## 5 Results and Discussions
### Effect of Profile Modifications  
According to Ref. [13], the radial clearance (\(\Delta c\)) between the tip and the root of the cycloid gear and the pin generated with PMs are \(\Delta c=\Delta R_{\text{rp}}-\Delta R_{\text{p}}\). To avoid the tooth interference, the radial clearance (\(\Delta c\)) should be a positive value. Thus, only the positive isometric modification (\(+\Delta R_{\text{rp}}\)), negative offset modification (\(-\Delta R_{\text{p}}\)), and three types of compound modification (\(-\Delta R_{\text{rp}}\) and \(-\Delta R_{\text{p}}\), \(+\Delta R_{\text{rp}}\) and \(-\Delta R_{\text{p}}\), and \(+\Delta R_{\text{rp}}\) and \(+\Delta R_{\text{p}}\)) are considered in this study. To quantitatively study the influence on the TE and backlash, a series of cases is applied to the proposed calculation method, as shown in Table 2. Cases 1-4 have positive isometric modification with different modification amounts, cases 5-8 have negative offset modification with different modification amounts, and cases 9-20 have three types of compound modification. Among them, case 4, case 8, and cases 9-20 have the same radial clearance. The results for different PMs are shown in Figure 8.  
According to the calculation results of cases 1-4, it is not difficult to find that as the modification amount increases with isometric modification, the absolute values of the MTE and MB increase. For the offset modification, the same conclusion can be drawn from cases 5-8. However, for the same modification amount, both of the absolute values of the MTE and MB of the isometric modification are greater than those of the offset modification. Compared with the MTE and MB, both the isometric modification and the offset modification have little influence on the PPTE and PPB. These results indicate that the transmission accuracy decreases with the increase in the modification amount for both the isometric modification and the offset modification, and the isometric modification has a greater influence on the transmission accuracy than the offset modification with the same modification amount. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multicolumn{4}{c}{\(+\Delta R_{\text{rp}}\)} & \multicolumn{4}{c}{\(-\Delta R_{\text{p}}\)} & \multicolumn{4}{c}{\(-\Delta R_{\text{rp}}\)} & \multicolumn{4}{c}{\(-\Delta R_{\text{p}}\)} & \multicolumn{4}{c}{\(+\Delta R_{\text{rp}}\) and \(-\Delta R_{\text{p}}\)} & \multicolumn{4}{c}{\(+\Delta R_{\text{rp}}\) and \(+\Delta R_{\text{p}}\)} \\ \cline{2-13}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** &  
For the compound modification, cases 9-20 have the same radial clearance (5 \(\upmu\)m). According to the results of the compound modification, the compound modification of the negative isometric and negative offset (\(-\Delta R_{\text{rp}}\) and \(-\Delta R_{\text{p}}\)) makes it easier to obtain a smaller backlash, and the absolute value of the MTE is also smaller. Similarly, the compound modification has little influence on the PPTE and PPB compared to their mean values. Additionally, the radial clearances of case 4 and case 8 are also 5 \(\upmu\)m. Comparing the results of case 4, case 8, and cases 9-12, the compound modification of the negative isometric and negative offset is more conducive to improving the transmission accuracy than the isometric modification and the offset modification. To summarize, in order to obtain higher transmission accuracy, the compound modification of the negative isometric and negative offset should be preferable. In addition, Figure 8c,d shows the mean of the number of contact pins and the MCS. Overall, when the PMs are considered, the number of contact pins is greatly reduced compared with Figure 7b, and the MCS is greatly increased compared with Figure 7e,f. This indicates that some of the original contact pins lose contact under the influence of the PMs, and the load distributed on each contact pin increases.