Friction and Dynamics of Verge and Foliot: How the Invention of the Pendulum Made Clocks Much More Accurate

The tower clocks designed and built in Europe starting from the end of the 13th century employed the "verge and foliot escapement" mechanism. This mechanism provided a relatively low accuracy of time measurement. The introduction of the pendulum into the clock mechanism by Christiaan Huygens in 1658-1673 improved the accuracy by about 30 times. The improvement is attributed to the isochronicity of small linear vibrations of a mathematical pendulum. We develop a mathematical model of both mechanisms. Using scaling arguments, we show that the introduction of the pendulum resulted in accuracy improvement by approximately pi/mu approximate to 30 times, where mu approximate to 0.1 is the coefficient of friction. Several historic clocks are discussed, as well as the implications of both mechanisms to the history of science and technology.