Feedback control in ancient water and mechanical clocks

Abstract

Attention is focused on Ktesibios' water clock and the outstanding mechanical clocks based on the crown wheel escapement that first appeared in Europe at the end of the thirteenth century. Specifially, block diagrams and the related equations are derived for both the Ktesibios and the verge and foliot clock. The essential role of feedback for controlling the speed of such devices is pointed out. In particular, each mechanical clock discussed can be regarded as a sampled-feedback control system. This explains why the average angular velocity of the wheel would be constant even in the absence of friction. The operation of the verge and foliot clock is compared to that of the pendulum clock built by Ch. Huygens in the seventeenth century.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>