# Design and Analysis of a Novel Floating Docking Mechanism for On-Orbit Refueling
## 4 Analysis and Discussion of Simulations and Experiments
### Dynamics Analysis of the Docking Mechanism  
A dynamic simulation and experiment on the contact force and driving force of the docking mechanism are performed in this section to verify the positive influence of the elliptical-helical refueling pipe on the docking mechanism with bias loading. The simulation and experiment took no account of gravity. As discussed in Section 2.3, the driving force is determined by the preloading and axial stiffness of the spring pins, and these characteristics of the spring pins are determined by the spring force of the refueling pipe. Therefore, decreasing the spring force of the refueling pipe can significantly decrease the driving force of the docking mechanism. A helical structure can decrease the resistance further for motion in a straight line, so a circular-helical pipe with center loading is proposed for such an application. By considering the loading point and the design space, as shown in Figure 7, three other types of analogical pipes can be proposed: a circular-helical pipe with bias loading, elliptical-helical pipe with center loading, and elliptical-helical pipe with bias loading, as shown in Figure 21. In addition, the preloading condition (Equation (1)) and the resetting condition (Equation (5)), each type of pipe can be matched with a set of spring pins, as shown in Tables 5 and 6. Figure 19: Components of the kinematic/dynamic (**a**) simulation system (**b**) experiment system. Figure 20: Kinematic results of tolerance range of the docking mechanism. \(\Delta d\) represents the two linear deviations, \(\Delta\theta\) represents the three angular deviations, the dashed line represents the estimate tolerance range, the circles represent successful docking, and the triangles represent failed docking. Empty symbols are considered according to the central symmetry of structure to be extrapolated results. force is thus to show the superiority of the configuration using the elliptical-helical pipe. The 3D model is the same as that used in the kinematic simulation. For the simulations of contact force, four types of working conditions are sufficient to verify the validity of the dynamic model, including three typical decoupling conditions, (\(X\)\(-\)2 mm), (Roll \(-\)1\({}^{\circ}\)), (Yaw \(-\)1\({}^{\circ}\)), and one typical coupling condition, (\(X\)\(-\)2 mm, Roll \(-\)1\({}^{\circ}\), Yaw \(-\)1\({}^{\circ}\)). Then, corresponding experiments were performed to validate the results of the simulations. The dynamic experimental system is the same as that used in the kinematic experiment system, as shown in Figure 19. A six-component force sensor installed at the root of the probe is used to detect contact forces. The key positions of the docking are shown in Figure 22, used to support dynamic results. The results of the contact force simulations and experiments are shown in Figure 23. Four types of working condition are setting, which can cover the whole docking conditions. The points worth noticing are points B, C, and D, which are the turning points of docking state. The curve worth noticing is \(F_{y}\), which is the contact force of the docking direction and influence the driving force directly. As shown in Figure 23, the trends (especially curve \(F_{y}\)) and most of the values (especially points C and D) of the experiment curves can correspond by the simulation curves. In view of machining errors, sensor accuracy and the estimation of friction coefficient, the agreements between simulations and experiments are more than 70% and the key points and curves are more than 85%, which reciprocally verifies the validity of the simulations and experiments. Therefore, the driving forces of the mechanism with four types of pipes above can be obtained from the simulations instead of experiments, which can save time and resources, to verify the superiority of the proposed elliptical-helical refueling pipe and meet the requirement R3 in Section 2.