Kinematics and dynamics of planar multibody systems with fully Cartesian coordinates and a generic rigid body
Ivo Roupa, Sérgio Gonçalves, Miguel Silva
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.