Is There Something Missing from the Antikythera Mechanism? Was It a Mechanical Planetarium–Positioner? Or a Luni-Solar Time Calculator Device? Reconstructing the Lost Parts of b1 Gear and Its Cover Disc

Abstract

We present the observations and the results of our experience from many hours of constructing, assembling, handling, and interacting with our functional reconstruction models of the Antikythera Mechanism. The parts were constructed and the models were assembled by applying a strict Constructional Protocol for a Research Grade functional reconstruction, after a careful study of the Personal Constructional Characteristics/Design Style of the (unknown today) ancient craftsman, retracted from the mechanical parts of the Mechanism’s fragments. During the extensive use of our models, it was concluded that two important and mandatory indicators are missing from all current reconstructions of the Mechanism. The two indicators are necessary for the Antikythera Mechanism to be considered as a complete and self-contained operational time-measuring device which provided direct astronomical and calendar information without additional calculations. The two operations related to the preserved remains were located on gear b1 and its lost Cover Disc. The reconstruction of those missing parts was done according to the Constructional Protocol. The extensive analysis of the Antikythera Mechanism’s operations leads to the understanding of the Mechanism as a luni-(solar) time-measuring device, as opposed to the notion that it was a mechanical planetarium presenting the hypothesized planetary motions and positions.

1. Introduction

1.1. A Brief History of the Antikythera Mechanism

For about 2000 years, the Antikythera Mechanism, a unique geared time-computing device of the Hellenistic era, was settled on the bottom of the Antikythera Island gulf [1,2,3,4,5,6,7]. After the extraction of the Antikythera Mechanism from the sea bottom during the underwater excavation of 1900, and its discovery as a rotten and heavily corroded device with gears and inscriptions in 1901/1902 [5] pp. 47 and 49; [6] p. 83, many opinions were expressed about the operation of this unique device. The general assumption in the 1920s was that it was an astrolabe for ship navigation or some related function [3,4,6]. Through time and after the discovery and recognition of new mechanical and inscriptional findings, the idea of an astrolabe was abandoned in favor of a mechanical calendar/astronomical calculator. The partially/poorly preserved engraved inscriptions with the names of the five known planets during antiquity brought forward the hypothesis that this geared device was a mechanical planetarium, which should have had spheres and pointers on its Front Central Dial to represent the planets’ motion and their position on the Ecliptic [8,9,10,11,12]. In 2004, following the initiative of M. Edmunds, J. H. Seiradakis, and X. Moussas, new data were collected during the Antikythera Mechanism Research Project (AMRP), via the Microfocal X-ray Computed Tomography (CT). The fragments were recorded in digital volumes [13,14,15] and the CTs led to better knowledge about this geared device. The study of the Mechanism’s CTs and the visual photographs of the fragments helped us to detect, recognize, and present the Personal Constructional Characteristics of the ancient craftsman: the specific style of the ancient craftsman in design/construction/assembly/stabilization of the Mechanism’s parts according to its experience and knowledge (presented in Section 3.1).

This paper presents an examination of the preserved mechanical remains on gear b1 to determine two lost but required operations of the Antikythera Mechanism. Gear b1 is the largest gear of the Mechanism (see Figure 1, Fragment A), with a diameter of about 129 mm, and it is not a robust design/one-piece bronze disc as is the e3 gear.

1.2. The Measuring Units of the Antikythera Mechanism

The Antikythera Mechanism was a computing device capable of carrying out complex (time) calculations, providing immediate information on the timing of astronomical, social, and religious events, without additional calculations by the user. This unique time-measuring device is a ΧΡΟΝΟΥ ΑΥΤΟΜΑΤΟΝ (Time Automaton), a Time “Robot” of Antiquity, in line with the ideas and constructions of Heron of Alexandria [16]. The calculated results were presented via several pointers, which rotated around calibrated dials (i.e., scales with subdivisions). The motion of the Mechanism’s pointers was achieved by the engagement of a number of gears, each having a specific number of teeth related to characteristic astronomical numbers, e.g., 223 teeth on gear e3 (related to the 223 synodic months of one Saros cycle), the engaged gears d2, d1, and c1 = 127 × (48/24) = 254 (related to the Metonic cycle of 254 sidereal months), etc.

Today, four measuring dials are preserved, in a circular distribution (Zodiac month ring, Egyptian calendar ring, Athletic Games circle, Exeligmos circle), which are divided into subdivisions of equal dimension and two dials in spiral distribution, the Metonic and the Saros spirals, which are divided into constant angular frequency.

