I'd expect the rope to wear very quickly.
Is that a problem?

Mike Halloran
Stratford, CT, USA

Nope, it's very low duty cycle, it's only to pull a curtain open/closed.

I'd loop the rope around a wider pulley 1.5 or even 2.5 turns.

At 2.5 turns, you could probably use a smooth pulley, which also provides some overload relief for when the drapery gets stuck

Mike Halloran
Stratford, CT, USA

Why not have fixed nubs in the pulley groove to increase friction, and not more expensive movable ones?

Walt

This is often handled with bead-chain and a pulley with a matching molded surface or using a spring loaded-counter pulley at the bottom end or a pinch point to maintain tension at the pulley.

If i have more than 1 turn of rope it's going to get tangled up trying to rotate 10 times to open/close the curtains. Since the rope will move sideways until it hits the end and bunchs up.
I could have a multi turn spiral type pulley but then it needs to be large enough to handle fully opening and fully closing the curtains without running out of spiral groves.

I did consider a single turn pulley that has the channel oscillating from side to side and very narrow so the rope jams in it a bit.
That might work but i was trying to locate something off-the-shelf that would grip the rope without needing to design and 3D print a pulley myself.

Or, you could use a multi-turn wrap on a smooth pulley, with smooth flanges.

Make the tangent ropes at the ends of the pulley run in different planes, basically adjacent each flange.
I.e. put joggles in the part of each traveler that connects the rope.

Mike Halloran
Stratford, CT, USA

You do not need moving pieces to grip the cord. Many possible pulley designs could work, but the common element that is required to make any of them work is that you have to have a device the will apply some initial tension to the slack side of the cord. Without some initial tension you cannot count on the cord staying on the pulley, let alone developing friction. A simple example would be a flat spring-steel strip pressing the cord against the pulley.

A v-groove pulley with a 15 degree included angle will cause the cord to wedge in the groove and multiply the cord tension. Additional frictional grip can be added by putting teeth or other texture on the surfaces of the v-groove.

There are some smaller marine anchor windlass' that have a "Wildcat" that can pull up rope, then the chain the is connected to the anchor.
I believe Maxwell is a brand that has this type of wildcat.
I also see some companies calling them Gypsy heads.

Link
These maybe a little over kill.