Watt Speed Governor
In the device described in this Demonstration, four rods are attached to each other with hinges at the vertices of a rhombus. Two of the sides are extended, with balls attached at their ends. The top vertex has a constant height. As you rotate the whole assembly, the balls move upward due to centrifugal force. The bottom vertex rises in proportion to the speed; therefore, this can be used to control the speed. A similar arrangement, called a flyball governor, was used by James Watt in his steam engine.[more]
If the engine gains too much speed, centrifugal force drives the balls upward and chokes the steam valve, slowing down the engine. If the engine slows down too much, the balls go down and open up the steam valve.
This device is of great importance because it was one of the first examples in the development of automatic controls.[less]
The height of the bottom vertex is , where is the angular speed of the assembly, is the length of the arms, and and are factors that depend on the geometry of the assembly.
Snapshot 1: lowest speed and longest arms: regulator is completely down
Snapshot 2: highest speed and shortest arms: regulator is completely up
Snapshot 3: highest speed and longest arms: regulator is not fully up
Based on the Demonstration "Rhombic Drive for Speed Governor" by Sándor Kabai.
The formula was taken from S. K. Bose, Theory of Machines, pp. 120–121, 2004.
"Watt Speed Governor"
Wolfram Demonstrations Project
Published: August 11 2011