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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.

Tires have been taking an important role in vehicle safety in the last years. A lot of efforts have been taken in the way that we can understand, predict and follow its behavior, in the way that this could be useful for vehicle safety increasing. In this direction, several models describe the tire interaction with ground, considering the steering angle, pressure, temperature, friction coefficient and thread as well. Inside this analysis, there is the tire slip angle value, that is consequence of lateral forces acting over the tire. This characteristic is predicted in some cases, and evaluated on another ones. This paper brings to community another point of view of slip angle. We propose a mathematical model that describes a constraint linking slip angles and steering angle, in the way that makes the vehicle turns. We present the kinematic model that makes all three angles compatibles each other, function of the radius' corner.