Mini-Lathe Metric Threading: 21 Tooth Gear

Mini-lathes sold everywhere except the USA have hard-metric leadscrews with a 1.5 mm pitch, so they can cut metric threads without any trouble at all. USA-ian mini-lathes have hard inch leadscrews with a 1/16 inch pitch and require gymnastics to cut decent metric threads.

For inch threads:

Mini-lathe - inch thread equation
Mini-lathe – inch thread equation

For metric threads, it’s upside-down and converted:

Mini-lathe - metric thread equation
Mini-lathe – metric thread equation

Including a 21 tooth change gear at A or C in the train will get closer to metric threads, but the stud holding the B-C gears on my lathe imposes a minimum B gear size. Here’s a 1 mm thread with a 21-30-45-50 train:

Mini-Lathe change gears - 1 mm - 21 vs 30 tooth - AB
Mini-Lathe change gears – 1 mm – 21 vs 30 tooth – AB

Oops.

You can interchange the AB and CD gear pairs, but the CD pair also has a minimum spacing:

Mini-Lathe change gears - 1 mm - 21 vs 30 tooth - CD
Mini-Lathe change gears – 1 mm – 21 vs 30 tooth – CD

If it worked, the 1 mm thread would be off by -125 ppm, which is surely close enough.

Without the 21 tooth gear, the LittleMachineShop gear calculator produces a 45-55-50-65 train that fits much better, albeit with +875 ppm thread error:

Mini-Lathe change gears - 1 mm - 45 55 50 65
Mini-Lathe change gears – 1 mm – 45 55 50 65

Dropping the 21 tooth gear into the LMS calculator produces a (barely) workable 21-50-60-40 train with -125 ppm error:

Mini-Lathe change gears - 1 mm - 21 50 60 40
Mini-Lathe change gears – 1 mm – 21 50 60 40

The very very snug fit of the screw (omitted here) on the 21 tooth gear nearly hits the 60 tooth gear. Your mileage may vary, of course.

Various sources suggest the gears are module 1, 20° pressure angle, 12 mm bore, and 8 mm thick (mine measure a scant 7.75 mm), with a 3 × 1.4 mm keyway (the key itself is 3 mm square, but it’s half-buried in the shaft).

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