1. Introduction
Although a small satellite has limited dimensions, it has shown promising potential to observe the earth [
1,
2,
3] with many advantages, i.e., lower launching expenses [
4], less energy consumption [
5,
6], and shorter lead-times [
7], etc. Recently, small satellites have been able to accommodate an expanding range of functions due to the rapid development of device miniaturization, including advances in chipsets. Hence, despite its limited volume, the small satellite can perform various missions in space [
8,
9,
10]. For these reasons, small satellites have been emerging as a new and energy-efficient technology, enabling them to replace bulkier, more expensive and less efficient conventional satellites.
For small satellites, an optical system is crucial to perform observations towards the earth or space, providing both high image resolution and minimum geometric distortion. However, the optimization of these optical systems is still a challenge due to their limited dimensions and the extreme environmental conditions, i.e., vibrations [
11], shock loading during launch [
12,
13], a dramatic temperature change [
14], or high vacuum pressure in space [
15], etc. Also, these harsh environments could cause mechanical damage, i.e., material failures of the system [
16,
17]. For instance, high vacuum pressure in space causes outgassing between the mounted (assembled) surfaces [
18,
19]. The extremely high temperature causes the evaporation of atomic oxygen distributed on the surface of the secondary mirror, which possibly leads to distortion and mis-alignment of the optical system [
20]. Consequently, such mis-alignment causes degradation of the image quality and/or resolution [
21].
In light of these constraints, optical systems should have features that ensure consistent performance in harsh environments, and rigorous design is needed to successfully integrate the specified type of optics. In particular, the performance of the optical system should be evaluated in terms of image resolution (i.e., pixel, MTF, etc.). Among the evaluation parameters, MTF (Modulation Transfer Function) has been commonly used to quantify optical alignments [
22,
23,
24]. By forecasting and anticipating these quantified mis-alignments, high-resolution pictures can be obtained by means of mechanical or systemic compensation solutions [
25,
26,
27].
In the case of the former, by investigating the novel mechanisms or identifying the optimal structures, the performance of the optical system can be improved. Indeed, many structural designs for small satellites have been studied [
28,
29,
30]. Among them, Lee et al. approximated the deflection of the primary mirror due to its own weight and presented an optical system based on an evaluation of optical tolerance [
31]. The error (0.0015° in deflection) that occurred between the primary mirror and supporting shaft was well-defined, yet these measurements and the resulting bulky structure of the optical system cannot be accommodated or adapted for small satellites. On the other hand, Franzoso et al. proposed a refocusing mechanism that can be controlled by means of thermal expansion [
32]. The degradations of Tilt and De-center were only 0.5 arcsec and ±10 µm, respectively. The main advantage of this design was to implement the accurate actuation of the inner and outer cylinders, and its mechanical characteristics are independent of the environmental conditions. Despite these efforts, both cooling and heating actions could consume lots of energy to operate. To decrease working temperatures of the thermally-driven refocusing mechanisms, Selımoglu et al. presented a novel mechanism that produces 30 µm of De-space, with respect to 10 °C variation in temperature [
33]. Here, they reduced energy consumption, but the stroke was relatively small, compared to the size of the secondary mirror (Diameter: 144 mm). In summary, such thermally driven refocusing mechanisms need to be further developed in order to achieve low energy consumption and adequate performance. In addition, a material with properties that resist fatigue, thermal expansion, hysteresis, and other failures should be further studied [
34].
In contrast to thermally driven systems, Kuo et al. presented a direct transmission-based refocusing mechanism [
35]. The secondary mirror (M2) was controlled by linear motion, and the Tilt was achieved by controlling rotational motion. The proposed design allowed not only the De-space to displace 25 µm in a longitudinal direction with a resolution of 0.5 µm, but also the Tilt to rotate ±3° with 6 s of arc of resolution. However, by using two actuators, the energy consumption of such mechanisms could be quite high, in contrast to a single actuator-driven mechanism.
