## 5 Results and Discussions
### Effect of Assembly Errors  
AEs are also another major factor affecting the TE and backlash. According to the definition of the AEs in Section 2, the AEs are divided into the center distance deviations (\(\Delta x\) and \(\Delta y\)) and the misalignment deviations (\(\varphi\) and \(\gamma\)). Since \(\Delta x\) and \(\Delta y\) have similar effects on the TE and backlash, only the influences of \(\Delta y\), \(\varphi\), and \(\gamma\) are investigated in this section. To ensure the lubrication requirements and the compensation for the AEs, the compound modification of the negative isometric and negative offset is applied, and the PM parameters of the cycloid gear are also determined to be \(\Delta R_{\rm rp}=-0.004\) mm and \(\Delta R_{\rm p}=-0.0017\) mm. The calculation results for the TE and backlash considering different center distance deviations are shown in Figure 13.  
Figure 12: Number of contact pins and load distribution on pins with different types of MEs: (**a,b**) pitch deviation, (**c,d**) profile deviation, (**e,f**) pin center circle diameter deviation. According to Figure 13a,b, the waveforms of the curves of the TE and backlash change significantly under the influence of the center distance deviation, which is similar to the harmonic function curve. According to Figure 13c,d, as the absolute value of \(\Delta y\) increases, the PPTE, PPB, and MTE increase, while the MB decreases, and the influence of the center distance deviation on the MB is greater than that on the MTE. Figure 14 shows the number of contact pins when \(\Delta y\) = 9 and \(-9\)\(\upmu\)m, as well as the load distribution on the pins when \(\Delta y\) = 9 \(\upmu\)m. According to Figure 14a, when \(\Delta y\) = 9 \(\upmu\)m, the number of contact pins first decreases and then increases with the change of \(\theta_{t}\), which is caused by the change of the initial gap between the tooth surfaces. In addition, the load on the pins increases significantly with the decrease in the number of contact pins (e.g., when \(\theta_{t}\) = 90\({}^{\circ}\) in Figure 14b), which will increase the MCS and shorten the contact fatigue lifetime of the tooth surface. At the same time, this will also produce vibration and noise in the gear system. The calculation results of the TE and backlash considering the misalignment deviations \(\varphi\) and \(\gamma\) are shown in Figure 15. Similar to the center distance deviation, both the misalignment deviations \(\varphi\) and \(\gamma\) have a greater effect on the waveform of the curves of the TE and backlash. The curves of the TE and backlash considering the misalignment deviations \(\varphi\) and \(\gamma\) are also similar to the harmonic function curve. When \(\varphi\) and \(\gamma\) have the same value, the PPTE and PPB considering the misalignment deviation \(\varphi\) are equal to the PPTE and PPB considering the misalignment deviation \(\gamma\), while their phase difference is 90\({}^{\circ}\). With the increase in \(\varphi\) and \(\gamma\), both the PPTE and PPB increase and the MB decreases, while the misalignment deviations \(\varphi\) and \(\gamma\) have little effect on the MTE. Although the  
Figure 13: Results with center distance deviation: (**a**) TE, (**b**) backlash, (**c**) MTE and PPTE, and (**d**) MB and PPB. misalignment deviations \(\varphi\) and \(\gamma\) are conducive to reducing the MB, the adverse effect of the increase in the PPTE and PPB on the transmission accuracy cannot be ignored. Figure 14: Effect of center distance deviation on (**a**) number of contact pins, and (**b**) load distribution on pins. Figure 15: Results with misalignment deviations: (**a**) TE (\(\varphi\)), (**b**) backlash (\(\varphi\)), (**c**) TE (\(\gamma\)), and (**d**) backlash (\(\gamma\)). Figure 16 shows the number of contact pins and the load distribution on pins when the misalignment deviations \(\varphi\) and \(\gamma\) are equal to \(0.02^{\circ}\).