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 pendulum’s backandforth movement to rotary movement must take this variance in swing angle into account. Click here to learn how.
