 122, 484–488 (2000) CrossRefGoogle Scholar
  22. 22.
    Chunmei, J., Yang, Q., Ling, F., Ling, Z.: The nonlinear dynamic behavior of an elastic linkage mechanism with clearances. J. Sound Vib. 249(2), 213–226 (2002) CrossRefGoogle Scholar
  23. 23.
    Mukras, S., Kim, N.H., Mauntler, N.A., Schmitz, T.L., Sawyer, W.G.: Analysis of planar multibody systems with revolute joint wear. Wear 268(5–6), 643–652 (2010) CrossRefGoogle Scholar
  24. 24.
    Glocker, C.: Set-Valued Force Laws: Dynamics of Non Smooth Systems. Lectures Notes in Applied and Computational Mechanics. Springer, Berlin (2001) zbMATHCrossRefGoogle Scholar
  25. 25.
    Ambrosio, J.C.: Impact of rigid and flexible multibody systems: deformation description and contact models. In: Schiehlen, E.W., Valásek, M. (eds.) Virtual Nonlinear Multibody Systems, vol. II, pp. 15–33 (2002) Google Scholar
  26. 26.
    Flores, P., Ambrosio, J., Claro, J.P.: Dynamic analysis for planar multibody mechanical systems with lubricated joints. Multibody Syst. Dyn. 12, 47–74 (2004) zbMATHCrossRefGoogle Scholar
  27. 27.
    Jia, X., Jin, D., Ji, L., Zhang, J.: Investigation on the dynamic performance of the tripod-ball sliding joint with clearance in a crank-slider mechanism. Part 1. Theoretical and experimental results. J. Sound Vib. 252(5), 919–933 (2002) CrossRefGoogle Scholar
  28. 28.
    Bing, S., Ye, J.: Dynamic analysis of the reheat-stop-valve mechanism with revolute clearance joint in consideration of thermal effect. Mech. Mach. Theory 43(12), 1625–1638 (2008) zbMATHCrossRefGoogle Scholar
  29. 29.
    Flores, P.: Modeling and simulation of wear in revolute clearance joints in multibody systems. Mech. Mach. Theory 44(6), 1211–1222 (2009) MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Flores, P., Ambrosio, J., Claro, J.C.P., Lankarani, H.M., Koshy, C.S.: Lubricated revolute joints in rigid multibody systems. Nonlinear Dyn. 56(3), 277–295 (2009) zbMATHCrossRefGoogle Scholar
  31. 31.
    Tian, Q., Zhang, Y., Chen, L., Flores, P.: Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Comput. Struct. 87, 913–929 (2009) CrossRefGoogle Scholar
  32. 32.
    Nikravesh, P.E.: Computer-Aided Analysis of Mechanical Systems. Prentice Hall, Englewood Cliffs (1988) Google Scholar
  33. 33.
    Shabana, A.: A. Computational Dynamics. Wiley, New York (1994) Google Scholar
  34. 34.
    Baumgarte, J.: Stabilization of constraints and integrals of motion in dynamical systems. Comput. Methods Appl. Mech. Eng. 1, 1–16 (1972) MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Kim, J.K., Chung, I.S., Lee, B.H.: Determination of the feedback coefficients for the constraint violation stabilization method. Proc. Inst. Mech. Eng., Part C, J. Mech. Eng. Sci. 204, 233–242 (1990) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringJomo Kenyatta University of Agriculture and TechnologyNairobiKenya

Personalised recommendations