# Structural Design, Simulation and Experiment of Quadruped Robot
## 2 Structure Designs
### Selection of Actuators  
The choice of actuator largely determines the locomotion performance of the quadruped robot. Due to the weight of the robot itself, the actuator has to generate high torque with a fast response and a compact size. Brushless motors are widely used because of their excellent dynamic characteristics, but they are generally less affordable and large in size. Since the main focus of this paper is the implementation and preliminary evaluation of the gait algorithm on the desktop-level model, the rudder servo is selected as the drive source. While the servo does not provide feedback for the angular displacement signal directly, the very high built-in gear ratio of the servo makes it acceptable for low-speed gait and self-balancing tests. The servo model is SPT-5425, as shown in Figure 7, and its specific parameters are shown in Table 1.  
To verify the torque rating of the chosen rudder servo, the following analysis is performed. Based on the analysis in Section 2.4, influence of the torque on the lower leg is most significant. Denote the angle between the normal ground contact force \(F_{N}\) and \(L_{AB}\) as \(\alpha\), and the angle between \(L_{DC}\) and \(L_{EC}\) (i.e., the length of the ball-head linkage) as \(\beta\), shown in Figure 8. Then, the following holds:  
\[F_{N}L_{AB}\sin(\alpha)=F^{\prime}{}_{t}L_{CB} \tag{2}\]  
where \(F^{\prime}{}_{t}\) is the projection of the ball-head linkage force \(F_{t}\) on \(L_{DC}\), namely,  
\[F^{\prime}{}_{t}=F_{t}cos(\beta) \tag{3}\]  
For the given linkage force, when DE is perpendicular to CE, the torque on the servo shaft reaches the maximum, which is calculated by:  
\[T_{max}=F^{\prime}{}_{t}L_{DE} \tag{4}\]  
During the low-speed trot gait, there are always two feet contacting the ground as support. Therefore,  
\[F_{Nmax}=Mg/2 \tag{5}\]  
where \(M\) is the total mass of the quadruped robot and \(g\) is the gravitational constant.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Model** & **Weight** & **Size (L\(\times\)W \(\times\) H)** & **Operation** & **Max Signal** & **Range of** & **Max Speed** & **Max Torque** \\ \hline SPT- & 5425 & 40.5 \(\times\) 20 \(\times\) & 4.8 V & 330 Hz & 10–180\({}^{\circ}\) & 0.22 s/60\({}^{\circ}\) (@4.8 V) & 24 kg\(\cdot\)cm (@4.8 V) \\
5425 & 57 g & 40.5 mm & 6 V & 330 Hz & 10–180\({}^{\circ}\) & 0.18 s/60\({}^{\circ}\) (@6 V) & 26 kg\(\cdot\)cm@6 V) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters for rudder servo actuator.  
Figure 7: Servo actuator (model SPT-5425) for quadruped robot.  
Substituting Equations (2), (3) and (5) for Equation (4) and considering the dynamic impact contact with the ground yields:  
\[T_{max}=\eta MgL_{AB}L_{DE}sin(\alpha)/(2L_{CB}) \tag{6}\]  
where \(\eta\) (\(>\)1) is the dynamic load coefficient. By plugging in \(M\) = 2.3 kg, \(L_{AB}\) = 0.11 m, \(L_{DE}\) = 0.024 m, \(L_{CB}\) = 0.025 m, \(\eta\) = 1.2, \(\alpha\) = 45\({}^{\circ}\) and \(g\) = 9.8 m/s\({}^{2}\) into the right hand side of Equation (6), \(T_{max}\) is found to be 1.01 N-m or 10.3 kg-cm, which is below the rating of the chosen servo (SPT-5425).