Lathe spindle dividing - resolution calculations and help!

Evening
I’m taking on a project to fit a stepper to the back of a lathe spindle for dividing when clock wheel cutting. I have the physical dividing electronics sorted, but I’m struggling with the resolution.

In the past I’ve done this by using a 90:1 reduction in a cheap dividing head and fitting this to the back of the lathe.
With 200 steps x 2 for mixrostepping x90 for the reduction = 36000 steps per revolution of the spindle.

This new lathe is far too small to use a dividing head and the worm and wheel is t really an option due to space. Therefore my plan was to go with day a 1:10 reduction using a planetary gear on a stepper motor and then on top of that a 1:6 belt drive reduction giving a similar number of steps per revolution as the example above. However, the problem is money. A cheapo stepper can be purchased for £50 with a planetary gear box attached but these have upto 1.2degrees if backlash!! My understanding is that this would really mess things up when reversing (which I sometimes need to do).

So I was doing a few more calculations and just though what about a standard stepper and then timing belt.

200 steps x 2 microstepping x 6 reduction = 2400 steps per revolution.

Now in my head that seems quite high precision at about 0.15 deg movement per step and seems like it would be highly suited to say 60-200 divisions on a clock wheel!

Before I part with my money, I’m just concerned I’m missing something. I feel 2400 steps per revolution seems a decent resolution but compared to 36000 steps I’m use to on my other lathe, it seems very low!

Any opinions or thought would be appreciated.
Thank you.
Chris

What are your requirements?

1-250 divisions for clock wheels.

A timing belt will allow you to disengage the stepper easily so you can use the lathe as normal. Nothing stopping you doing a 4:1 reduction and then doing 10 or even 16 or 32 microsteps. As the rotational speeds will be low, 32microsteps will be fine if you selected driver allows them.

In theory your resolution would be: 360/(200*4*16)=0.026deg which equates to 1minute 33.6sec of a degree or half that with 32 microstepps

If you are concerned about back driving then you will need a worm gear.