I would start by gluing a small dab of epoxy to a popsicle stick, or something similar, and setting it down onto the penny. Let that cure for a good couple of hours, then try to pull it up. This has a better chance of working if there's a little room to let you slide the coin back and forth. If it's wedged in tight or if it's caught under a metal tab, you may have to use the stick to tip the coil a little to get it passed what it is hooked on.
If the glue pulls loose and leaves the coin behind, don't panic. Try it again. Pennys commonly get a dark brown coating that is a film of corrosion. The glue will pull that coating off without really adhering to the coin. A second attempt may find the coin is shiny now and the glue will stick to it better.
Next is to try using a vacuum cleaner to suck the coin out, but don't be surprised if that doesn't work. You need air flow through the socket to make that work.
The last trick is to use a thin screwdriver to hold the coin from spinning, then drill a small hole through it. Run a wood screw into the hole, then use it to pull the coin up. I have a huge bucket of 3"-long screws for all kinds of projects. A 1/16" hole would be just right to fit those screws. Also consider using a sheet rock screw. Those come as long as 2" which should still be long enough to let you screw it in, then pull it out with a needle nose pliers. Use something sticky, like chewing gum, on a stick to pull out any metal chips from the socket or use compressed air to blow the chips out.
Let me know if any of those methods work for you.
The last resort is to remove the socket so you can turn it upside down and knock the coin out. I'll find the instructions for socket removal for you if it comes to that.
Sunday, December 18th, 2022 AT 5:36 PM