## 4 Mechanism Analysis
### Rotation Process  
The rotation process is one of the most important parts to verify the elevation angle adjustment for the FCRA. From the scale lines on the transparent side plate of the model, the relative motion angles \(\gamma\) of the trolley and the rotation angles \(\varphi\) of the back frame can be recorded. The elevation angle \(\beta\) can be further calculated according to \(\beta+\varphi=90^{\circ}\). The same relative motion angles \(\gamma\) in prototype tests are selected in the software simulation. These moments of rotation processes are listed in Figures 8 and 9. In order to observe the elevation angle and the position of the trolley better, the software simulation results are given in front view. Further, the kinematic relationships between \(\gamma\) and \(\beta\) based on the model test and software simulation are compared with the theoretical results from Equation (2) in Section 3. The error analysis for the three is listed Table 4.  
Figure 6: Prototype model.  
Figure 7: Analysis model. (**a**) Model in axonometric view, (**b**) Model without shell.  
Figure 9: Rotation process of simulation. (**a**) \(\gamma=0^{\circ}\), \(\beta=90^{\circ}\), (**b**) \(\gamma=12.5^{\circ}\), \(\beta=80.13^{\circ}\), (**c**) \(\gamma=20^{\circ}\), \(\beta=74.21^{\circ}\), (**d**) \(\gamma=32.5^{\circ}\), \(\beta=64.18^{\circ}\).  
From Figures 8 and 9, it is obvious that the results of software simulation match the rotation process of the model test well. In the model test, the central angle \(\theta\) between the model and the water's surface is 120\({}^{\circ}\) when the trolley is at the initial position. Since \(\beta_{\text{min}}\) is equal to half of the central angle \(\theta\), the value of \(\beta_{\text{min}}\) can be obtained as 60\({}^{\circ}\). The lower-limit \(\beta_{\text{min}}\) calculated by the water's surface constraint is 63.6\({}^{\circ}\). It is approximately 6% larger than the test result. It is inferred that the reasons for these differences have two parts. One part is about the manufacturing errors in the prototype model and the other is the numerical error of this theoretical solution to the transcendental equation Equation (3).  
It can be seen from the differences in Table 4 that the errors between model test results and theoretical results are kept within 0.55%, indicating that the model test also matches theory well. The reason for the slight error may be because the scale line interval on the transparent side plate is so large that the reading accuracy is not high enough.  
The error of the software simulation is larger than the error of the model test, which may be related to the contact setting between the trolley and the track in the software. Another reason is that the method of measurement in the model test is to wait for the trolley to reach a certain point until finding an equilibrium before reading the data, while the method of measurement in the software simulation involves real-time monitoring data. The structure is still in the motion state and does not reach the balance, which also results in a certain error. In general, compared with the results from Equation (2), the errors of the model test and software simulation are relatively small and within the acceptable range. It is indicated that the theory is correct and the moving mass gear drive method is feasible.