# Design and Research of a Flexible Foot for a Multi-Foot Bionic Robot
## 2 Flexible Foot Mechanism Design  
According to the principles of bionics, we designed the flexible foot unit to mimic the composition and movement characteristics of an insect's foot. The robot's foot end first absorbs the terrain through the flexible sole, slows the contact impact between the legs and the ground, and then weakens the impact by the spring mechanism, achieving secondary absorption of the impact force. According to this principle, a two-degrees-of-freedom foot mechanism, as shown in Figure 1, was designed. The mechanism consisted of six parts: a flexible sole, a base, a push-pull rod, a compression spring, a pressure sensor, and a bottom plate. The pedestal, the bottom plate, and the sole mold were made from photosensitive resin using 3D-printing technology, and the printing precision was 0.1 mm. After the foot mold was printed, the flexible robot foot was formed by injecting silica gel HC9000 (Shinebon Company in Anhui Province, China. HC9008 and HC9015 mentioned below are produced by the same company). The diameter of the foot tip was 13 mm, the height of the base was 40 mm, and the overall mass was 45 g.  
The rationality of the spring directly determines the motion performance of the entire foot mechanism. Therefore, the spring was designed in detail. The structure of the spring is shown in Figure 2. The parameters are shown in Table 1. The small hexapod robot used in the experiment had a single leg support force of less than 10 N, and, considering the low stress factor, the selected spring material was a B-grade carbon spring steel wire, and the tensile strength limit of \(\sigma_{\mathrm{B}}\)\(=2059\) Mpa was obtained. The maximum stroke was f\({}_{\mathrm{b}}\)\(=18\) mm; the outer diameter D was 8 mm; the maximum load was about P\({}_{\mathrm{max}}\)\(=20\) N; the minimum was P\({}_{0}\)\(=0\) N; the spring ends were flattened; and the number of support turns was one turn. Other parameters are listed below:  
* Spring wire diameter D: \[\mathrm{A_{2}}\mathrm{=KC^{3}=\frac{\pi\tau_{\mathrm{P}}}{8P_{\mathrm{max}}}D^{ 2}=\frac{\pi\times 823}{8\times 15}\times 8^{2}\mathrm{=1378}\] (1) where \[\tau_{\mathrm{P}}\mathrm{=0.4\sigma_{\mathrm{B}}}\mathrm{=823\ Mpa,\ C=10.2, \ d=}\frac{D}{C}\approx 0.8\mathrm{mm}.\] (2)
* Elastic coefficient K, effective number of turns N: \[\mathrm{k_{1}=\frac{F}{S}=\frac{P_{\mathrm{max}}-P_{0}}{15}=\frac{20-0}{15} \approx 1.3\ N/\mathrm{mm},}\] (3) \[\mathrm{n=\frac{Gd^{4}}{8k_{1}D_{2}{}^{3}}=\frac{78.5\times 10^{3} \times 0.8^{4}}{8\times 1.3\times 8^{3}}=6.0.}\] (4)
* Total number of laps: \[\mathrm{n_{1}}\mathrm{=n+2=8.}\] (5)  
Figure 1: Simplified model of foot mechanism: (**a**) foot tip mechanical structure; (**b**) foot tip sectional view.  
Total load shape variable:  
\[\mathrm{f=}\frac{\mathrm{P_{max}}}{\mathrm{k_{1}}}=\frac{20}{1.3}=15\;\mathrm{mm}. \tag{6}\]  
Pressure height:  
\[\mathrm{H_{b}=(n_{1}-0.5)d=}(8-0.5)0.8=6\;\mathrm{mm}. \tag{7}\]  
Freedom height:  
\[\mathrm{H_{0}=H_{b}+f_{b}}=18+6=24\;\mathrm{mm} \tag{8}\]  
Pitch:  
\[\mathrm{t=}\frac{\mathrm{H_{0}-1.5d}}{\mathrm{n_{1}}}=\frac{24-1.5\times 0.8}{8} =2.85\;\mathrm{mm} \tag{9}\]  
After selecting a suitable compression spring, a Honeywell FSS (Honeywell in Morris town, New Jersey, USA) pressure sensor was placed between the compression spring and the bottom plate. When the flexible material is deformed by force, the push-pull rod passes through the spring structure and finally acts on the FSS pressure sensor. The foot-end force information is fed back through the pressure sensor in real time. This can effectively improve the environmental adaptability and stability of the robot in complex terrain.