# Transmission Efficiency of Cycloid-Pinion System Considering the Assembly Dimensional Chain
## 5 Comparison of Transmission Efficiency of Different Structures
### Tolerance Analysis of Different Structure  
In the general state, the cycloid gear is in full contact with the pin teeth. However, under the action of the input torque, only half of the contact surface will be deformed to produce the contact force. In parallel, coupled with the effect of dimensional tolerances, the actual number of teeth engaged is less than half. For the cycloid pin gear system, the error distribution mainly lies in five parts: the cycloid, the input crank, the pin teeth, the pin gear, and the pinion sleeve. Due to dimensional tolerances, the cycloid gear must be turned through a certain angle to engage the pin teeth, defined as the tolerance clearance. To make up the tolerance clearance, the crankshaft and the cycloid gear are adapted to the assembly dimensional chain, and the pin tooth and pin gear or pinion sleeve fit assembly dimensional chain are established, respectively. Finally, the result of the solution is entered in the equation of the tooth profile to obtain the tolerance difference. Figure 8 shows the clearance at the part joints in relation to the number of teeth meshed. The matrix with a pitch of 0.5 and overall dimensions of 61 \(\times\) 61 can be obtained. When the clearance between the cycloid and the input crankshaft as well as the pin tooth is in the interval [0 \(\upmu\)m,11 \(\upmu\)m] in the main diagonal, a contact tooth number of 11 is the ideal meshing condition. In the XY-plane of Figure 8, it is observed that the number of contact teeth is more sensitive to the contact clearance between the housing and the pin tooth or the sleeve. The optimal area (i.e., red part) is shifted in the upper triangle of the matrix. In view of the economy of machining and assembly, the target optimal solution is set in the area around the point (26.5, 24.5, 9). The fit is first determined for the position of the relatively insensitive connection, i.e., the input crankshaft is connected to the cycloid. The basic dimension of the center circle diameter of the cycloid gear is 144 mm. The base-hole system is selected with a clearance fit, and a maximum clearance of 26.5 \(\upmu\)m and a minimum clearance of 0 \(\upmu\)m are adopted as design targets. Considering the economy of machining and assembly, H3/h5 is finally chosen. The upper deviation es and lower deviation ei of the hole are 8 \(\upmu\)m and 0 \(\upmu\)m, respectively; the upper deviation es and lower deviation ei of the shaft are 0 \(\upmu\)m and \(-\)18 \(\upmu\)m, respectively. The maximum clearance of the final design is 26 \(\upmu\)m and the minimum clearance is 0 \(\upmu\)m. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Load torque, T (N m) & 100 & Number of cycloidal teeth, \(\mathrm{z_{a}}\) & 23 \\ Density, \(\rho\) (Kg/m\({}^{3}\)) & 7830 & Number of pin tooth, \(\mathrm{z_{b}}\) & 24 \\ Poisson’s ratio \(v\) & 0.3 & Pin pitch radius, \(\mathrm{r_{b}}\) (mm) & 30 \\ Yield limit, (MPa) & 518 & Cycloid pitch circle radius, \(\mathrm{r_{a}}\) (mm) & 27 \\ Elastic modulus, E (GPa) & 208 & Pin radius, \(\mathrm{r_{p}}\) (mm) & 10 \\ Transmission ratio & 24 & Eccentricity, e (mm) & 3 \\ Pin center circle radius, \(\mathrm{R_{b}}\) (mm) & 100 & Cycloid tooth width, b (mm) & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cycloid design parameters. After selecting a clearance value of 26 \(\upmu\)m for this region, the maximum assembly clearance of the pin tooth is 24 \(\upmu\)m according to the calculation results corresponding to Figure 8. This ensures that the number of teeth engaged is 9 and that a stable power transmission is maintained. The hole where the pin tooth is placed in the housing is named and machined to an accuracy of IT5, which corresponds to the diameter of \(\varphi 20^{+0.009}_{0}\) mm. The accuracy of the corresponding shaft is slightly lower; so, IT6 is adopted here, which corresponds to the diameter of \(\varphi 20^{+0}_{-0.013}\) mm (based on the standard ISO 286).