# Numerical Analysis of the Kinematic Accuracy of the Hermetic Harmonic Drive in Space Vehicles
## 2 Impact of Type of Generator on Flexspline Deformation Form  
The correct work of the harmonic drive is possible by an adequate deformation of the flexspline by the wave generator. The neutral layer of the flexspline body under the toothing can take various forms of curvature, depending on the wave generator used. The obtained character of deformation is chosen based on the correctness of the toothing of circles and their influence on the quality of work of the harmonic drive. Therefore, it is important to choose the appropriate type of wave generator, which for the chosen harmonic drive allows obtaining the highest kinematic accuracy. There are generators, hydraulic, pneumatic, and electromagnetic options, but due to their simple structure and easy operation, mechanical generators are used most often [23; 32]. The generator can cause a different number of waves which allows one to determine them as single-wave, double-wave, or three-wave. The most often used are double-wave generators because additional waves on the circumferences of the flexspline make a significant increase in bending stresses in its body [33; 34]. Among mechanical generators, there are four main types shown in Figure 3, which are different in construction and operation principles. There are generators: two-roll, four-roll, disc, and cam generators. Using all listed types entails the determined benefits and limitations, and using them depends on the destination of the drive and the technology possibilities that make the type of generator. Roller generators in double-wave harmonic drives have a combined slider of two or four rolls, with the deformation of the toothed wheel rim of the flexspline to the form of a thin-walled ring loaded with two or four forces, respectively (Figure 3a,b). In a two-roll generator, the rolls face opposite one another and forces operate in the large axis of the generator. In the four-roll generator, the rolls are facing at an angle \(\gamma\) (Figure 3b) from its large axis, whereas the deformation forces of the neutral layer of the flexspline work at an angle \(\gamma\), which generally has a value within the limit of \(\gamma=25\div 35^{\circ}\)[34]. The outer diameter of the generator roll \(D_{r}=2R_{r}\) should be possibly as large as \(D_{r}=(0.25\div 0.3)d_{1}\) (where: \(d_{1}\)--pitch diameter of the flexspline). The advantage of roll generators is simple construction and the possibility of using them for anything, obtained from the calculation and the inner diameters of the flexspline. It allows us to obtain strictly calculated gear ratio values and makes it easier to select the parameters of the toothed rings and other dimensions of flexsplines. The disadvantage of this type of generator is the limited possibility of using them for large rotational speeds of generators and the impossibility of keeping a complex form of the toothed ring of flexspline after the loading of the harmonic drive by torque. The disc generator has the name of the disc installed on the eccentrics, which is deforming a flexspline. The two-wave generators of the harmonic drive have the discs shifted to each other at an angle of 180\({}^{\circ}\). Disc diameters are bigger than rolls in roller generators; therefore, the disc generator makes it possible to maintain the computational form  
Figure 3: Forms of deformation of the neutral layer of a flexspline deformed by the generator: (**a**) two-roll, (**b**) four-roll, (**c**) disc, (**d**) cam, where: 1—minor axis of generator, 2—large axis of generator, 3—neutral layer of flexspline body before deformation, 4—neutral layer of flexspline body after deformation, R—radius of undistorted interlayer of flexspline, R—radius of roll of generator, R—radius, e—eccentricity of the disc setting, F—force deformation of flexspline in roll generators, \(\beta\)—angle of action of forces in the roll generators, \(\beta_{r}\)—angle of settings of generator rollers, \(\gamma\)—angle of contact of generator with flexspline, w\({}_{0}\)—radial deformation of the neutral layer of flexspline.