CNC Cookbook: Astronomical Clock

Last modified: October 4, 2022

Antikythera Mechanism / Orrery Plans

I've always had a great interest in Astronomy, and I read with great interest recent articles about the Antikythera Mechanism, which was apparently an ancient orrery or simulator of motions of the heavenly bodies. The machine, which was constructed circa 80 BC, could represent the motions of most heavenly bodies known in its time using a clockwork consisting of 37 gears.

Antikythera mechanism diagram, ancient Greek mechanical calculator.Differential Gear Mechanism Was Way Ahead of Its Time.

The front dial would show the progression of the Sun and Moon through the Zodiac according to the ancient Egyptian calendar. The lower back dial gives the Metonic cycle, the Synodic cycle, and the Lunar
year of 12 Synodic months. Later researchers determined that the device could show the motion of the visible planets through the Zodiac, as well as predict Solar and Lunar eclipses using the Saros scale. It also displayed
the Calippic scale.

Ancient Greek astronomical calculator, Antikythera mechanism.

Antique brass mechanical device with glass front and wooden case, featuring dials and pointers.**
Front and Back of a Reconstructed Model of the Antykthera Mechanism**

Antique wooden safe front panel with brass circular dial and keyhole.

This Model May Be Closer. Note the Spiral Tracks on the Back Dials

Ancient Greek astronomical calculator, Antikythera mechanism, with intricate gears and dials.

The Sun and Moon Dials Tracking Against the Zodiac...

My Own Astronomical Clock Design: Bobtikythera

After reading some about the Antikythera Mechanism, I was inspired and got interested in designing an astronomical clock of
my own. I don't know if I will ever finish the design, let alone build it, but it is an interesting and challenging exercise. I'm learning a lot about clockwork, as well as refreshing some old memories about astronomy and learning for the first time more about how the Ancients dealt with heavenly bodies. Fascinating stuff!

Let's consider the ratios needed to produce the outputs. We will assume the input crank is 1 Egyptian calendar day each revolution:

**Mechanism Feature
**

Period

Purpose

Input Crank

1 rpm = 1 Egyptian
Day
= 1.0007 Solar Days

Moves all the other dials. In the Egyptian Calendar,
a solar year is exactly 365 days, so the clockwork need not account
for leap years.

Sideral Month Dial

1 rpm = 27.3 Egyptian Days

Motion of Moon Around the Zodiac.

Sidereal Year Dial

1 rpm = 365 Egyptian Days

Motion of Sun Around the Zodiac. This was the front
dial of the Antikythera Mechanism. Also provided was a slip dial that
could be used to correlate the Egyptian days back to regular calendar
days incorporating the leap year. This second dial was set manually.

Synodic Cycle or Month Dial

1 rpm = 29.5 Egyptian Days

1 rpm gives all the lunar phases

Lunar Year Dial

1 rpm = 12 Synodic Cycles

Metonic
Cycle

1 rpm = 235 Synodic Cycles = 19 Tropical Years

Can be used to relate lunar and solar calendars.
For example, a Metonic cycle is 1:19 Tropical Years and 1:235 Synodic
Cycles.

Saros Cycle

1 rpm = 223 Synodic Cycles

Used to predict lunar and solar eclipses. If an eclipse
occurs, another will occur exactly one Saros cycle later. By marking
off relative positions of eclipses (both lunar and solar) on this
wheel, and having the wheel turn at the Saros Cycle rate, we can show
when eclipses will occur.

Calippic
Cycle

1 rpm = 76 Tropical Years = 940 Synodic Cycles

A more accurate way to relate lunar and solar calendars
than the Metonic Cycle.

Mercury

Motion of Mercury Around the Zodiac.

Venus

Motion of Venus Around the Zodiac.

Mars

Motion of Mars Around the Zodiac.

Jupiter

Motion of Jupiter Around the Zodiac.

Saturn

Motion of Saturn Around the Zodiac.

A Geartrain Schematic:

Here is a schematic that I use to represent the inter-relationship between the various gears or wheels in the Mechanism I'm designing. I think it simplifies the understanding of how it would work:

Complex gear system of Antikythera mechanism.

Gear Mechanism Schematic...

Each of the light blue circles represents a major gear and dial in the system. In other words, it is both a gear that others may engage as well as an output of some kind. For example, the Synodic Cycle is a dial showing the lunar phases as well as an important gear that is driven through a 29.5:1 ratio from the input shaft and goes on to drive7 subsequent major gear/dials and 4 auxilliary reduction gears.

The dark blue circles represent what I'm calling auxilliary reduction gears. In my more detailed design, I estimated
the diameter of each gear in the system given a 20 tooth per inch gear pitch. Based on that estimate, I added auxilliary gearing to keep the largest gears from exceeding much more than 8" in diameter. The largest gear/dial is that governing the motion of Mars through the Zodiac at 8.4". The smallest gear/dials (doesn't count the aux reduction gears) have 10 teeth each and correspond to the Input in days and the Tropical Year.

