Welcome to the forum. Just decide on a reasonable rotation in degrees and then use two arcs that will give the lift in that desired angular rotation. The fewer degrees the harder it will be to compress the springs so the more torque the motor will need to do the work. Just select a degree of rotation and an offset from that center to the "cam" grooves.
Kinda like the pic attached, but you are not limited to 180deg, just make the total offset of the rotational travel of the "cam" to be 1" of lift from it's starting point. This design will probably bind as the working pressure from the "cam" will be at 90-deg to the movement of the spring, so not a good thing. Perhaps if you can give us a better idea (sketch or picture) of what you are trying to achieve we can give you a better idea on how to do it.
eedge sprint cams 01.png