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What are the sprocket modules? How is the circle of graduation calculated?

Chain transmission only has the concept of "pitch" and does not talk about "modulus". The definition of pitch can be understood as the name implies. Commonly used pitches are 12.7, 15.875, 19.05, 25.4, 31.75, 38.1, 44.45, 50.8,..., and the relationship with inches can be seen at a glance.

Sprocket indexing circle diameter d=p/(sin(180°/z)), where p is the pitch and z is the number of teeth.