The type of calculations performed by the Antikythera Mechanism can be determined by checking the measuring units and subdivisions engraved on their corresponding dials. For example, by observing the units on the measuring scale of a multimeter, someone can figure out that this measuring instrument measures Volts, Amperes, and Ohms. These units are directly correlated to the nature of the electric current.

The concept of relevance governs a measuring device, i.e., the procedures of the measurements are made on inter-correlated phenomena: it is difficult to find a real scientific multimeter for electric current measurements and at the same time for this device to offer the ability to measure distance in kilometers or the intensity of an earthquake in Richter’s scale.

According to

Table 1. Preserved dials of the Antikythera Mechanism and their corresponding units. The type of measurement for each scale is the same: measurement of time.

Measuring Dial	Antikythera Mechanism Scale	Scale Subdivisions/Units	Type of Measurement
Egyptian calendar ring	Egyptian year of full 365 Days	1 Day	Time
Parapegma plates 1, 2	1 Year = 2 Plates = 2 × 2 (corner) columns 1 column = 1 Season = 3 month Each Parapegma event corresponds to a specific Date = 1 Day per index letter	1 Day	Time
Lunar Phases sphere	The lunar phases are measured in days (e.g., Full Moon = 15 day Moon, not Moon at 180°)	colors B&W: Black, White, half black-half white	Time
Zodiac month ring	1 tropical year of 365.25 Days (365 equal subdivisions + 0.25 or 365.0 subdivisions with a correction procedure).	1 Day	Time (instead of arc degrees-space)
Metonic spiral	19 Years/235 Synodic months	1 Synodic month/cell	Time
Saros spiral	18.03 Years/223 Synodic months	1 Synodic month/cell	Time
Exeligmos dial	54.09 = 3 × Saros (=3 × 223 Synodic months)	18.03 Years/sector	Time
Athletic Games dial	4 Years (=alternately 49/50 Synodic months)	1 Year/quadrant	Time

, all currently preserved scales of the Antikythera Mechanism measure time in units of days, synodic months, and years. Each measuring scale is subdivided into equal time durations.

Regarding the units of the Zodiac dial ring, it was also suggested the division of the Zodiac ring in 360 un-equal subdivisions, i.e., arc degrees (units of space) [17] in order to represent the solar anomaly, but the Parapegma events occurred in days, not in degrees [18,19,20,21]. Therefore, the Parapegma index letters which are engraved on some of the Zodiac ring subdivisions should correspond to days (equal subdivisions), instead of arc-degrees (unequal subdivisions). By dividing the Zodiac ring in 365.25 or rounded in 365.0 equal subdivisions and in different numbers of subdivisions per each Zodiac month, the solar anomaly is represented on the Antikythera Mechanism [22].

Based on the characteristics of these units, the Antikythera Mechanism is related to the procedures of a mechanical time-measuring calculator.

1.3. Regarding the Ancient Craftsman of the Antikythera Mechanism

There is no clear information available regarding the identity of the ancient craftsman who created the Antikythera Mechanism. Undoubtedly he was highly skilled in geometry, mechanical design, engineering, constructions, and likely astronomy. The craftsman would also have required exceptional finger dexterity and, most importantly, a great deal of patience [23].

In a previous publication, we identified the likely starting date for the initial calibration position of the Mechanism’s pointers as 22/23 December 178 BC [24]. This suggests that the craftsman likely lived, at least as an adolescent or young adult, before/after this period. Notably, Hipparchos of Rhodes (190-120 BC) lived in Alexandria and Rhodes, would have been contemporary with this timeframe.

In contrast, scientists such as Posidonius of Rhodes (c. 135-c. 51 BC) and Geminus (1st century BC-c. 50 BC) lived significantly later, making them unlikely candidates.

Archimedes of Syracuse (287–212 BC) has also been proposed as the creator of the Mechanism [25,26]; however, analysis of the Back Cover Inscription Part-2 renders this hypothesis improbable [27].

To date, the identity of the craftsman who created this remarkable geared device remains unknown.

2. Materials and Method

2.1. Present Day Missing Parts of the Antikythera Mechanism

Today, 7 large and 75 smaller fragments of the Mechanism are preserved as shown in Figure 1. These fragments comprise about <44% of the Mechanism. For example, Fragment B is about one third of the Metonic spiral, i.e., 15% of the entire Back Plate. By applying symmetry and geometry to the Design, the dimension and the shape of the Back and Front Plates can be calculated and the partially preserved parts can be reconstructed [28,29].

