Analytical Design of an Ackermann Steering Linkage

Abstract

A method is outlined whereby the dimensions of an Ackermann steering linkage may be determined analytically. The theoretical relation between the angles of rotation of the front wheels of a vehicle is derived and it is shown how this relation may be approximated by a symmetrical four-bar linkage. The method is briefly as follows: The basic relation between the angles of the four-bar linkage is derived and the theoretically correct relation between the angles is used to express the four-bar linkage equation as a function of one variable. If this derived equation can be made equal to zero for a suitable range of wheel-turning angle by proper adjustment of the coefficients, then the magnitudes of the coefficients will determine the physical dimensions of the linkage. A direction solution as indicated does not seem possible so an approximate solution is developed by expressing the derived equation as a power series and adjusting the coefficients of this series so that the sum of the lower order terms deviates the least from zero.