Monoservo robot - second problem

Hi guys,
this is my next robot of the series "simple robots", it should be easy :) .

After having my robot "Big M" built, I showed him my friend. He said: This is not difficult to build a robot with three motors. He would use only two motors.
This was challenge:)
I decided: I build a robot with only one motor. But how???????????????
Helped me my "Big M stepper".

First I'll show you only the lateral movement

And here are a few photos:

He is built from wood and plywood.

 Here you can see one magnet, he pulling the stick.

and here is a rad which the robot moves to the side

I built second version, but it was not perfect, he did not just work:(