# Design and Analysis of a Novel Floating Docking Mechanism for On-Orbit Refueling
## 2 Description of the Mechanism
### Mechanical Analysis  
In Section 2.1.1, the design requirements R1 and R2 have been met. As another core design criteria, R3 must decrease the driving force during the docking process to decrease the power consumption of the motor and facilitate successful docking. In this section, the mechanical analysis of the system, which was used to guide the design of the driving force, is discussed. The drogue is in a state of low speed and uniform motion throughout the docking process; thus, the docking can be considered as a quasi-static process. The kinematic diagram of the mechanism is shown in Figure 9.  
Figure 9: Kinematic diagram of the docking mechanism. The red arrows and the red points represent the preloading spring forces and the points at the corresponding spring pins acted on the drogue, respectively; the 3D model and the principles of the mechanism can be seen in Figures 4 and 5. From the viewpoint of the docking process, as shown in Figure 8, the mechanical analysis can be divided into three parts:  
1. Free stretching The (a) initial and (b) approach stages of docking comprise the process of free stretching and do not involve contact. The drogue stretches and breaks away from the anti-overload strengthening to float. Owing to the characteristics of the elliptical-helical configuration with bias loading of the refueling pipe, the bias torque generated by the pipe acts on the drogue. To maintain the initial attitude of the drogue, the corresponding spring pins must have sufficient preloading to compete with the bias loading of the pipe, or the drogue will slant, and the initial deviations will increase, resulting in failed docking. The free-body diagram of the initial floated state is shown in Figure 10a, and the preloading conditions of the corresponding spring pins can be obtained by the following equation: \[\left\{ \begin{array}{l}F_{is1}>-\frac{F_{r}\cdot z_{r}+h_{s}\cdot F_{r}\cdot r _{s24}}{z_{s1}}\\ F_{is2}>-\frac{F_{r}\cdot z_{r}-h_{s}\cdot F_{r}\cdot r_{s13}}{x_{s2}}\end{array} \right.\] (1)  
where \(F_{is1}\) and \(F_{is2}\) are the preloading of the resetting spring pins for pitching and yawing respectively, \(F_{r}\) is the axial force of the refueling pipe, \(\mu_{s}\) is the friction coefficient of the spring pins and frame, \(r_{s}\) is the radius of spring pins, \(S_{1}\) is the point at which the resetting pitching spring pin acts on the yawing spring pin, \(S_{2}\) is the point at which the resetting yawing spring pin acts on the pitching spring pin, \(R\) is the point at which the refueling pipe acts on the drogue, \(S_{1}S_{3}\) and \(S_{2}S_{4}\) represent the yawing and pitching spin axes respectively, and \(x\) and \(z\) represent the distance between a point corresponding to the subscript and another axis; for instance, \(z_{s1}\) represents the distance between point \(S_{1}\) and \(x_{r}\)-axis. Then, the drogue stretches at a constant, continuous speed until it contacts the probe. The servo motor generates the driving force of the drogue to compete with the resistance forces, including the axial force of the refueling pipe and the friction of the linear guide-way. The spur gears and trapezoidal screw of the driving subassembly lead to an efficiency loss of the driving force.