Input: yellow pulley.
Internal gear (35 teeth) is stationary. Pink nut is fixed to the pink gear (30 teeth). The nut (lead = t1) rotates in eccentric hole (in pink) of the yellow pulley. The nut can roll on the screw thus reduces the friction.
Output: green screw (lead = t2 = t1) moving linearly an amount of S in 1 revolution of the input.
S = t2+(Z2/Z1)*t1
If no grey internal gear, the output motion depends on the friction between the nut and the screw. If no friction the screw does not move.