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.

这项工作旨在以全面的方式介绍使用经典拉格朗日公式对闭环拓扑进行建模和仿真的几种方法。拉格朗日方法的最大优点之一是它的简单性和获得运动方程的容易性。但是，当机械系统包括闭环拓扑时，就会出现一个关键方面，因为推导运动方程的过程变得很复杂。本研究的重点是将闭环性质转换为开放系统，从而最终在利用拉格朗日公式时简化了建模过程。为此，考虑了三种不同的方法，即使用基于切缝方法，间隙关节约束模型和弹性关节公式的方法。在此过程的后续过程中，使用曲柄滑块机构作为演示应用示例，并将主要结果与通过完善的约束多体系统的Newton-Euler方法获得的结果进行比较。而且，该示例允许比较所描述的方法的主要特征和特性。