Mathematical model establishment of irregular plantar surface of ostrich didactyl foot

Abstract: African ostrich (Struthio camelus) is the fastest long-distance runner with two feet in the desert. Plantar surface morphology of ostrich foot is one of the key effect factors on the superior travelling performance of ostrich didactyl foot on sand. The research of the ostrich plantar surface characteristics, will help to apply the superior characteristics to the wheels which travell on the soft grounds, and will help to improve the passing ability of current conventional sand wheel on soft grounds. Ostrich didactyl foot has two toes, the third toe and the fourth toe. During ostrich walking or running in the desert, the third toe supports the heavy weight and provides locomotor propulsion, while the fourth toe maintains balance as an outrigger. Therefore, the mathematical model of the third toe plantar surface of ostrich foot was studied. The ostrich foot of an adult male ostrich was gained from Changchun Lushengyuan mountain villa, Jilin Province, P.R. China. The geometric point clouds of the ostrich foot were obtained by using a 3D hand-held non-contact laser scanner. And then, the point cloud data were imported into Geomagic Studio software to analyze and reconstruct. Using the cutting function of the software, the reconstructed model of the third toe plantar surface of ostrich foot was divided into three typical characteristic areas, including the forefoot gradual surface, the middle groove and the heel spherical cap. In order to reduce the amount of calculation of the fitting curved surfaces, the digitized shape editor module of CATIA was utilized to filter the dense point clouds and retain the characteristic points. The retained characteristic points could reflect the third toe plantar surface morphology of ostrich foot through adopting the reasonable filtering way. The 3D characteristic point data of the three typical characteristic areas were then exported. The forefoot gradual surface and the middle groove were fitted by using the surface fitting module of MATLAB software. The equations of the curved surfaces and the solution fitted parameters were achieved. Because the heel spherical cap looked like a part of an ellipsoid from appearance, an ellipsoid model was used to fit the heel spherical cap by using the nonlinear regression module of SAS software. The fitted solution parameters of three curved surfaces were satisfactory, R2 is the parameter for measuring the mathematical model conformed to original model or not. The fitting results would be more accurate if R2 is more close to 1. According to the fitting results R2 of three curved surface fitting results was 0.95, 0.96 and 0.95, which are all close to 1. That is to say, the third toe plantar surface of ostrich foot were successfully transformed from the biological model to the mathematical model. The establishment of the mathematical model of the third toe plantar surface of ostrich foot provides the foundation for applying the superior travelling performance of ostrich foot to designing the wheels driving on the soft grounds, including desert, lunar or Martian surface. At the same time, this research will provide a new research direction for studying walking machinery on the soft grounds.