An accurate clock only matches a sundial 4 times per year.
Wait, what? An accurate clock should be right. But the sun can't be wrong, can it?
Both are "right" but they aren't supposed to be the same. A clock is showing the mean (average) day with 24 hours. The solar day varies from the average day by +16:25 minutes to -14:15 minutes throughout the year. Yes, the length of time between successive noons varies by over 30 minutes per year. By the late 1600's after Christiaan Huyghens patented his accurate pendulum clock, the accuracy of clocks had improved to the point where people noticed that the clock time didn't match the sundials. So they doubted the clocks.
A category of clocks called Equation Clocks provided a mechanism driven display that let people reconcile between solar time and clock time. These clocks use a variety of different mechanisms to calculate and display the Equation of Time (EoT). Most equation clocks use a kidney shaped cam to push a follower wheel inside or outside the zero radius of a circle. The clock's EoT display only crosses the zero mark four times per year and that is when a solar day is exactly 24 hours long.
This video shows the Lego Astronomical Clock EoT solution using a new mechanism: the "parallel whippletree". A standard whippletree has been used in the past for many applications including an EoT mechanism. This new parallel whippletree is a significant modification that removes some of the error of a standard whippletree allowing for a more accurate summing of the input shafts.
Of course with Lego plastic gears there is some gear looseness and inaccuracies but this mechanism would work quite well in "real" clock.
