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)


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.


rolling surfaces contact kinematics bivariate B-splines kinetostatic transmission elements 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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