# A New Tooth Profile Modification Method of Cycloidal Gears in Precision Reducers for Robots
## 5 Examples and Discussion
In addition, the minimum backlash angle of each modification method corresponds to the No. 31 tooth, indicating that the No. 31 tooth first comes into contact with the cycloidal profile in reverse rotation. It can be determined that the lost motions of the cycloid-pin gear after the modification by the traditional method and the proposed method are 0.6 and 0.99 arcmin, respectively. The above results indicate that under the same initial clearance requirement, the shape of the modified tooth profile had the greater influence on the transmission error and less influence on the backlash. For the traditional modification method, although the initial clearance condition is the same as that of the proposed method, the modifications of the meshing area cannot be determined in advance, thus resulting in the larger backlash in the meshing area, which indirectly affects the repeated positioning error of the precision reducer. Furthermore, a measurement experiment of the transmission error and the lost motion of the robot precision reducer were carried out on a RV reducer tester shown in Figure 14. The transmission error and lost motion were measured with the static measurement method [23]. Under low-speed and no-load conditions, the high-precision circular grating installed at the input and output shafts was used to acquire the angular changes in real time. The reducer used in the measurement had 40 pins. Therefore, within the angle range (360\({}^{\circ}\)) of the output shaft, the rotation angle of one point was measured every 9\({}^{\circ}\) to obtain the actual output rotation angles at 40 positions. The cycloidal gear in this reducer was respectively replaced by the cycloidal gears modified by the traditional method, straight line method, cycloid method and  
It can be seen from Figures 12, 13, 15 and 16 that the error values obtained from actual measurements were greater than those obtained from theoretical modeling. The reasons might be as follows. The actual measurement process was affected by many influencing factors, such as installation errors, tooth profile errors, tooth pitch errors, and radial runout. The combined effects of these factors were complex and could not be accurately determined. However, before the test, a series of measures were taken to minimize these effects. For example, through the adjustment and detection of the tooling and precision instruments for many times, the high installation accuracy could be ensured. Through many times of precision grinding, the high processing accuracy could be ensured (the maximum profile and pitch errors of the cycloidal gear were respectively limited to 0.02 mm and 0.006 mm). However, we can see that the overall trends of transmission errors and backlashes measured in actual measurements are similar to the results of the theoretical modeling. The changing trend of the transmission error and lost motion of the new modification method is significantly smaller than that of the traditional modification. Among them, the transmission error after the second cycloid method is the least and the lost motions of the straight line method and the traditional method are basically the same. In summary, compared with the tooth profile obtained with the traditional modification method, the modified tooth profile obtained by the proposed method can reflect smaller transmission error and backlash, indicating the higher motion accuracy and repeated positioning accuracy. Based on the working conditions and transmission requirements of robot reducers in engineering practices, the appropriate modification function can be selected to carry out the modification design of the cycloidal gear.