Skip to main content
SpringerLink
Log in

A rotationless formulation of multibody dynamics: Modeling of screw joints and incorporation of control constraints

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

In the present work, a new energy-momentum conserving time-stepping scheme for multibody systems comprising screw joints is developed. In particular, it is shown that the underlying rotationless formulation of multibody dynamics along with a specific coordinate augmentation technique makes possible the energy-momentum discretization of the screw pair. In addition to that, control (or servo) constraints are treated within the rotationless framework of multibody dynamics. The control constraints are used to partially prescribe the motion of a multibody system. In particular, control constraints, in conjunction with the coordinate augmentation technique, make possible to solve inverse dynamics problems by applying the present simulation approach.

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. Gonzalez, O., Simo, J.C.: On the stability of symplectic and energy-momentum algorithms for non-linear Hamiltonian systems with symmetry. Comput. Methods Appl. Mech. Eng. 134, 197–222 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ibrahimbegović, A., Mamouri, S., Taylor, R.L., Chen, A.J.: Finite element method in dynamics of flexible multibody systems: Modeling of holonomic constraints and energy conserving integration schemes. Multibody Syst. Dyn. 4(2–3), 195–223 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bottasso, C.L., Trainelli, L.: An attempt at the classification of energy decaying schemes for structural and multibody dynamics. Multibody Syst. Dyn. 12(2), 173–185 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Lens, E., Cardona, A.: An energy preserving/decaying scheme for nonlinearly constrained multibody systems. Multibody Syst. Dyn. 18(3), 435–470 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Betsch, P., Leyendecker, S.: The discrete null space method for the energy consistent integration of constrained mechanical systems. Part II: Multibody dynamics. Int. J. Numer. Methods Eng. 67(4), 499–552 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Betsch, P.: The discrete null space method for the energy consistent integration of constrained mechanical systems. Part I: Holonomic constraints. Comput. Methods Appl. Mech. Eng. 194(50–52), 5159–5190 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Leyendecker, S., Betsch, P., Steinmann, P.: The discrete null space method for the energy consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics. Multibody Syst. Dyn. 19(1–2), 45–72 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Betsch, P., Uhlar, S.: Energy-momentum conserving integration of multibody dynamics. Multibody Syst. Dyn. 17(4), 243–289 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Uhlar, S., Betsch, P.: Conserving integrators for parallel manipulators. In: Ryu, J.-H. (ed.) Parallel Manipulators, pp. 75–108. I-Tech Education and Publishing, Vienna (2008). Chap. 5, www.books.i-techonline.com

    Google Scholar 

  10. García de Jalón, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge. Springer, Berlin (1994)

    Google Scholar 

  11. Géradin, M., Cardona, A.: Flexible Multibody Dynamics: A Finite Element Approach. Wiley, New York (2001)

    Google Scholar 

  12. Bauchau, O.A., Bottasso, C.L.: Contact conditions for cylindrical, prismatic, and screw joints in flexible multibody systems. Multibody Syst. Dyn. 5, 251–278 (2001)

    Article  MATH  Google Scholar 

  13. Bottasso, C.L., Croce, A.: Optimal control of multibody systems using an energy preserving direct transcription method. Multibody Syst. Dyn. 12(1), 17–45 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Blajer, W., Kołodziejczyk, K.: A geometric approach to solving problems of control constraints: Theory and a DAE framework. Multibody Syst. Dyn. 11(4), 343–364 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. Betsch, P., Steinmann, P.: Constrained integration of rigid body dynamics. Comput. Methods Appl. Mech. Eng. 191, 467–488 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  16. García de Jalón, J.: Twenty-five years of natural coordinates. Multibody Syst. Dyn. 18(1), 15–33 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  17. Gonzalez, O.: Mechanical systems subject to holonomic constraints: Differential-algebraic formulations and conservative integration. Physica D 132, 165–174 (1999)

    MATH  MathSciNet  Google Scholar 

  18. Betsch, P., Steinmann, P.: Conservation properties of a time FE method. Part III: Mechanical systems with holonomic constraints. Int. J. Numer. Methods Eng. 53, 2271–2304 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Gonzalez, O.: Time integration and discrete Hamiltonian systems. J. Nonlinear Sci. 6, 449–467 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  20. Greenspan, D.: Conservative numerical methods for \(\ddot{x}=f(x)\) . J. Comput. Phys. 56, 28–41 (1984)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chair of Computational Mechanics, Department of Mechanical Engineering, University of Siegen, Siegen, Germany

    Stefan Uhlar & Peter Betsch

Authors
  1. Stefan Uhlar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Betsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Betsch.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Uhlar, S., Betsch, P. A rotationless formulation of multibody dynamics: Modeling of screw joints and incorporation of control constraints. Multibody Syst Dyn 22, 69–95 (2009). https://doi.org/10.1007/s11044-009-9149-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-009-9149-3

Keywords

Search

Navigation