# New Construction Solutions of Gear Using in Space Vehicle Control Systems
## 3 Results  
The results for stresses obtained for many analyzed construction solutions differed considerably from each other. Many of the researched shapes of the flexspline turned out to be completely useless because of their little durability. Therefore, they were considered inappropriate for application in space vehicles and they were not included as part of the analysis. Therefore, only the most characteristic cases were presented, for which key information was obtained. Using this as a basis, a new shape for the flexspline body was designed. Table 1 shows figures of model shapes of the flexspline considered in the next steps of calculation. It also includes the values of the most important geometric parameters, which were changed in the next variant of the flexspline. \begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Sleeve Shape Diagram** & **Parameters to Be Changed** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Shapes of flexsplines used in the next part of the calculation. The results of the numerical calculations obtained using FEM in the program for the model in the flexspline in basis variant (variant I) are presented in Figure 5. The distribution of stresses in the flexspline is an effect of its deformation by the wave generator. The basic variant of the flexspline has dimensions similar to the standard construction offered by leading manufacturers of harmonic drives [30; 34]. The flexspline in variant I has a total length equal to L = 150 [mm], which is comparable to the pitch diameter. The length L was the main parameter modified in the next calculation variants for the flexspline. An important geometric parameter assumed based on variant I was the fillet radius at the bottom equal to R\({}_{2}\) = 5 [mm]. The highest stress values occurred directly near the wave generator, in its major and minor axes. The stress level is not high and confirms the correctness of such a structure. However, it is clear that increased stress values occurred in areas of the toothed wheel rim, but are low in other parts of the wheel. Therefore, the cylindrical sleeve of the flexspline was shortened by about half, and this solution was marked as variant II. The length of the shortened flexspline was equal to L = 75 [mm] and was significantly affected by the reduction in the size of the total harmonic drive. After the calculations, the results obtained indicate a large increase in the maximum stress values in the body. Especially dangerous accumulation of stresses occurred on the main axis of the flexspline (Figure 6). This design solution is not appropriate, as it would result in very quick damage to the compliant wheel in this area. Except for the toothed wheel rim, increased stress also occurred with the radius of transition from the cylindrical part to the bottom of the flexspline. \begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Sleeve Shape Diagram** & **Parameters to Be Changed** \\ \hline  & & \\  & & \\  & & \\  & & \\ \hline \end{tabular}
\end{table} 
Table 1: Cont. To reduce the shape impact of the change in the bottom area of the flexspline with stresses in its body, the next calculation variants were proposed with the following names: variant III and variant IV. These solutions are based on previously analyzed constructions of the flexspline (variants I and II). Only the radius value between the cylindrical body and the flat bottom was changed. When modeling the flexspline in variant III and variant IV, the maximum possible value of this radius was assumed to be R\({}_{2}\) = 35 [mm]. The results on the distribution of the stresses in the flexspline model with a large radius between the bottom and the body are shown in Figures 7 and 8. Figure 5: The distribution of the stresses in the flexspline base model—variant I.  
Figure 6: The distribution of the stresses in the flexspline model—variant II. In the case of the long model (variant III), this change did not bring significant benefits.