Length of Path of Approach Calculator

Calculate Length of Path of Approach







Formula

The formula to calculate the Length of Path of Approach is:

\[ P1 = \sqrt{RA^2 - R_{wheel}^2 \cdot (\cos(\Phi_{gear}))^2} - R_{wheel} \cdot \sin(\Phi_{gear}) \]

Where:

Definition

Path of approach is the portion of the path of contact from the beginning of contact to the pitch point.

Example Calculation

Let's assume the following values:

Using the formula:

\[ P1 = \sqrt{0.022^2 - 0.0124^2 \cdot (\cos(0.55850536063808))^2} - 0.0124 \cdot \sin(0.55850536063808) \]

Evaluating:

\[ P1 = 0.0127530282978548 \text{ m} \]

The Length of Path of Approach is 0.0127530282978548 meters.

Conversion Chart

Radius of Addendum Circle of Wheel (m) Radius of Pitch Circle of Wheel (m) Pressure Angle of Gear (rad) Path of Approach (m)
0.02 0.0124 0.55850536063808 0.010441291570
0.021 0.0124 0.55850536063808 0.011606405400
0.022 0.0124 0.55850536063808 0.012753028298
0.023 0.0124 0.55850536063808 0.013884270035
0.024 0.0124 0.55850536063808 0.015002550350
0.025 0.0124 0.55850536063808 0.016109786521
0.026 0.0124 0.55850536063808 0.017207521394
0.027 0.0124 0.55850536063808 0.018297013232
0.028 0.0124 0.55850536063808 0.019379300279
0.029 0.0124 0.55850536063808 0.020455248111