Skip to main content
SpringerLink
Log in

From Neweul to Neweul-M2: symbolical equations of motion for multibody system analysis and synthesis

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

The state-of-the-art for deriving symbolical equations of motion for multibody systems is reviewed. The fundamentals of formalisms based on Newton–Euler equations are presented and the recent development of a research software called Neweul-M2 is highlighted. The modeling approach with commands and a graphical user interface are discussed as well as system analysis options, control design by export to Matlab/Simulink, and parameter optimization for system synthesis. The alternatives within the program using symbolic and numeric approaches are emphasized. A double pendulum is used to explain the program features and a vehicle benchmark model is presented as an example. Advanced applications include closed kinematic loops and flexible bodies.

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. Bestle, D.: Analyse und Optimierung von Mehrkörpersystemen. Springer, Berlin (1994) [in German]

    Google Scholar 

  2. Burkhardt, M.: Implementierung flexibler Mehrkörpersysteme in MATLAB/SIMULINK auf Basis von Neweul-M2. Studienarbeit STUD-292. Institute of Engineering and Computational Mechanics, University of Stuttgart (2008) [in German]

  3. Burkhardt, M.: Versuchsstand flexibler Roboterarm: Modellierung und Beobachterentwurf. Studienarbeit IST-110. Institute for Systems Theory and Automatic Control, University of Stuttgart (2009) [in German]

  4. Eberhard, P.: Zur Optimierung von Mehrkörpersystemen. Dissertation, VDI Fortschritt-Berichte, Reihe 11, Nr. 227. VDI Verlag, Düsseldorf (1996) [in German]

  5. Fisette, P.: Génération Symbolique des Equations du Mouvement de Systèmes Multicorps et Application dans le Domaine Ferroviaire. PhD Thesis, Université Catholique de Louvain, Louvain-La-Neuve (1994) [in French]

  6. Fleissner, F., Lehnart, A., Eberhard, P.: Dynamic simulation of sloshing fluid and granular cargo in transport vehicles. Veh. Syst. Dyn. 48, 3–16 (2010)

    Article  Google Scholar 

  7. Henninger, C.: SYMBS—eine Matlab-Umgebung zur Simulation von Mehrkörpersystemen. Zwischenbericht ZB-149. Institute of Engineering and Computational Mechanics, University of Stuttgart (2007) [in German]

  8. Kane, T.R., Levinson, D.A.: Dynamics: Theory and Applications. McGraw-Hill, New York (1985)

    Google Scholar 

  9. Kreuzer, E.: Symbolische Berechnung der Bewegungsgleichungen von Mehrkörpersystemen. Dissertation, VDI Fortschritt-Berichte, Reihe 11, Nr. 32. VDI-Verlag, Düsseldorf (1979) [in German]

  10. Kurz, T.: Entwicklung eines Optimierungsmoduls mit Sensitivitätsanalyse für die symbolische Mehrkörpersimulationsumgebung SYMBS. Diplomarbeit DIPL-122. Institute of Engineering and Computational Mechanics, University of Stuttgart (2007) [in German]

  11. Kurz, T., Henninger, C.: Program documentation to Neweul-M2. http://www.itm.uni-stuttgart.de/research/neweul/neweulm2_en.php. Institute of Engineering and Computational Mechanics, University of Stuttgart (2009)

  12. Léger, M., McPhee, J.: Selection of modeling coordinates for forward dynamic multibody simulations. Multibody Syst. Dyn. 18, 277–297 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Legland, D.: Graphics Library geom3d. http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=8002&objectType=file (2005)

  14. Leister, G.: Beschreibung und Simulation von Mehrkörpersystemen mit geschlossenen kinematischen Schleifen. Dissertation, VDI Fortschritt-Berichte, Reihe 11, Nr. 167. VDI-Verlag, Düsseldorf (1993) [in German]

  15. Lennartsson, A.: Efficient multibody dynamics. PhD thesis, Royal Institute of Technology, Stockholm (1999)

  16. Levinson, D.A.: Equations of motion for multi-rigid-body systems via symbolic manipulations. J. Spacecr. Rockets 14, 479–487 (1977)

    Article  Google Scholar 

  17. Levinson, D.A., Kane, T.R.: Autolev—a new approach to multibody dynamics. In: Schiehlen, W. (ed.) Multibody Systems Handbook, pp. 81–102. Springer, Berlin (1990)

    Google Scholar 

  18. Lu, X., A Lie Group Formulation of Kane’s equations for multibody systems. Multibody Syst. Dyn. 20, 29–50 (2008)

    Article  MathSciNet  Google Scholar 

  19. Lutz, M.: Erstellung einer symbolischen Mehrkörpersimulationsumgebung in Matlab mit grafischer Benutzeroberfläche und verschiedenen Schnittstellen. Studienarbeit STUD-263. Institute of Engineering and Computational Mechanics, University of Stuttgart (2007) [in German]

  20. Maes, P., Samin, J.-C., Willems, P.-Y.: Autodyn & Robotran-computer programms. In: Schiehlen, W. (ed.) Multibody Systems Handbook, pp. 225–264. Springer, Berlin (1990)

