Standard methods to model multibody systems are aimed at systems with configuration spaces isomorphic to Rn. This limitation leads to singularities and other artifacts in case the configuration space has a different topology, for example in the case of ball joints or a free-floating mechanism. This paper discusses an extension of classical methods to allow for a very general class of joints, including all joints with a Lie group structure. The model equations are derived using the Boltzmann-Hamel equations and have very similar structure and complexity as obtained using classical methods, but they do not suffer from singularities. Furthermore, the equations are explicit differential equations that can be directly implemented in simulation software.