# New Construction Solutions of Gear Using in Space Vehicle Control Systems
## 3 Results
The short solution (variant IV) was considered to be more correct owing to the values of the stresses at the radius R\({}_{2}\). The maximum stress values in the rim area have increased slightly compared with variant III, due to the greater stiffness of this solution. The previous results of the calculations showed that excessive shortening of the body is not favourable for the durability of the gear wheel and such a solution should be rejected. Changing the radius at the bottom of the flexspline has resulted in a lower stress in this area, so further changes should take place in this area. The literature contains theoretical descriptions of other flexspline design solutions with a shape significantly different from the classical one [20; 35]. Some of them, instead of being cup-shaped, have a flange located outside the body of the compliant wheel. Therefore, for this model, a strength analysis was carried out considering the possibility of its application in spacecraft. One of the expected solutions is the construction of dimensions reduced to relatively standardized; therefore, for the next computational models (variant V and V), the effect of the stress on the stability of the system is not significant. Figure 8: The distribution of the stresses in the flexspline model—variant IV. Figure 7: The distribution of the stresses in the flexspline model—variant III. variant IV), the less assumed about the length of the flexspline was reduced by half, which is L = 75 [mm], for the two constructions with an assumed value of the fillet radius of R\({}_{2}\) = 5 [mm]. Figure 9 shows the shortened length results obtained for the flexspline model in variant V. The highest stress values were on the radius between the cylindrical body and the flexspline flange. In the next VI variant shown in Figure 10, the flexspline corpus changed from cylindrical to conical. However, this modification of the shape did not have any beneficial effects. Due to the modification of the structure and the use of a small fillet radius, the highest stress values were obtained in this solution. After these trials, the length of the model is too small because the total length, which is half of the pitch diameter, does not guarantee the required strength. Figure 10: The distribution of the stresses in the flexspline model—variant VI. Figure 9: The distribution of the stresses in the flexspline model—variant V.  
Based on the results obtained for the previously presented computation variants, it was concluded that the desired state of stress occurs in situations where the body has the shape of a thin-walled cylindrical sleeve in places near the toothed wheel rim. On the other hand, the transition to the collar or bottom is achieved on an arc with the largest possible radius. A combination of these requirements provided the answer that the shape that can best meet expectations would be a quarter of an ellipse, limited by its major and minor axes. The large axis of the ellipse will be parallel to the axis of the flexspline and would decide its total length. The radially directed minor axis has a length limited by the inside diameter (d\({}_{w}\)) of the flexspline with a bottom and the diameter of the thickening of the bottom (d\({}_{2}\)), which are used to fix the flexspline to the case. For the wheel with the outer flange, the minor axis would have length limits based on the outer diameter (d\({}_{2}\)) of the flexspline. This new shape of the body was used to model the harmonic drive at the bottom (variant VII) and the outer flange (variant VIII). In these models, we assumed the total length of the flexspline as in the basic solution (variant I), so L = 150 [mm]. The results of the numerical calculations using FEM for the proposed constructions are presented in Figures 11 and 12, as appropriate for variants VII and VIII. For both constructions, we obtained satisfying low-stress values on the flexspline model.