## 4 Dynamic Analysis of the Docking Process
### Dynamic Model and Simulation Analysis of the Docking Process
Under the vertical docking mode, the mass of the moving object is the equivalent mass of the passive motion simulator and the passive docking mechanism, but in the horizontal docking mode, the mass of moving object is only the mass of the passive docking mechanism. Hence, when the initial conditions and the retracting speed of the locking jaw are the same, the impacting force generated by vertical docking is larger, and the effect on the related components is larger. Therefore, we need only perform an analysis of impacts during the docking process in vertical docking mode. In this paper, a set of initial limit conditions are taken for co-simulation in the two docking cases of frontal impact and oblique impact, respectively. The initial conditions are shown in Table 1.  
The mass and inertia characteristics of each part of the motion simulator and the docking mechanism are shown in Table 2. The data in the table are obtained from previous theoretical research and experiments [48]. The movement of the locking jaw of the active docking mechanism is realized by controlling the lifting speed of the screw-thread lifting platform. Here, the three locking jaws abide by the same law of motion. In order to make the boundary conditions closer to \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(\mathbf{X/mm}\) & \(\mathbf{Y/mm}\) & \(\mathbf{Z/mm}\) & \(\mathbf{\psi}^{\circ}\) & \(\mathbf{\theta}^{\circ}\) & \(\mathbf{\varphi}^{\circ}\) \\ \hline Frontal Impact & 0 & 0 & 50 & 5 & 0 & 0 \\ Oblique Impact & 40 & 40 & 50 & 5 & 5 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial condition of attitudes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{m}\) (\(\mathbf{Kg}\)) & \(\mathbf{I_{x}}\) (\(\mathbf{Kg}\cdot\mathbf{m^{2}}\)) & \(\mathbf{I_{y}}\) (\(\mathbf{Kg}\cdot\mathbf{m^{2}}\)) & \(\mathbf{I_{z}}\) (\(\mathbf{Kg}\cdot\mathbf{m^{2}}\)) \\ \hline Active Docking Mechanism & 12.9 & 0.624 & 0.827 & 0.827 \\ Passive Docking Mechanism & 2 & 0.198 & 0.198 & 0.285 \\ Mandrel Balancing Assembly & 25 & 2.25 & 2.25 & 5.635 \\ End-Effector & 21.2 & 1.96 & 1.96 & 4.79 \\ Rotating Hanger & 18.5 & 0 & 0 & 3.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristic parameters of mass and inertia. the follow-up experiments and the required design indicators, the speed of the upper and lower thread lifting platforms is defined as 0.01 m/s. The corresponding number of change curves under the two initial docking conditions are obtained through simulation, as shown in Figures 8 and 9. It can be seen from Figure 8a-f that the force trend of the three locking claws is almost the same. It can be seen that the three locking claws receive almost the same force at the same time. Impact force indicates that the three pawls were stable after impact for an impact from the front. It can be seen from Figure 8d that, when the platform is hit by the frontal impact, the force from the impact direction, which was the \(Z\) direction, is relatively large, which is in line with the force situation at the time of design. Although there are forces in the \(Y\) and \(Z\) directions, the force amplitude difference was not big, since the \(X\) and \(Y\) directions are on the same horizontal plane, when the spherical pair is subjected to a force in one direction, due to the action of the structure, it is bound to produce a resultant force of the same size and opposite direction, so that the whole docking mechanism can achieve balance in the horizontal direction, without overturning or horizontal translation. This indicates that the designed structure will not be subjected to too much force in individual directions to cause attitude deviation after being hit. Figure 8: Curves of corresponding quantities under the frontal impact (**d**) for locking jaw 1 (**a**) for locking jaw 2 (**b**) for locking jaw 3 (**c**) between the passive docking mechanism and the matching surface (**e**) showing the angular velocity of the spherical joint (**f**) spherical joint.