So the question still stands...Why 540? Why did the ASAE in April of 1927 decide that the PTO rotational speed was to be 536 +/- 10 rpm?
I don't understand the 60 cycle electric motor explanation...the common speeds for AC motors are 1725 and 3450 rpm.
I believe the early engine speed comment has merit and could be a good starting point for the ASAE logic.
Electric motors speeds are determined by the number of poles;
16 pole 60 Hz = 450 rpm unloaded
12 pole 60 Hz = 600 rpm unloaded
10 pole 60 Hz = 720 rpm unloaded
8 pole 60 Hz = 900 rpm unloaded
6 pole 60 Hz = 1200 rpm unloaded
4 pole 60 Hz = 1800 rpm unloaded
2 pole 60 Hz = 3600 rpm unloaded
of course we shouldn't forget the Europeans with their 50 Hz power
12 pole 50 Hz = 500 rpm unloaded 50 Hz 3000 1500 1000 750 600 500
10 pole 50 Hz = 600 rpm unloaded 60 Hz 3600 1800 1200 900 720 600
8 pole 50 Hz = 750 rpm unloaded
6 pole 50 Hz = 1000 rpm unloaded
4 pole 50 Hz = 1500 rpm unloaded
2 pole 50 Kz = 3000 rpm unloaded
And then there are DC motors of all types and variations,
of course then we can start with VFD's for most any and all speeds.