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You really want it to scre wup tight just before it tightend on the arm so the plain length should be just over the 0.312"Personally I would make it with a shoulder making the unthreaded section 0.156" for alength of 0.314" and increase the hole in the arm to the same 0.156"
If you make a second one exactly the same as the one you have already done so you have a pair with female threads. You can then make a separate "spacer tube" 1/8" ID x 5/32" OD and 0.314" long. Take a piece of threaded rod, screw it into one of the pair, slip on the spacer and then screw the other end onto the threaded rod and it can all be tightened up with just the right amount of space between the two faces.