# A Single Motor-Driven Focusing Mechanism with Flexure Hinges for Small Satellite Optical Systems
## 4 Conclusions and Discussion  
In this paper, the SMFH was proposed to correct the mis-alignments of an optical system in small satellites. The presented SMFH corrects the alignment of a secondary mirror in a Schmidt-Cassegrain optical system. A novel structure with radial slits was proposed to reinforce the bending stiffness and maintain compliant axial stiffness. To investigate its mechanical characteristics, a static structural analysis was carried out. As a result, the FlexHe that features five slits was identified as the optimal design. Then, an extension test for a single optimized FlexHe was performed to determine its reaction force. The reaction force applied on the three FlexHes was measured to 30 N. The desired pushing force for the linear screw was measured at approximately 45 N, while multiplying a safety factor of 1.5. Based on the obtained reaction force, a geared motor having a torque of 230 mN\(\cdot\)m was employed. The SMFH integrating three FlexHes was fabricated. To identify the proper preload, optimization was performed through an experimental study. By using six different pre-stretched lengths, we obtained  
Figure 9: Experimental results for the input versus the optical alignments; (**a**) De-space, (**b**) De-center, and (**c**) Tilt.  
a different hysteresis for each case. Among them, Case 4, having a pre-stretched length of 3 \(\upmu\)m, showed a minimized hysteresis of 6.52%. For further investigation, the cyclic compression/extension test was repeated in ten trials, and we numerically compensated for any structural deformations caused by gravity. As a result, the proposed SMFH was not only able to generate a 23.93 \(\upmu\)m stroke in a longitudinal direction (De-space), but also to achieve a maximum De-center and Tilt of 5.20 \(\upmu\)m and 88.45 \(\upmu\)rad, respectively. Moreover, given the resolution of the geared motor, the control system allowed the proposed device to achieve a high resolution of De-space control at a maximum of 0.1 \(\upmu\)m. The SMFH ensures the requirement of optical alignment. The control resolution for the De-space was not over 0.1 \(\upmu\)m; thereby, the minimum control step of MTF identified 0.22%, allowing the maximum MTF to achieve 37%.  
Consequently, the proposed SMFH showed promising feasibilities. Among them, the primary contribution of this study is to present a simplified structure that embeds a single motor, and it is anticipated to consume less satellite power. Moreover, in light of our findings on the interpolated relation of the input versus the De-space, a simple yet precise feedback control system can be achieved, without embedding exteroceptive sensors. These promising advantages could provide opportunities that the proposed SMFH will be able to perform the desired objectives passively, and to complete an advanced mechanism ensuring low-cost and simplicity.  
However, the need still remains for further studies on the mechanical behaviors of the structure in extreme space environments (i.e., extremely high/low temperature, vacuum, vibration, etc.). With this in mind, our future works will focus on furthering the objectives of simplifying SMFH, reducing satellite size, power consumption, and expense.