Rotating Ballnut - design ideas

[Jonathan]

But factors aren't the only factor...
Ideally you don't want to be using less than a 15T pulley as that bends the belt a lot and gets lower tooth engagement, so if you need a 1:2 ratio then you've got to go with at least 30T. However if you're happy with ratios from 15:24 and you can fit the ballscrew shaft through the 24T, then use it as it's inertia will be about 60% less than the 30T pulley. That will help get high acceleration, although you need to consider the system as a whole not just the pulley.