The mechanism consists of 2 movable links, 2 screw joints and 1 revolution joint.
In 1 rev of the blue crank:
The nut’s displacement s = -h2.h3/(h3-h2)
The nut’s rotation φ = -h2/(h3-h2) revs.
h2: pitch of the screw joint of the blue screw and the green nut.
h3: pitch of the screw joint of the green nut and the base.
h2, h3 carry negative sign in case of left-handed thread and vice-versa.
For this case, h2 = 3 and h3 = 4 so s = -12, φ =.-3
Wanted s and φ values can be obtained by combination of appropriate h2, h3 and the thread direction.