The formula to calculate the Length of Path of Recess is:
\[ P_2 = \sqrt{r_A^2 - r^2 \cdot (\cos(\Phi_{gear}))^2} - r \cdot \sin(\Phi_{gear}) \]
Where:
Path of recess is the portion of the path of contact from the pitch point to the end of contact.
Let's assume the following values:
Using the formula:
\[ P_2 = \sqrt{0.02^2 - 0.0102^2 \cdot (\cos(0.55850536063808))^2} - 0.0102 \cdot \sin(0.55850536063808) \]
Evaluating:
\[ P_2 = 0.0126274587238916 \text{ m} \]
The Length of Path of Recess is 0.0126274587238916 m.
| Radius of Addendum Circle of Pinion (m) | Radius of Pitch Circle of Pinion (m) | Pressure Angle of Gear (rad) | Path of Recess (m) |
|---|---|---|---|
| 0.019 | 0.0102 | 0.55850536063808 | 0.011511558797 |
| 0.02 | 0.0102 | 0.55850536063808 | 0.012627458724 |
| 0.021 | 0.0102 | 0.55850536063808 | 0.013730547503 |