Mini-Lathe: Metric Change Gear Tables

Running my assortment of custom 3D printed change gears through the LittleMachineShop calculator and copying the results into a spreadsheet for E-Z formatting produces a useful table:

The same table in text-ish format, minus the colored highlights marking the custom gears:

Pitch	A	B	C	D	Actual	Error	In 10 pitches
0.10
	20	80	20	80	0.099	0.786%	0.008
	20	79	20	80	0.100	0.468%	0.005
	20	80	20	79	0.100	0.468%	0.005
0.20
	20	79	40	80	0.201	0.473%	0.009
	20	80	40	79	0.201	0.473%	0.009
	40	79	20	80	0.201	0.473%	0.009
	40	80	20	79	0.201	0.473%	0.009
0.25
	20	55	35	81	0.249	0.225%	0.006
	20	81	35	55	0.249	0.225%	0.006
	35	55	20	81	0.249	0.225%	0.006
0.30
	20	57	35	65	0.300	0.023%	0.001
	20	65	35	57	0.300	0.023%	0.001
0.40
	20	55	45	65	0.400	0.088%	0.004
	20	65	45	55	0.400	0.088%	0.004
0.50
	21	50	45	60	0.500	0.012%	0.001
	21	60	45	50	0.500	0.012%	0.001
	21	80	60	50	0.500	0.012%	0.001
	42	35	21	80	0.500	0.012%	0.001
	60	50	21	80	0.500	0.012%	0.001
0.60
	35	57	40	65	0.600	0.022%	0.001
	35	65	40	57	0.600	0.022%	0.001
	40	57	35	65	0.600	0.022%	0.001
	40	65	35	57	0.600	0.022%	0.001
0.70
	35	55	45	65	0.699	0.087%	0.006
	35	65	45	55	0.699	0.087%	0.006
	45	55	35	65	0.699	0.087%	0.006
	45	65	35	55	0.699	0.087%	0.006
	50	77	55	81	0.700	0.006%	0.000
	50	81	55	77	0.700	0.006%	0.000
	55	77	50	81	0.700	0.006%	0.000
0.75
	42	50	45	80	0.750	0.012%	0.001
	42	80	45	50	0.750	0.012%	0.001
	45	50	42	80	0.750	0.012%	0.001
	45	80	42	50	0.750	0.012%	0.001
0.80
	40	55	45	65	0.799	0.088%	0.007
	40	65	45	55	0.799	0.088%	0.007
	45	55	40	65	0.799	0.088%	0.007
	45	65	40	55	0.799	0.088%	0.007
	20	55	79	57	0.800	0.010%	0.001
	20	57	79	55	0.800	0.010%	0.001
1.00
	21	50	60	40	1.000	0.012%	0.001
	42	50	45	60	1.000	0.012%	0.001
	42	60	45	50	1.000	0.012%	0.001
	42	80	60	50	1.000	0.012%	0.001
	45	50	42	60	1.000	0.012%	0.001
	45	60	42	50	1.000	0.012%	0.001
	60	50	42	80	1.000	0.012%	0.001
1.25
	21	50	60	32	1.250	0.013%	0.002
	35	40	45	50	1.250	0.013%	0.002
	42	40	45	60	1.250	0.013%	0.002
	42	80	60	40	1.250	0.013%	0.002
	45	40	42	60	1.250	0.013%	0.002
	60	20	21	80	1.250	0.013%	0.002
	60	40	42	80	1.250	0.013%	0.002
1.50
	42	40	45	50	1.500	0.013%	0.002
	45	40	42	50	1.500	0.013%	0.002
1.75
	65	42	57	80	1.751	0.029%	0.005
2.00
	42	40	60	50	2.000	0.012%	0.003
	42	50	60	40	2.000	0.012%	0.003
	60	40	42	50	2.000	0.012%	0.003
2.50
	42	32	60	50	2.500	0.012%	0.003
	42	40	60	40	2.500	0.012%	0.003
	42	50	60	32	2.500	0.012%	0.003
	60	20	42	80	2.500	0.012%	0.003
	60	32	42	50	2.500	0.012%	0.003
3.00
	65	50	80	55	3.002	0.061%	0.018
	65	55	80	50	3.002	0.061%	0.018
	80	50	65	55	3.002	0.061%	0.018
3.50
	57	40	65	42	3.501	0.029%	0.010
	57	42	65	40	3.501	0.029%	0.010
	65	21	57	80	3.501	0.029%	0.010
	65	40	57	42	3.501	0.029%	0.010
	65	42	57	40	3.501	0.029%	0.010
4.00
	60	20	42	50	4.000	0.012%	0.005
5.00
	55	21	60	50	4.989	0.215%	0.107
	55	35	80	40	4.989	0.215%	0.107
	55	40	80	35	4.989	0.215%	0.107
	60	21	55	50	4.989	0.215%	0.107
	80	35	55	40	4.989	0.215%	0.107
	80	40	55	35	4.989	0.215%	0.107
	35	45	81	20	5.001	0.012%	0.006
	45	55	77	20	5.001	0.012%	0.006
	77	20	45	55	5.001	0.012%	0.006

The basic formulas:

TPI = 16 / ((A/B) x (C/D))
Pitch = 25.4 / TPI = 1.5875 x ((A/B) x (C/D))

So, for example, a 45-50-42-60 train will produce a 1 mm thread pitch with 120 ppm error adding up to a mere 1 micron in 10 pitches:

Overall, the errors are so low as to not matter, even without using the custom gears, but it’s the principle of the thing …