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Archive of Mechanical Engineering

The Journal of Committee on Machine Building of Polish Academy of Sciences

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Implementation of A Geometric Constraint Regularization For Multibody System Models

Implementacja Geometrycznej Regularyzacji Więzów w Układach Wieloczłonowych

Andreas Müller
  • University of Michigan - Shanghai Jiao Tong University Joint Institute, 800 Dong Chuan Road, Shanghai, 200240, P.R. China
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Published Online: 2014-08-15 | DOI: https://doi.org/10.2478/meceng-2014-0021


Redundant constraints in MBS models severely deteriorate the computational performance and accuracy of any numerical MBS dynamics simulation method. Classically this problem has been addressed by means of numerical decompositions of the constraint Jacobian within numerical integration steps. Such decompositions are computationally expensive. In this paper an elimination method is discussed that only requires a single numerical decomposition within the model preprocessing step rather than during the time integration. It is based on the determination of motion spaces making use of Lie group concepts. The method is able to reduce the set of loop constraints for a large class of technical systems. In any case it always retains a sufficient number of constraints. It is derived for single kinematic loops.


Nadmiarowe więzy w układach wieloczłonowych (MBS) powaŻnie pogarszajĄ wydajność obliczeniowĄ i dokładność numerycznych metod symulacji systemów MBS. Klasycznym podejściem do rozwiĄzania tego problemu jest numeryczna dekompozycja Jakobianu więzów w kolejnych krokach całkowania cyfrowego. Dekompozycje takie sĄ jednak kosztowne obliczeniowo. W artykule zaprezentowano metodę eliminacji, która wymaga tylko pojedynczej dekompozycji na etapie wstępnego przetwarzania modelu, a nie w trakcie integracji czasowej. Metoda jest oparta na wyznaczaniu przestrzeni ruchu przy wykorzystaniu koncepcji grup Liego. Pozwala ona zredukować zbiór więzów pętli dla szerokiej klasy systemów technicznych, przy czym w kaŻdym przypadku zachowuje ona dostatecznĄ liczbę więzów. Metoda została wyprowadzona i zilustrowana dla pojedynczych pętli kinematycznych.

Key words:: multibody systems; constraints; redundancy; Lie groups; screw systems; numerics; dynamics


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About the article

Published Online: 2014-08-15

Citation Information: Archive of Mechanical Engineering, ISSN (Online) 2300-1895, DOI: https://doi.org/10.2478/meceng-2014-0021. Export Citation

© 2014 Andreas Müller. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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