A benchmark problem with singularities for multibody system dynamics formulations with constraints

When performing the numerical integration of multibody systems (MBS) dynamics, it is possible to choose from a wide variety of methods and implementations. Selecting the most appropriate option for a particular application is not a straightforward task; as a consequence, several benchmark examples have been formulated by the MBS research community with the intent to assess the accuracy and performance of different solution methods when applied to certain kinds of mechanical problems. This paper introduces a variation of the slider-crank mechanism, already employed as a benchmark problem in the MBS literature, intended to evaluate the performance of formulations that feature kinematic constraints. Three cases, featuring singular configurations and external actions, were defined. The example is used to illustrate some necessary elements in the definition of a benchmark problem and in the process of comparing different solution methods, as well as difficulties that can arise during this task. The use of the proposed example was demonstrated in the evaluation of the behaviour of different solution methods, which employed both fixed- and variable-step integration formulas.