Equation clock

An equation clock is a mechanical clock which includes a mechanism that simulates the equation of time, so that the user can read or calculate solar time, as would be shown by a sundial. The first accurate clocks, controlled by pendulums, were patented by Christiaan Huyghens in 1657. For the next few decades, people were still accustomed to using sundials, and wanted to be able to use clocks to find solar time. Equation clocks were invented to fill this need.

Early equation clocks have a pointer that moves to show the equation of time on a dial or scale. The clock itself runs at constant speed. The user calculates solar time by adding the equation of time to the clock reading. Later equation clocks, made in the 18th Century, perform the compensation automatically, so the clock directly shows solar time. Some of them also show mean time, which is often called "clock time".

All equation clocks include a mechanism that simulates the equation of time, so a lever moves, or a shaft rotates, in a way that represents the variations of the equation of time as the year progresses. There are two frequently-used types of mechanism:

In this type of mechanism, a shaft is driven by the clock so it rotates once a year, at constant speed. The shaft carries a cam, which is approximately "kidney shaped" such that its radius is essentially a graph of the annual variation of the equation of time. A follower and lever rest against the cam, so that as the cam rotates the lever moves in a way that represents the changing equation of time. This lever drives other components in the clock.

To a close approximation, the equation of time can be represented as the sum of two sine waves, one with a period of one year and the other with a period of six months, with the relative phase varying very slowly (marginally noticeable over the course of a century). See the explanation in Equation of time for more detail.

The double shaft mechanism has two shafts rotating at constant speeds: one turns once a year, and the other twice a year. Cranks or pins attached to the two shafts move the two ends of a combining lever (sometimes referred to as a whippletree) sinusoidally; if the dimensions are chosen correctly, the midpoint of the rod moves in a way that simulates the equation of time.

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