Construction of a Mathematical Model of the Irregular Plantar and Complex Morphology of Mallard Foot and the Bionic Design of a High-Traction Wheel Grouser

To improve the traction performance of mobile mechanisms on soft ground, such as paddy fields, tidal flats, and swamps, a mallard (Anas platyrhynchos) foot was adopted as a bionic prototype to explore the influence and contribution of the plantar morphology of the toes and webbing on the anti-subsidence function during its locomotion on wet and soft substrates and to apply this to the bionic design of high-traction wheel grousers. A handheld three-dimensional laser scanner was used to scan the main locomotion postures of a mallard foot during ground contact, and the Geomagic Studio software was utilized to repair the scanned model. As a result, the main three-dimensional geometric models of a mallard foot during the process of touching the ground were obtained. The plantar morphology of a mallard foot was divided into three typical parts: the plantar irregular edge curve, the lateral webbing surface, and the medial webbing surface. The main morphological feature curves/surfaces were extracted through computer-aided design software for the fitting and construction of a mathematical model to obtain the fitting equations of the three typical parts, and the mathematical model construction of the plantar irregular morphology of the mallard foot was completed. In order to verify the sand-fixing and flow-limiting characteristics of this morphological feature, based on the discrete element method (DEM), the numerical simulation of the interaction between the plantar surface of the mallard foot and sand particles was carried out. The simulation results show that during the process of the mallard foot penetration into the loose medium, the lateral and medial webbing surfaces cause the particles under the foot to mainly move downward, effectively preventing the particles from spreading around and significantly enhancing the solidification effect of the particles under the sole. Based on the principle and technology of engineering bionics, the plantar morphology and movement attitude characteristics of the mallard were extracted, and the characteristics of concave middle and edge bulge were applied to the wheel grouser design of paddy field wheels. Two types of bionic wheel grousers with different curved surfaces were designed and compared with the traditional wheel grousers of the paddy field wheel. Through pressure-bearing simulation and experiments, the resistance of different wheel grousers during the process of penetrating into sand particles was compared, and the macro–micro behaviors of particle disturbance during the pressure-bearing process were analyzed. The results show that a bionic wheel grouser with unique curved surfaces can well encapsulate sand particles at the bottom of the wheel grouser, and it also has a greater penetration resistance, which plays a crucial role in improving the traction performance of the paddy field wheel and reducing the disturbance to the surrounding sand particles. This paper realizes the transformation from the biological model to the mathematical model of the plantar morphology of the mallard foot and applies it to the bionic design of the wheel grousers of the paddy field wheels, providing a new solution for improving the traction performance of mobile mechanisms on soft ground.