# 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 Leg Structure
#### 3.1.2 Structural Analysis  
Figure 4a is a simplified schematic of the leg mechanism derived from the analysis of Figure 3; the red sections B and C represent the knee and hip joints. We perform a force analysis on the schematic diagram of the leg mechanism based on the contents of Section 3 in _Machine Design_ by [PERSON] [43]. In Figure 4b, the motor at location 1 is subjected to not only torque \(M_{\text{Cl}}\) but also a radial force \(F_{\text{C2}}\), which is a component of the force \(F_{\text{C}}\), exerted on the motor. At location 2, the force \(F_{\text{C}}\) generates a bending moment \(M\) on the motor's output shaft.  
It is necessary to optimize the design of this structure in light of the robot's own weight, the various devices it must carry under various operating scenarios, and the types of motors it can choose from. We carry out the following structural optimization designs for structural units I and II.  
Structural unit I: As shown in Figure 5a, adjust the position of the power source and adapt the structure of rods AB and BC in Figure 4a to form a new leg-lifting mechanism.  
Figure 3: Spider leg joint motion diagram.  
As depicted in Figure 5a, the motor drives the screw as the driving element. Since the slider is restricted, it will not rotate by itself. When the leg is under force, the motor does not need to be in a stalled state, which reduces the loss of the motor. In addition, the support structure should be used as a direct load-bearing unit for the screw, and the motor has no additional load loss. When designing the screw, we adopted a large pitch to ensure that it withstands a large load and degrades the motor selection requirements.  
Freedom degree analysis is conducted for this mechanism. We adopted the planar freedom degree calculation formula, i.e., Equation (1), to analyze the freedom degree of structural unit I, given that components 2 and other mechanisms are in parallel planes:  
\[F=3n-2P_{l}-P_{h} \tag{1}\]  
In Equation (1), \(F\) is the degree of freedom, \(n\) is the number of active components, \(p_{l}\) is the number of lower-pair joints, and \(p_{h}\) is the number of higher-pair joints.  
Consequently, the degree of freedom \(F_{1}\) at structural unit I is 1.  
As displayed in Figure 5b, the motor drives the worm as the driving element. The self-locking performance of the worm gear mechanism can ensure that the leg will not rotate when it is stationary, and the motor does not need to be in a stalled state; then, since the maximum rotation angle is 120 degrees, the larger transmission ratio can reduce the starting torque of the motor and provide a sufficient torque, so as to achieve a fast and powerful rotation of the leg and reduce the selection requirements of the motor.  
Similarly, the degree of freedom \(F_{2}\) of structural unit II is 1.  
Figure 4: (**a**) Schematic diagram of the overall leg structure; (**b**) force analysis of the leg.  
Figure 5: (**a**) Schematic diagram of structural unit I; (**b**) schematic diagram of structural unit II.  
In summary, the degree of freedom of each mechanical leg is \(F=F_{1}+F_{2}=2\), which meets the freedom design requirements of Section 3.1.1 for the movement of the leg.