Need mechanism for connect from handle to controlled object (please see pic)

[lemd]

Please see the above picture, I need a mechanism to connect handle to a controlled object below. While the handle moves from a to b (~10cm) the object needs to move from c to d (about 25 - 30 cm) and when handle moves back from b to a, the object needs to moves back from d to c. They are both restricted in a box 3 to 4 cm high.

The mechanism should be simple and reliable for repeat operation. So I prefer rod, bar connection over gear or wire link.

Is there something like mechanical telescopic rod on the market where you can extend the whole rod length by moving a little control distance?

 

[OldEngr63]

How about a slotted vertical lever arrangement, pivoted between the two paths such that the motion of the lower end is 2 or 3 times the motion of the upper end?

 

[Danger]

In this case, I honestly can't think of anything better than just running some fishline through a 2:1 or 3:1 (depending upon what you end up having as your actual final path) pulley arrangement.
A couple of wheels, a couple of knots, and Bob's your uncle.