Speed difference in the pulleys in a block and tackle setup

[Rhettoric]

I am designing a block and tackle system (because I can't think of anything more simple) to take up the slack in a loop of cordage for a machine I am tinkering on. The loop only travels in one direction due to a set of cam cleats.

I am trying to figure out if all the pulleys in a block need their own bearing or if I can fix them all on a shared axle. My mind is pretty fried at the moment and google isn't helping me out much so I figured I ask you guys :)

 

[Rhettoric]

actually, i just realized that the pulley nearest the "fixed" end should rotate slower than the side giving up the rope.

please correct me if I am wrong.