Kinematics and dynamics of planar multibody systems with fully Cartesian coordinates and a generic rigid body. (February 2023)

• Record Type: Journal Article
• Authors: Roupa, Ivo; Gonçalves, Sérgio B.; da Silva, Miguel Tavares
• Is Part Of: Mechanism and machine theory. Volume 180(2023)
• Publication Date: 2023-02
• Subjects: Multibody dynamics formulations -- Fully Cartesian coordinates -- Generic rigid body -- Planar systems -- Advanced education; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2022.105134
• Languages: English
• ISSNs: 0094-114X

Abstract

Abstract: This work describes in detail the theoretical basis of the fully Cartesian coordinates formulation with a generic rigid body and evaluates its performance in the dynamic analysis of planar multibody systems. The topological features of the generic rigid body and the most relevant kinematic constraint equations are presented, aiming its application in the dynamic analysis of complex multibody systems and in advanced teaching. Contrarily to natural coordinates, in which the present formulation lays its foundation, planar rigid bodies are defined with a predetermined kinematic structure that resorts only to the Cartesian coordinates of one point and one unit vector. The introduction of the generic rigid body systematizes the discretization of the multibody system, simplifies the kinematic constraints required for its description, and renders higher physical meaning and sparsity to its mass matrix. However, it also slightly increases the number of generalized coordinates and kinematic constraints, required to model the multibody system, when compared to other global formulations. The present formulation was applied to the analysis of four planar models with different complexity levels, namely the slider-crank, double four-bar linkage, Jansen mechanism and a biomechanical model of the human body, presenting high agreement scores with benchmark and literature data. Highlights: Multibody formulation with Fully Cartesian coordinates (FCC) for planar systems. Theoretical basis and description of the most relevant features of FCC. Discussion of the advantages and limitations of FCC over other multibody formulations. Detailed description of the formulation, aiming RD&I and advanced education purposes. Examples of FCC as a systematic formulation to analyze planar multibody systems.