Minimum Number of Teeth for Involute Rack and Pinion Arrangement
Involute rack and pinion arrangement is a common mechanism used in various mechanical systems. In this arrangement, the pressure angle is an important parameter that determines the smooth operation and efficiency of the system.

Pressure Angle of 20 Degrees
The pressure angle is the angle between the line of action and the line tangent to the pitch circle. A commonly used pressure angle is 20 degrees in mechanical systems.

Calculation of Minimum Number of Teeth
The minimum number of teeth required for an involute rack and pinion arrangement with a pressure angle of 20 degrees can be calculated using the formula:
\[ N = \frac{2}{\sin(\phi)} \]
Where:
- \( N \) = Number of teeth
- \( \phi \) = Pressure angle in radians
For a pressure angle of 20 degrees (approximately 0.349 radians), the minimum number of teeth required would be:
\[ N = \frac{2}{\sin(0.349)} \approx \frac{2}{0.342} \approx 5.85 \]
Therefore, the minimum number of teeth required for an involute rack and pinion arrangement with a pressure angle of 20 degrees is approximately 6 teeth.

Conclusion
In summary, the minimum number of teeth for an involute rack and pinion arrangement is determined by the pressure angle, with a higher pressure angle requiring fewer teeth for smooth operation. In this case, with a pressure angle of 20 degrees, a minimum of 6 teeth is needed to ensure efficient functioning of the mechanism.