What is the reciprocal of the diameter pitch in relation to pitch diameter and number of teeth?

The reciprocal of the diameter pitch is known as the module in gear design. The module is a crucial parameter that relates the pitch diameter of the gear to the number of teeth on the gear. It is defined as the ratio of the pitch diameter (in millimeters) to the number of teeth. Essentially, it provides a standardized way to specify the size of a gear in metric units, making it easier to design and manufacture gears that will mesh correctly.

When calculating the module, you can express it mathematically as:

[ \text{Module} = \frac{\text{Pitch Diameter}}{\text{Number of Teeth}} ]

This relationship highlights how the module serves as an indicator of the size of the teeth on a gear; as the number of teeth increases while keeping the pitch diameter constant, the module decreases, indicating smaller teeth. This is why the concept of the module is integral to gear design and why it is recognized as the reciprocal of the diameter pitch when considering the pitch diameter and number of teeth.

In contrast, other options like lead, involute, and clearance have their specific definitions and applications in gear design, but they do not represent the relationship derived from dividing the pitch diameter by the number of teeth in the same manner.