-- Last Updated: Jun-24-13 10:05 AM EST --
GBG is correct, pulley diameter is irrelevant to the kinematics of a pulley system. If the motion of a system requires friction at the hub to generate the desired motion, that indicates improper design.
Friction at the rim is needed to keep the rope and pulley moving at the same speed. To remove it from the analysis, the pulley system can be modeled (mentally) as toothed belts turning gears.
For the system described by the OP, a cog-belt system with frictionless hubs would still be unstable, so it is under-designed, i.e. improperly constrained.
Per pilotwingz' comment, the pulleys in mine and grayhawks designs are NOT compound pulleys, but single pulleys mounted in sequence. A compound pulley is a single wheel with multiple grooves - not needed in this design.
EDIT - this last statement is incorrect - a compound pulley is a multiple pulley system. See pilotwingz' explanation below.
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