[en] This paper presents a reduction method to build closed-form dynamic equations for rigid multibody systems with a minimal kinematic description. Relying on an initial parameterization with absolute displacements and rotations, the method is able to tackle complex topologies with closed-loops in a systematic way and its extension to flexible multibody systems will be investigated in the future. Thus, it would be of great use in the framework of model-based control of mechanisms. The method is based on an interpolation strategy. The initial model is built and reduced for a number of selected points in the configuration space. Then, a piecewise polynomial model is adjusted to match the collected data. After the presentation of the reduction procedure and of the interpolation strategy, two applications of the reduction method are considered: a four-bar mechanism and a parallel kinematic machine-tool called "Orthoglide".