Role of MMS and IFToMM in Multibody Dynamics

  • Javier Cuadrado
  • Jose Escalona
  • Werner Schiehlen
  • Robert Seifried
Chapter
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 1)

Abstract

An important application of multibody dynamics is mechanism theory. Rigid and flexible bodies are widely applied for modeling of planar and spatial machines, for their dynamical analysis with respect to motion and strength, vibration and control, and for their optimization. Interacting machine parts result in a variety of contact problems. Some fundamentals and typical mechanism and machine problems will be presented.

Keywords

Multibody System Ordinary Differential Equation Absolute Nodal Coordinate Formulation Multibody Dynamic Normal Contact Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Schiehlen, W.: Multibody system dynamics: roots and perspectives. Multibody Sys. Dyn. 1, 149–188 (1997)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Shabana, A.A.: Flexible multibody dynamics: review of past and recent developments. Multibody Sys. Dyn. 1, 189–222 (1997)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Uicker, J.J.Jr.: On the dynamic analysis of spatial linkages using 4 by 4 matrices. Ph.D. thesis, Northwestern University, Evanston (1965)Google Scholar
  4. 4.
    Magnus, K. (ed.): Dynamics of Multibody Systems. Springer, Berlin (1978)MATHGoogle Scholar
  5. 5.
    Bianchi, G., Schiehlen, W. (eds.): Dynamics of Multibody Systems. Springer, Berlin (1986)MATHGoogle Scholar
  6. 6.
    Schiehlen, W. (ed.): Multibody Systems Handbook. Springer, Berlin (1990)MATHGoogle Scholar
  7. 7.
    Shabana, A.A.: Dynamics of Multibody Systems. Cambridge University Press, New York (2005)MATHCrossRefGoogle Scholar
  8. 8.
    Geradin, M., Cardona, A.: Flexible Multibody Dynamics. A Finite Element Approach. Wiley, West Sussex (2000)Google Scholar
  9. 9.
    Shabana, A.A.: Computational Continuum Mechanics. Cambridge University Press, New York (2008)MATHCrossRefGoogle Scholar
  10. 10.
    Kim, S.S., Haug, E.J.: Selection of deformation modes for flexible multibody dynamics. Mech. Struct. Mach. 18, 565–586 (1990)CrossRefGoogle Scholar
  11. 11.
    Romero, I.: The interpolation of rotations and its application to finite element models of geometrically exact rods. Comput. Mech. 34, 121–133 (2004)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Lugris, U., Naya, M.A., Perez, J.A., Cuadrado, J.: Implementation and efficiency of two geometric stiffening approaches. Multibody Sys. Dyn. 20, 147–161 (2008)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Escalona, J.L., Hussien, A.H., Shabana, A.A.: Application of the absolute nodal co-ordinate formulation to multibody system dynamics. J. Sound Vib. 214, 833–851 (1998)CrossRefGoogle Scholar
  14. 14.
    Schwab, A.L., Meijaard, J.P.: Comparison of three-dimensional flexible beam elements for dynamic analysis: classical finite element formulation and absolute nodal coordinate formulation. J. Comput. Nonlinear Dyn. 5, 011010-1 to 011010-10 (2010). doi: 10.1115/1.4000320 CrossRefGoogle Scholar
  15. 15.
    Pfeiffer, F., Glocker, C.: Multibody Dynamics with Unilateral Contacts. Wiley, New York (1996)MATHCrossRefGoogle Scholar
  16. 16.
    Glocker, C., Studer, C.: Formulation and preparation for numerical evaluation of linear complementarity systems in dynamics. Multibody Sys. Dyn. 13, 447–463 (2005)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Lankarani, H., Nikravesh, P.: Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn. 5, 193–207 (1994)Google Scholar
  18. 18.
