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. (June 2021)

• Record Type: Journal Article
• Authors: Marques, Filipe; Roupa, Ivo; Silva, Miguel T.; Flores, Paulo; Lankarani, Hamid M.
• Is Part Of: Mechanism and machine theory. Volume 160(2021)
• Publication Date: 2021-06
• Subjects: Newton-Euler method -- Lagrangian formulation -- Closed loop kinematic chains -- Open systems -- Multibody system dynamics; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2021.104294
• Languages: English
• ISSNs: 0094-114X

Abstract

Highlights: The classical Newton-Euler method and Lagrangian formulation are revisited in this work. The Lagrangian formulation can be quite complex when applied to closed loop systems. Three approaches are presented to transform the closed loop topologies into open-loop systems. The cut joint, the clearance joint constraint, and the elastic joint formulations are utilized. The different approaches described are applied and the results are compared for a closed loop system. Abstract: 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 becomes 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 Lagrangian 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 mechanism is utilized as a demonstrative application example, and the main results are compared with those obtained with the well-established Newton-Euler method for constrained multibody systems. Moreover, this example allows the comparison of the main characteristics and peculiarities of the described approaches.