Abstract :
[en] This talk will start with a brief overview of the current research activities undertaken at the Multibody & Mechatronic Systems Laboratory with a number of applications in the fields of wind turbines, deployable space structures, robotics and human motion analysis.
Then, the presentation will focus on some recent results related with the modelling of dynamic contact conditions in multibody systems. Typical applications include the modelling of non-ideal joints with backlash and friction, the analysis of mechanical transmission systems and gearboxes, the modelling of grasping tasks or the description of the foot-ground contact in gait analysis.
The proposed formalism relies on the nonsmooth contact dynamics method. Accordingly, the condition of impenetrability of the bodies in contact is expressed as a unilateral constraint, with the consequence that impacts and/or instantaneous changes in the velocities may arise in the dynamic response. Also, the resulting set of equations is solved in the time domain using a time-stepping strategy, which is known its robustness and its ability to deal with a large number of events in an efficient way.
After a review of the time-stepping method originally proposed by Moreau and Jean, a number of improvements are addressed during the talk. Firstly, a splitting method is introduced to isolate the contributions of impacts, which can only be integrated with first-order accuracy, from smooth contributions, which can be integrated using a higher order scheme. Secondly, following the idea of Gear, Gupta and Leimkuhler, the equation of motion is reformulated so that the bilateral and unilateral constraints appear both at position and velocity levels. This strategy leads to an algorithm which exactly satisfies the constraints at both levels, i.e., no penetration is allowed in the numerical response. After time discretization, the equation of motion involves two complementarity conditions and it can be solved at each time step using a monolithic semi-smooth Newton method. The numerical behaviour of the proposed scheme is studied and compared to other approaches for a number of numerical examples. It is shown that the formulation offers a unified and valid approach for the description of contact conditions between rigid bodies as well as between flexible bodies.
