Kinematic and dynamic analysis of spatial multibody systems based on a formulation with fully Cartesian coordinates and a generic rigid body

Abstract

This work introduces the Fully Cartesian Coordinates Formulation with a Generic Rigid Body (FCC-GRB), a novel global multibody formulation for three-dimensional mechanical system analysis. The formulation's intrinsic characteristics are thoroughly detailed and compared with other widely-used global formulations, enabling its application in both kinematic and dynamic analysis of complex mechanical systems and as a teaching tool in advanced multibody dynamics courses.

FCC-GRB formulation is founded on two main premises: multibody systems are described using only Cartesian coordinates, and the rigid bodies are modeled with a fixed and predetermined structure. Consequently, the kinematic constraints are described by lower-degree equations and the system mass matrix is highly sparse. Additionally, the introduction of the generic rigid body simplifies the modeling process by making the definition of the bodies independent of system topology. To reduce the number of generalized coordinates, a reduced modeling approach using less coordinates for describing the generic rigid body is also introduced and compared with the fully-defined alternative.

The formulation's accuracy was validated through forward dynamic analysis of benchmark problems. Simulations demonstrated excellent agreement with reference data, with both modeling approaches yielding comparable kinematic results. The reduced approach offered faster computational performance, particularly in more complex models.