Some light hints that may point you in the right direction:
Hint 1
The assembly is a part of a larger machine.
Hint 2
Several assemblies are meant to move side by side in unison.
Hint 3
The square-ish shaped piece is plastic that will wear down and be replaced.
Is this like a part of something off the marble machine x?
https://youtu.be/qjkIMxmSeIc
Is it playing music from a large drum? Haha
Lol, that's a no. It's for an industrial machine.
Does this push paper along a track or converor by its edge? For like a newspaper or something?
Spot on.
Answer
It's for pushing mail into an envelope. Three or four of them work in unison to push a stack of papers/inserts into an envelope.God damn. That's the hardest one I've seen in a long time. Very nice.
I figured it would be a tough one.
These are mail insertion machines I worked on for several months as a mechanic. It's a little blurry since that were moving, but here it is in action:
That's cool. Never seen anything like that. I love big industrial machines that exist only to recreate an action a single human can do easily lol
Look up a Pitney Flowmaster if you're curious for more.
Collates the inserts into stacks, aligns and opens the envelopes, pushes the insert stack into the envelope, folds and seals the flap, flips the envelope, applies a stamp, prints addresses or data, reads the barcode, ejects any flagged envelopes, and finally stacks them all in a neat row.