James Watt used the so-called "flyball governor" to regulate the speed of his steam engines (1787). It consists of two flyballs which are connected to the spindle by two flyball arms. The spindle of the governor is directly connected to the shaft of the steam engine. The flyballs move upward when the spindle speed increases due to the centrifugal forces. The flyball arms are connected to a throttle valve that regulates the steam input to the engine. If the spindle speed increases, then the flyballs arms move upward thereby closing the throttle valve, which reduces the steam input and the engine is therefore slowed down. The flyball governor therefore regulates the speed of the steam engine. It is in fact one of the first feed-backward mechanisms. The amount of feed-backward, i.e. the "gain", is determined by the kinematics between the flyball arms and the throttle valve. The stationary movement of the combined engine-governor system is an equilibrium of the system. If everything goes well, then this equilibrium is asymptotically stable, i.e. a disturbance in the load of the engine will die out and the system returns to stationary movement with a constant desired engine speed. However, if the gain is taken too large (if the flyballs influence the throttle valve too much), then the equilibrium becomes unstable and a stable limit cycle is created. This is what we call a Hopf bifurcation. The speed of the engine as well as the height of the flyballs will therefore not be constant for a large gain but will oscillate (which is undesirable).
In order to show the students of my Nonlinear Dynamics class what a Hopf bifurcation is, I designed a model of a Watt Governor using only ordinary LEGO bricks as well as the LEGO Mindstorms Robotic set (RCX). Below, you find two video's. The first video has been made with a parameter setting for which the equilibrium is unstable and for which a stable limit cycle exists (the flyball arms go up and down). The other video has been made with a parameter setting for which the equilibrium is stable. The only difference between the two cases is the value of the gain in the feed-back loop.