The reconstruction of the Mechanism’s Back Plate is based on the preserved Fragments A, B, F, and E and the Front Plate is based on the remaining parts of Fragments A and C, as well as a large number of small fragments. The center of gear b1 (b_out axis) is the geometrical center of the Front Plate (see Figure 1).

Most of the Front Central Face parts of the Mechanism are missing. The only preserved part is the Lunar Disc (or Lunar Cylinder) located on Fragment C (Figure 2). Close to the perimeter of the Lunar Cylinder, a cavity is preserved, which was formed by the lost Lunar Phases sphere [30,31,32]. The lost Lunar Phases sphere was probably made of an organic material, such as wood or ivory. The gear z (depicted by the red arrow in Figure 2E) is broken in half, with 10 out of 20 teeth remaining. The gear is attached on its axis z, and these are the two preserved parts of the Lunar Phases sphere gearing [13,30,32].

As inferred by the well-preserved shape of the Lunar Cylinder surface, the specific position of gear z seems to be in its original position, i.e., the gear teeth aiming towards the perimeter of the Lunar Cylinder [32], and its adaptation into an inverted position it cannot be convincingly justified. In [11,12,30], the gear z is presented an in inverted position, i.e., with the gear teeth aiming toward the center of the Lunar Disc; their suggestion requires a large number of hypotheses and the assumption that someone made the wrong adaptation of gear z. This cannot be justified (see Introduction and Section 2 in [32]). Moreover, the current material of the Mechanism fragments is atacamite, a rocky material [29], and most of the parts are stacked together as “one piece”. Thus, it is difficult to detach a part unscathed. Taking into account the current/original position of the gear z, this means that the Lunar Phases sphere gearing needs three additional hypothetical gears and one shaft in order to operate [33].

If gear z were to be placed in inverted position, then only one additional gear would be necessary for the Lunar sphere rotation and not two additional gears. But the specific position of gear z seems to be its original position [32].

The imprint in a horseshoe shape at the internal area of the Lunar Cylinder (Figure 2E) implies the existence of a spacer in a horseshoe design. The spacer should be attached between two plane surfaces/plates: the Lunar Cylinder and its base, which is not preserved today.

The question arises: “Why didn’t the craftsman of the AM invert the gear position to avoid the construction and assembly of two additional gears and their shaft?”

As the base of the Lunar Cylinder is not preserved, a new question arises: Could the original design of the Lunar Cylinder and its gearing be different than the present-day hypotheses?

The lack of answers leaves these two questions open today…

There are also some poorly preserved mechanical formations on gear b1 (presented further below), the remains from a mechanical structure just above gear b1, with unknown operation and design, and totally missing today (also discussed below).

Since the Zodiac month dial is a ring, there is a central circular hole in the Front Central area [28], with a diameter of about 135 mm. This central hole should be filled by the lost structures of gear b1 and the Cover Disc of gear b1, which is also missing today.

Figure 2. (A) X-ray CT of the Lunar Cylinder gear z, its axis, and the Lunar Phases sphere cavity, located on Fragment C. (B) The outline of the area in which the (lost) Lunar Phases sphere once existed; the gear z and its axis are attached. (C) A close-up of the gear z. Note that the outline of this area precisely follows the outline of the gear. Attaching gear z in inverted position cannot be realistic (see also [32]). The CT was aligned to the Lunar Cylinder surface (CT was generated from AMRP Raw volumes using the Real3D VolViCon V.4.31.0422 software [34] and it was further processed by the authors). (D) Gear z, its axis, and the Lunar Phases sphere cavity are the preserved parts of the Lunar Cylinder’s lost gearing. CTs processed by the authors. (E) A close-up of the internal area of the Lunar Cylinder on Fragment C (photo by the first author, Copyright ©Hellenic Ministry of Culture & Sports/Archaeological Receipts Fund). The white arrows depict the imprint of the lost horseshoe spacer. The black arrow depicts the Lunar Phases sphere cavity. The red arrow depicts the half-preserved gear z. Note that the colors of the corrosion are the dark green shades and any other color (mostly brighter colors) should be a result of the part’s/area’s cleaning.

