Abstract: According to the different force directions of the upper and lower ends of the steering knuckles and the balance state of the two forces on the tie rod in a steering trapezoid mechanism of a vehicle, the tilted axis model, which assumes that the axes of the two pairing elements of revolute kingpin are not coincident but inclined each other, and the variable length rod model of the tie rod are firstly addressed to describe the joint clearances in the steering trapezium. The screw theory is used to analyze the force situation acting on the steering knuckle from the reactions of the ground to the tires and the exponential product formula of an interesting point on the steering knuckle around the revolute pair with clearance. The constraint reactions of the kingpin and the steering angles of left and right wheels are calculated, and the additional steering error and the sensitivity index are proposed to evaluate the influence of parameters on the steering error and sensitivity to the joint clearances. The variations of steering errors and the sensitivity of 12 parameters to the joint clearances are analyzed by an example. The results show that when vehicle steering to the driving side at a larger angle, the steering error analyzed by the case of the mechanism with the joint clearance is relatively smaller than that calculated by the clearance-free case; the kingpin caster angle, vehicle speed and other factors related to the lateral force acting on tires are significantly sensitive to the clearance; the longitudinal and the normal forces acting on tires and the factors related to their moments about kingpin are relatively small insensitive. The results can provide guidance for reasonable design of the parameter values sensitive to the joint clearances, appropriate manufacturing tolerances and allowable sizes of the clearances.

Key words: joint clearance, steering trapezium, screw theory, force analysis, steering error, additional steering error