## 2 Design of the Non-Circular Gear
### 2.2. Tooth Profile Design
#### 2.2.1 Calculation of Minimum Module  
In order to determine module for each section, it is necessary to calculate the minimum module that can be used in the operating environment. In the case of non-circular gears, the distance from the center of rotation to the pitch point continuously changes during the rotation of gears which are engaged with each other. The largest changes in angular velocity occur in the section with the largest curvature, and in order to accurately represent the angular velocity, module was based on the position with the smallest radius in the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Section** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline \hline \begin{tabular}{c} Pinion rotation \\ angle (\({}^{\circ}\)) \\ \end{tabular} & 0–67.5 & 67.5–90 & 90–112.5 & 112.5–157.5 & 157.5–202.5 & 202.5–315 & 315–337.5 & 337.5–360 \\ \begin{tabular}{c} Gear rotation \\ angle (\({}^{\circ}\)) \\ \end{tabular} & 0–67.5 & 67.5–93.37 & 93.37–115.87 & 115.87–160.89 & 160.89–205.87 & 205.87–318.04 & 318.04–340.54 & 340.54–360 \\ \begin{tabular}{c} Radius of Driving \\ Gear (mm) \\ \end{tabular} & 50 & \(\uparrow\) & 66.67 & \(\downarrow\) & \(\uparrow\) & \(\downarrow\) & 33.33 & \(\uparrow\) \\ \begin{tabular}{c} Radius of Driven \\ Gear (mm) \\ length (mm) \\ \end{tabular} & 50 & \(\downarrow\) & 33.33 & \(\uparrow\) & \(\downarrow\) & \(\uparrow\) & 66.67 & \(\downarrow\) \\ \
\begin{tabular}{c} Pitch curve \\ length (mm) \\ \end{tabular} & 58.90 & 22.17 & 22.20 & 28.60 & 27.18 & 29.09 & 114.75 & 20.42 \\ \hline \hline
\begin{tabular}{c} Total pitch curve \\ length (mm) \\ \end{tabular} & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications of driving gear and driven gear according to the sections. driving gear, and a sufficient safety factor was given in consideration of the specificity of non-circular gears. For the transfer load (\(W\)), the minimum module is given by Equation (8). \[\text{m}=\frac{w}{sf_{p}by\sigma_{b}} \tag{8}\]  
The minimum module is obtained from Equation (8), where \(w\) is the transfer load, \(s\) is the safety factor, \(f_{v}\) is the velocity factor, \(y\) is the tooth form factor, and \(\sigma_{b}\) is the bending stress in gear tooth. The torque load required in the field is 50\({}^{\prime}\)000 N\(\cdot\)mm in the viscera removal section, and the transfer load \(W_{n}\) is calculated by Equation (9). Each interval of driving gear is shown in Figure 6, and theoretically calculated module is shown in Table 3.  
\[W_{n}=\frac{w}{\cos(\alpha)}\div R_{\text{min}} \tag{9}\]  
\[\text{m}=\frac{\text{P}}{\text{z}\pi}(z=1,2,3,\ldots\text{Natural number}) \tag{10}\]  
The minimum module obtained from Equation (8) was adjusted by Equation (10) because the number of teeth within each section must be a natural number. Design procedures of non-circular gear are composed of 4 steps and are as follows. 1. Creation of involute tooth according to the modules calculated (Figure 7a). 2. Equal division of pitch curve at each section according to the modules adjusted (Figure 7b). 3. Arrangement of centers (pitch points) of circle in the equal points by translation and rotation (Figure 7c). 4. Connection of roots between designed teeth (Figure 7d).