Mechanical systems are typically described through multi-body models with redundant coordinates, related by imposed constraints, where the dynamics is expressed with Differential Algebraic Equations. Alternatively, for rigid models, it may be preferable to employ minimal coordinates that do not require additional constraints, thus leading to Ordinary Differential Equations. However, to reduce a general multibody model to minimal coordinates and perform the simulation in the reduced space, the mapping between the minimal coordinates and the full coordinates is required. In this work, it is proposed to approximate such mapping using a neural network. In order to avoid overfitting and guarantee a continuous description of the solution manifold, the multibody dynamics information are included in the neural network training. The particular case where periodic minimal coordinates are required is treated and validated. In general, the methodology can be used when the mapping is unknown such as for spatial mechanisms with closed loops.