Piano keys are linear (or some curve that is close).
Key travel is usually up to 1/2".
Actuation and break is usually at the middle of the stroke -- but it actuates only if you press hard enough, as the hammers move only from the force of your strokes.
Usually ...
There are several types of mechanisms for both vertical and horizontal pianos. Some pianos have
hysteresis.
There are some diagrams on
Wikipedia.