The earliest mechanical clocks appeared in Europe in the 13th century. From about 1250 CE to 1670 CE, these simple clocks consisted of a weight suspended from a rope or chain that was wrapped around a horizontal axle. To tell time, the weight must fall with a slow uniform speed, but, under the action of gravity alone, such a suspended weight would accelerate. To prevent this acceleration, an escapement mechanism was required. The best such escapement mechanism was called the verge and foliot escapement, and it was so successful that it lasted until about 1800 CE. These simple weight‐driven clocks with verge and foliot escapements were accurate enough to mark the hours but not minutes or seconds. From 1670, significant improvements were made (principally by introducing pendulums and the newly invented anchor escapement) that justified the introduction of hands to mark minutes, and then seconds. By the end of the era of mechanical clocks, in the first half of the 20th century, these much‐studied and much‐refined machines were accurate to a millisecond a day.1

1.
For a general history of mechanical clock and pocket watch evolution, see Eric Bruton, The History of Clocks and Watches (Little, Brown and Co., London, 2000). For a brief historical summary and technical account of anchor escapements, see Mark Denny, Ingenium: Five Machines that Changed the World (Johns Hopkins University Press, Baltimore, 2007), Chap. 4, and
Mark
Denny
, “
The pendulum clock: A venerable dynamical system
,”
Eur. J. Phys.
23
,
449
458
(
2002
).
2.
The comprehensive study of verge and foliot escapement is that of
Alexander V.
Roup
et al., “
Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and Poincaré maps
,”
Int. J. Control
76
,
1685
1698
(
2003
).This paper contains 94 equations and makes use of advanced mathematical techniques.
3.
There is a wonderful YouTube video that shows the action of a simple wooden clock verge and foliot escapement very clearly: seewww.youtube.com/watch?v=7HgAtCn3VUU&feature=related. The action of a 14th‐century verge and foliot clock (that of Salisbury Cathedral, in England) can be seen at the following website, where the historical importance of clocks of this period is well explained: www.youtube.com/watch?v=HdLTUxx4xq8&feature=related.
4.
See the online appendix at . EPAPS ID: E-PHTEAH-48–019006
5.
The single hand of a medieval clock was connected to the horizontal axle of Fig. 1 via gears. The gear transmission ratio was chosen so that, typically, the hand would make one complete revolution in one hour. Some clocks had no hands, but instead struck a bell on the hour.
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