Skip to main content
SpringerLink
Log in

Modeling and simulation of closed loop multibody systems with bodies-joints composite modules

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

Modular approaches are effective in improving the modeling efficiency in multibody system dynamics. A modular method, called bodies-joints composite simulation (BJCS) is presented in this paper. Two types of bodies-joints composite modules, i.e., f modules and 0 modules, are defined according to topology design rules of closed loop mechanisms. By this module partitioning, the differential-algebraic equations of motion of the system can be separated into purely algebraic and differential equations by structure decomposition. The stability criterion for the simulation is derived and a closed-form formulation to solve the algebraic loop problem is proposed. Simulation results of the forward dynamics of a 5R mechanism and a 6-UPS platform are presented to show the feasibility of the method. The CPU times of these two case studies are provided and compared with the generalized coordinate partitioning of Wehage and Haug and the modular simulation method of Kübler and Schiehlen, which indicate that the closed-form algebraic loop solver is more efficient than the numerical ones.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kübler, R., Schiehlen, W.: Modular simulation in multibody system dynamics. Multibody Syst. Dyn. 4, 107–127 (2000)

    Article  MATH  Google Scholar 

  2. Eberhard, P., Schiehlen, W.: Hierarchical modeling in multibody dynamics. Arch. Appl. Mech. 68, 237–246 (1998)

    Article  MATH  Google Scholar 

  3. Bremer, H.: Subsystem computation of large mechanical systems. In: Garcia-Lomas, J., Bautista, E., Navarro, A. (eds.) Proceedings of the 7th World Congress on Theory of Machines and Mechanisms, vol. 1, pp. 413–416 (1987)

  4. Schiehlen, W.: Recent developments in multibody dynamics. J. Mech. Sci. Technol. 19(1), 227–236 (2005)

    Article  MathSciNet  Google Scholar 

  5. Schmitke, C., McPhee, J.: Forming equivalent subsystem components to facilitate the modelling of mechatronic multibody systems. Multibody Syst. Dyn. 14, 81–109 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Schmitke, C., McPhee, J.: Effective use of subsystem models in multibody and mechatronic system dynamics. International J. Multiscale Comput. Eng. 1(2), 139–159 (2003)

    Article  Google Scholar 

  7. Diaz-Calderon, A., Paredis, C., Khosla, P.: Automatic generation of system-level dynamic equations for mechatronic systems. J. Comput.-Aided Des. 32, 339–354 (2000)

    Article  Google Scholar 

  8. Kecskemethy, A., Hiller, M.: An object-oriented approach for an effective formulation of multibody dynamics. Comput. Meth. Appl. Mech. Eng. 115, 287–314 (1994)

    Article  Google Scholar 

  9. Bonaventura, C.S., Jablokow, K.W.: A modular approach to the dynamics of complex multirobot systems. IEEE Trans. Robot. 21(1), 26–37 (2005)

    Article  Google Scholar 

  10. Kim, S.S.: A subsystem synthesis method for efficient vehicle multibody dynamics. Multibody Syst. Dyn. 7, 189–207 (2002)

    Article  MATH  Google Scholar 

  11. Romano, R.: Real-time multibody vehicle dynamics using a modular modeling methodology. SAE Technical Paper Series 2003-01-1286, Society of Automotive Engineers (2003)

  12. Suh, C.H., Radcliffe, C.W.: Kinematics and Mechanisms Design. Wiley, New York (1978)

    Google Scholar 

  13. Schiehlen, W.: Multibody system dynamics: roots and perspectives. Multibody Syst. Dyn. 1, 149–188 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  14. Wang, H., Lin, Z.Q., Lai, X.M.: Composite modeling method in dynamics of planar mechanical system. Sci. China Ser. E 51(5), 576–590 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Wehage, R.A., Haug, E.J.: Generalized coordinates partitioning for dimension reduction in analysis of constrained dynamic system. J. Mech. Des. 104(1), 247–255 (1982)

    Article  Google Scholar 

  16. Ji, Z.M.: Study of the effect of leg inertia in Stewart platforms. In: Proceedings of IEEE Intrenational Conference on Robotic and Automation, pp. 121–126 (1993)

  17. Dasgupta, B.: Closed-form dynamic equations of the general Stewart platform through the Newton–Euler approach. Mech. Mach. Theory 33(7), 993–1012 (1998)

    Article  MathSciNet  Google Scholar 

  18. Wittenburg, J.: Dynamics of Systems of Rigid Bodies. Teubner, Stuttgart (1977)

    MATH  Google Scholar 

  19. Yang, T.L., Yao, F.H.: The topological characteristics and automatic generation of structural analysis and synthesis of planar mechanism, Part 1: Theory, Part 2: Application. Proc. ASME Mech. Conf. 15(1), 179–190 (1988)

    Google Scholar 

  20. Tsai, L.W.: Robot Analysis—The Mechanics of Serial and Parallel Manipulators. Wiley, New York (1999)

    Google Scholar 

  21. Cellier, F.E., Kofman, E.: Continuous System Simulation. Springer, Berlin (2006)

    MATH  Google Scholar 

  22. Kincaid, D., Cheney, W.: Numerical Analysis: Mathematics of Scientific Computing. 3rd ed. Wadsworth Group, Hartford (2002)

    Google Scholar 

  23. Bathe, K.J., Wilson, E.L.: Numerical Methods in Finite Elements Analysis. Prentice-Hall, New York (1976)

    Google Scholar 

  24. Wang, H., Chen, G.: Forward dynamics analysis of 6-PUS platform based on composite simulation method, In: Proceedings of the 8th International Conference on Frontiers of Design and Manufacturing, September, pp. 23–26, Tianjin, P.R. China (2008)

Download references

Author information

Authors and Affiliations

  1. Institute of Automobile Engineering, Shanghai Jiao Tong University, 200240, Shanghai, P.R. China

    Hao Wang

  2. Institute of Engineering and Computational Mechanics, University of Stuttgart, 70569, Stuttgart, Germany

    Peter Eberhard

  3. State Key Laboratory of Mechanical Systems and Vibration, Shanghai Jiao Tong University, 200240, Shanghai, P.R. China

    Zhongqin Lin

Authors
  1. Hao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Eberhard
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhongqin Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Eberhard.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, H., Eberhard, P. & Lin, Z. Modeling and simulation of closed loop multibody systems with bodies-joints composite modules. Multibody Syst Dyn 24, 389–411 (2010). https://doi.org/10.1007/s11044-010-9208-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-010-9208-9

Keywords

Search

Navigation