Why not 500 or 632 or whatever?
There must be some mechanical basis for standardizing on 540 rpm for PTO speed.
Let's light it up, tractor gurus!
I think its due mostly to engine RPM. Early motors were designed to run at 1800 rpm max. Put on a 3:1 gear box and that gives you 600 rpm at the PTO. Most engine torque curves peak before the max rpm then drop off. 540 PTO rpm is the closest to max engine torque curve peak for maximum power output without redlining the motor.