I wanted wheels on an Amazon basics wire shelving unit and had some extra office chair casters (11mm stem), so enter this adapter. It uses the screw-in feet that come already attached to the shelving unit which snugly fits into a matching shape on the adapter.  In the end you wind up with a caster that screws in just like the foot.

I intentionally made the fit tight so no adhesives are necessary on the caster end, you will need a standard hammer:
- Put the shelf foot into the adapter first, tapping the end of the thread and the body of the foot until it's all the way in. It will probably take a couple tries to line it up right.  You may want to use epoxy or a strong adhesive for this connection, the foot can stress the adapter and tilt out of it if there's enough weight - see the important note at the bottom.
- Next, start the caster in the other end. You will need to hold the caster in place and again hammer the end of the thread to get the caster fully inserted, and it may take some effort.  This does not need any adhesive.

If you're using the tightest design, it's meant to be heat set - take a heat gun or hair dryer and heat both the stem and the adapter, then hammer them together. If you'd prefer not to do that, I included a couple size adjustments that will be easier to assemble, and you can always scale the X and Y axes if needed.  The last thing you want is a shelf that fails, so don't overdo the scaling.

Important - the base design is not suitable for supporting a lot of weight.  I added a robust version that's significantly thicker, however depending on the caster design it can still be an issue.  “Potting” the foot-adapter connection with epoxy has solved the issue, I suggest you flip the rack upside down to apply it and let it cure overnight.

It's probably a good idea to use some epoxy with the base design as well.