I need to animate a production line simulation (several rotating cylinders pushing a rubbery gasket material forward) I basically need to animate about 5 or 6 cylinders that push a rubbery sealing material down the production line in a somewhat complex pattern so doing it by hand with keyframes is not an option. The cylinders are not in a straight line 
 or only below the substance which complicates things.

My idea is to use physics and cloth with the correct constraints, settings and options to achieve this effect.

I require the cylinders to rotate constantly at the same speed troughout the animation giving off kinetic energy to the cloth, not affected by the cloth weight, pushing it forward. The cloth needs to be stiff and not buckle inward under the strain because that just wouldn't happen. It's a gasket sealing material and that wouldn't happen IRL. It's several mm thick and very

I need some help and helpful tips from people who're experienced in animation.

List of requirements:

Extremely rigid "cloth" that acts like rubber. I am fine working with extensions.

rotating cylinders that are not afected by physics in their rotation but do transmit energy via friction

Can you give me some helpful pointers? The tests i've been making  have been somewhat abysmal and it's a pretty specific thing so there aren't many tutorials around.
I'm sorry, the question was way too broad.

I've gotten a partial solution from Duarte Farrajota Ramos by experimenting with presets and ramping up bending to 1000 and structural to 500 for the rubbery material.

I'll create a new question for how to propel the piece of ruber track in the animation forward.