I have seen printing press rollers that were designed to oscillate on their own while turning. the mechanism inside is quite simple and you might be able to make something like it if you do a lot of them.
If you picture a really coarse thread that is cut from left to right and back to left again. there is a dog that follows this track. the dog has a spring that holds just a bit of tension on it . The dog then goes from left to right, turns slighty, following the "thread" where it then goes back to the left and so on.
I am interested in lathes too. we have 4 of them between my two brothers and my dad. I don’t actually own one or have one at home but the odds are good that I will one day 🙂 one is a south bend , one a Hurcus , and two are boxford. These are all south bend clones so most of the parts are interchangeable.
If you look for one I would advise looking for one of these old machines used. They tend to come from high school shops and places like that and if you watch you will likely find one for around 1000- 1500 which is comparable to one of these newer ones, but much more sturdy. watch the auctions and such , the do come up.
If you buy one used, try to get the tools, cutters, knurling tools, three and four jaw chucks, dividing head, toolpost grinder, boring bar, large drill bits with morse tapered shanks, etc.
All the accessories are expensive so if you can get them with the original purchase you are ahead of the game.
This machine Ed has is not a toy it is still very useful and as he says if you don’t put too much of a load on it, it will do nice work. where you will wish it is larger is when you want to remove a lot of material. you will sometimes want o make a part that is such a shape that more material removal is needed. sometimes the stock you find around your shop is quite a bit larger than your intended project. Whatever you end up with will be very handy, even just to make the odd little bushing or washer a certain size. you’ll turn to your lathe rather than driving all over trying to buy one. I don’t mean to knock ed’s machie because I know that someone who is precise and patient can create beutiful work, you just need to compensate. likewise if you find on e that is big and heavy but quite worn, there are workarounds and you can still usually do some fairly precision work if you get to know how to work around any shortcomings.
The great big huge ( but old) monsters can sometimes be even cheaper as no one has room for them ( like ones with a 12 foot bed) if you happen to have that kind of space..
CNC is the way of industry so these old machines are sometimes getting pushed aside, but you don’t need CNC for home projects, repairs etc.
I think a milling machine would be just as useful. of course one of each would be nice.. and there are some lathes with milling attachments. My brother set his up by making a milling attachment which is basicly a third axis to move the workpiece vertically ( the workpiece being mounted on the carriage , and the cutter in the chuck. he makes all kinds of parts with that setup.