## 6 Conclusions  
In this study, a novel approach for calculating the transmission accuracy of a cycloid-pin gear pair based on a three-dimensional error tooth surface model has been proposed. Compared with the traditional analysis method for a cycloid-pin gear pair, this method has the capability to consider the influence of some abnormal meshing phenomena caused by PMs, MEs, and AEs on the tooth contact state, TE, and backlash, such as the instantaneous mesh-apart of tooth pairs and the eccentric load on a tooth surface. The feasibility and effectiveness of this method is validated by comparison with the theoretical analysis results and the results in the literature.  
Based on this method, a series of cases is simulated to quantitatively study the influence of PMs, MEs, and AEs on the TE, backlash, the number of contact pins, load distribution on pins, contact stress, and instantaneous contact lines on the tooth surface of a pin. The obtained results show that the compound modification of the negative isometric and negative offset should be preferred in order to avoid the tooth interference and to obtain higher transmission accuracy. With this compound modification method, although the increase in the modification amount improves the transmission accuracy; this increase also leads to a decrease in the mean of the number of contact pins and an increase in the MCS. Among the MEs and AEs, the pitch deviation, the center distance deviation, and the misalignment deviations are the main influencing factors of the TE and backlash. They not only change the waveform of the TE and backlash curves, but also the main source of the peak-to-peak values of the TE and backlash, while the profile deviation and the pin center circle diameter deviation mainly affect the mean values of the TE and backlash. In addition, the pitch deviation and the center distance deviation will cause the number of contact pins to fluctuate in a large range, and they will cause the load on some pins to increase significantly. Under the influence of the misalignment deviations, although the mean of the number of contact pins increases and the load distribution on the pins does not change significantly, a serious eccentric load occurs on the tooth surface of some contact pins. The increase in the load on the pins and the occurrence of the eccentric load not only increase the MCS and shorten the contact fatigue lifetime of the tooth surface, but they also accelerate the tooth surface wear and reduce the transmission accuracy lifetime of the cycloid-pin gear pair.  
The proposed method and the above conclusions are of great significance for the optimal design of the tooth profile of a cycloid gear, the tolerance allocation during the installation of a gear pair, and the accurate prediction of the TE and backlash of a cycloid-pin gear pair. The error tooth surface in this study is obtained through different probability distribution functions based on the tolerance range of various errors, and this method is expected to be used for the prediction of the transmission accuracy range of the gear pair in engineering practice. The error tooth surface can also be generated using the measurement coordinates of the element control point on the tooth surface, and this method can provide more accurate internal excitation data for the dynamic analysis of a cycloid-pin gear pair, which will be implemented in future research.  
Conceptualization, C.L. and W.S.; methodology C.L. and W.S.; validation, L.X.; data curation, K.L.; writing--original draft preparation, C.L.; writing--review and editing, W.S. and L.X.; funding acquisition W.S.; All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 51675061.  
Not applicable.  
The authors declare no conflict of interest.