A comparison of spherical joint models in the dynamic analysis of rigid mechanical systems: ideal, dry, hydrodynamic and bushing approaches

Spherical joints, usually known as ball and socket joints, are utilized in several engineering applications. On the one hand, these types of joints may be found in mechanical systems acting as a pivot element between the wheels and the suspension in cars. On the other hand, ball and socket joints can also be used to model human articulations, as in the case of the hip and shoulder. From more simplistic to more complex scenarios, spherical joints might be modeled using different approaches. Therefore, the objective of this work is to provide a comparative analysis of different spherical joint models and to examine their influence on the dynamic response of mechanical multibody systems. For this purpose, ideal or kinematic formulation, dry, lubricated, and bushing approaches are revised. Additionally, the formulation of the dynamic equations of motion for constrained mechanical multibody systems is succinctly described. Afterward, the kinematic and dynamic characteristics of the considered spherical joint models are comprehensively described. In this regard, normal, tangential, hydrodynamic lubrication and bushing forces experienced by the multibody systems in such cases of spherical joints are examined. The application of the spherical joint models in the dynamic modeling and simulation of multibody systems is investigated. Considering two multibody models as demonstrative examples of application from the outcomes, it is observed that the influence of the spherical joint modeling strategy on the dynamic simulation of mechanical multibody systems strongly depends on the nature of the multibody model analyzed, both in terms of dynamic response and computational efficiency.