Aemilius
you could use a limit switch to energize a solenoid.
http://www.galco.com/buy/NTE-Electronics/54-403-BP 
http://www.galco.com/buy/Deltrol-Controls/53754-87 the solenoid could pivot the device.
you can connect a counter to the electrical system to
time the iterations.
http://www.galco.com/buy/Redington-Counters/6330-1000 
I believe that you can adjust the voltage going to the solenoid
on some solenoids so that the speed of the solenoid plunger can be adjusted , this way you could have a speed control switch attached.
http://www.galco.com/buy/Dart-Controls/SA-STOK-WO 
my first thoughts for a application was a pump.
with a spring loaded piston inside the outer weight thing.
the piston would be forced outwards 2 times per rev , to
provide the pumping action.
like I said theses a lot of force in whipping that outer weight around like it does , this could easily be transmitted to a gas.
