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Imperial to Metric and Metric to Imperial
Transposing Gears
by Evan Lewis

How to calculate what changewheels are needed to make an imperial lathe cut metric threads - and a metric lathe cut imperial

I had noticed the large number of compound gears used for metric-imperial conversion (other than the standard 127/100) and so I have been studying the question for some time. As I wanted to generate a list of possible conversion gears for any lathe, I've written a program to do the job called and derived a general equation as shown below.
The starting point was to make an imperial lathe with an 8 t.p.i. leadscrew behave like a metric lathe with a 3 mm pitch leadscrew and to do this - from the table below - a gear ratio of 1.058333 is needed. Enter this ratio in the program to generate a list of compound gears that can produce this ratio (approximately). Then, choose one of the compound gears and use it in the geartrain calculator to see how well it works.

The general equation is:
R = 25.4 / ( Li * Lm )
Where Lm is the pitch of the desired metric leadscrew, and Li is the t.p.i. of the imperial leadscrew. I then made the following table using this equation:

Table of gear ratios for Metric-Imperial Conversion-Large-WEB.jpeg
In, if you click the menu button 'Metric-Imperial-Conversion' it displays this table so you can copy and paste your chosen ratio into the INPUT box and the program runs through gear sizes from about 12 to 400 teeth and for each one finds the nearest matching gear that approximates this ratio, and displays the error beside it. By choosing the lowest error in a reasonable gear size you can make your own 'transposing' gear.
This works for any lathe, with or without a gearbox and the same ratio is used for converting imperial to metric or metric to imperial (just flip the compound pair over to invert the gear ratio).


Once on there are some very useful vidoes that take you, step-by-step through the various options; it's suggested that you look at these first.
To take an example: if you have an imperial lathe, look across the top row to find the column which matches the t.p.i. of your leadscrew. Look down the left column and decide which leadscrew pitch (in mm) that you would like your lathe to produce. Find the ratio where the row and column meet. Copy and paste this ratio into the INPUT box below.
If you have a metric lathe, look down the first column to find the mm pitch of your leadscrew. Look across the top row and decide which leadscrew t.p.i. you would like your lathe to produce. Find the ratio where the row and column meet. Use copy and paste to use this ratio in the INPUT box below.
The program on this page will list all the pairs of gears that approximate the ratio you requested, and the amount of error that is introduced. This error is caused by the fact that the number of teeth on any gear must be an integer. works for any lathes without a gearbox and also has a quite a few lathes with gearboxes listed e.g. Myford, Grizley, Logan, etc, after people asked to have their lathe added. Actually the user can add a gearbox using code on the site, but it seems to be a bit too complicated for most users so I usually end up doing it myself. There are so many lathe designs with their own quirks! Some of them are really challenging, but all I need are photos of the labels on the gearbox.  I should really go through your site to see how many of the lathes have photos of the tables and info about the standard gear train and leadscrew pitch.

Unfortunately, the list of conversion gears is not complete because compound gears can be combined with a wide range of stud and leadscrew gears - or gearbox settings - to produce the same overall gear ratio, sometimes with even greater accuracy, such as 76/65 on the Boxford. But, still, it may give the user more useful options.