# Pattern Classification and Gear Design of Spatial Noncircular
## 2 Pattern Classification of Spatial Noncircular gear CVT  
Spatial noncircular gear CVT pattern can be divided into two categories, with a total of five subcategories, as shown in Table 1 and Figure 2. Type I is the addition method, including classes A, B, and C, named NG-PBGT, NG-PCGT, and CFG-BG-PCGT, respectively. Type II is the multiplication method, including classes D and E, named CFG and NG, respectively.  
In Figure 2, \(\omega_{\text{i}}\) and \(\omega_{\text{o}}\) are the input and output angular velocities, respectively. The spatial noncircular gear CVT mechanism includes three parts. The first part is the phase switching mechanism, which is responsible for adjusting the phase angle between the two driving spatial noncircular gears and synchronizing their rotation speed at the same time. The second part is the transmission ratio changing part, which is responsible for integrating the transmitted variable transmission ratio to achieve a constant speed output within a certain range of input rotation angle. The third part is the transmission selection mechanism, which is responsible for selecting the transmission ratio transmitted in order to only output a constant rotation speed during the transmission. Through the transmission selection mechanisms of multiple branches, the transmission ratio of each branch at different input rotation angles was integrated, and finally a constant rotation speed output with the input rotation angle in the range of 0 to 360\({}^{\circ}\) was realized.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multicolumn{3}{c}{**I: Addition Method**} & \multicolumn{2}{c}{**II: Multiplication Method**} \\ \cline{2-5}  & **Class A** & **Class B** & **Class C** & **Class D** & **Class E** \\ \hline
**Name** & **NG-PBGT** & **NG-PCGT** & **CFG-BC-PCGT** & **CFG** & **NG** \\ \hline \multirow{3}{*}{\begin{tabular}{c} Transmission ratio \\ changing mechanism \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} Noncircular gear pair \\ and planetary \\ gear train \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} Noncircular gear pair \\ and planetary \\ cylindrical gear train \\ \end{tabular} } & Curve face gear pair & \multirow{3}{*}{
\begin{tabular}{c} Noncircular gear pair \\ gear train \\ \end{tabular} } \\  & & & & gear train \\ \hline \hline \end{tabular}
\end{table}
Table 1: CVT pattern of spatial noncircular gear.  
Figure 1: Research workflow of spatial noncircular gear CVT.  
The structure of the phase switching mechanism and the transmission selection mechanism of the five patterns are the same, but the transmission ratio changing part is different. For the three classes included in type I, the transmission ratio changing part is composed  
Figure 2: CVT pattern of spatial noncircular gear. (**a**) Type I: Addition method. (**b**) Type II: Multiplication method.  
of different spatial noncircular gear mechanisms and differential mechanisms. Through the addition method, the transmission ratios of gear pairs were integrated to achieve a constant speed output. For the two classes included in type II, the transmission ratio changing part is composed of different spatial noncircular gear mechanisms. Through the multiplication method, the transmission ratios of gear pairs were integrated to achieve a constant speed output. The structural composition of the transmission ratio changing part of each pattern is shown in Table 1.