bladehunter over at CNCZone has come up with an interesting approach to fitting a ballscrew to the X axis of a mini lathe.
There is hardly any room, and it's quite difficult to do. Various solutions have been used including:
1. Tiny ballscrews - hard to find, expensive
2. Screw off to the side of the cross slide - fiddly, exposed screw, not ideal but workable.
bladehunter has found a solution by having the nut fixed to the carriage, whilst the screw, bearing assembly and motor move in and out with the cross slide.
He's used a 12mm THK ballscrew, second hand I'm guessing.
An alternative might be a 12mm ballscrew from eBay. I've dealt with Chai (linearmotionbearings2008) a number of times and he's quite reliable. The 12mm ballscrew bladehunter got appears to be different measurements to some of the ones I've seen on eBay.
It's a bit difficult to be sure of the 12mm chinese ballscrew measurements, as often the listing have specs for all the screws except the 12mm screws. If you do this, you'll need to make sure you are getting a screw with the smallish nut as bladehunter got.