A combined penalty and semi-recursive formulation for closed-loops in MBS

The continuously improved performance of personal computers enables the real-time motion simulation of complex multi-body systems, such as the whole model of an automobile, on a conventional $1,200 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 formulation and one of the most systematic topological formulation. In this way, it is developed a new formulation which 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 analysis of three examples is carried out using the three formulations and the corresponding results are compared: a planar mechanism which goes through a singular position, a car suspension with stiff behaviour, and a 6-dof robot with changing configurations.