Figure 2. (A) X-ray CT of the Lunar Cylinder gear z, its axis, and the Lunar Phases sphere cavity, located on Fragment C. (B) The outline of the area in which the (lost) Lunar Phases sphere once existed; the gear z and its axis are attached. (C) A close-up of the gear z. Note that the outline of this area precisely follows the outline of the gear. Attaching gear z in inverted position cannot be realistic (see also [32]). The CT was aligned to the Lunar Cylinder surface (CT was generated from AMRP Raw volumes using the Real3D VolViCon V.4.31.0422 software [34] and it was further processed by the authors). (D) Gear z, its axis, and the Lunar Phases sphere cavity are the preserved parts of the Lunar Cylinder’s lost gearing. CTs processed by the authors. (E) A close-up of the internal area of the Lunar Cylinder on Fragment C (photo by the first author, Copyright ©Hellenic Ministry of Culture & Sports/Archaeological Receipts Fund). The white arrows depict the imprint of the lost horseshoe spacer. The black arrow depicts the Lunar Phases sphere cavity. The red arrow depicts the half-preserved gear z. Note that the colors of the corrosion are the dark green shades and any other color (mostly brighter colors) should be a result of the part’s/area’s cleaning.

2.2. Clues for the Hypothesis of the Planets’ Rotating Spheres on the Antikythera Mechanism: Objections and Contradictions

Many researchers believe that the Antikythera Mechanism had a planet indication gearing system on the Central Front Face which represented the motion of the 5 planets, but today is lost [9,10,11,12]. This hypothesis is based on four clues which are presented below:

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Clue I: On the Back Cover plate of the Mechanism, the engraved Instruction manual of the device (Back Cover Inscription—BCI) is given in two parts and is partially or poorly preserved [19]. The operational parts of the Front Plate are presented in the text of BCI Part-1, while the operational parts of the Back Plate are presented on the BCI Part-2.

The names of the 5 known planets during antiquity, or with their theophoric names, are preserved on the text of the BCI Part-1:

[ΕΡΜΟΥ ΣΤΙΛΒΟΝ]ΤΟΣ (Hermes Stilbon—Mercury),

ΑΦΡΟΔΙΤΗ<Σ> ΦΩΣΦΟΡΟΥ (Aphrodite Phosphoros—Venus),

ΑΡΕΩΣ ΠΥΡΟΕΝΤΟΣ (Ares Pyroes—Mars),

[ΔΙΟΣ ΦΑ]ΕΘΟΝΤΟΣ (Dias/Zeus—Phaethon—Jupiter), and

[ΚΡΟΝΟΥ ΦΑ]ΙΝΟΝΤΟΣ (Kronos Phainon—Saturn).

-

Clue II: The (theophoric) names of the five planets can also be found on the Front Cover inscription [35], with information for each planet, related to the planet’s timed position on the Ecliptic, e.g., Ο ΔΕ ΦΩ[ΣΦΟΡΟΣ, Ο ΔΕ Φ̣Α̣ΕΘΩ̣Ν ΕΝ . . . . . ̣ΑΠΟΚΑΤΑΣΤ̣Α̣Σ̣[ΕΙΣ , [Ε]ΣΠΕΡΙΝΟΝ ΣΤΗΡΙΓΜΟΝ etc.

-

Clue III: Fragment D is an unplaced part of the Mechanism. It consists of a gear with 63 teeth (r1), with a circular plate attached to it and an independent oblong/curved plate that are visible in the CTs (see Fragment D analysis in [36]. It was suggested that these parts can be related to the gearing of the planet Venus, after its engagement with an additional number of hypothetical/non-existent gears [11,12].

-

Clue IV: There are preserved mechanical remains fixed on gear b1 (Figure 3A,D,E), which lead to the conclusion that a mechanical structure existed on the b1 gear and extended above it (Figure 3A–C). These lost structures and the lost Cover Disc of gear b1 occupied the space of the large central large hole of the Front Plate.

Based on these four clues, the hypothesis of the planet indication gearing on the Antikythera Mechanism appeared over time. It was suggested that the Antikythera Mechanism was a mechanical planetarium device, representing the motions of the five planets and their position on the Ecliptic (only their ecliptic longitude) via their corresponding colored spheres and pointers attached on their arms or rings, on the Central Front Face [9,10] in a bronze model; ref. [12] in 3D computer simulation).

This paper challenges this hypothesis of the planet indication gearing–mechanical planetarium, for a number of reasons presented and discussed below.

Instead of the hypothesis of the planetarium device, this paper presents arguments leading to the conclusion that the Antikythera Mechanism is a luni-solar time calculator (also taking into account the analysis in Section 2), which had only the Moon and Sun spheres and their pointers, located on the Central Front Face of the Mechanism, as only these two celestial bodies were necessary for the time measurement of the calendar calculation (lunar/solar cycles, years, months, days, hours) and eclipse predictions during the Hellenistic Era.

