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 the great advantages of the Lagrangian approach is its simplicity and easiness of obtaining the equations of motion. However, a critical aspect arises when the mechanical systems include closed loop topologies, since the process of deriving the equations of motion be-comes a complex task. The key point of the present study is to convert the closed loop nature into open systems, which ultimately simplifies the modeling process when the La-grangian formulation is utilized. For this purpose, three different methods are considered, namely those based on the cut joint approach, the clearance joint constraint model, and the elastic joint formulation are used. In the sequel of this process, a slider-crank mech-anism is utilized as a demonstrative application example, and the main results are com-pared with those obtained with the well-established Newton-Euler method for constrained multibody systems. Moreover, this example allows the comparison of the main character-istics and peculiarities of the described approaches. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This study presents several approaches to model and simulate closed loop topologies using the Lagrangian formulation, focusing on converting closed loop nature into open systems to simplify modeling. The methods considered include the cut joint approach, the clearance joint constraint model, and the elastic joint formulation, with a slider-crank mechanism used as a demonstrative example and comparison with the Newton-Euler method for constrained multibody systems.