    Google Scholar 

  21. Maplesim by Maplesoft: http://www.maplesoft.com/products/maplesim/ (2009)

  22. Melzer, F.: Symbolisch-numerische Modellierung elastischer Mehrkörpersysteme mit Anwendung auf rechnerische Lebensdauervorhersagen. Dissertation, VDI Fortschritt-Berichte, Reihe 20, Nr. 139. VDI-Verlag, Düsseldorf (1993) [in German]

  23. Mitiguy, P., Reckdahl, K.: Autolev Tutorial. Online Dynamics Inc., Sunnyvale (2005)

  24. Mupad by Mathworks: http://www.mathworks.com/products/symbolic/ (2009)

  25. Popp, K., Schiehlen, W.: Ground Vehicle Dynamics. Springer, Berlin (2010)

    Book  Google Scholar 

  26. Rill, G.: Vergleich von Integrationsverfahren am Beispiel eines ebenen PKW-Modells. Institutsbericht IB-40, Institute of Engineering and Computational Mechanics, University of Stuttgart (2008) [in German]

  27. Rosenthal, D.: Triangulization of equations of motion for robotic systems. J. Guid. Control Dyn. 11(3), 278–281 (1988)

    Article  MATH  Google Scholar 

  28. Samin, J.-C., Fisette, P.: Symbolic Modeling of Multibody Systems. Kluwer, Norwell (2003)

    MATH  Google Scholar 

  29. Sayers, M.W.: Symbolic computer methods to automatically formulate vehicle simulation codes. PhD Thesis, The University of Michigan (1990)

  30. Sayers, M.W.: Symbolic computer language for multibody systems. J. Guid. Control Dyn. 14(6), 1153–1163 (1991)

    Article  Google Scholar 

  31. Sayers, M.W.: Symbolic vector/dyadic multibody formalism for tree-topology systems. J. Guid. Control Dyn. 14(6), 1240–1250 (1991)

    Article  MATH  Google Scholar 

  32. Schaechter, D.B., Levinson, D.A.: Interactive computerized symbolic dynamics for the dynamicist. J. Astronaut. Sci. 36(4), 365–388 (1988)

    Google Scholar 

  33. Schiehlen, W. (ed.): Multibody Systems Handbook. Springer, Berlin (1990)

    MATH  Google Scholar 

  34. Schiehlen, W., Eberhard, P.: Technische Dynamik. B.G. Teubner, Wiesbaden (2004) [in German]

    MATH  Google Scholar 

  35. Schiehlen, W.: Recent trends in multibody system dynamics. Multibody Syst. Dyn. 18, 3–13 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  36. Schiehlen, W., Kreuzer, E.: Rechnergestütztes Aufstellen der Bewegungsgleichungen Gewöhnlicher Mehrkörpersysteme. Arch. Appl. Mech. 46, 185–194 (1977) [in German]

    MATH  Google Scholar 

  37. Schiehlen, W., Kreuzer, E.: Symbolic computational derivation of equations of motion. In: Magnus, K. (ed.) Dynamics of Multibody Systems, pp. 290–305. Springer, Berlin (1978)

    Google Scholar 

  38. Schirm, W.: Symbolisch-numerische Behandlung von kinematischen Schleifen in Mehrkörpersystemen. VDI Fortschritt-Berichte, Reihe 20, Nr. 20. VDI-Verlag, Düsseldorf (1993) [in German]

  39. Schmoll, K.P.: Modularer Aufbau von Mehrkörpersystemen unter Verwendung der Relativkinematik. Dissertation, VDI Fortschritt-Berichte, Reihe 18, Nr. 57. VDI-Verlag, Düsseldorf (1988) [in German]

  40. Schwertassek, R., Wallrapp, O.: Dynamik flexibler Mehrkörpersysteme. Friedr. Vieweg & Sohn, Braunschweig (1999) [in German]

    Google Scholar 

  41. Shi, P., McPhee, J.: Symbolic programming of a graph-theoretic approach to flexible multibody dynamics. Mech. Struct. Mach. 30(1), 123–154 (2002)

    Article  Google Scholar 

  42. Woernle, C.: Ein systematisches Verfahren zur Aufstellung der geometrischen Schließbedingungen in kinematischen Schleifen mit Anwendung bei der Rückwärtstransformation. VDI Fortschritt-Berichte, Reihe 18, Nr. 59. VDI-Verlag, Düsseldorf (1988) [in German]

Download references

Author information

Authors and Affiliations

  1. Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569, Stuttgart, Germany

    T. Kurz, P. Eberhard, C. Henninger & W. Schiehlen

Authors
  1. T. Kurz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Eberhard
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Henninger
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. W. Schiehlen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Eberhard.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kurz, T., Eberhard, P., Henninger, C. et al. From Neweul to Neweul-M2: symbolical equations of motion for multibody system analysis and synthesis. Multibody Syst Dyn 24, 25–41 (2010). https://doi.org/10.1007/s11044-010-9187-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-010-9187-x

Keywords

Search

Navigation