Computational efficiency of multi-body systems dynamic models

For several decades, simulation and analysis of mechanisms have been performed with dedicated computer-aided engineering software that implements general dynamic formulations, known in the literature as multi-body systems (MBS) formulations. The MBS name is related to the structure of the mechanism, which is often considered to be a collection of bodies interconnected by mechanical joints (pairs). Nevertheless, only a few formulations are really based on a true multi-body mechanical model, while many others instantiate mathematically quite different mechanical concepts. This paper aims to identify and discuss the mechanical models that fundament the main multi-body mathematical formulations known in the literature. The main features of each model are outlined, based on a detailed presentation of the structure and equations of motion, together with their link with the kinematic and dynamic formulations. A comparative study related to computational efficiency is then presented for the identified main models, based on a test mechanism. Comparative advantages and disadvantages are discussed at the end, considering the identified mechanical models.