I tried to animate a pantograph just for fun, but it didn't work. I have tried lot of ideas particularly with the observation of this pages:

• How can a mechanical linkage with a closed loop be rigged?

• https://blenderartists.org/t/animating-a-rigid-linkage/685592

The best result i obtain is this one :

But there is still a mistake, the pantograph bow does not keep a vertical position.
The root bone to make the animation is this one selected on the picture.

The perfect movement is here : https://youtu.be/w_9YgDjfohc?t=55

Here is the Blend file: http://www.wfr.zone/w/blender_animation_images/pantographe_pli%C3%A9.blend

Thank's !