The following arguments address the above-mentioned clues, and contradict the hypothesis of the planet indication gearing on the Antikythera Mechanism:

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First argument against the planet gearing hypothesis: A reference to the planets’ names is not enough to prove the existence of a planet indication gearing. It is possible to reconstruct the text on the Back Cover inscription related to the names of the planets, although the relative text is partially/poorly preserved. This text is given below, taken from [19] p. 234. It corresponds to Back Cover Inscription (BCI) Lines 16–25 (the left/right boundary of the following table corresponds to the Cover plate boundary):

(16) ΠΡΟΕΧΟΝ ΑΥΤΟΥ ΓΝΩΜΟΝΙΟΝ Σ[………………………………………………….…… ΠΕΡΙ (17) ΦΕΡΕΙΩΝ Η ΜΕΝ ΕΧΟΜΕΝΗ ΤΩΙ ΤΗΣ […………………………………. ΕΡΜΟΥ ΣΤΙΛΒΟΝ- (18) ΤΟΣ ΤΟ ΔΕ ΔΙ ΑΥΤΟΥ ΦΕΡΟΜΕΝ[ΟΝ …………………………………..……………………… (19) ΤΗΣ ΑΦΡΟΔΙΤΗ<Σ> ΦΩΣΦΟΡΟΥ . . .[ ……………………………………..………….….……… (20) ΤΟΥ [ΦΩ]ΣΦΟΡΟΥ ΠΕΡΙΦΕΡΕΙΑΝ .[……………………………..………..………………..….… (21) ΓΝΩΜΩ[.]ΚΕΙΤΑΙ ΧΡΥΣΟΥΝ ΣΦΑΙΡΙΟΝ . .[………………..……………………………..…….. (22) ΗΛΙ[ΟΥ] ΑΚΤΙΝ ΥΠΕΡ ΔΕ ΤΟΝ ΗΛΙΟΝ ΕΣΤΙΝ […………………………….……….…….…… (23) [---ΤΟ]Υ ΑΡΕΩΣ ΠΥΡΟΕΝΤΟΣ ΤΟ ΔΕ ΔΙΑΠΟΡΕ[ΥΟΜΕΝΟΝ …………………………………… (24) [ΔΙΟΣ ΦΑ]ΕΘΟΝΤΟΣ ΤΟ ΔΕ ΔΙΑΠΟΡΕΥΟΜΕΝΟΝ̣[…………………………… Ο ΤΟΥ ΚΡΟ- (25) [ΝΟΥ ΦΑ]ΙΝΟΝΤ̣ΟΣ ΚΥΚΛΟΣ ΤΟ ΔΕ ΣΦΑΙΡΙΟΝ ΦΛ̣[……………………………………..…

As the phrase ΚΡΟΝΟΥ ΦΑ]ΙΝΟΝΤ̣ΟΣ ΚΥΚΛΟΣ (Kronos Phainon circle—Orbit) is preserved, then the word ΚΥΚΛΟΣ—orbit should exist for the planets Mars and Jupiter.

Therefore the text restoration is as follows:

(22) ΗΛΙ[ΟΥ] ΑΚΤΙΝ ΥΠΕΡ ΔΕ ΤΟΝ ΗΛΙΟΝ ΕΣΤΙΝ [………………………..…….…… ΕΣΤΙΝ Ο ΚΥΚ- (23) ΛΟΣ ΤΟ]Υ ΑΡΕΩΣ ΠΥΡΟΕΝΤΟΣ ΤΟ ΔΕ ΔΙΑΠΟΡΕ[ΥΟΜΕΝΟΝ ΣΦΑΙΡΙΟΝ….. ΕΣΤΙΝ Ο ΚΥΚΛΟΣ ΤΟΥ (24) ΔΙΟΣ ΦΑ]ΕΘΟΝΤΟΣ ΤΟ ΔΕ ΔΙΑΠΟΡΕΥΟΜΕΝΟΝ̣ [ΣΦΑΙΡΙΟΝ ………….. ΕΣΤΙΝ Ο ΤΟΥ ΚΡΟ- (25) ΝΟΥ ΦΑ]ΙΝΟΝΤ̣ΟΣ ΚΥΚΛΟΣ ΤΟ ΔΕ ΣΦΑΙΡΙΟΝ ΦΛ̣[………………….………………………………

The names of the planets are directly connected to the word ΚΥΚΛΟΣ—orbit of planet. At this point, the ancient craftsman presents the names of the planets and the corresponding orbit/position of each planet. There is not a clear and distinct presentation for the spheres and the pointers of the planets. The ancient craftsman uses the word ΚΥΚΛΟΣ/orbit for each of the superior planets Mars, Jupiter, and Saturn and the word ΠΕΡΙΦΕΡΕΙΑ/circumference for the orbit of the inferior planets Mercury and Venus ([19] p. 233, lines 17 and 20) and probably for the orbit of the Sun–Golden Sphere.

