Such schemes are accurate for the free flight smooth motions, but fail to handle frequent transitions in a short time. At this time instant, the event is solved with the help of an impact law.
Eventdriven schemes are based on an accurate event detection and the time step is adapted such that the end of the step coincides with an event. There exist two main groups of numerical integration schemes for nonsmooth systems, namely, event-driven schemes and time-stepping schemes. In multibody dynamics, contact conditions can lead to impacts and/or abrupt changes in the velocities and, as a consequence, the design of a consistent and stable time integration scheme requires great care.
The results obtained show that the existence of clearance joints in the modeling of multibody systems influences their dynamics response. Finally, the classical slider-crank mechanism is considered as a demonstrative application example and numerical results are presented. The resulting contact-impact problem is formulated and solved as a linear complementarity problem, which is embedded in the Moreau's time-stepping method. In this work, the unilateral constraints are described by a set-valued force law of the type of Signorini's condition, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb's law for dry friction. The equations of motion are complemented with constitutive laws for the normal and tangential directions. The dynamics of rigid multibody systems are stated as an equality of measures, which are formulated at the velocity-impulse level. In the following, the most fundamental issues of the nonsmooth dynamics theory are revised. The methodology is based on the nonsmooth dynamics approach, in which the interaction of the elements that constitute a translational clearance joint is modeled with multiple frictional unilateral constraints. The main purpose of this paper is to present and discuss a methodology for a dynamic modeling and analysis of rigid multibody systems with translational clearance joints.
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