After seeing the failed MTs utilizing what I call ball-tracks - freely rolling weights, etc. I wrote them all off as nothing to be gained from them.
Despite numerous mechanical approaches with many failures, I find going back to explore them reasonable since I never gave them a second thought.
Doing some deep research, I chanced upon a Dutch mathematician named Frans van Schooten.
His parabola mechanism for drawing can be found here:
https://www.fransvanschooten.nl/fvs_java.htm
Notice the top mechanism has this neat drawing which I've included. I like the 5 loops which overlap each other in mobius fashion.
Also, I see 2 hammer toys in the parallelogram as well as a bow and arrow (try out the applets to see what I mean.)
I've been trying to wrap my head around what could happen with balls in the tracks and if this could create a permanent imbalance. Each ball has a constant path it will take, but it will be interwoven with the other balls on their tracks so that it will take several revolutions until one ball visits each loop.
I have a really hard time getting my head around these movements, but it's a rabbit hole I wish to explore because I'm sure others stayed away because they couldn't think that hard nor grasp it.
No promises - only speculations.