Tac, the Hooke Joint, Universal Joint, Universal Coupling, U Joint and Cardan Joint are essentially the same thing just different names. Hooke however was the first to realize that this type of joint accelerated/decelerated when there was an angle involved and how that related to shadows casting across sundials. The design with the outer ring is geometrically no different to what we find on a car tailshaft. I suspect the rings act centrifugally to take side load of the bearings.
90 degree difference on each side of the engine block does make a difference as the joint pivot pins would be 90 degrees different on each side which would then make each side shaft near out of phase during the accelerate/decelerate cycle. (Equivalent to overlaying the above chart by 1/4) That would produce opposing vibration effect rather than a compounded one. That’s why I figure they chose 45 degrees to dampen things out. It has nothing to do with the square shaft but everything to do with the joints and the way the pins are oriented. The square shaft rotation appearance is just a product of where the pivot pins are on the joint.
Have you noticed that at each end of a regular drive shaft the pins are the same way so when there is a similar angle at each end the shaft will accelerate/decelerate twice per revolution after the first joint but the opposite will happen through the second joint therefore the result/wheels will not accelerate/decelerate. If the pins were 90 degrees out on each end of the shaft the accelerate/decelerate effect would double at the result/wheels rather than canceling the accelerate/decelerate effect out.
Therefore, there is a correct way we should slide the square shafts together on our model shays although it is not critical if we have slip clutches etc, the engine crank will just accelerate/decelerate around corners when not correct. That may be another reason why some people got excessive wind up and busted things on earlier models.
I think I got all that right. It has been an education pondering this. Thanks for posing the question. I will attempt to confirm all when I next chat to a loco engineer than knows his shays. They drive through the bottom of my yard regularly.
The movie is just an animated ‘gif’ courtesy of wikipedia commons. It’s good to visualize these things although it will do your head in eventually…
Andrew
(http://upload.wikimedia.org/wikipedia/en/thumb/b/bc/SonoraUJoints.jpg/640px-SonoraUJoints.jpg)