ThomD
>Precision machinery, or for that mater my Ford truck, do not feel the need to be limited in the size of threads they specify. My belt tensioner uses an easily available 8.7 MM star drive cap screw.

Probably there was a time when 37/128th was standard. :) If it is whitworth the threads will be 55 degrees with more rounding on them than the American which is 60. So if it looks a more acute thread that may be what it is.

You really can't measure a machine cut thread (if that is what it is) by the outside diameter. The machinist can't do the rounding of the threads with a single point tool so he will probably hand finish the external diameter to get the correct fit. So the outside diameter means nothing. You can measure the exact thread by using know rods that fit into three of the valleys and running the numbers. Good luck with that. If your fix doesn't work, you might try running a few pictures up the flagpole. Sounds like a simple thing, but it might require some custom work.