In the present work, an introduction to the contact phenomena in multibody systems is made. The different existing approaches are described, together with their most distinctive features. Then, the term of coefficient of restitution is emphasized as a tool to characterize impact events and the algorithm for calculating the relative indentation between two convex-shaped bodies is developed. Subsequently, the main penalty contact models developed in the last decades are presented and developed, analysing their advantages and drawbacks, as well as their respective applications. Furthermore, some models with specific peculiarities that could be useful to the reader are included. The aim of this work is to provide a resource to the novice researcher in the field to facilitate the choice of the appropriate contact model for their work.

This work presents and discusses a general approach for the dynamic modeling and analysis of a passive biped walking robot, with a particular focus on the feet-ground contact interaction. The main purpose of this investigation is to address the supporting foot slippage and viscoelastic dissipative contact forces of the biped robot-walking model and to develop its dynamics equations for simple and double support phases. For this investigation, special attention has been given to the detection of the contact/impact between the legs of the biped and the ground. The results have been obtained with multibody system dynamics applying forward dynamics. This study aims at examining and comparing several force models dealing with different approaches in the context of multibody system dynamics. The normal contact forces developed during the dynamic walking of the robot are evaluated using several models: Hertz, Kelvin-Voight, Hunt and Crossley, Lankarani and Nikravesh, and Flores. Thanks to this comparison, it was shown that the normal force that works best for this model is the dissipative Nonlinear Flores Contact Force Model (hysteresis damping parameter - energy dissipation). Likewise, the friction contact/impact problem is solved using the Bengisu equations. The numerical results reveal that the stable periodic solutions are robust. Integrators and resolution methods are also purchased, in order to obtain the most efficient ones for this model.

The hunting phenomenon is an intrinsic swaying motion appearing in railway vehicles due to the vehicle’s forward speed and the wheel–rail contact forces. Hunting motion consists of wheelset and other vehicle’s components oscillations that arise above a certain vehicle’s speed known as critical or hunting speed. These oscillations are of unstable nature and represent a safety hazard as they could lead to the vehicle’s derailment. This article analyses the stability of a bogie nonlinear model for a Spanish high-speed train when this is travelling at speeds near the hunting speed. The vehicle’s stability is studied by means of root loci methods, and the value of the critical speed is found. In addition to this, the behaviour of the vehicle is studied in both stable and unstable regions and the existence of limit cycles is discussed in this work. Finally, a sensitivity analysis of the axle load and suspension parameters is performed. The results show that the axle load, the vertical stiffness of the primary suspension and the lateral damping of the secondary suspension have a significant influence on the value of the critical speed.