Clayton Boyer Clock Designs
"Ferguson's Mechanical Paradox Orrery"
Here is an easy weekend project that is truly amazing. I spent less than ten hours of shop time, over two days, building this wonderful mechanism, and yet it can illustrate so much. For example, it shows the consistence of the tilt of the earth that is responsible for the seasons as the earth progresses around the sun throughout the year.
This simple mechanism also shows the retrograde motion of the nodes of the Moon’s orbit throughout its 18.6 year cycle, called the Precession of the Nodes, from which one can predict both solar and lunar eclipses. There is also an indicator for the Recession of the Line Of Apsides, which is the ellipse of the lunar orbit slowly rotating counterclockwise in about 8.85 years. In addition the Orrery allows one to determine the hours of daylight or darkness on any place on earth at any time of the year, and the Annual Index on the Moveable Frame points to the day of the month, the month, and the sun’s location in the zodiac.
The accuracy of the complex and various workings of these five simple gears is phenomenal. For example, the Moon’s Nodes indicator is only off by 41 days in one full cycle of 18.6 years, and the Moon’s Apogee period indicator is only off about 20 days in the cycle’s 8 years 290 days. Included are Ferguson’s explanations on how to compensate for these slight errors to get correct predictions.
Not interested in all that science? This is still a truly amazing, and elegantly simple project that is just fun to watch all the movement as you crank it around. It is also a great project to begin learning how to cut wooden gears, since there are only five required in this mechanism.
Also included is an excerpt, in Ferguson’s own words, explaining his Mechanical Paradox and the operation and use of his Orrery.
After reading Ferguson’s explanation of his Mechanical Paradox, I just had to build one. Briefly, the Mechanical Paradox is made of three wheels – Ferguson later added another two wheels to create his orrery. So we start with just three wheels, and all have the same number of teeth. We will call these wheels D, E, and F - because that’s what Ferguson called them. Wheel D is stationary and wheel E turns around D. Now here’s the part I couldn’t get my head around – when wheel E makes one trip around stationary wheel D, E rotates twice! How is that possible when all the wheels have the same number of teeth? And lastly, wheel F, which is turned by wheel E, does not rotate at all in reference to wheel D. Ferguson was certainly right in calling it a “paradox”.