Ran across this great Youtube video showing how a pair of u-joints, when timed, produce a smooth output. Each joint cancels the pulsation of the other, perfectly. It also shows that if the input and output shafts aren't parallel there will be vibration (and lots of it). Most people know this from "lifting" a 4x4 truck. It's much less critical on a PTO shaft.
This video shows the effect of the input shaft and output shafts NOT parallel. You can't always control this on a PTO implement because the 3-point travels up and down in an arc, NOT vertical. And in many cases the top link is a variable length. But if you CAN choose a setting (3-point height, or top link adjustment) where the implement is operating with the implement shaft/yoke parallel to the PTO output shaft/yoke, this will be the smoothest operation, and everything will last longer. Bearings, u-joints, chains, sprockets, gearboxes. Everything.
For anyone
cutting or extending a PTO shaft, the main issue in welding it back together is
the u-joint timing. It's easy, and it's not critical to be accurate. You can be a few degrees either way. But only a few. A hand-drawn straight line on the shaft (before you cut it) is all the accuracy you need. Towards the end it shows what happens when a u-joint pair is "OUT of time". For example if a PTO shaft was lengthened or shortened and welded back together with the U-Joint pair "OUT of TIME"