How does the mechanical linkage of the ASI convert dynamic pressure into KIAS?
I understand the underlying principle of an ASI, ie. that it uses the Pitot-static system to measure the dynamic pressure as the difference between total pressure and static pressure.
Knowing that the dynamic pressure is proportional to the square of airspeed, any (linear) immediate variation in the measure of dynamic pressure will be a linear variation in the square of airspeed, not in airspeed alone. Yet the ASI markings are themselves uniformly spaced and still, they show airspeed, not airspeed squared.
Therefore: how does the mechanical linkage convert a linear variation (change) in the dynamic pressure into airspeed?
That is, how is the square root transformation of dynamic pressure performed at the clockwork level of the ASI to obtain the KIAS?
My guess is that one of the gearwheels will be responsible for this but I haven't actually been able to find any information on this online. Any help or insight would be greatly appreciated