Core Definitions
Mathematical Definition 1: The module is the ratio of the gear's pitch circle diameter to the number of teeth; the formula is $m = d/z$, where $d$ is the pitch circle diameter and $z$ is the number of teeth.
Mathematical Definition 2: The module is the ratio of the pitch (measured along the pitch circle) to pi ($\pi$); the formula is $m = p/\pi$, where $p$ is the arc length between corresponding points on the profiles of adjacent teeth along the pitch circle (the circular pitch).
Unit Attribute: The standard unit for the module is the millimeter (mm); it is a standardized measurement parameter derived through abstract convention.
Core Basis of the Definition
The definition of the module is based on the gear's **pitch circle**. The pitch circle serves as the theoretical reference circle for gear design and manufacturing; standard module and standard pressure angle values refer specifically to parameters at the pitch circle.
The concept of the module was first proposed by French engineers in the mid-19th century to unify dimensional standards for gear design and manufacturing, thereby enabling the interchangeable production of gears.
