CURVATURE ANALYSIS OF LINEAR AND CIRCULAR TRACTRICES FOR THE PLANAR MOTION OF VEHICLES

The curvature analysis of the linear and circular tractrix curves for the planar motion of vehicles is formulated as based on the application of the classical differential geometry, along with the Bresse and return circles. In particular, a two-wheel (bicycle) model of four wheels vehicles was assumed and the evolutes of the corresponding fixed centrodes, being the related moving centrodes represented by straight lines, are determined, along with the evolutes of the linear and circular tractrix curves. The proposed formulation has been implemented in Matlab, in order to simulate and analyze the vehicle behavior in terms of curvature, when the front wheel center follows a straight line or a circle. Significant numerical and graphical results allowed the validation of the proposed formulation in different conditions.