# Design and Analysis of a Novel Floating Docking Mechanism for On-Orbit Refueling
###### Abstract
Capture--the service spacecraft captures the client spacecraft using a robotic manipulator. 3. Pullback--the robotic manipulator pulls back and adjusts the attitude of the client spacecraft toward the service spacecraft until the position of the spacecraft falls within  
Figure 1: Steps of berthing and joining by stretching: (**a**) approach, (**b**) capture, (**c**) pullback, (**d**) docking. the docking conditions. By this time, the relationship between the service spacecraft and client spacecraft is relatively stationary. 4. Docking--the active part of the docking mechanism stretches and eventually docks with the passive part to build a propellant transfer pipeline. For berthing and joining by stretching, the initial position and attitude deviations be-tween the two spacecraft may occur owing to the flexibility and control error of the robotic manipulator. To eliminate these deviations, it is necessary to enable the alignment of the docking mechanism. Moreover, the self-resetting capability of the docking mechanism is also required to return the docking subassembly back to its initial position and attitude after docking and prepare for the next refueling operation. In addition, a refueling pipe connected to the docking subassembly can be stretched synchronously with a docking subassembly during stretching. Considering the compatibility between propellants and the refueling pipe and the high pressure of propellants, the refueling pipe can be generally composed of hard metals, such as titanium or aluminum alloys, rather than flexible materials [27]. Thus, a nonnegligible additional force on the driving assembly of the refueling pipe should be considered in the design of the docking mechanism. Owing to the single stretching direction of the refueling pipe--that is, the docking direction--a helical configuration is a suitable choice for the refueling pipe to decrease the additional force, as shown in Figure 2. The mechanical properties of helical pipes--especially axial stiffness--need to be researched, which directly affect the additional force. At present, scholars have mainly focused on circular-helical structures, such as helical springs. [PERSON] [28] derived spring rates by [PERSON]'s second theorem. [PERSON] et al. [29] proposed a type of shape memory alloy (SMA) helical spring for an SMA actuator. [PERSON] et al. [30] derived the exact stiffness matrix of curved beams with nonuniform cross-sections by a direct method. [PERSON] [31] studied the relationship between helical spring compliances and free- and fixed-end rotations. [PERSON] [32] derived the classical formula for a circular-helical spring using an energy-based method. For the on-orbit mechanism, its design space is limited and irregular. An elliptical-helical refueling pipe is more appropriate in compact docking mechanisms than a circular-helical refueling pipe to further decrease the additional force by increasing the envelope of the pipe (decreasing the axial stiffness of the pipe). However, there is almost no research on elliptical-helical structures. For further design and analysis, the axial stiffness of elliptical-helical pipes must be researched, and the expression of the additional force can be derived by analogy with helical springs. This paper presents a novel floating docking mechanism for on-orbit refueling by berthing. The capacities of the proposed docking mechanism with passive five-DOF alignment for initial deviations and passive self-resetting for multiple refueling are realized using several spring pins. The mechanism is lightweight, simple, and compact in structure based on the probe-drogue configuration. An elliptical-helical pipe configuration with bias loading was proposed to decrease the additional force on the driving subassembly. Then, the influence mechanism of the additional force of the proposed pipe on the docking process is obtained by mechanical analysis, which determines the design of the spring pins and the driving force.