An improved methodology to restrict the range of motion of mechanical joints

Joints with rotational degrees of freedom, for instance, revolute, spherical, or universal joints, are commonly utilized in real-world scenarios. In the multibody systems methodology, mechanical joints usually are formulated as classical kinematic constraints such that there is no restriction of the range of motion (RoM) of the joint. Thus, the formulation must include additional restrictions to prevent the joints from performing unacceptable movements and to avoid unrealistic configurations of the connected bodies. Therefore, the aim of this work is to propose a methodology to restrict the RoM of mechanical joints. Joint resistance moments are applied to the bodies connected by the joint to mimic the dissipative behavior of the materials constituent of joints and to prevent unacceptable configurations of those bodies. The proposed methodology aims to extend and improve a previously published study, specifically in the definition of the RoM limits, calculation of the penalty moments, and establishment of their direction of application. Enhanced methods to deal with the detection of unacceptable joint configurations, namely the elliptical and polynomial approaches, are proposed. A parametrization procedure is described to correctly calculate the direction of the penalty moments to apply to the connected bodies. The methodology is investigated in the dynamic modeling and simulation of one demonstrative example of application, namely a simple pendulum. A parametric analysis is performed to assess the influence of the methodology parameters in the response of the model. The methodology allows the correct restriction of the RoM of joints, while preserving the mechanical energy of the system.