Editing Antikythera mechanism (section)

==== Known gear scheme ====
[[file:AntikytheraMechanismSchematic-Freeth12.png|thumb|upright=1.4|A hypothetical schematic representation of the gearing of the Antikythera Mechanism, including the 2012 published interpretation of existing gearing, gearing added to complete known functions, and proposed gearing to accomplish additional functions, namely true sun pointer and pointers for the five then-known planets, as proposed by Freeth and Jones, 2012.<ref name=freeth-12/> Based also upon similar drawing in the Freeth 2006 Supplement<ref name=freeth-06-1/> and Wright 2005, Epicycles Part 2.<ref name="wright-05-1"/> Proposed (as opposed to known from the arte<!-- 'e' - this article uses British spelling -->fact) gearing crosshatched.]]

It is very probable there were planetary dials, as the complicated motions and periodicities of all planets are mentioned in the manual of the mechanism. The exact position and mechanisms for the gears of the planets is unknown. There is no coaxial system except for the Moon. Fragment D that is an epicycloidal system, is considered as a planetary gear for Jupiter (Moussas, 2011, 2012, 2014) or a gear for the motion of the Sun (University of Thessaloniki group).

The Sun gear is operated from the hand-operated crank (connected to gear a1, driving the large four-spoked mean Sun gear, b1) and in turn drives the rest of the gear sets. The Sun gear is b1/b2 and b2 has 64 teeth. It directly drives the date/mean sun pointer (there may have been a second, "true sun" pointer that displayed the Sun's elliptical anomaly; it is discussed below in the Freeth reconstruction). In this discussion, reference is to modelled rotational period of various pointers and indicators; they all assume the input rotation of the b1 gear of 360 degrees, corresponding with one tropical year, and are computed solely on the basis of the gear ratios of the gears named.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The Moon train starts with gear b1 and proceeds through c1, c2, d1, d2, e2, e5, k1, k2, e6, e1, and b3 to the Moon pointer on the front face. The gears k1 and k2 form an [[epicyclic gearing|epicyclic gear system]]; they are an identical pair of gears that do not mesh, but rather, they operate face-to-face, with a short pin on k1 inserted into a slot in k2. The two gears have different centres of rotation, so the pin must move back and forth in the slot. That increases and decreases the radius at which k2 is driven, also necessarily varying its angular velocity (presuming the velocity of k1 is even) faster in some parts of the rotation than others. Over an entire revolution the average velocities are the same, but the fast-slow variation models the effects of the elliptical orbit of the Moon, in consequence of [[Kepler's laws of planetary motion#Position as a function of time|Kepler's second and third laws]]. The modelled rotational period of the Moon pointer (averaged over a year) is 27.321 days, compared to the modern length of a lunar sidereal month of 27.321661 days. The pin/slot driving of the k1/k2 gears varies the displacement over a year's time, and the mounting of those two gears on the e3 gear supplies a precessional advancement to the ellipticity modelling with a period of 8.8826 years, compared with the current value of precession period of the moon of 8.85 years.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The system also models the [[lunar phase|phases of the Moon]]. The Moon pointer holds a shaft along its length, on which is mounted a small gear named r, which meshes to the Sun pointer at B0 (the connection between B0 and the rest of B is not visible in the original mechanism, so whether b0 is the current date/mean Sun pointer or a hypothetical true Sun pointer is unknown). The gear rides around the dial with the Moon, but is also geared to the Sun—the effect is to perform a [[differential gear]] operation, so the gear turns at the synodic month period, measuring in effect, the angle of the difference between the Sun and Moon pointers. The gear drives a small ball that appears through an opening in the Moon pointer's face, painted longitudinally half white and half black, displaying the phases pictorially. It turns with a modelled rotational period of 29.53 days; the modern value for the synodic month is 29.530589 days.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The Metonic train is driven by the drive train b1, b2, l1, l2, m1, m2, and n1, which is connected to the pointer. The modelled rotational period of the pointer is the length of the 6939.5 days (over the whole five-rotation spiral), while the modern value for the [[Metonic cycle]] is 6939.69 days.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The [[Olympiad]] train is driven by b1, b2, l1, l2, m1, m2, n1, n2, and o1, which mounts the pointer. It has a computed modelled rotational period of exactly four years, as expected. It is the only pointer on the mechanism that rotates anticlockwise; all of the others rotate clockwise.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The Callippic train is driven by b1, b2, l1, l2, m1, m2, n1, n3, p1, p2, and q1, which mounts the pointer. It has a computed modelled rotational period of 27758 days, while the modern value is 27758.8 days.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The Saros train is driven by b1, b2, l1, l2, m1, m3, e3, e4, f1, f2, and g1, which mounts the pointer. The modelled rotational period of the Saros pointer is 1646.3 days (in four rotations along the spiral pointer track); the modern value is 1646.33 days.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

The Exeligmos train is driven by b1, b2, l1, l2, m1, m3, e3, e4, f1, f2, g1, g2, h1, h2, and i1, which mounts the pointer. The modelled rotational period of the exeligmos pointer is 19,756 days; the modern value is 19755.96 days.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>

It appears gears m3, n1-3, p1-2, and q1 did not survive in the wreckage. The functions of the pointers were deduced from the remains of the dials on the back face, and reasonable, appropriate gearage to fulfill the functions was proposed and is generally accepted.<ref name=freeth-06/><ref name=freeth-08/><ref name=ieeecomp1/>