Moreover, the word (ΔΙΑΠΟΡΕΥΟΜΕΝΟΝ) ΣΦΑΙΡΙΟΝ (preserved in Line 25 and implied in Lines 23 and 24) can be well correlated to the ΧΡΥΣΟΥΝ ΣΦΑΙΡΙΟΝ as it is well presented in the previous lines 21–22: ΚΥΚΛΟΣ ΕΣΤΙΝ ΤΟΥ ΑΡΕΩΣ ΠΥΡΟΕΝΤΟΣ. ΤΟ ΔΕ ΔΙΑΠΟΡΕΥΟΜΕΝΟΝ (ΧΡΥΣΟΥΝ) ΣΦΑΙΡΙΟΝ ΕΝ ΣΥΝΟΔΩΙ ΒL Ζ (there is a circle of Mars. The rotating Golden Sphere is in conjunction (to Mars) in 2 Years + 1/7^y; see the analysis in [37] https://arxiv.org/pdf/2207.12009, pp. 42–43, (accessed on 1 February 2026).

A dominant question arises: Why did the ancient craftsman present the orbits of the planets, instead of their spheres and pointers (if such components indeed existed)?

Each of the planetary orbits was (probably) engraved by a simple circular line on the b1 Cover Disc, but it is less important than its sphere and pointer. Between the planet’s sphere and its orbit, the importance of the planet’s sphere is dominant!

The ΣΦΑΙΡΙΟΝ (sphere) and the pointer are operational parts, whereas the ΚΥΚΛΟΣ/orbit does not affect the planet’s positional calculation and its existence is not necessary.

A proper text about the planets’ sphere/pointer presentation should be ΕΣΤΙΝ ΣΦΑΙΡΙΟΝ ΤΟΥ ΑΡΕΩΣ ΠΥΡΟΕΝΤΟΣ, ΕΠΙ ΤΟΝ ΑΥΤΟΥ ΚΥΚΛΟΝ ΔΙΑΠΟΡΕΥΟΜΕΝΟΝ, (there is the sphere of Ares Pyroes which travels through its circle) or ΕΣΤΙΝ ΤΟ ΤΟΥ ΚΡΟΝΟΥ ΦΑΙΝΟΝΤΟΣ ΣΦΑΙΡΙΟΝ, ΕΠΙ ΤΟΝ ΑΥΤΟΥ ΚΥΚΛΟΝ ΦΕΡΟΜΕΝΟΝ (there is the sphere of Kronos Phainon which travels through its circle), since the ancient craftsman presents the Sun as ΧΡΥΣΟΥΝ ΣΦΑΙΡΙΟΝ (Golden Sphere) and ΗΛΙ[ΟΥ] ΑΚΤΙΝ (sun ray-pointer).

From the statistical analysis, it shows that the ancient craftsman uses the following (see

Table 2. A part of the preserved Back Cover inscription (Lines 10–26) of the Antikythera Mechanism Instruction Manual (Part-1) [19], pp. 232–233. The preserved letters are in bold.

