## 4 Dynamic Simulation Analysis of the Vehicle Side-Door Latch
#### Analysis of Simulation Results of Spatial RRURR Mechanism  
We simulated the electric releasing process of the vehicle side-door latch by ADAMS. The joint angle and corresponding time of the electric releasing mechanism during the releasing and reset processes are plotted as shown in Figure 13. In electric releasing mode, the motor-drive phase lasts from 0 to 118 ms. The ratchet and pawl start disengaging at 86 ms and separate at 108 ms. The ratchet resets under the force of the torsion spring and rotates to 70.53\({}^{\circ}\), releasing the door latch. The gear crank reaches its maximum angle of 56.99\({}^{\circ}\), and the pawl reaches its maximum angle of 12.66\({}^{\circ}\) at 118 ms. The incomplete gear and crank gear separate at 118 ms. The crank gear and pawl rotate back to their original positions under the force of the torsion spring at 122.4 ms and finish the electric releasing process. During the electric releasing process, the actuating torque of the crank gear continuously increases due to the torsion spring force, its actuating-torque variation curve of the crank gear in electric releasing mode, as shown in Figure 14. The maximum actuating torque of the crank gear obtained from the simulation is 352.73 N\(\cdot\)mm. Under the transmission ratio of 1:120, considering the overall motion/force transmission performance index \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Stiffness Coefficient (N\(\cdot\)mm/\({}^{\circ}\))** & **Preload (N\(\cdot\)mm)** \\ \hline Pawl torsion spring & 2.2 & 380 \\ Ratchet torsion spring & 0.5 & \(-\)510 \\ Crank gear torsion spring & 2.2 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Spatial RRUPRR mechanism torsion-spring stiffness coefficient and preload parameter table. Figure 13: Joint angle and corresponding time of the electric releasing mechanism during the releasing and reset processes. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Mass (g)** & **Material** \\ \hline Crank gear \(l_{AB}\) & 0.52 & 7500 Nylon \\ U joint connecting bar \(l_{BC}\) & 0.21 & 7500 Nylon \\ Grooved connecting bar \(l_{CD}\) & 0.15 & 7500 Nylon \\ Pawl plate \(l_{DE}\) & 10.3 & 45 Steel \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The connecting bar mass parameters of the electric releasing mechanism. of the serial mechanism proposed above, the rated torque required for the motor during electric releasing is calculated as follows:  
\[ \begin{split} T_{motor}&=\frac{T_{\text{cmd}}\;\text{gur }}{\gamma_{T}\cdot\text{I}}\\ &=\frac{352.73}{120\times 0.93}\approx 3.16\;\text{N}\cdot\text{mm} \end{split}  \tag{20}\]  
The MABUCHI MOTOR FC-280 SC (Matsudo City, Japan) is a typical motor for vehicle side-door latches, and its rated torque is 3.95 \(\text{N}\cdot\text{mm}\). The rated torque is larger than the simulated torque required, demonstrating that the mechanism has practical feasibility. As shown in Figure 14, the actuating torque during electric releasing increases with input rotation angle \(\theta_{1}\) due to the pawl and ratchet torsion springs. Notably, the trend of the actuating-torque curve is coincident to that of the motion/force transmission performance curve. When the crank gear reaches \(\theta_{1}=92.88^{\circ}\), the actuating torque becomes zero because of the acceleration generated by the pawl torsion spring when the ratchet and pawl separate. Despite this transient torque discontinuity, the motion/force transmission performance index remains unaffected, indicating its sole dependence on input angular displacement. When the crank gear reaches \(\theta_{1}=101^{\circ}\) at 118 ms (corresponding to Figure 13), the incomplete gear and the crank gear separate and the maximum actuating torque occurs. At this moment, the overall motion/force transmission performance index of the electric releasing chain is 0.93.