Kinematic Analysis of the Planar Motion of Vehicles when Traveling Along Tractrix Curves

Abstract

The kinematic analysis of the planar motion of vehicles, such as common cars, buses, and trucks, when traveling along linear and circular tractrices at low speeds, is proposed here based on the fundamentals of the kinematics of planar mechanisms. In particular, the analysis of the vehicle chassis motion, with chassis represented as a drawbar connecting the back and front-wheel centers, is developed and formulated by determining the moving and the fixed centrodes. The proposed formulation was implemented in matlab to simulate and analyze the vehicle motion at low speeds, as the front-wheel center follows a straight line or a circle and, correspondingly, the back-wheel center traces a linear tractrix or one of the inner and outer circular tractrices, according to the exit from or entrance of the vehicle into a roundabout. Significant numerical and graphical results allow the validation of the proposed formulation, which represents useful tool to predict the vehicle behavior at low speeds during parking, changing of lanes, and entering and leaving roundabouts, thereby increasing the safety for bicycles, motorcycles, and pedestrians, along with the design of safe roads and highways.