## 7 Conclusions  
The present study proposed a design optimization large-scale moving framework approach for an L5 AMC to solve the contradiction between the moving mass, material costs, and structural stiffness. Based on the conducted analyses, the following conclusions can be drawn.  
1. To design an optimized large-scale moving framework for the L5 AMC, an improved approach, named the 3-step design optimization, was introduced to obtain the optimum framework structures based on multi-objective optimization and finite element analysis.
2. The structural stiffness of the framework after optimization increased by 89% compared with before optimization, although the mass increased by 6% and the material costs increased by 9%. The finite element simulation results showed that the displacements of the milling head were less than the design requirement of 0.25 mm in all load cases.
3. The actual verification results indicated that the large-scale moving framework based on the proposed 3-step design optimization approach fully met the design requirements of the L5 AMC and reduced energy consumption.
4. The proposed 3-step design optimization approach based on multi-objective optimization and finite element analysis can be considered as a guide for optimizing large-scale moving structures to balance the moving mass, material costs, and structural stiffness.  
**Author Contributions:** [PERSON] hosted the project and drafted the present report. [PERSON] contributed the analysis ideas. [PERSON] checked the test data. [PERSON] carried out the finite element analysis. [PERSON] conducted the prototype test. And [PERSON] proposed the analytical method.  
**Funding:** This work was supported by the State Key Laboratory for Manufacturing Systems Engineering at Xi'an Jiaotong University of China (grant number: sklms2017008), the National Torch Plan of China (grant number: 2012 GH040610), and the Jiangsu Kunshan Cultivation Project of Scientific and Technological Achievements of China (grant number: KH1003).  
**Acknowledgments:** This work was supported by the State Key Laboratory for Manufacturing Systems Engineering at Xi'an Jiaotong University of China (grant number: sklms2017008), the National Torch Plan of China (grant number: 2012 GH040610), and the Jiangsu Kunshan Cultivation Project of Scientific and Technological Achievements of China (grant number: KH1003). The authors are also grateful to the Kunshan Dynapro Technology Co., Ltd for their support.  
**Conflicts of Interest:** The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript; nor in the decision to publish the results.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Test Content** & **Design Request** & **Measured Value** \\ \hline \multirow{3}{*}{Stroke} & \(x\) axis (m) & 40 & 40.02 \\  & \(y\) axis (m) & 6 & 6.01 \\  & \(z\) axis (m) & 4 & 4.01 \\ \hline \multirow{3}{*}{Positioning accuracy and repeatability} & Translational axes & Testing equipment: laser interferometer \\ \cline{2-3}  & Taking the \(y\) axis as an example, maximum positioning error and repeatability (mm)/full stroke & 0.25/0.04 & Forward: 0.041/0.021 \\ \cline{2-3}  & Rotational axes & Testing equipment: laser tracker \\ \cline{2-3}  & Taking the \(B\) axis as an example, maximum positioning error and repeatability (\({}^{\circ}\))/full stroke & 1/0.4 & 0-110\({}^{\circ}\): 0.079/0.034 \\ \hline \multirow{3}{*}{Sample machining} & Roughness \(R_{\text{e}}\) (mm) & 3.2 & No abnormality, \(<\)3.2 \\  & Contour accuracy (mm) & \(\pm\)0.05 & No abnormality, \(<\)\(\pm\)0.05 \\ \hline \multicolumn{3}{c}{Total mass of the framework (kg): 2199.81 (proposed in this study)} \\ \hline \hline \end{tabular}
\end{table}
Table 8: Inspection results of the L5 AMC prototype related to the framework.