Input: blue pulley having eccentric hole for orange nut.
The pulley rotates in bearings concentrical with the screw axis. Orange nut has circular grooves (not helical).
The blue pulley has revolution joint (rolling bearing in pactice) with the nut so the latter can rotate in relation with the pulley.
The nut rolls on the screw to reduce the friction.
Output: green screw of lead t1 fixed to popcorn slider moves
t1 in 1 rev. of the input.
If the nut has helical grooves (threaded) the output motion will be unstable subject to the nut - screw friction.