The period of swing of a gravity pendulum depends upon its length, the local force of gravity, and to a small degree the maximum angle that the pendulum swings away from the vertical. Since gravity is constant, we can ignore that factor.  And since for most pendulum clocks the swing angle is small and does not vary significantly, it can often be ignored.  So the period is set solely by the length of the pendulum.  Accurate timekeeping is achieved by fine adjustments to the effective length of the pendulum, by adjusting the pendulum bob or weight up and down.

But all that assumes a perfect pendulum, with no friction and no expansion or contraction of the pendulum due to temperature and humidity. In fact, these factors change, causing changes to the period and timekeeping accuracy, particularly in wood gear clocks. 

What can be done?

The Mystery Clock uses that last factor - the maximum swing angle of the pendulum - to maintain precise time.

The nominal swing angle of the Mystery Clock is about 20 degrees.  The weight on the pendulum is initially adjusted so that the period - the time that it takes for a complete back and forth motion - is exactly 1 second. 

What would happen if the swing were increased to 25 degrees? Because of the greater distance traveled, it would take a little longer - not quite 0.5% longer - for a complete cycle.  On the other hand, if we reduced the swing to only 15 degrees, the period would be shortened by somewhat less than 0.5%.  So, if we allowed the swing angle to vary between about 15 and 25 degrees, we could adjust the speed of the clock almost 1%, actually up to about 10 minutes per day.

This is exactly what the Mystery Clock does. A microcontroller precisely measures the period of each and every swing of the pendulum.  Then, using a modified PID (proportional - integral - differential) control algorithm, it adjusts the swing angle of the pendulum to speed up or slow down the pendulum and therefore the clock.  Timekeeping accuracy is kept to within the tolerance of the watch crystal used by the microcontroller, which is within a few parts per million.

To make this work, the ratchet mechanism which converts the pendulumís back-and-forth movement to rotary movement must take this variance in swing angle into account.  Click here to learn how.


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