2. ## ..this might help

Here I think you can see that the middle wheels rotate
by same angle

---The wheel Y moves an equal distance as the smaller middle wheel

---Similarly the wheel Z moves the same distance as that moved by the bigger middle wheel

Now try again, I think you should get the result
If you still have trouble feel free to ask

3. hi there,

i certainly appreciate your help, but i am completely lost from the beginning. what you are describing is a little too far beyond what i understand.

would it be possible to see step by step what to do? if not, i completely understand.

4. Lets first take wheel Y
It rotates 360 degrees to complete one rotation hence
the first string rotates by a length 4pi
now this rotates the inner wheel by
distance $=4\pi$ hence angle moved $= \frac{360}{6\pi} *(4\pi) degrees$
this rotates the outer wheel by the same angle
(as they are mutually joined)

on moving by 240 degrees
the distance moved by outer wheel , $x= \frac{2}{3} *2*\pi*7$
which is same as the wheel Z
so the revolution by Z $= \frac {x}{2*\pi*5}$