# Design Analysis of a Passive Buffer System for Space-Assembled Segmented Mirrors
## 3 Buffer System Validation  
At present, one of the important factors restricting the development of on-orbit PM assembly is how to connect the modular PMAs, which can ensure that the assembled telescope achieve optical performance requirements. The mechanical strength and precision need to be satisfied between PMAs, so the design of the connection mechanism plays an important role. In this section, the proposed double-elastic contact model is considered for the androgynous connection mechanism, SMALL. This modularization scheme is a critical conceptual upgrade attached to the optical elements, as illustrated in Figure 4.  
It is predominantly comprised of: A chamfered entrance hole and a grooved protruding pin which increase docking tolerances; a positioning channel to correct alignment error by limiting five degrees of freedom (DOFs); a latch lock to connect two adjacent modules rigidly; and a linear actuator to control the clearance between combined parts. This compact and simple interface is attached to the outer wall of the PMA base, which solves the defects, such as high energy consumption, high operation difficulty, insufficient locking force, and low adjustment precision, compared with the traditional connection mechanism. The operation principle of SMALL is explained as shown in Figure 5. In the capture stage, under the monitoring of the camera, two SMALLs are simultaneously close to each other. The pins will make contact with the opposing holes, as shown in Figure 5a. During the positioning stage, the pins enter the positioning channels to limit five DOFs of the combination. Only one DOF is left along the axis hole direction, as shown in Figure 5b. In the locking and adjustment stage, the groove of the pin engages with the locking mechanism, which has twelve locking teeth [21]. After the lock is completed, the internal actuators of SMALLs start to align the gap between the two mirror segments to a reasonable range, as shown in Figure 5c. In the separation stage, the locking teeth expand outwards, with the assistance of the extended semi-rigid stick within the grooved pin, separating the two connection mechanisms from each other as shown in Figure 5d. The SMALL adopts a flexible design of the inner-wall of the tapered cone. Eight flexure sections are evenly distributed on the chamfered surface. As shown in Figure 4, the gap between the flexible sections and the tapered surface is consistent. According to the design requirements, the deformation of the buffer system should be within 0.002 m according to the material properties and structural characteristics. Taking the actual working environment into account, it is assumed that the driving force is with the range of 100 N-500 N, and the protruding pin and the inner-wall of the hole are made of TC4. The docking parameter specifications are shown in Table 1.  
Figure 4: Introduction of a modular PMA (**left**) and the design scheme of SMALL (**right**). Figure 5: Operation principle of SMALL: (**a**) capture, (**b**) positioning, (**c**) locking & adjustment, (**d**) separation. According to the double-elastic model, the deformation and compressive stress can be acquired from  
\[\left\{ \begin{array}{l}\delta=1.99e-7\left[\frac{F^{2}(0.02+R_{1})}{R_{1}}\right] ^{\frac{1}{3}}\\ f_{0}=0.12e9\left[\frac{F(0.02+R_{1})^{2}}{R_{1}^{2}}\right]^{\frac{1}{3}}\end{array}  \right.. \tag{11}\]  
Depending on the location of the collision point, the value of the \(R_{1}\) is changing. Assuming that the \(Z\)-axis is along with the center axis of the conical hole, and the propulsion depth of the pin head is denoted by \(z\), the elastic pin head makes the first collision with the elastic inner wall. Then there is:  
\[R_{1}=\frac{(0.020-z)\tan\beta}{\cos\beta} \tag{12}\]  
With the different values of \(F\), the maximum deformation and the maximum compressive stress are shown below. The line graph, illustrated in Figure 6, demonstrates the relationship between the maximum collision deformation and the driving force under different depths of propulsion.