Preserved Inscription	Related to the	Number of Sentences
(10) [- - - - - - - - - - -]Ε̣Π ΑΚΡΟΥ Δ[ …………………………….…………..…. (11) [- - - - - - - - - - -].ΩΣΜΕΝΩΝ .[……….………………………….………… (12) [- - - - - - - - - - - -]Ε̣ ΜΕΛΑΝ ΟΤ .[………………………………..……….. (13) [- - - - - - - - - - -]. . . . . . Λ̣Ω̣ΝΓΕΓ[………………………………….……….. (14) [- - - - - - - - - -]. Ε . ΔΥΠΟΛΑΒΕΙ[Ν…………….……………..…………… (15) [ ̣ ̣]ΟΘ̣Ε ̣ ̣ ΤΟ ΣΦΑΙΡΙΟΝ ΦΕΡΕ ̣[…………..…………………..…..…..…. (16) ΠΡΟΕΧΟΝ ΑΥΤΟΥ ΓΝΩΜΟΝΙΟΝ Σ[………………………..… ΠΕΡΙ	Lunar Cylinder	7+
(17) ΦΕΡΕΙΩΝ Η ΜΕΝ ΕΧΟΜΕΝΗ ΤΩΙ ΤΗΣ …. […ΕΡΜΟΥ ΣΤΙΛΒΟΝ-	Lunar Cylinder + Mercury	1+
(18) ΤΟΣ ΤΟ ΔΕ ΔΙ ΑΥΤΟΥ ΦΕΡΟΜΕΝ[ΟΝ………………….….…………	Mercury + Venus
(19) ΤΗΣ ΑΦΡΟΔΙΤΗ<Σ> ΦΩΣΦΟΡΟΥ . . .……..……….……….…………	Venus	1+
(20) ΤΟΥ [ΦΩ]ΣΦΟΡΟΥ ΠΕΡΙΦΕΡΕΙΑΝ .[……………….…….……..……..	Venus + Sun
(21) ΓΝΩΜΩ[.]ΚΕΙΤΑΙ ΧΡΥΣΟΥΝ ΣΦΑΙΡΙΟΝ . .[………..……………..… (22) ΗΛΙ[ΟΥ] ΑΚΤΙΝ ΥΠΕΡ ΔΕ ΤΟΝ ΗΛΙΟΝ ΕΣΤΙΝ ……….……………	Sun	2+
(23) [---ΤΟ]Υ ΑΡΕΩΣ ΠΥΡΟΕΝΤΟΣ ΤΟ ΔΕΔΙΑΠΟΡΕ[ΥΟΜΕΝΟΝ…..….	Mars	1
(24) [ΔΙΟΣ ΦΑ]ΕΘΟΝΤΟΣ ΤΟ ΔΕΔΙΑΠΟΡΕΥΟΜΕΝΟΝ̣[…. Ο ΤΟΥ ΚΡΟ	Jupiter	1
(25) [ΝΟΥ ΦΑ]ΙΝΟΝΤ̣ΟΣ ΚΥΚΛΟΣ ΤΟ ΔΕ ΣΦΑΙΡΙΟΝ ΦΛ̣[………….…	Saturn	1
(26) [- - - - - - -]Ε̣ΡΑ ΔΕ ΤΟΥ ΚΟΣΜΟΥ ΚΕΙΤΑΙ . . .[………………………….	Beyond Cosmos

Note. The preserved letters are in bold.

):

• About seven sentences (Lines 10–16) to describe the Lunar Cylinder + the Lunar Phases sphere + the lunar pointer + its operation;
• About three sentences (Lines 20–22) to describe the Golden Sphere–Sun and its position + its pointer + its operation; and
• Definitely, one sentence each is used for the planets Mars (Line 23), Jupiter (Line 24), and Saturn (Line 25), in order to describe the planet’s position + its (hypothetical) colored sphere + its pointer + its operation, and also for Mercury (Lines end of 17–18) and Venus (Line 19), see Table 2.

The rest of the planets should have a similar mechanical design to that of the Sun, i.e., spheres in different colors (e.g., red for Mars), with pointers; they should have a similar text description as the Golden Sphere–Sun description and be in equal length in the text (as the Sun was one of the planets according to Hellenistic Astronomy; [21,38].

The description of the Sun’s orbit with its Golden Sphere, its position and pointer, and its operation occupies three lines. But there is not enough space for the description of the rest of the planets with their orbits, spheres, pointers, and operation in one sentence (of ~ 86 letters) per each planet.

-

Second argument against the planet gearing hypothesis: The preserved text on the Front Cover Inscription (FCI) describes the motion of the planets but there is no reference to a mechanical part related to a planet on the Mechanism, e.g., there should be a phrase such as ΓΝΩΜΟΝΙΟΝ ΚΡΟΝΟΥ (Saturn pointer) or ΣΦΑΙΡΙΟΝ ΔΙΟΣ (Sphere of Jupiter) or ΓΝΩΜΟΝΙΟΝ ΜΕΤΑ ΣΦΑΙΡΙΟΥ ΤΟΥ ΑΡΕΩΣ (Mars’ sphere attached on the arm), etc.

The total absence of any mechanical reference in the inscription of the Front Cover plate related to the planets’ spheres and their pointers can be justified if the Front Cover Inscription was an introductory informative text to the planetary phases, conjunction, morning station, greatest elongation, i.e., the characteristic motions of the planets and their positions on the Ecliptic, as the planets were part of the Cosmos in that era. This text seems somewhat unrelated to the operation of the Antikythera Mechanism as there is no direct connection/relation to parts of the Mechanism.

