# Optimal Dimensional Synthesis of Ackermann Steering Mechanisms for Three-Axle, Six-Wheeled Vehicles
###### Abstract
Many types of vehicle or robot steering mechanisms were proposed in the literature, such as non-circular gear steering [2; 3], differential gear steering [4], pure rolling steering [5], rack-and-pinion steering mechanisms [6; 7; 8], Ackermann trapezoidal steering mechanisms [9; 10; 11; 12; 13; 14; 15; 16; 17], Ackermann-type steering mechanisms [18] and multi-link steering mechanisms [19; 20; 21; 22; 23; 24; 25; 26; 27; 28]. [PERSON] [9] proposed an analytical method for determining the dimensions of a planar Ackermann four-bar steering mechanism. [PERSON] and [PERSON] [2] proposed a new steering mechanism using noncircular gears capable of turning a carrier with a small radius. To facilitate analysis, the concept of a virtual two-wheeled vehicle was introduced. It was shown that the noncircular gear in the mechanism is an elliptical gear with a pitch curve represented by a simple equation. This mechanism is applicable to wheeled carrier robots in industrial production lines. [PERSON] et al. [4] presented a differential steering mechanism, derived from a six-bar steering linkage, with the addition of a differential mechanism. The differential mechanism, coupled with a higher pair, converts the single input from the steering wheel into two outputs, ensuring the condition for correct steering is satisfied. [PERSON] et al. [6] developed a kinematic model for synthesizing the rack-and-pinion steering linkage of a four-wheel-drive light tractor and applied the Nelder-Mead Simplex optimization method to optimize the objective functions, which included the Ackermann motion criteria and motion transmissibility. [PERSON] et al. [7] employed a local optimization method based on exact gradient determination, which requires an initial guess for the design variables, to synthesize four types of steering mechanisms used in road vehicles: rack-and-pinion, four-bar, six-bar, and double four-bar mechanisms. [PERSON] and [PERSON] [8] proposed a multi-objective optimization approach for a rack-and-pinion steering linkage, aiming to simultaneously minimize steering error and turning radius. The optimization problem was addressed using a hybrid method that combines multi-objective population-based incremental learning with differential evolution. [PERSON] and [PERSON] [10] proposed a computational kinematics approach based on elimination procedures to synthesize a steering four-bar mechanism. The goal was to minimize the root-mean-square of the structural error within the steering motion range. The minimization problem was reformulated into two polynomial equations with two variables, and by eliminating one variable, a univariate polynomial equation was derived. The roots of this equation provided all locally optimal linkages. However, the global optimum identified from the locally optimal solutions exhibited dimensional unbalance. They addressed this drawback by employing a kinematically equivalent focal six-bar mechanism. [PERSON] and [PERSON] [11] utilized [PERSON]'s optimization algorithm to synthesize the [PERSON] steering mechanism and developed parametric design charts to assist in selecting the optimal initial angles for implementing an [PERSON] steering mechanism in a new vehicle for practical applications. [PERSON] and [PERSON] [12] employed a gradient-based sequential quadratic programming (SQP) algorithm, which requires an initial estimate of variables, to optimize the objective function of a four-bar function generator and achieve five precision points within the range of motion. In the study, the distribution of precision points served as the optimization parameter. An Ackermann steering mechanism was successfully optimized. [PERSON] [13] applied two optimization methods, Simulated Annealing, and Differential Evolution, to synthesize the trailing Ackermann steering linkage and leading Ackermann steering linkage, respectively. The study considered two optimal criteria, the maximum absolute steering error and the root mean square (RMS) of the steering error.