    Seifried, R., Schiehlen, W., Eberhard, P.: The role of the coefficient of restitution on impact problems in multibody dynamics. Proc. Inst. Mech. Eng. [K] J Multibody Dyn 224, 279–306 (2010)Google Scholar
  19. 19.
    Flores, P., Ambrosio, J.: Revolute joints with clearance in multibody systems. Comput. Struct. 82, 1359–1369 (2004)CrossRefGoogle Scholar
  20. 20.
    Garcia de Jalon, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems. Springer, New York (1994)Google Scholar
  21. 21.
    Hernandez, A., Altuzarra, O., Aviles, R., Petuya, V.: Kinematic analysis of mechanisms via a velocity equation based in a geometric matrix. Mech. Mach. Theor. 38, 1413–1429 (2003)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Fumagalli, A., Masarati, P.: Real-time inverse dynamics control of parallel manipulators using general-purpose multibody software. Multibody Sys. Dyn. 22, 47–68 (2009)MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Sancibrian, R., Garcia, P., Viadero, F., Fernandez, A.: A general procedure based on exact gradient determination in dimensional synthesis of planar mechanisms. Mech. Mach. Theor. 41, 212–229 (2006)MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Korkealaakso, P., Mikkola, A., Rouvinen, A.: Multi-body simulation approach for fault diagnosis of a reel. Proc. Inst. Mech. Engi. [K] J. Multibody Dyn. 220, 9–19 (2006)Google Scholar
  25. 25.
    Negrut, D., Ortiz, J.L.: A practical approach for the linearization of the constrained multibody dynamics equations. J. Comput. Nonlinear Dyn. 1, 230–239 (2006)CrossRefGoogle Scholar
  26. 26.
    Popp, K., Schiehlen, W.: Ground Vehicle Dynamics. Springer, Berlin (2010)CrossRefGoogle Scholar
  27. 27.
    Cuadrado, J., Gutierrez, R., Naya, M.A., Gonzalez, M.: Experimental validation of a flexible MBS dynamic formulation through comparison between measured and calculated stresses on a prototype car. Multibody Sys. Dyn. 11, 147–166 (2004)MATHCrossRefGoogle Scholar
  28. 28.
    Schiehlen, W., Seifried, R., Eberhard, P.: Elastoplastic phenomena in multibody impact dynamics. Comput. Meth. Appl. Mech. Eng. 195, 6874–6890 (2006)MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    Kovalev, R., Lysikov, N., Mikheev, G., Pogorelov, D., Simonov, V., Yazykov, V., Zakharov, S., Zharov, I., Goryacheva, I., Soshenkov, S., Torskaya, E.: Freight car models and their computer-aided dynamic analysis. Multibody Sys. Dyn. 22, 399–423 (2009)MATHCrossRefGoogle 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, 277–295 (2009)MATHCrossRefGoogle Scholar
  31. 31.
    Fisette, P., Peterkenne, J.M., Vaneghem, B., Samin, J.C.: A multibody loop constraints approach for modelling cam/follower devices. Nonlinear Dyn. 22, 335–359 (2000)MATHCrossRefGoogle Scholar
  32. 32.
    Ziegler, P., Eberhard, P.: Simulative and experimental investigation of impacts on gear wheels. Comput. Meth. Appl. Mech. Eng. 197, 4653–4662 (2008)MATHCrossRefGoogle Scholar
  33. 33.
    Kerkkanen, K.S., Garcia-Vallejo, D., Mikkola, A.: Modeling of belt-drives using a large deformation finite element formulation. Nonlinear Dyn. 43, 239–256 (2006)CrossRefGoogle Scholar
  34. 34.
    Pedersen, S.L., Hansen, J.M., Ambrosio, J.A.C.: A roller chain drive model including contact with guide-bars. Multibody Sys. Dyn. 12, 285–301 (2004)MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Javier Cuadrado
    • 1
  • Jose Escalona
    • 2
  • Werner Schiehlen
    • 3
  • Robert Seifried
    • 3
  1. 1.University of La CoruñaFerrolSpain
  2. 2.Escuela de Ingenieros, Dept. Ingeniería Mecánica y de los MaterialesUniversity of SevilleSevilleSpain
  3. 3.University of StuttgartStuttgartGermany

Personalised recommendations