# Numerical Analysis of the Kinematic Accuracy of the Hermetic Harmonic Drive in Space Vehicles
## 4 Results
The graph obtained by numerical calculations for this calculated variant has a green color (2). Almost every time, the charts for these two types of cause overlap. Larger discrepancies occurred in the case of loading the circular spline of torque in the opposite direction. The red-colored figure (2) corresponds to this case. The largest differences are noticeable after crossing a torque angle equal to 1 radian. Figure 13: Kinematic errors of the circular spline are the result of the generator excitation of different types of generators. At this point, the generator stopped and started to rotate in the opposite direction, which also caused the circular spline to rotate in the opposite direction. Differences in the chart regarding the reversing and return movement of the generator indicate for both types of generators the largest differences from the no-load solution. However, the waveform of the graph for the return rotation (from 1 to a \(-\)1 rad) refers to the model with a load opposite to the direct torque of the wave generator that is mostly parallel to the case without load. Based on this, it can be assumed that the kinematic error occurs during the change of directions of the rotating generator. Since during further cooperation the deceleration of the circular spline did not increase, it was a consequence of the backlash of the cooperating teeth of both gears and the deformation of the flexspline. In the presented charts concerning hermetic harmonic drive with the do generator differences and cam generator, we can notice both the shape of the graph and the error values. The harmonic drive with a cam generator should be rated as more accurate, also  
Figure 14: Rotation angle of circular spline resulting from double-disc generator work. Figure 15: The rotation angle of the circular spline resulting from the cam generator work. in the case of its load with torque. It can be concluded that the load of the hermetic harmonic drive had a significant impact on its kinematic accuracy. This factor can have little importance by using harmonic drives in space vehicles where gravitation is low, so a large part of the load can be omitted at a low level. It is also worth paying attention to the direction of the load of flexspline by outer torque because this factor influences accuracy in reverse motion. Harmonic drives are used in the control mechanisms of antennas or manipulators of space vehicles where there is a continuous change in the direction of rotation. The kinetic accuracy of reversing movement is in this case a parameter decisive for the usefulness of harmonic drive. To more accurately check what kinematic errors occurred during the change of the rotation direction of the generator, the charts of kinematic errors for circular spline dependent on the rotation angle of the generator were prepared. The charts presented in Figures 16 and 17 refer to computational models of hermetic harmonic drive with double disc and cam generator. The charts show the results read based on calculations FEM for circular spline without outer load. The kinematic errors were shown, so the difference between the nominal and calculated value of the rotation angle of the circular spline result of rotate generator about the angle. The graphs include the range of rotating angle \(\varphi\) from \(-1\) to \(1\) radian relative to the major axis of the generator, which corresponds to the value \(\varphi=0\) radian. For this purpose, the computational model forced the generator to rotate initially by \(1\) radian in the positive direction and then by \(2\) radians in the negative direction. In the graphs of both analyzed types of generators, it can be seen that the initial motion from \(0\) to \(A\) does not follow the same curves as the return motion of the circular spline from point B to C. After the direction of rotation of the wave generator was changed, the circular spline was in its position due to the backlash occurring in the meshing. This state corresponds to the fragment of the graph between points A and B in Figures 16 and 17.