Algodoo

your thyme is broken, because you used non scene.my.variables. It will probably only work for you, maybe not even for you after you download the scene. Do this:
Press F10, write

scene.my.length = 1.18

on the console. this will declare a variable called scene.my.length, and it will put it the initial number of 1.18. Global variables (a.k.a easily accessed) are stored within the simulation, this means that if you copy the 'box and paste it on another scene it will stop working. Now press F10 again to close the console

Now, on the spring's length property, write

{scene.my.length}

this will make the length equal to scene.my.length. Now go to each laser and write
(e)=>{scene.my.length= whatevernumbercomeshere}
a.k.a lengths of the springs at different gears
You don't really need the second variable. Make a cam out of some circles and make it rotate when you need the clutch, so that the whole thing goes up. Keep it as simple and variable-free as possible if you can

Yep exactly what I was about to comment.

Thank you a lot!