Judging by the metal filings in between the threads on the screw in the last picture (the screw removed from the machine) I would say the screw is fine but the piece it goes through is shot. You might be able to repair it with a helicoil insert, but if you have to enlist the help of a machinist the expense could exceed the value of the machine.
Speaking of machinists, in lieu of trying to find a local machine shop and talking them into doing something like this, you might post to a machine shop forum online and see if anyone contacts you via direct message with an offer.
I agree... If you happen to have a metal bristled brush (or just any firm bristled brush), try to clean up the threads on the bolt. If they are intact, then the hole is shot. However, if it really is only happening in a limited range of travel, that doesn't make sense... Unless this is at the far end of travel and only half of the hole is damaged.
Either way, though - this actually isn't as bad to recreate as it looks. You don't
really need an identical part if the threaded hole on the yoke isn't trashed.
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McMaster-Carr is the complete source for your plant with over 595,000 products. 98% of products ordered ship from stock and deliver same or next day.
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A little luck needs to be involved, but this looks like a partially threaded thumb screw with a pilot point tip. My guess is that the unthreaded area near the knob is going to be standard sized for the thread that was cut, and the other end of the bolt actually doesn't really matter
if you can fit a bushing on the other end. I'm linking mcmaster carr here for inspiration (and figuring out what stuff is named), but you really only need to match the length of the bolt. The screw and washers do all the work of holding the threaded rod in place in your machine, and as that screw moves, the carriage is pulled/pushed along by the threads. If the holes are snug on both ends, I'd take a look to see if there's any inserts in the machine. It appears that the left (red circled) surface is narrower diameter than the rest of the bolt. If worse comes to worse, I'd drill out the hole on the other end and drop in a (sacrificial) bushing and call it a day. The bushing is just there to keep the bolt shaft in the correct alignment and provide a surface to ride on. Note that you don't need to retain the bolt in the same way (with a screw from the other end). As mentioned, the screw is just there to keep the bolt from floating in and out. You can just cut the thumbscrew down to length, and then use a nylock nut with the same results. It's more ideal if you can remove the threads, but you're not likely to get that done precisely without some machine work... You
could buy a way longer bolt than you need, chuck it up in a drill, and then grind it with a carbide cutter, or something, but at that point, custom machining is fine.
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Edit: Next steps if you still can't find help on this is to take that bolt to a hardware store and ID what the machine thread is. I'm guessing it's metric, maybe M6 from the looks of it... Then do your best to measure the lengths of the threaded area, the unthreaded areas, and if you can (calipers), the diameters of the unthreaded areas.