Lathe precision for making aluminum yoyos?

I recently talked with a friend who studied engineering about buying a lathe to make yoyos, and he told me those small lathes normally under $700 are probably not precise enough for making aluminum yoyos.
So anyone who have made yoyos before, how precise should the lathe be to make acceptably smooth yoyos? Is there a guide number like “at least 0.001mm” something?

Am I approaching this the right way?

I’m talking about this kind of lathe:

I bought a mini lathe some time back, not necessarily specifically for yoyos although I have modded my fair share of old yoyos with it. If you buy a good mini lathe (ie from littlemachineshop, sherline, maybe grizzly etc) with DRO and/or put a significant amount of care in setting up the machine and work piece, you can achieve decent tolerances. Maybe not .0001in (.0025mm) or anything on a large/long piece, but closer to .0005in-.001in in most cases. Several manufactures I’ve heard comments from have said they aim for +/-.0002in (.005mm) tolerances with CNC production runs. Of course the biggest issue with using a mini lathe is that they are all manual lathes, so precisely turning two separate halves of a yoyo without CNC is quite tricky, especially if you hope to avoid significant vibe or maintain tight tolerances.

Mini lathes are honestly probably only suited for modding yoyos for recessed silicone grooves, shmoove grooves, adding bearing spacer kits etc, and with some skill making wood or delrin yoyos from scratch (although they still probably wont be the smoothest). To get the best results you’d really need CNC, especially for tight tolerances and consistency with aluminum

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