# Optimization Design of the Spaceborne Connecting Structure for a Lightweight Space Camera
## 5 Conclusions  
This paper presents an optimization design method for designing spaceborne connecting structures. Drift of line of sight (LOS) is the movement of an image point on the image plane under external loads. In order to meet the design requirements of the camera's LOS drift under 1 g of gravity and a temperature rise load, the LOS drift was qualitatively analyzed. The main factor that affects the LOS drift is the relative displacements between the secondary mirror and primary mirror. The specific expressions of the relative displacements between mirrors were derived. In order to obtain the optimal configuration of the spaceborne connecting structure, a topology optimization model was established with the mass as the objective and the fundamental frequency and relative displacements between mirrors as constraints. The topology optimization model was solved by using MMA. Based on the topology optimization results, the sensitivity analysis of size parameters was carried out. The analysis result showed that the size parameters have an obvious influence on the performance of the system. To obtain the optimal size parameters combination, a size parameter optimization model was established, and it was solved by using GA. In order to further evaluate the effect of the optimization, engineering analysis was carried out. The performance was compared with the traditional flexible structure after size parameter optimization. The results showed that the camera mounted by the designed connecting structure in this paper has better comprehensive performance. The relative linear displacements and angular displacements between mirrors are within 10 \(\upmu\)m and 10\({}^{\prime\prime}\) respectively, which meet the design requirements, and the lightweight ratio of the connecting structures reached 54%, which verifies the effectiveness of the proposed optimization design method. In this paper, the relative displacements between mirrors were analyzed in detail, which is the main factor affecting the camera's LOS drift. By integrating the relative displacements into the optimization design model of the spaceborne connecting structures, effective optimization results were obtained. If the other structures in the optomechanical system have an obvious influence on the camera's LOS drift, this method can also be used for their optimization design, which can significantly improve the LOS stability and lightweight ratio of the structure. However, if a structure in the optomechanical system has little effect on the LOS drift, it should consider other targeted design methods and conduct specific analysis. The camera's system performances also include other optical metrics such as optical transfer function and energy distribution. In the future, if the optical transfer function under external loads can be integrated in the optomechanical structure optimization, the design will be more effective. Conceptualization, M.S. and L.Z. ; methodology, M.S., L.Z. and X.J. ; software, L.Z. ; validation, M.S., L.Z. and X.J. writing--original draft preparation, M.S. ; writing--review and editing, M.S. ; \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Response** & \(R_{1}^{G}\)/\(\upmu m\) & \(R_{1}^{T}\)/\(\upmu m\) & \(R_{5}^{G}\)/\(\upnu\) & \(R_{5}^{T}\)/\(\upnu\) & \(f_{1}\)/Hz & _MASS_/kg \\ \hline The traditional structure & 15.1 & 16.7 & 7.3 & 9.1 & 121.6 & 1.2 \\ Optimized structure in this paper & 9.8 & 9.6 & 4.2 & 6.5 & 112.1 & 1.1 \\ Requirements & \(\leq\)10.0 & \(\leq\)10.0 & \(\leq\)10.0 & \(\leq\)10.0 & \(\geq\)100 & Min \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance comparisons of different flexure mountings. Figure 11: Conventional flexure configurations. supervision, M.S. ; project administration, L.Z. ; funding acquisition, L.Z. All authors have read and agreed to the published version of the manuscript. This research was supported by the National Key Research and Development Program from Ministry of Science and Technology of the People's Republic of China under Grant No. 2016 YFB0500904.