20B sprocket dimensions: pitch, outside and root diameters from 9 to 120 teeth

The 20B chain (ISO 606 B series) has a pitch of 31.8 mm and a roller of 19.1 mm. These two numbers set every diameter of the sprocket that runs it.

The table gives, for every tooth count, the diameters a sprocket cut from plate must have: the pitch diameter the rollers sit on, the outside diameter at the tooth tips, the root diameter at the bottom of the gaps and the measurement a caliper reads across the gaps. Every row opens the sprocket generator with that chain and tooth count, for the 1:1 template and the DXF.

Dimensions in mm. The outside diameter is the middle of the ISO 606 range; ANSI catalogues print a slightly larger figure, for the tighter ANSI tooth, and the pitch and root diameters are the same. The caliper check is the root diameter on an even tooth count and d × cos(90°/z) − d1 on an odd one, read across the two gaps nearest to opposite.

How the numbers are worked out

Pitch diameter

d = p / sin(180° / z) p is the chain pitch and z the number of teeth.

Outside diameter

da = d − d1 + p × (1.125 − 0.8 / z) d1 is the roller diameter. The middle of the ISO 606 range, from d + p (1 − 1.6/z) − d1 to d + 1.25 p − d1.

Root diameter

df = d − d1 The bottom of the tooth gap, which is what the chain sits on.

Caliper check

even z: df ; odd z: d × cos(90° / z) − d1 On an even tooth count one gap faces another and the caliper reads df; on an odd one it reads across the two gaps nearest to opposite.

Questions

What is the pitch diameter of a 20-tooth %{chain} sprocket?

%{d20}: d = p / sin(180° / 20) with p = %{pitch}. The outside diameter is %{da20} and the root diameter %{df20}.

How do I check a %{chain} sprocket after cutting it?

With a caliper across the tooth gaps. On an even tooth count it reads the root diameter, d − d1 with d1 = %{roller}; on an odd one, across the two gaps nearest to opposite, it reads d × cos(90°/z) − d1. The table gives the figure for every tooth count.

Why is the outside diameter in the table different from the catalogue?

The table is the middle of the ISO 606 range, which is the nominal a plasma or laser cut should aim at. ANSI catalogues print the outside diameter of the tighter ANSI tooth, a few tenths of a millimetre larger; the pitch and root diameters, which are what the chain sits on, are the same.