# Numerical Analysis of the Kinematic Accuracy of the Hermetic Harmonic Drive in Space Vehicles
## 5 Discussion  
The calculations performed confirm the generally known advantage of harmonic drive--namely, its high kinematic accuracy. Thanks to this study, harmonic drives are used so eagerly in control mechanisms of machine tools, control systems, robots, and manipulators [38; 39; 40]. The hermetic harmonic drive combines these advantages with the possibility of tight separation of the engine from the ambient space, which is not allowed by harmonic drives with standard construction. This opens the possibility of a wider application of these devices in vehicles and devices operating in space than before. There, hermetic harmonic drives could be an essential component of antenna, camera, or solar panels, ensuring high precision in their positioning. The harmonic drives used should, in addition to hermeticity, ensure the highest possible kinematic accuracy. The previous studies of the authors and knowledge of the construction show that the type of generator to make the greatest extent of influences the kinematic accuracy is the harmonic hermetic drive. The quality of work in hermetic drive also depends on the shape of the tooth or the construction shape of the flexspline, but the deformation form of the toothed wheel rim influences the correct operation of the entire transmission. In the FEM numerical calculation performed, the four types of mechanical generators were analyzed. Models forcing different forms of deformation were selected but also significantly different in construction and manufacturing technology. These were two-wave generators: two-roller, four-roller, double-disc, and cam. Each of the generators has different operating  
Figure 17: Kinematic error of the circular spline in reversing motion relative to the angle of rotation of a cam generator. characteristics, so it is necessary to determine whether it is possible to use them in control devices with the required highest kinematic accuracy. Research on the generator impact of the type on the kinematic accuracy of the harmonic drive was realized by using the numerical finite element method. The calculations were realized in the Abaqus program using flat models of a hermetic harmonic drive. The computational models of all basic elements of the hermetic harmonic drives were their cross sections created on the basis of full spatial models in the CAD program. The calculations of kinematic error were done for the nonloaded gear and loaded gear by torque with a changed direction of action. The size of the backlash that occurs when changing the direction of rotation of the wave generator was also analyzed. The results of FEM calculations also stresses distributions on the models but were not the purpose of the analysis, so they were not discussed in detail. The highest stress levels were observed on the wheel rim of the flexspline after it was deformed by a two-roll wave generator. In the first step of the analysis, it was checked how the type of wave generator and the form of deformation of the flexspline obtained affect the kinematic accuracy of the gear. For each of the four types of generators, read the values of kinematic error, so the difference between the expected and real value of the rotation angle of the circular spline and relative angle of rotation of the generator. The largest kinematic error occurred in the case of roller generators, and the harmonic drive with a cam generator was the most accurate. However, the production of the cam generator is much more difficult than that of the roller generators, which can be easily made by conventional methods. The harmonic drives with roller generators, although worse results, can still be successfully used as power transmission gears and in normal quality control mechanisms. However, the kinematic error values for models with roller generators exceed the recommendations of the literature [23] and manufacturers of harmonic drives [37; 41], so they were not included in the next part of the analysis.