We purchased an old Mitchell lathe a while back and have been running it as a general purpose maintenance lathe. I am now at the point where I want to do some slightly more advanced things and am running into some difficulties. I am research engineer and not a machinist so apologies for my gaps in knowledge. I spent a lot of my free time at university in the machine shop hanging out with the staff there but I have no formal training. Yes, it needs a clean, yes, a three jaw chuck held in the 4 jaw is janky and has a lot of runout, I am not the only user of this guy...

To the issue: The threading chart seems to bear little connection to what actually happens on the workpiece.

The change gear arrangement is as follows:

I am trying to make an M16x2mm drawbar for the mill I just purchased (It has a 40 taper and 5/8"-11 drawbar and would like to run cheap import tooling). The change gears that came with the lathe seem to be 12DP with a 3/4" bore. I only have those pictured available currently which are 40, 40, 42, 42, 48. I imagine these can be found used or from McMaster etc. if I need more, or someone on Alibaba sells sets I could substitute in.
Anyways, the chart lists 4 gears which is my first confusion, I see only one driver and one driven gear in this arrangement. The second problem is that of course I don't have a 45 or 60 tooth gear available. I tried running it with 42 and 40 and it wasn't even close, roughly 2.6mm pitch. I messed around with settings and couldn't get it close. I tried with 48-42 which got me close enough (levers set A-D but in position 6) that I could probably run a die over a shallow thread and get something workable.
Time is on my side here so if possible I would like to understand what is going on at minimum and hopefully grab a gear off ebay to get me 100% of the way there.
Thank you for the help.
-Stephen
Also, if you have battery or chemistry questions I am the person to ask.

To the issue: The threading chart seems to bear little connection to what actually happens on the workpiece.

The change gear arrangement is as follows:

I am trying to make an M16x2mm drawbar for the mill I just purchased (It has a 40 taper and 5/8"-11 drawbar and would like to run cheap import tooling). The change gears that came with the lathe seem to be 12DP with a 3/4" bore. I only have those pictured available currently which are 40, 40, 42, 42, 48. I imagine these can be found used or from McMaster etc. if I need more, or someone on Alibaba sells sets I could substitute in.
Anyways, the chart lists 4 gears which is my first confusion, I see only one driver and one driven gear in this arrangement. The second problem is that of course I don't have a 45 or 60 tooth gear available. I tried running it with 42 and 40 and it wasn't even close, roughly 2.6mm pitch. I messed around with settings and couldn't get it close. I tried with 48-42 which got me close enough (levers set A-D but in position 6) that I could probably run a die over a shallow thread and get something workable.
Time is on my side here so if possible I would like to understand what is going on at minimum and hopefully grab a gear off ebay to get me 100% of the way there.
Thank you for the help.
-Stephen
Also, if you have battery or chemistry questions I am the person to ask.