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.