# Optimal Dimensional Synthesis of Ackermann Steering Mechanisms for Three-Axle, Six-Wheeled Vehicles
###### Abstract
[PERSON] and [PERSON] [14] carried out an optimal synthesis of an Ackermann four-bar steering mechanism using an artificial immune system (AIS) algorithm and a genetic algorithm (GA). In their approach, the link length was selected as the optimization parameter in the first method, whereas the precision point distribution was employed in the second method. The optimal results revealed that the AIS algorithm outperformed the GA in the first method, whereas the GA produced superior results compared to the AIS algorithm in the second method. [PERSON] et al. [15] studied the optimization of a steering trapezoid mechanism by minimizing the sum of absolute differences between the actual and theoretical rotational angles of the anterolateral steering wheel. An improved particle swarm optimization (IPSO) algorithm is introduced with over-flow exception handling to address nonlinear constraints. Performance comparisons demonstrated that IPSO outperforms traditional PSO and simulated annealing-based PSO (SA-PSO) in convergence speed and computational efficiency, though it slightly lags behind SA-PSO in calculation accuracy. [PERSON] and [PERSON] [16] presented the kinematic synthesis of a crossed four-bar mechanism for four-wheel automotive steering using the Hooke and Jeeves optimization method to achieve five precision points. The mechanism, incorporating two equal spur gears to coordinate outer wheel motion, achieved a maximum steering error of 0.12 degrees, making it suitable for long-wheelbase vehicles. [PERSON] et al. [17] optimized the design of a steering trapezoid mechanism for an agricultural tractor using the Powell Hybrid Genetic Algorithm (HGA), which combines the global search capability of genetic algorithms with the efficient local search ability of the Powell method. This approach enhanced the accuracy and efficiency of the tractor's steering mechanism design. Experimental verification demonstrated the reliability and feasibility of the HGA method for optimizing tractor steering mechanisms. [PERSON] et al. [18] proposed the synthesis of an Ackermann-type steering mechanism incorporating a five-bar mechanism coupled with incomplete noncircular gears, designed to precisely satisfy the Ackermann steering geometry. The synthesis process involved designing the pitch curves, addendum curves, dedendum curves, tooth profiles, and transition curves of the noncircular gear pair. The optimized design enhances vehicle steering performance while maintaining a structure similar to existing four-bar steering linkages. The literature on the dimensional synthesis of three-axis, six-wheeled, or multi-axis, multi-wheeled steering mechanisms is relatively scarce. [PERSON] and [PERSON] [29] proposed a dual-axle steering system for a three-axle, six-wheeled vehicle with a rear non-steerable axle. The steering system comprised two symmetrical planar six-bar mechanisms integrated with a planar four-bar mechanism serving as the double-shaft linkage. The Newton-Raphson iterative method was utilized to linearize and solve the design equations, resulting in an optimized design with a maximum structural error of 0.8 degrees. [PERSON] et al. [30] conducted the design and error analysis of a steering device consisting of five axles of a Watt-II center-arm six-bar mechanism for a multi-wheel heavy vehicle. [PERSON]'s iterative algorithm was employed, with an appropriate initial value selected, to solve the linear simultaneous equations through seven precision points, ensuring compliance with the Ackermann steering principle. Additionally, ADAMS v2015 software was utilized for the kinematic simulation of the designed steering mechanism. [PERSON] et al. [31] explored the optimization of a five-axle steering mechanism for heavy vehicles using a hybrid approach that combines the global search capabilities of the Bees algorithm with the local refinement efficiency of the Hooke-Jeeves algorithm. This method improved steering accuracy and performance, validating its effectiveness for complex multi-axle systems in heavy vehicles. [PERSON] et al.