# New Construction Solutions of Gear Using in Space Vehicle Control Systems
## 4 Discussion  
The analysis of the flexspline body shape allowed one to assess the possibility of reducing the dimensions of harmonic drives without limiting their strength.  
Multiple studies of different construction variants allowed us to draw conclusions that are useful for future research. Our search for the new corpus shape of the flexspline was aimed at reducing its length. However, as shown in the results on stress distribution in FEM calculations, too short a flexspline body causes a transgression of its strength and could lead to its eventual damage. Additionally, in harmonic drives with short flexsplines, problems with the accuracy of the wheels in the mesh area may occur. Flexsplines with an outer flange have lower strength for the same length as cup-type models. The sleeve body of the flexsplines must be able to deform during operation, but the flange stiffens the structure, causing a significant increase in the stress value.  
Figure 16: Stress values in the longitudinal section through the major axis of the wave generator for selected long variants of the flexspline.  
Figure 17: Stress values in the longitudinal section through the large axis of the generator for selected short variants of flexsplines.  
During the determination of the geometric parameters of the toothed wheel rim, it is necessary to avoid solutions in which there exists the possibility of stress concentrations occurring, for example, small rounding radii or sharp changes in body thickness.  
Note that the stresses are not distributed symmetrically on the rim of the toothed wheel. They are much higher on the bottom side than on the free end of the flexspline. This nature has already been pointed out in previous studies [36; 37], and solutions have been proposed, for example, in the form of intermediate rings to improve the cooperation between the flexspline and the wave generator [19; 38]. The starting point for the analysis was a flexspline with a bottom modeled with commercial solutions (variant I). This model obtained a uniform stress distribution, and its level was not too high. Therefore, large dimensions of the gears are not a problem, and this solution can be used successfully.  
However, there are often limitations concerning the size and weight of toothed wave gears, as these devices are launched into space. Therefore, as a result of the analysis, a new type of flexspline (variant X) was proposed.  
This solution allows for shortening the flexspline by about 25% from the starting solution. In the modified construction, correct stress distribution was achieved without threat of destruction in strategic places for the strength of the flexspline. The maximum stress values after deformation of the flexspline occurred in the area of the toothed rim, but they are at a safe level, lower than the allowable stress.  
The proposed design solution in terms of the shape of the flexspline body extends the scope of their application, while maintaining all the unique advantages of the wave gear, such as kinematic accuracy or the possibility of transferring heavy loads. The new shape of the flexspline is characterized by high mechanical strength and durability, and the reduced dimensions mean that it can be used successfully in the drive of space vehicles.  
Conceptualization, J.P. and A.P.; methodology, J.P.; software, J.P. and D.S.; validation, D.S., A.P. and J.P.; formal analysis, J.P.; investigation, D.S.; resources, D.S.; data curation, A.P.; writing--original draft preparation, J.P. and D.S.; writing--review and editing, A.P.; visualization, D.S.; supervision, A.P. and J.P.; project administration, A.P. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.