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This work presents a mathematical model for a three-wheeled narrow vehicle that will serve as a platform for mobility engineering experiments, conducted by the Mechanical and Automation curses of the Federal University of Santa Catarina. This document presents a cinematic and dynamic model of the vehicle, whose main feature is the leaning movement of its body and wheels. In spite of the enhanced mechanical and control projects complexity, the capacity to lean on curves offers better directional stability, which is a limitation for narrow vehicles. The ability to lean the entire vehicle allows the reduction of transversal loads on the wheels, which reduces their mechanical solicitations. Some simplifications were made in the mathematical model to facilitate the analysis of physical aspects inherent to this type of vehicle.