Robots are controlled mechanisms, and their analysis and control requires adequately accurate but at the same time efficient models. While in the past, the computational efficacy of the kinematic and dynamic models were addressed, there is a recent interest in efficient and modular modeling procedures and model parameterizations. The representation of spatial kinematic and dynamical entities largely dictates the computational effort of a mathematical model. 

The last decades have seen two parallel developments, namely the increasing use of parallel kinematic machines (PKM) and the increasing use of Lie group methods for dynamics modeling. The latter gives rise to coordinate invariant formulations that are computationally efficient and further allow for a flexible model description, which does not rely on the Denavit-Hartenberg convention, for instance. 

In this presentation a systematic approach to the modeling of PKM using Lie group methods is presented. The modularity of this approach is discussed and it is shown how this leads to geometric modeling concepts that allow for a simple and intuitive modeling. A salient feature is that it admits model description in terms of readily available data without compromising computational efficiency.