Based on the introduced scope, the main objective of the focusing mechanism is to achieve a simple yet reliable control system that integrates a single-geared DC motor. The proposed single motor-driven focusing mechanism can save the energy consumption and control the De-space precisely using a Flexure Hinge (FlexHe) that features zig-zag patterned slits in a radial direction. The FlexHe can ensure its structural elasticity, and its novel design was conceived to reinforce bending stiffness, as well as to provide relatively compliant axial stiffness. First, the mechanical behaviors (i.e., elasticity, stress concentration, strain energy, etc.) of the FlexHe were investigated. Through a Finite Element Method (FEM) simulation, optimization was performed. For further investigation, a fatigue analysis was carried out, and the available life cycle was determined. Then, we fabricated the FlexHe, and a novel focusing mechanism was proposed by integrating three FlexHes, radially arranged at 120° from each other. The so-called Single Motor-driven Focusing mechanism with Flexure Hinges (SMFH) was successfully assembled. By using a single-geared DC motor and LVDT (Linear Variable Differential Transformer) sensors, SMFH demonstrated their potential to expand into practical use in space as well as to provide more insights into the future of small satellites. To demonstrate its feasibility, the targeted optics type is Schmidt-Cassegrain, which has been widely addressed as a suitable optical system for small satellites [
36,
37]. Its specifications are summarized in
Table 1.
3. Experimental Results
As a result of the rotation body measurements, the relation between the input of the linear screw and the displacements of the rotation body showed a linear behavior. Based on this relationship, the dynamic characteristics of the SMFH were identified by using the SMFH characterization platform. As shown in
Figure 8, the hysteresis of the De-space was observed to 8.73%. Such a hysteresis of a flexible structure has been commonly observed, yet it can be reduced by means of a preload in the opposite direction of deformation. Here, the stretched length of 5 µm ensures the unlimited fatigue cycle described in the fatigue analysis section. To investigate the variation of hysteresis, a cyclic loading/unloading was performed. Six comparison groups were made, with steps of 1 µm pre-stretched lengths, ranging from 0 to 5 µm. Here, since the cyclic traveling begins from the offset origin due to its pre-stretched length, the initial point (
Pi) of the secondary mirror was defined. Then, starting from the initial point (
Pi), a top point (
Pt) and a bottom point (
Pb) were defined.
Where Pt and Pb indicate that the De-space is maximized (Positive) and minimized (Negative) from the initial point. Based on these two points, a single cycle was divided into four steps, from Travel 1 to 4, and each phase is as follows: the secondary mirror moves from Pi to Pt (Travel 1), back from Pt to Pi (Travel 2), and moves from Pi to Pb (Travel 3), back again from Pb to Pi (Travel 4). Namely, Travels 1 and 4 represent loading, while Travels 2 and 3 represent unloading.
As shown in
Figure 8, Case 4 showed a minimum hysteresis of 6.52% at a pre-stretched length of 3 µm, which represents 25.3% lower hysteresis than Case 1, a non-pre-stretched condition. The maximum error for the loading and unloading cycles was only 1.44 µm. Therefore, the optimal pre-stretched length for the secondary mirror supporter was defined to 3 µm (Case 4). For all cases, the hysteresis and the displacements were summarized in
Table 5.
In addition to the investigations of cyclic travel, an evaluation in a zero-gravity environment was performed, as addressed in
Supplementary Material (Text S1). Indeed, since the objects on earth are influenced by gravity, SMFH can deflect under their own weight (See
Figure S2). These undesired deformations may affect the mechanical behavior of the structure. Accordingly, by compensating for gravity, it is possible to mimic a zero-gravity space environment in the experiment. The derived equation with the defined parameters (See
Table S1) eliminates the deflections of SMFH that could occur along the
x,
y, and
z-axes, respectively. To obtain each deflection measurement, the cyclic experiments were performed in 10 trials on each axis.
As shown in
Figure 9a, the De-space can range from −10.93 to 13 µm with a hysteresis of 10.46%, and the maximum error for loading and unloading was 2.47 µm. The loading and the unloading cycles were characterized by means of 5th polynomial fitting, in order to avoid the possible errors between the desired and the current De-space due to the hysteresis. As summarized in
Table 6, the agreement between the interpolated curve and the experimental curve was very good, with R-square of 99.99%. In the case of De-center, its distribution can range from 0 to 5.2 µm, and the hysteresis was 41.60% (
Figure 9b). Conversely, Tilt showed a relatively large hysteresis of 73.63%, yet its response achieved the range of between 0 to 88.45 µrad (
Figure 9c).
4. Conclusion 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·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 a different hysteresis for each case. Among them, Case 4, having a pre-stretched length of 3 µm, 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 µm stroke in a longitudinal direction (De-space), but also to achieve a maximum De-center and Tilt of 5.20 µm and 88.45 µrad, 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 µm. The SMFH ensures the requirement of optical alignment. The control resolution for the De-space was not over 0.1 µm; 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.