Optimal Dimensional Synthesis of Ackermann and Watt-I Six-Bar Steering Mechanisms for Two-Axle Four-Wheeled Vehicles
This study investigates the dimensional synthesis of steering mechanisms for front-wheel-drive, two-axle, four-wheeled vehicles using two metaheuristic optimization algorithms: Differential Evolution with golden ratio (DE-gr) and Improved Particle Swarm Optimization (IPSO). The vehicle under conside...
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MDPI AG
2025-07-01
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| author | Yaw-Hong Kang Da-Chen Pang Dong-Han Zheng |
| author_facet | Yaw-Hong Kang Da-Chen Pang Dong-Han Zheng |
| author_sort | Yaw-Hong Kang |
| collection | DOAJ |
| description | This study investigates the dimensional synthesis of steering mechanisms for front-wheel-drive, two-axle, four-wheeled vehicles using two metaheuristic optimization algorithms: Differential Evolution with golden ratio (DE-gr) and Improved Particle Swarm Optimization (IPSO). The vehicle under consideration has a track-to-wheelbase ratio of 0.5 and an inner wheel steering angle of 70 degrees. The mechanisms synthesized include the Ackermann steering mechanism and two variants (Type I and Type II) of the Watt-I six-bar steering mechanisms, also known as central-lever steering mechanisms. To ensure accurate steering and minimize tire wear during cornering, adherence to the Ackermann steering condition is enforced. The objective function combines the mean squared structural error at selected steering positions with a penalty term for violations of the Grashoff inequality constraint. Each optimization run involved 100 or 200 iterations, with numerical experiments repeated 100 times to ensure robustness. Kinematic simulations were conducted in ADAMS v2015 to visualize and validate the synthesized mechanisms. Performance was evaluated based on maximum structural error (steering accuracy) and mechanical advantage (transmission efficiency). The results indicate that the optimized Watt-I six-bar steering mechanisms outperform the Ackermann mechanism in terms of steering accuracy. Among the Watt-I variants, the Type II designs demonstrated superior performance and convergence precision compared to the Type I designs, as well as improved results compared to prior studies. Additionally, the optimal Type I-2 and Type II-2 mechanisms consist of two symmetric Grashof mechanisms, can be classified as non-Ackermann-like steering mechanisms. Both optimization methods proved easy to implement and showed reliable, efficient convergence. The DE-gr algorithm exhibited slightly superior overall performance, achieving optimal solutions in seven cases compared to four for the IPSO method. |
| format | Article |
| id | doaj-art-c81b1ebdb9754971a341a9b39e681333 |
| institution | Kabale University |
| issn | 2075-1702 |
| language | English |
| publishDate | 2025-07-01 |
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| series | Machines |
| spelling | doaj-art-c81b1ebdb9754971a341a9b39e6813332025-08-20T03:32:32ZengMDPI AGMachines2075-17022025-07-0113758910.3390/machines13070589Optimal Dimensional Synthesis of Ackermann and Watt-I Six-Bar Steering Mechanisms for Two-Axle Four-Wheeled VehiclesYaw-Hong Kang0Da-Chen Pang1Dong-Han Zheng2Department of Mechanical Engineering, National Kaohsiung University of Science and Technology, 415 Jiangong Rd., Sanmin District, Kaohsiung 80778, TaiwanDepartment of Mechanical Engineering, National Kaohsiung University of Science and Technology, 415 Jiangong Rd., Sanmin District, Kaohsiung 80778, TaiwanDepartment of Mechanical Engineering, National Kaohsiung University of Science and Technology, 415 Jiangong Rd., Sanmin District, Kaohsiung 80778, TaiwanThis study investigates the dimensional synthesis of steering mechanisms for front-wheel-drive, two-axle, four-wheeled vehicles using two metaheuristic optimization algorithms: Differential Evolution with golden ratio (DE-gr) and Improved Particle Swarm Optimization (IPSO). The vehicle under consideration has a track-to-wheelbase ratio of 0.5 and an inner wheel steering angle of 70 degrees. The mechanisms synthesized include the Ackermann steering mechanism and two variants (Type I and Type II) of the Watt-I six-bar steering mechanisms, also known as central-lever steering mechanisms. To ensure accurate steering and minimize tire wear during cornering, adherence to the Ackermann steering condition is enforced. The objective function combines the mean squared structural error at selected steering positions with a penalty term for violations of the Grashoff inequality constraint. Each optimization run involved 100 or 200 iterations, with numerical experiments repeated 100 times to ensure robustness. Kinematic simulations were conducted in ADAMS v2015 to visualize and validate the synthesized mechanisms. Performance was evaluated based on maximum structural error (steering accuracy) and mechanical advantage (transmission efficiency). The results indicate that the optimized Watt-I six-bar steering mechanisms outperform the Ackermann mechanism in terms of steering accuracy. Among the Watt-I variants, the Type II designs demonstrated superior performance and convergence precision compared to the Type I designs, as well as improved results compared to prior studies. Additionally, the optimal Type I-2 and Type II-2 mechanisms consist of two symmetric Grashof mechanisms, can be classified as non-Ackermann-like steering mechanisms. Both optimization methods proved easy to implement and showed reliable, efficient convergence. The DE-gr algorithm exhibited slightly superior overall performance, achieving optimal solutions in seven cases compared to four for the IPSO method.https://www.mdpi.com/2075-1702/13/7/589Ackermann steering mechanismWatt-I six-bar steering mechanismcentral-lever steering mechanismIPSODE-grADAMS |
| spellingShingle | Yaw-Hong Kang Da-Chen Pang Dong-Han Zheng Optimal Dimensional Synthesis of Ackermann and Watt-I Six-Bar Steering Mechanisms for Two-Axle Four-Wheeled Vehicles Machines Ackermann steering mechanism Watt-I six-bar steering mechanism central-lever steering mechanism IPSO DE-gr ADAMS |
| title | Optimal Dimensional Synthesis of Ackermann and Watt-I Six-Bar Steering Mechanisms for Two-Axle Four-Wheeled Vehicles |
| title_full | Optimal Dimensional Synthesis of Ackermann and Watt-I Six-Bar Steering Mechanisms for Two-Axle Four-Wheeled Vehicles |
| title_fullStr | Optimal Dimensional Synthesis of Ackermann and Watt-I Six-Bar Steering Mechanisms for Two-Axle Four-Wheeled Vehicles |
| title_full_unstemmed | Optimal Dimensional Synthesis of Ackermann and Watt-I Six-Bar Steering Mechanisms for Two-Axle Four-Wheeled Vehicles |
| title_short | Optimal Dimensional Synthesis of Ackermann and Watt-I Six-Bar Steering Mechanisms for Two-Axle Four-Wheeled Vehicles |
| title_sort | optimal dimensional synthesis of ackermann and watt i six bar steering mechanisms for two axle four wheeled vehicles |
| topic | Ackermann steering mechanism Watt-I six-bar steering mechanism central-lever steering mechanism IPSO DE-gr ADAMS |
| url | https://www.mdpi.com/2075-1702/13/7/589 |
| work_keys_str_mv | AT yawhongkang optimaldimensionalsynthesisofackermannandwattisixbarsteeringmechanismsfortwoaxlefourwheeledvehicles AT dachenpang optimaldimensionalsynthesisofackermannandwattisixbarsteeringmechanismsfortwoaxlefourwheeledvehicles AT donghanzheng optimaldimensionalsynthesisofackermannandwattisixbarsteeringmechanismsfortwoaxlefourwheeledvehicles |