Mathematical Modeling of the Spatial Steering Linkage of a Wheeled Vehicle

The value and steer angle ratio, steering effort of the steerable wheels while operating the vehicle are determined by the steering linkage and steering drive ratio. Since the kingpins of the real vehicle have a combined slope, the trapezoidal steering linkage is a four-bar spatial mechanism, all points of which are rotated in three dimentions during rotation. The paper proposes a mathematical model of the spatial steering linkage, which allows to calculate the steer angles and its steering linkage ratio in the full range of steer angles. The spatial model provides a higher accuracy of calculations comparing with the flat model. It is proved that it is permissible to use a flat model, which is simpler, to analyze the kinematics of steerable wheel rotation with sufficient accuracy. When using a flat model, the calculation of trapezoidal steering mechanism gear ratios the fallibility is up to 35%. To calculate the power parameters of the steering, such as the effort on the steerable wheel and the total steering resistance torque of the steerable wheels, it is more appropriate to use a spatial model that is more complex but it provides high accuracy. The accuracy of the calculations is confirmed by the results of 3D modeling in Creo software.