Examination and comparison of different methods to model closed loop kinematic chains using Lagrangian formulation with cut joint, clearance joint constraint and elastic joint approaches

This work aims at presenting, in a comprehensive manner, several approaches to model and simulate closed loop topologies using the classical Lagrangian formulation. One of great advantages approach is its simplicity easiness obtaining equations motion. However, critical aspect arises when mechanical systems include topologies, since process deriving motion becomes complex task. The key point present study convert nature into open systems, which ultimately simplifies modeling formulation utilized. For this purpose, three different methods are considered, namely those based on cut joint approach, clearance constraint model, elastic used. In sequel process, slider-crank mechanism utilized as demonstrative application example, main results compared with obtained well-established Newton-Euler method for constrained multibody systems. Moreover, example allows comparison characteristics peculiarities described approaches.