Analytical Method of Examining the Curvilinear Motion of a Four-wheeled Vehicle

We obtained equations for the curvilinear trajectory of a four-wheeled vehicle in the parametric form of a function of turning angle of the machine frame. The equations are suitable for the sections of entering a turn and exiting a turn. The proposed equations make it possible to build the trajectories taking into account the intensity of turning the front steered wheels. For this purpose, the course angle is represented as a function of the turning angle of the body of a machine. For example, in the case of a linear dependence, the proportionality factor (coefficient of intensity of change in the course angle, predetermined by the rotation speed of steered wheels) depends on the turning angle of a steering wheel. The solution was found based on the projections of velocity of the center of mass of a machine onto the inertial coordinate axes. In this case, the integrand functions are represented through a single variable – turning angle of the machine frame. For this purpose, we employed a special substitution, which replaces the differential of time with the differential of turning angle of the machine frame. Following the decomposition of integrand functions into the Maclaurin series, the integration becomes possible. We also found the equation of motion along a circular trajectory at fixed position of a steering wheel. Along with the equations for entering a turn and exiting a turn, they allow us to build complex trajectories of u-turns in a unified coordinate system. For the conjugation of separate sections of the trajectory, we applied formulas of change in the coordinates at parallel carry and turn of the coordinate axes. The coordinates of points along the trajectory can be calculated by using the software tools.The impact of the phenomenon of wheels slip under the action of lateral forces on the trajectory of curvilinear motion is accounted for by introducing to the equations the intensity coefficients that represent dependence of the course angle, caused by the slip, on the turning angle of the machine fram