Well guess what!  I just put together a 5 wheel / 5 rod machine all rotating and sliding in sync just by turning the first wheel... But when I ran the animation everything started getting crazy, so I spent an hour trying to clear all keyframes to start fresh with my perfect first-frame setup, but it kept getting out of whack the moment I advanced the frames.  Why can't there be a 'CLEAR ALL KEYFRAMES AND START OVER' button?  Is that too much to ask for?  Anyway, I gave up this whole project in disgust... I already wasted too much time on it. 

"An Example is worth Ten Thousand Words"