# Design of a Bionic Spider Robot with a Two-Degrees-of-Freedom Leg Structure and Body Frame
## 3 Design and Analysis of Structure
### Design and Analysis of Body Structure
#### 3.2.3 Analysis of the Layout of Body and Leg Connection Points  
After performing kinematic forward and inverse analyses of the legs, considering the impact of the installation position of the legs on the overall machine's motion performance and load-bearing capabilities, an analysis of the connection points between the legs and the body is conducted, with a primary focus on the position of the center of gravity, etc. In calculating the position of the center of gravity, the relationship between the triangle's coordinate positions and the center of gravity is utilized, as shown in Equation (23).  
\[\overline{x}=\frac{\int xd\sigma}{\int d\sigma};\overline{y}=\frac{\int yd \sigma}{\int d\sigma} \tag{23}\]  
In the case where the coordinates of the triangle are known, the central position of the triangle can be determined using Formula (24).  
\[x_{z}=\frac{x_{1}+x_{2}+x_{3}}{3};y_{z}=\frac{y_{1}+y_{2}+y_{3}}{3} \tag{24}\]  
In Equation (24), \((x_{z},y_{z})\) represents the coordinates of the center of gravity, while \((x_{1},y_{1})\), \((x_{2},y_{2})\), and \((x_{3},y_{3})\) correspond to the vertices of the triangle. This approach is numerically straightforward in principle, yet its complexity arises in the acquisition of the coordinate information at the foot's endpoint. Due to the unknown environmental information of the biomimetic spider robot and the inability to predict the conditions of the landing site during rapid movement, whether it is on yielding ground or slippery surfaces, controlling the placement of the foot's endpoint is quite challenging.  
In conclusion, this paper intends to reduce the size of the support triangle by defining its position at the connection points between the leg mechanism and the body, namely \(a_{1}\sim a_{3}\), \(b_{1}\sim b_{3}\), to determine its location, as shown in Figure 12. This arrangement forms a triangle between the support phase and the body's connecting part, which stabilizes the center of gravity of the body within the triangle. Consequently, this ensures that the overall center of gravity of the biomimetic spider robot remains within the support triangle formed by the foot end of the support phase.  
In Figure 12, \(L_{1}\)\(\sim\)\(L_{3}\) represent the three legs in the swing phase, while \(R_{1}\)\(\sim\)\(R_{3}\) represent the three legs in the support phase. \(a_{1}\)\(\sim\)\(a_{3}\) and \(b_{1}\)\(\sim\)\(b_{3}\) are the connection points between the leg structures and the torso.  
The common arrangements of the body-leg connections are shown in Figure 13. Figure 13a depicts legs on the same side not aligned on a straight line, with the middle leg on the outer side; Figure 14b shows legs on the same side aligned on a straight line; and  
Figure 12: Support phase and swing phase.  
Figure 13c shows legs on the same side not aligned on a straight line, with the middle leg on the inner side.  
When arranging the supporting triangle, if the overall width is the same, the distance from the vertex \(a_{2}\) to the bottom \(a_{1}a_{3}\) of the triangle in Figure 13b is the largest. In Figure 13a, \(a_{1}a_{3}\) is located inside the frame, while in Figure 13c, it is located at the edge of the frame. It can be concluded that the center of gravity of the triangle is biased towards the bottom edge; compared to the c scheme, the center-of-gravity coincidence of the supporting triangles on both sides of the a scheme is higher.