The Instability of Verge-Foliot Clocks in Contrast with the Isochronicity of Pendulum Clocks: A Study of Verge-Foliot Kinematics

Abstract

The tower clocks of Europe starting in the 13th century CE employed a verge-foliot mechanism, which was low in both precision and accuracy due to the sensitivity of frictional losses in the system. The pendulum and Huygens’ introduction of the Theory of Involutes is shown to be a mechanism with a linear relationship to frictional losses in the system, instead of the non-linear relationship between frictional losses in verge-foliot mechanisms. The isochrone nature of vibrations of the pendulum are discussed in contrast to the variance in oscillation seen in verge-foliots. The introduction of the pendulum resulted in an improvement of accuracy of around π/µ≈31 times, where µ=0.1 is the coefficient of friction. In this thesis a CAD model is developed for both the verge-foliot and pendulum with a verge, and it is found that FEA analysis produces a sufficiently approximate result to the theoretical models. A discussion of CAD and DFM principles in relation to clocks is also discussed.