# Numerical Analysis of the Kinematic Accuracy of the Hermetic Harmonic Drive in Space Vehicles
## 2 Impact of Type of Generator on Flexspline Deformation Form
of deformation of the neutral layer of the flexspline, even under the load of the harmonic drive. Its disadvantage is that the disc of the generator does not support the toothed ring across its full width, allowing additionally stresses to occur. In designing a wave generator, it is necessary to designate the generator angle \(2\gamma\) of which the disc comes into contact with the flexspline and radius \(\mathrm{R_{t}}\) of the generator disc. Due to the most favorable stress distribution, it is recommended to use the angle value \(\gamma=20\div 40^{\circ}\)[22]. Currently, the most commonly used harmonic drives are cam generators. Their characteristic element is the elastic bearing, which is placed in the corpus of the cam-shaped generator. The elastic bearings used in these generators are special with thinner rings and separators centered by rolling elements. The cam deforms the bearing, giving its ring shape and allowing the form of deformation of the neutral layer of the flexspline to be required. The cam generator can deform the flexspline into any form of deformation described by the equation at the assumed, unchanged value of the cam circumference [34]. The bearing of the cam generator adheres to the inner surface of the flexspline, allowing its deformation to form all over the perimeter; hence, there are no additional deformations of the toothed ring after loading the harmonic drive with torque. The neutral layer of the flexspline is deformed cyclically during operation and takes the appropriate shape for the type of generator used. Figure 4 shows the momentary displacement of segment \(A_{0}B_{0}\) of the neutral layer of the corpus of flexspline before the deformation position of \(A_{2}B_{2}\) and after its deformation by the generator. The occurring radial displacement \(w\), the circumferential displacements \(v\), and rotation angle \(\theta\) of the normal for the neutral layer of flexspline depend on angle \(\varphi\) measured from the major axis of the generator. Figure 4: The angle of rotation of the normal exposed, in point \(A_{0}\), to the neutral layer of flexspline deformed by the generator. The segment \(A_{0}B_{0}\) of the undeformed neutral layer of the flexspline corpus, after its deformation with a generator, moves to position \(A_{2}B_{2}\). At this time, the normal point \(A_{0}\) will rotate about angle \(\theta\), which is the difference between the angles \(\theta_{1}\) and \(\theta_{2}\) (Figure 4). The radial and circumferential displacements and rotation angle of the normal in point \(A\) of the neutral layer allow its location to be determined in relation to the flexspline origin of the polar coordinate system. Because the impact of different generators on the neutral layer of the flexspline is different, the forms of deformation for different types of generators are different, and therefore their respective displacements differ from each other. Analytical calculations contain geometric simplifications and ignore the impact of the load on the torque, resulting in additional deformation of the neutral layer. In these calculations, the toothed ring is replaced by the smooth ring and the influence of the flexspline body sleeve is ignored. Equations allowing for the calculation of geometric parameters of the neutral layer of flexspline for different types of generators are available in many publications [12; 14; 17] and will not be discussed in more detail because the analysis used more advanced computational tools. During the operation of the harmonic drive, the wave generator rotates, causing the mating of successive pairs of teeth of both gears. Each of the teeth of the flexspline moves from one interdental notch to the next with the circular spline.