# 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
#### 3.2.2 Analysis of Support Triangle Gait  
According to the findings of Section 2.2.2 in this paper, the biomimetic spider robot employs a triangular gait for walking. In existing research, many scholars have also adopted the triangular gait as the walking gait for biomimetic robots, such as [PERSON], [PERSON] [44], [PERSON], [PERSON] [45], [PERSON], [PERSON] [46], etc., who have all used the triangular gait in the walking control of their designed hexapod robots. However, the triangular configurations chosen and the different legs that form the triangle vary during the design process. If only the different legs that form the triangle are considered, there are six possible configurations, as shown in Figure 11, the point a,b,c represent the three vertices of a triangle.  
The triangle structure in Figure 11 is expressed in a matrix to assist in judging its stability margin. An equilateral hexagon is selected as the prototype of the support triangle analysis. Its side length is \(2m\), and it corresponds to Figure 11a-f, respectively.  
\[\begin{pmatrix}-m&\sqrt{3}m\\ -2m&0\\ -m&-\sqrt{3}m\end{pmatrix}\begin{pmatrix}-m&\sqrt{3}m\\ m&\sqrt{3}m\\ 2m&0\\ \end{pmatrix}\begin{pmatrix}-m&\sqrt{3}m\\ -2m&0\\ m&-\sqrt{3}m\\ 2m&0\end{pmatrix}\begin{pmatrix}-m&\sqrt{3}m\\ -m&\sqrt{3}m\\ 2m&0\\ \end{pmatrix}\begin{pmatrix}-m&\sqrt{3}m\\ -m&\sqrt{3}m\\ 2m&0\\ \end{pmatrix}\begin{pmatrix}-m&\sqrt{3}m\\ -m&-\sqrt{3}m\\ 2m&0\\ \end{pmatrix}\begin{pmatrix}-m&\sqrt{3}m\\ -m&-\sqrt{3}m\\ 2m&0\\ \end{pmatrix}\begin{pmatrix}-m&\sqrt{3}m\\ -m&-\sqrt{3}m\\ 2m&0\\ \end{pmatrix}\begin{pmatrix}-m&\sqrt{3}m\\ -m&-\sqrt{3}m\\ 2m&0\\ \end{pmatrix}\begin{pmatrix}-m&\sqrt{3}m\\ -m&-\sqrt{3}m\\ 2m&0\\ \end{pmatrix}\begin{pmatrix}2m&0\\ \end{pmatrix}\] (a) (b) (c) (d) (e) (f)  
In the triangles shown in Figure 11a,b, the center of gravity (COG) of the support triangle is located outside the triangle, and the stability margin is negative, indicating that the robot cannot maintain stability in the posture, hence this method is unreasonable. In the cases shown in Figure 11c-e, the support triangle passes through the center of gravity, and the stability margin is in a critical state. In this situation, the probability of the robot tipping over is high, which is not conducive to the robot's movement on uneven roads and reduces the robot's traversability. However, stability can be improved through stability-enhancement measures; thus, these support triangles are reasonable. In the support triangle shown in Figure 11f, the center of gravity of the legs on one side and the middle leg on the other side is located inside the triangle, and its stability margin is the best among the five support triangles mentioned earlier, indicating the best stability. This represents the maximum expectation for support, making this scheme the most reasonable. [PERSON] [47] conducted a study on the influence of center-of-gravity alterations on the walking stability  
Figure 11: Six types of support triangles, (**a**) the triangle formed by legs on one side, (**b**) the triangle formed by two front legs and a middle leg, (**c**) the triangle formed by the front and middle leg on one side and the rear leg on the other side, (**d**) the triangle formed by two middle legs and a front leg, (**e**) the triangle formed by two rear legs and a front leg, (**f**) the triangle formed by the front and rear leg on one side and the middle leg on the other side.  
of hexapod biomimetic mechanical devices and focused on center-of-gravity trajectory planning. The research also addresses control methods to ensure overall stable walking when any one of the six legs is problematic.