Well I never! I know Pat Barker well, although I haven't seen him since my father died. Both Pat and the other John Riley worked with my father (J B B Johnston) in Structures Dept at RAE Bedford. I used to fly at Twinwood Farm and then at Thurliegh, both gliders and the Tiger Moth, until we sold it. I now fly at Gransden Lodge, gliding and tugging.
One key question about the change gears is the pressure angle. Given the age of the lathe the PA is most likely 14½°. It is possible to machine gears on a CNC mill to save the effort of making, or buying, special cutters:
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And the final gear set:
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I live a few miles west of Cambridge, and regularly visit Bedford as my mum lives in Brickhill. PM me if you'd like to meet up.
Andrew