Sprocket Pitch Diameter (ANSI B29.1)
The pitch diameter a sprocket blank is laid out from, straight from the chain pitch and tooth count: PD = p / sin(180 deg / N). It is the circle through the chain-pin centers when the chain wraps, and it -- not the tip diameter -- sets the drive's speed ratio and center distance. A 17-tooth #40 sprocket (0.5 in pitch) is 2.7211 in pitch diameter, with a maximum outside (tip) diameter OD = p(0.6 + cot(180 deg / N)) = 2.9748 in to turn the blank. A design aid; the manufacturer's tooth form and hub govern the sprocket you cut.
Formula and source
PD = p / sin(180 deg / N); OD = p (0.6 + cot(180 deg / N)).
The ANSI B29.1 roller-chain sprocket pitch-diameter and maximum-outside-diameter relations, by name; the manufacturer's tooth form and hub govern.
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