Abstract
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 π/μ ≈ 30 times, where μ ≈ 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.
Highlights
Accurate time measurement was among the most important technological problems throughout the history of humankind
A different principle is employed by mechanical clocks, which emerged in Europe by the end of the 13th century [2,3,4,5]
The invention of the oscillating verge and foliot escapement mechanism at the end of the 13th century was a breakthrough in the development of time measuring technology
Summary
Accurate time measurement was among the most important technological problems throughout the history of humankind. To achieve accurate time measurement, mechanical clocks rely on a periodic motion (oscillation) of a mechanical shaft called the verge. The weights could be moved to different positions on the crossbar, tuning its moment of inertia, so that the period of oscillations was dependent on the distance of the weights from the center It is not known who invented the verge-and-foliot escapement mechanism. The introduction of the pendulum is viewed as a revolutionary invention, whereas the emergence of the verge-and-foliot escapement mechanism is often treated as an. The question of why the accuracy of the verge escapement mechanism remains so low in comparison with the pendulum-based clock has not been addressed in most of these studies. We will study mathematically the effect of friction on the accuracy of both mechanisms: the verge and foliot escapement and the pendulum. We will discuss its application to numerical modeling and to some known historical clocks
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