## 4 Numerical Analysis and Discussion  
### Parameter Effects  
The effects of the design parameters in Table 1 on the lockable maximum load of the closing spring \(F_{\rm ml}\) and the permissible stroke of the locking tab \([L]\), respectively, are analyzed in this section. Assume that the parameters of the low-power holding mechanism are: \(\lambda=45^{\circ}\), \(\varphi=5.7^{\circ}\), \(S=850\) mm, \(R=183\) mm, \(F_{\rm D}=1600\) N, the required working stroke of the locking tab \(L=8\) mm, and the design variable ranges are listed in Table 3.  
Figure 10 shows the variable effects on the lockable maximum load of the closing spring \(F_{\rm ml}\). \(F_{\rm ml}\) can be increased by increasing \(r_{2}\) and/or reducing \(\alpha\). According to Equations (5), (10) and (11), in the holding process, the resistance arm, \(r\), increases with the increase in \(r_{2}\) or decrease in \(\alpha\), while the resistance force, \(F_{\rm t}\), decreases with the increase in \(r_{2}\) or decrease in \(\alpha\), and the reduction in \(F_{\rm t}\) is greater than the increment in \(r\), resulting in the decrease in the total resistance torque \(T\). Thus, with a given maximum lockable load, \(F_{\rm ml}\), the required force, \(F_{\rm D}\), of the electromagnet can be reduced by increasing \(r_{2}\) and/or decreasing \(\alpha\); in other words, with a given output force, \(F_{\rm D}\), of the electromagnet, the maximum lockable load, \(F_{\rm ml}\), can be increased by increasing \(r_{2}\) and/or decreasing \(\alpha\).  
As shown in Figure 10, \(F_{\rm ml}\) decreases with the increase in \(r_{3}\) and \(l\). According to Equations (5), (10) and (11), both \(r\) and \(F_{\rm t}\) increase with the increase in \(r_{3}\) and \(l\), resulting in the increase in the total resistance torque \(T\). Thus, with a given output force, \(F_{\rm D}\), of the electromagnet, the maximum lockable load, \(F_{\rm ml}\), can be decreased by increasing \(r_{3}\) and \(l\).  
Figure 10: The lockable maximum load of the closing spring with (**a**) effects of \(r_{2}\) and \(l\); (**b**) effects of \(r_{3}\) and \(\alpha\).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Design Variable Description** & **Variable** & **Variable Range** \\ \hline Radius of the actuator working cavity & \(r_{1}\) & 130–150 mm \\ Radius of the notch of the locking ring & \(r_{2}\) & 130–150 mm \\ Radius of the locking tab & \(r_{3}\) & 10–20 mm \\ Center distance between the actuator working cavity and the locking ring notch & \(l\) & 30–40 mm \\ Radial deflection angle of the center of the locking ring notch & \(\alpha\) & 35–45\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The design variable ranges.  
Figure 11 shows the variable effects on the permissible stroke of the locking tab [\(L\)]. [\(L\)] increases with the increase in \(r_{1}\) and \(\alpha\) or decrease in \(r_{3}\). The reason is that the angle of the notch of the locking ring, \(\delta\), increases with the increase in \(r_{1}\) and \(\alpha\) or decrease in \(r_{3}\), resulting in the rise of the rotation angle, \(\theta\), of the locking ring in the locking or unlocking process. Thus [\(L\)] increases with the increase in \(r_{1}\) and \(\alpha\) or decrease in \(r_{3}\).  
As shown in Figure 11, [\(L\)] can be decreased by increasing \(r_{2}\) and/or decreasing \(l\). The reason is that as shown in Figure 9, the position of the contact point of the locking tab in the unlocking state, is not affected by the variation of \(r_{2}\) and \(l\), while the position of the contact point of the locking tab in the locking state show upward tendency with the increase in \(r_{2}\) or decrease in \(l\), resulting in the reduction in the relative position distance between the contact point in the locking state and that in the unlocking state. Thus [\(L\)] decreases with the increase in \(r_{2}\) or decrease in \(l\).