How would I build a Conveyor like this in blender?
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You can use Rigid Body physics with Constraints to replicate this:
Add a cylinder and make it an active Rigid Body object (CtrlR)
Add a cube and make it a passive rigid body object (CtrlShiftR), and move it to the side of the cylinder.
Constrain them together (Tool shelf > Rigid Body Tools > Connect) with Hinge constraint and rotate the resulting empty 90 degrees on the Y axis:
Constrain again with a Motor constraint and enable angular motor: