A combined penalty and recursive real-time formulation for multibody dynamics

The continuously improved performance of personal computers enables the real-time motion simulation of complex multibody systems, such as the whole model of an automobile, on a conventional PC, provided the. adequate formulation is applied. There exist two big families of dynamic formulations, depending on the type of coordinates they use to model the system: global and topological. The former leads to a simple and systematic programming while, the latter is very efficient. In this work, a hybrid formulation is presented, obtained by combination of one of the most efficient global formulations and one of the most systematic topological formulations. It shows, at the same time, easiness of implementation and a high level of efficiency. In order to verify the advantages that the new formulation has over its predecessors, the following four examples are solved using the three formulations and the corresponding results are compared: a planar mechanism which goes through a singular position, a car suspension with stiff behavior a 6-dof robot with changing configurations, and the full model of a car vehicle. Furthermore, the last example is also analyzed using a commercial tool, so as to provide the readers with a well-known reference for comparison.