# Design and Analysis of a Novel Floating Docking Mechanism for On-Orbit Refueling
## 2 Description of the Mechanism
### Mechanical Analysis
The free-body diagram of the free stretching process is shown in Figure 10b, and the driving force can be obtained using the following equation:  
\[F_{d}=\frac{1}{\eta_{g}\cdot\eta_{s}}\cdot\frac{\mu_{L}(x_{L1}-z_{L1}-x_{r}-z _{r})+y_{L1}}{\mu_{L}(-x_{L1}+z_{L1}+x_{d}+z_{d})-y_{L1}}\cdot F_{r} \tag{2}\]  
where \(F_{d}\) is the driving force, \(\eta_{g}\) and \(\eta_{s}\) are the efficiency of the spur gears and trapezoidal screw, \(\mu_{L}\) and \(f_{L}\) are the friction coefficient and friction of the linear guideway, \(D\) is the point of action of the driving force, \(L_{1}\) and \(L_{2}\) are the endpoints of the linear guideway, \(N_{L1x}\) and \(N_{L2x}\) are the supporting forces of points \(L_{1}\) and \(L_{2}\) along \(x_{w}\)-axis, and \(N_{L1z}\) and \(N_{L2z}\) are the supporting forces of points \(L_{1}\) and \(L_{2}\) along \(z_{w}\)-axis. 2 Contact and alignment The drogue and probe must then make contact and self-align by completing steps (c), contact and alignment I; (d), probe insertion and alignment II; and (e), pin insertion  
Figure 10: Free-body diagram of (**a**) the preloading condition of spring pins and (**b**) free stretching. and alignment III. Through this process, the drogue makes contact with the probe and must compete with the spring force of the pipe, the friction of the linear guideway and linear spring pins, and the contact force is affected by the spring force of the spring pins. Considering step (c) as an example to summarize the factors influencing the driving force, a free-body diagram of this step is shown in Figure 11, and the driving force can be obtained by the following equation:  
\[\left\{ \begin{array}{c}F_{d}-F_{r}-f_{L}=N_{cy}+f_{cy}\\ F_{s3}+f_{s13}=N_{c2}-f_{c2}\\ F_{s4}+f_{s24}=N_{cx}-f_{cx}\end{array} \right. \tag{3}\]  
where \(N_{c}\) and \(f_{c}\) are the component forces of the contact force, representing the normal contact force and the tangential contact force, respectively, acting on the drogue through the probe. The subscripts represent the direction of the component force, representing the component force of \(N_{c}\) along the \(y\)-axis, and \(F_{s}\) and \(f_{s}\) are the spring force and the friction of the linear spring pins along the corresponding axis acting on the drogue. In step (c), the contact force is related to the spring forces of the two linear spring pins. Similarly, the contact force of process (d) is related to the spring forces of the yaw and pitch spring pins and (e) to that of the roll spring pins; thus, the driving force is determined by the contact force. Therefore, decreasing the spring force (preloading and axial stiffness) of the spring pins decreases the driving force. 3. Accomplishing and resetting  
After the process of contact and alignment, the drogue has achieved the correct alignments and is ready for step (f) and connector docking. By this time, the spring pins have reached the maximum amount of compression, and the spring forces compressed the drogue on the probe. Thus, the driving force of process (_f_) can be obtained using the following equation:  
\[F_{d}=F_{r}+f_{L}+f_{dp}+F_{ie} \tag{4}\]  
where \(f_{dp}\) is the friction between the drogue and probe, and \(F_{ie}\) is the insertion and extraction forces of the fluidic and electric connectors. After process (f), the docking process is complete, and the mechanism refuels the client craft. The drogue will separate from the probe after refueling, and to ensure that the docking mechanism can be reused, the preloading of the spring pins must be high enough to reset the drogue. Considering the extreme case, the drogue does not reset until it completely breaks away from the probe.