## 6 Conclusions  
In this work, a floating cylindrical reflector antenna driven by a moving mass gear is developed to realize the elevation angle adjustment of the reflector surface. The specific structural design parameters are stated for the back frame structure of this FCRA while considering the kinematic relationship and water surface limitation. The effects of a single control variable on the elevation angle and the stability parameter are discussed, respectively. The prototype model test and software simulation are conducted to verify the feasibility of the moving mass gear drive method and the accuracy of parametric design. The deformation analyses for the back frame structure of the FCRA are carried out. And the iFEM algorithm with sub-region divisions is used for shape sensing of the over-constrained back frame structure during the angle adjustment process by four quasi-static sampling moments.  
Based on the parametric analysis of the FCRA, the optimal parameter combination for the maximum rotation range is \(a\) = 0.02, \(b\) = 2, \(c\) = 0.3, \(n\) =1, \(a_{1}\) = 0.02, and \(b_{1}\) = 0.4 while ensuring the stability of the FCRA. The errors in the rotation process between the theoretical calculation, software simulation, and prototype test are within 1.5%, which indicated that the parametric design is correct and the moving mass gear drive method is feasible. The deformation analysis of the back frame revealed that the total displacement increases with the growth of the rotation angle \(\varphi\). The average differences in deformation reconstruction by iFEM are below 6.5%. It suggests that the iFEM algorithm with sub-regions is very suitable for the shape sensing of the over-constrained back frame structure. It is also confirmed that the iFEM algorithm by several quasi-static sampling can fulfill the deformation reconstruction with high precision during the rotation process.  
Further work will focus on the influence of deformation on the reflector surface accuracy and technology development for the future applications of the FCRA.  
Figure 15: The iFEM contour of total displacement for coarse mesh at \(\beta\) = 90\({}^{\circ}\), \(\varphi\) = 0\({}^{\circ}\).  
**Author Contributions:** Conceptualization, H.H. and Y.L.; methodology, H.H. and M.M.; investigation, M.M. and Z.Z.; model analysis, M.M.; test, M.M. and Z.Z.; validation, Y.L.; writing--original draft preparation, M.M. and H.H.; writing--review and editing, H.H. and Y.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported by the National Natural Science Foundation of China (Grant No. 11902253 and 52278218), the Natural Science Foundation of Shaanxi Province, China (2021 JM-065), and the Fundamental Research Funds for the Central Universities of China (310201906 zy008).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data available on request due to restrictions, e.g., privacy or ethical.  
**Acknowledgments:** The authors would like to thank the support of the aforementioned fund committees.  
**Conflicts of Interest:** The authors declare that there are no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.