Measuring touch-weight resistance in piano keys
Here's an idea: use two levers, one driven by a gear motor or large RC servo, the other resting on the key, rotating on the same axle, connected to each other with a spring.  Think of something along the lines of the non-clamping end of a clothespin, just a lot bigger and less stiff.  The idea is that the spring with convert the position of the driven lever into a force based on the separation between the two levers (F = kx).  Measuring the force can be done in a couple of different ways.  The most straightforward would be a load cell between the lever and the key.  Another option would be to measure the length of the spring, perhaps with encoders on both levers, and then calibrate the spring with a scale so you can get the corresponding force for the measured separation of the levers.  It would be possible to use potentiometers as encoders since you don't need continuous rotation.  You will also need to measure the position of the free (non-driven) lever continuously so you can figure out exactly when it starts moving.  

There are two ways of using it.  The first is open loop, where you simply run the driven lever through one complete cycle while logging the position of the free lever and the force applied to the key, and extracting the data afterwards.  The second method is closed loop, where you run the motor until the key starts to move, record the force at that point, run it a bit more until the key stops, then reverse, and measure the force when the lever starts to move back up again.