Geartrain Details:

To work out the details of the geartrain, I designed an Excel spreadsheet that tracked the following for each gear/dial:

Here are the details I came up with:

Name

Input

Ratio

Aux. Gear
Ratio

Teeth

Circum-

ference

Diameter

Purpose
& Calibration

Sidereal Month

Input Crank

27.3

273

13.650"

4.345"

Lunar position on Zodiac

Synodic Cycle

Input Crank

29.5

295

14.750

4.695

Lunar Phases

Sidereal Year

Input Crank

365

10

365

18.250

5.809

Position of Sun in Zodiac

Sidereal Year Sub-Wheel

On Sidereal Year Hub

10

0.500

0.159

Drives Sunspot Cycle

Input (Days)

Input Crank

10

0.500

0.159

Input Crank. Calibrated into 24 hours w/ Egyptian
sunrise/sunset

Tropical Year

Metonic Cycle Sub-Wheel

1:19

10

0.500

0.159

Standard Months & Seasons

Metonic Cycle Sub-Wheel

On Metonic Cycle Hub

190

9.500

3.024

Synodic Cycle Sub-Wheel

On Synodic Cycle Hub

10

0.500

0.159

Lunar Year

Synodic Cycle Sub-Wheel

12

120

6.000

1.910

Saros Cycle

Synodic Cycle Sub-Wheel

223

5

446

22.300

7.098

Lunar & Solar Eclipse Cycle. Calibrate
w/ historical eclipses that will repeat.

Metonic Cycle

Synodic Cycle Sub-Wheel

235

10

235

11.750

3.740

Divide into 19 Solar Years per revolution,
4 revolutions.

Metonic Cycle Sub-Gear #2

On Metonic Cycle Hub

10

0.500

0.159

Calippic Cycle

Metonic Cycle Sub-Wheel
#2

4

40

2.000

0.637

Divide into 76 Solar Years per revolution.

Mercury

Input Crank

87.94

2

439.71

21.986

6.998

Position of Mercury on Zodiac

Venus

Input Crank

224.85

4

562.13

28.107

8.947

Position of Venus on Zodiac

Mars

Input Crank

686.51

13

528.08

26.505

8.405

Position of Mars on Zodiac

Jupiter

Synodic Cycle Sub-Wheel

93.03

2

465.16

23.258

7.403

Position of Jupiter
on Zodiac

Saturn

Synodic Cycle Sub-Wheel

64.43

7

520.61327

26.031

8.286

Position of Saturn on Zodiac

Sunspots

Sidereal Year

11

110

5.500

1.751

Relative % of Sunspots, With 100% being maxima
and 0% being minima

Rhino Geartrain Layout

Next, I tried laying out some of the gears using Rhino 3D, just to get an idea of how things might fit together. This was my
first attempt at a layout for the gears needed to drive the inner planets. It's everything in the gear schematic above that's tied directly to the input wheel except for the synodic wheel.

Antikythera mechanism interlocking gears diagram.

A first attempt at gear layout in Rhino. The exact center is the Input Gear, and the various other gear trains are color coded. I'm thinking I'll want something a little more compact!

I also sketched out an orrery hub mechanism in Rhino to see how that might work:

Mechanical solar system model with Earth at center and planetary spheres connected by rods.

Orrery front view. That's Earth in the center, Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn. That is the order the Ptolemaic universe worked in...

Three-dimensional model of the solar system with Earth as a central blue-green sphere.

A closer perspective view of the Orrery mechanism...

This orrery piece presents some real design issues. The drawing shows the heavenly bodies in the Ptolemaic perspective, with Earth at the center and all the other bodies revolving around it. As you recall, refuting this view is one of the things that put Gallileo (and others) in hot water with the Church.

The Ptolemaic perspective is more in keeping with the feel I'd like to have for the clock, which is a lot more astrological
and Ancient-looking than a more modern orrery. Frankly, I'd like to do both at some point and have them sit next to one another. The problem is that the planets display retrograde motion. In other words, at certain times of the year, their apparent motion against the stars reverses for a time and the planet "backs up". This happens as planets lap each other around the sun. In the Ancient view, this was accounted for by having the planets travel in little sub-circles called "epicycles" as they made their circuit around the big circle. You can imagine that this would make for complex motion to simulate with clockwork!

The easier way out is to have the orrery display the modern view, with Sun at center and planets circling around
it. To determine where a planet appears in the Zodiac would require sighting along the line from the Earth to the planet and extending that line into the zodiac. Not quite so elegant, although physically more realistic and also easier to construct a clockwork for.

Circular chart displaying zodiac signs, each represented by a different color, on a yellow background with white text.

A rendering of the baseplate for the orrery...

Three-dimensional illustration of the solar system with planetary orbits.

Astronomical Theory Notes

Ancient Astronomical Cycles:

A little extra explanation of some of these cycle sand why they are important.

Other Cycles:

Cycles not tracked by the original Antikythera Mechanism, but that would be interesting and straightforward to recreate.

Antikythera Links

Original 1959 Scientific American Article on Antikythera Mechanism

Details of the Antikythera Mechanism's Construction

The Antikythera Computing Device: Excellent data on internal functioning, especially the differential gear system.

The Wheels of Greek Astronomers: Excellent description of the Antikythera Mechanism.

Antikythera Animations

Lego Antikythera

Astronomical Cycle Links

Moon-Sun Glossary

[Eclipse Cycle Calculator](https://www.phys.uu.nl/~vgent/calendar/eclipsecycles.htm#An eclipse cycle calculator)

Almagest Emphemeris Calculator: Ptolemy's method.

Ancient Planetary Model Animations

Models of Planetary Motion from Antiquity to Renaissance

Encyclopedia Brittanica Description of Ancient Calendars

Many different kinds of months defined

Astronomy Formulas I: Periodicity Formulas

Astronomy Formulas II: Illumination Geometry

Babylonian Astronomy: Good info on how the Babylonians figured cycles for planets and such.

Introduction to Ancient Astronomical Concepts: Good info on synodic periods.

See also the Orrery Gallery...

Is Manual Machining Faster than CNC for Simple Parts?

Manual is Faster

CNC is Faster

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