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My crank puller doesn't fit the TA crank.
There is a thread (perhaps in "open toolbox") where people passed the appropriate puller around, failing which I think SJS stock them.
I have no idea about how to go about drilling the rear to accommodate a modern caliper.
I can't see the bridge clearly but even if there is enough reinforcement to allow the hole to be drilled, the chance of you accurately enlarging the hole with a flexible drive is vanishingly small.
Scroll down to "Mounting recessed-mounting calipers on older frames" on this page, if you don't fancy getting a new bridge installed.
I don't know if it's safe to drill the forks.
Yes, but without a drill press it's inadvisable for the same reasons as the rear.
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I have no idea about how to go about drilling the rear to accommodate a modern caliper
You don't need to, the centre bolt on a front caliper will be long enough to allow you to fit a hex nut.
https://www.lfgss.com/conversations/226321/?offset=125#10056988
Started having a fiddle with this tonight and made a tiny bit of headway...
I have taken the front chain-set off and flipped it over - both bolts were very loose which is worrying.
I measured the BB and both sides had 15mm showing so I didn't flip the BB axle over too. (I hope this is ok). Amazingly, almost 50 years after it was originally fitted the BB is still running smooth and free.
Problems:
My crank puller doesn't fit the TA crank.
I have no idea about how to go about drilling the rear to accommodate a modern caliper.
I don't know if it's safe to drill the forks.
The bolt that holds my seatpost is imperial.
In conclusion,
I have a lot of issues...