Advertisement

Minimal coordinate multibody dynamics of rolling surfaces using surface joints

  • Alina Stepken
  • Francisco Geu FloresEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

This paper describes a new method for modeling the dynamics of rolling rigid-bodies in the framework of object-oriented multibody dynamics with minimal coordinates. The method consists in modeling each rigid-body surface as a kinetostatic transmission element mapping the motion of the rigid-body as well as a two-parametric relative motion on its surface to the spatial motion of a corresponding Darboux frame. This allows for contact constraints to be handled as a subset of the closure conditions of a kinematical chain at position level and, hence, to be assembled into a multibody framework without further efforts. Furthermore, the paper shows two examples which use surface-fitting with bivariate B-Splines to define the surface joints, and discusses the advantages of solving the contact equations at position level.

Keywords

rolling surfaces contact kinematics bivariate B-splines kinetostatic transmission elements 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Bicchi and V. Kumar. Robotic grasping and contact: A review. In ICRA, 2000.Google Scholar
  2. 2.
    C. Cai and B. Roth. On the spatial motion of a rigid body with point contact. In Proceedings. 1987 IEEE International Conference on Robotics and Automation, volume 4, pages 686–695, March 1987.Google Scholar
  3. 3.
    M. B. Cline and D. K. Pai. Post-stabilization for rigid body simulation with contact and constraints. In Robotics and Automation, 2003. Proceedings. ICRA’03. IEEE International Conference on, volume 3, pages 3744–3751. IEEE, 2003.Google Scholar
  4. 4.
    P. Dierckx. Curve and Surface Fitting with Splines. Oxford University Press, Inc., New York, NY, USA, 1993.Google Scholar
  5. 5.
    F. Geu Flores. An Object-Oriented Framework for Spatial Motion Planning of Multibody Systems. VDI-Verlag, 2013.Google Scholar
  6. 6.
    F. R. Hogan and J. R. Forbes. Modeling of spherical robots rolling on generic surfaces. Multibody System Dynamics, 35(1):91–109, Sep 2015.Google Scholar
  7. 7.
    A. Jain. Minimal coordinates formulation of contact dynamics. Multibody dynamics, 2013.Google Scholar
  8. 8.
    A. Kecskeméthy and M. Hiller. An object-oriented approach for an effective formulation of multibody dynamics. Computer Methods in Applied Mechanics and Engineering, 115(3):287 – 314, 1994.Google Scholar
  9. 9.
    M. Millard and A. Kecskeméthy. A 3d foot-ground model using disk contacts. In Interdisciplinary Applications of Kinematics, pages 161–169. Springer, 2015.Google Scholar
  10. 10.
    H. K. Moffatt and Y. Shimomura. Classical dynamics: Spinning eggs — a paradox resolved. Nature, (385):416(6879), 2002.Google Scholar
  11. 11.
    D. J. Montana. The kinematics of contact and grasp. The International Journal of Robotics Research, 7(3):17–32, 1988.Google Scholar
  12. 12.
    F. Pfeiffer and C. Glocker. Contacts in multibody systems. Journal of Applied Mathematics and Mechanics, 64(5):773 – 782, 2000.Google Scholar
  13. 13.
    M. Tändl. Dynamic simulation and design of rol ler coaster motion. PhD thesis, Düsseldorf, 2009. Zugl.: Duisburg, Essen, Univ., Diss., 2008.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Chair for Mechanics and Robotics, University of DuisburgEssenGermany

Personalised recommendations