# Dynamic Synthesis of Three -- Point Circle Peripheral Docking Technology Pose
## 4 Dynamic Simulation Analysis
### Simulation Analysis of the Positive Docking Process  
The positive docking process of Condition 1 in Figure 11a indicates that, as the docking rod completely penetrates into the target body, the active vehicle successfully captures the target vehicle and completes the docking task. The simulation results of the docking processes of the two vehicles under Condition 1 are shown in Figure 11b. The target vehicle is represented by the red curve (CHE1), and the active vehicle is represented by the blue curve (CHE2). The simulation results show that when the active vehicle decelerates to approach the target vehicle, the kinetic energy decreases by 77.8%, from 2.35 N\(\cdot\)m to 0.52 N\(\cdot\)m. During the docking process of the docking rod, the kinetic energy oscillation of the driving vehicle rises to 0.57 N\(\cdot\)m. After the docking rod contacts the docking hole, the kinetic energy decreases from 0.57 N\(\cdot\)m to 0.25 N\(\cdot\)m, and after correction, the kinetic energy approaches 0.15 N\(\cdot\)m and tends to be stable. The kinetic energy of the active vehicle decreases by 93.6% in total. During deceleration upon approach, the total kinetic energy of the system decreases from 4.5 N\(\cdot\)m to 0.6 N\(\cdot\)m, which is an 86.6% decrease. After the docking rod contacts the docking hole, the kinetic energy decreases from 0.8 N\(\cdot\)m to 0.3 N\(\cdot\)m. After correction, the kinetic energy approaches 0.25 N\(\cdot\)m and tends to be stable. The total kinetic energy of the system decreases by 94.4%, as shown in Figure 11c. The maximum force on the butt bar for alignment is about 900 N, and the duration is relatively short, at about 0.2 s. The force on the connecting rod stabilizes at about 50 N, as shown in Figure 11d. The maximum reaction force during vehicle body docking is about 2300 N, as shown in Figure 11e. According to the relative speed change between the active vehicle and the target vehicle, the coefficient of restitution \(S\) of the vehicle body after the initial collision is about 0.68, and the coefficient of restitution \(S\) after two contact collisions is about 0, as shown in Figure 11f. The coefficient of restitution \(S\) refers to the ratio of the normal relative separation speed and the normal relative approach speed of the two car bodies at the contact point before and after the collision, expressed as follows:  
\[S=\frac{V_{2}^{{}^{\prime}}-V_{1}^{{}^{\prime}}}{V_{2}-V_{1}}\]  
\(V_{1}\) and \(V_{2}\) represent the speed of the active and target vehicles before the collision, and \(V_{1}^{{}^{\prime}}\) and \(V_{2}^{{}^{\prime}}\) represent the speed of the active and target vehicles after the collision.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & **Feed Range** & **Angle of** & **Initial Velocity** & **Final Velocity** \\  & **(mm)** & **Inclination (\({}^{\circ}\))** & **(m\(\cdot\)s\({}^{-1}\))** & **(m\(\cdot\)s\({}^{-1}\))** \\ \hline \multirow{2}{*}{1} & 2000–50 & 0 & 1 & 0.2 \\  & 50–0 & 0 & 0.2 & 0.2 \\ \hline \multirow{2}{*}{2} & 2000–50 & 3 & 1 & 0.2 \\  & 50–0 & 3 & 0.2 & 0.2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Initial Condition Parameters of Space Docking System.  
Figure 11: _Cont._