Two Novel Formulations for the Optimum Design of Rack-and-Pinion Steering Mechanisms

Abstract

A numerical and an analytical optimization formulations are presented for design of rack-and-pinion steering mechanisms. The distance between the uprights, the angle between the steering arm and wheel axles are assumed to be predesigned. The numerical method enables design of the steering arm, the rack, the rack offset and then the tie rod length can be computed using the symmetrical configuration of the mechanism. The analytical method results in a cubic polynomial equation, root of which gives only one parameter (steering arm or rack offset) based on the assumption that the rack offset is equal to the half of the difference between the distance between the uprights and the rack. Both methods optimize weighted sum of the least-squares of the error between wheel turning angle generated by the mechanism and desired angle according to Ackermann steering principle. The methods are illustrated with a numerical example. When numerical optimization is used, the error is less than 0.2° for 36° angle range. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.