## 5 Conclusions  
The main purpose of this study was to form an integrated theory for the clearance analysis of landing gear retraction mechanisms. Major contributions and comments are summarized as follows: \begin{table}
\begin{tabular}{c c} \hline \hline
**Components** & **Tolerances (mm)** \\ \hline \(\Delta_{AB}\) & \(\Delta_{AB}\sim(0,0.133^{2})\) \\ \(\Delta_{BC}\) & \(\Delta_{BC}\sim(0,0.083^{2})\) \\ \(\Delta_{CD}\) & \(\Delta_{CD}\sim(0,0.133^{2})\) \\ \(\Delta_{CK}\) & \(\Delta_{CK}\sim(0,0.083^{2})\) \\ \(\Delta_{KL}\) & \(\Delta_{KL}\sim(0,0.083^{2})\) \\ \(r_{CA}\) & \(r_{eA}\sim(0.024,0.00283^{2})\) \\ \(r_{eB}\) & \(r_{eB}\sim(0,0.0205,0.00242^{2})\) \\ \(r_{cC}\) & \(r_{cC}\sim(0.0205,0.00242^{2})\) \\ \(r_{eD}\) & \(r_{eD}\sim(0.024,0.00283^{2})\) \\ \(r_{eK}\) & \(r_{eK}\sim(0.0205,0.00242^{2})\) \\ \(r_{eL}\) & \(r_{eL}\sim(0.0205,0.00242^{2})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Primary tolerance design parameters. Figure 13: (**a**) The modified deviations; (**b**) The comparison of original and modified deviations. 1. A new integrated theory composed of tolerance design and robust analysis was presented. The Jacobian tolerance theories were adopted to deduce the kinematic accuracy model, while robust theories are used to analyze the tolerance effects of a mechanism. The procedures of the theory are also given. 2. A typical landing gear retraction mechanism was taken as a case to study the joint clearance effects. Using the presented theory, joint clearances were seen as tolerances. Through the procedures of tolerance design, robust analysis, and tolerance redesign, final results showed that modified deviations of the landing gear retraction mechanism were significantly reduced, which suggests that the integrated theory presented is a valid way to estimate the influences of joint clearances and keep the robustness of a mechanism. 3. The study has have found that the inner tendencies of joint clearances could be observed. This finding provides designers assistance for sound decisions and researchers' insights for future studies on joint clearances. According to the finding and the results of the study case, the designers are planning to modify the tolerance parameters to obtain a more robust mechanism and further research will continue. 4. Regarding landing gear retraction mechanism, the integrated theory and the study presented contribute in several ways to our understanding of tolerance design and robust analysis. This is the first study to integrate tolerance and robust theories and analyze the clearance effects on landing gear kinematic accuracy. The theory and the findings will be of great use for landing gears in the future design. 5. The jacobian model has the advantage of simplicity and clarity. This is also the first study to use the jacobian model for the tolerance analysis of the landing gear mechanism. Future studies regarding the role of the jacobian model are strongly recommended. Conceptualization: [PERSON], [PERSON], [PERSON]; Methodology: [PERSON]; Validation: [PERSON], [PERSON]; Formal analysis: [PERSON]; Investigation:[PERSON], [PERSON], [PERSON]; Resources: [PERSON], [PERSON], [PERSON]; Data curation: [PERSON]; Writing original draft: [PERSON]; Writing review & editing: [PERSON], [PERSON], [PERSON]; Visualization: [PERSON], [PERSON]; Supervision: [PERSON], [PERSON]; Project administration: [PERSON], [PERSON], [PERSON]; Funding acquisition: [PERSON], [PERSON] All authors have read and agreed to the published version of the manuscript. This work described in this paper is supported in part by The Fundamental Research Funds for the Central Universities (under Grant No.NF2018001), and in part by National Defense Outstanding Youth Science Foundation (under Grant No. 2018-JCJQ-ZQ-053). The authors would like to thank the anonymous reviewers, associate editor, and editor for their valuable and constructive comments and suggestions. The authors declare no conflict of interest.