The specific text is completely independent from the rest and could be a standalone text unrelated to the operation of the Antikythera Mechanism.

-

Third argument against the planet gearing hypothesis: The measurements of the gears’ rotational inertia in [33], and torques in [39] proves that “the Input of the Antikythera Mechanism is very doubtful from the axis a1, as it creates problems in the mechanical parts, has low torque and makes the handling difficult because of the lack of precision in the pointing”. The central hole of the contrate gear a1 has an oblong shape, and an axis with an oblong cross-section edge is attached. These two parts could have been previously made and come from a different machine or construction, i.e., scrap material/useless parts, and the ancient craftsman processed them into a gear and axis (as one part).

Starting from Price [8], most researchers assume that the input of the Mechanism is from crown gear a1 (see Figure 3A–C). However, in [39] it is shown that driving the Mechanism from gear a1 would be very difficult due to friction.

Additionally, when operating the Mechanism from gear a1, the Lunar pointer rotates very fast (if contrate a1 rotates by a single tooth, the Lunar Disc rotates ~21.5° in respect to the Zodiac month ring (i.e., ~71.75% of a Zodiac month of ≈30°), making it difficult to aim the Lunar pointer at a desired position with precision [36]. The design of any mechanical construction that a human will handle must obey the theory of biomechanics, bioengineering, and the motions of the human body [40].

Furthermore, the bronze Lunar Cylinder is notably heavy, with a large diameter (approximately 68 mm), resulting in substantial inertia during its rotation, particularly when positioned as the final element in the gear sequence. It is important to note that toward the end of the sequence, torque diminishes, which makes rotation more difficult and doubtful.

The proper and ideal input for the Antikythera Mechanism is the Lunar Cylinder/b_in axis (the axis b_in perforates the axis b_out; see gearing scheme of Figure 1 in [29], as it presents satisfactory torque [39] and also results in a high pointing accuracy of the Lunar pointer to any subdivision of the Zodiac month ring [36] p. 116.

The ancient Greek calendars and the time measurement during the Mechanism’s era were based on the lunar synodic month [20,41]. The Lunar Cylinder, as the input of the Mechanism, correlates the Mechanism’s calculations to the lunar synodic cycle. Additionally, all of the preserved dials of the Mechanism are mostly based on the lunar synodic cycle.

Today, only three lunar cycles are represented on the Antikythera Mechanism: Sidereal, Synodic, and Anomalistic. The fourth, the very important, critical, and decisive Draconic cycle for the solar eclipses’ calculation (well known in the Hellenistic era), is missing. The unplaced Fragment D/gear r1 can satisfactorily cooperate with the preserved gears b1-a1-(r1) and three hypothetical (lost) gears [42]. (The authors’ first paper describing the idea for the Draconic gearing existence on the Antikythera Mechanism was initially submitted to a journal on 14 January 2020, and it was eventually published in a different journal (Mediterranean Archaeology and Archaeometry) in December 2022). By this engagement, the Draconic cycle is represented and so the four lunar cycles are present on the Antikythera Mechanism, Figure 4.

By introducing the Draconic lunar cycle on the Antikythera Mechanism, the lost eclipse events on the Saros spiral can be recalculated, using the relative positions of the Lunar pointer (to the Golden Sphere–Sun or opposite position) and the Draconic pointer (between the ecliptic limits of the Draconic scale); [45]. For this correlation, three hypothetical gears are needed [42].

The scenario that the ancient craftsman includes in his creation three out of the four lunar cycles, but that he does not include the very important Draconic cycle, and he also includes the five planets, is inadequate and astronomically inconsistent and unjustified.

In [45], it was shown that the sequence of eclipse events, engraved in the Saros cells, was calculated using the (missing/lost) Draconic gearing on the Antikythera Mechanism, i.e., through a purely mechanical procedure.

Freeth et al., 2021 [12], suggest a hypothetical Draconic gearing on the Front face of the Mechanism, without a typical dial. In this suggestion, the Draconic pointer is referred to as The Dragon Hand, and gets motion from the b1 gear (via a number of additional hypothetical gears). The b1 gear rotates in constant angular velocity and therefore this Draconic pointer also rotates with constant angular velocity. But all the lunar cycles have a variable angular velocity, due to the variable velocity of the Moon (Anomalistic cycle). As the lunar motion is variable, the lunar nodes change their position in the sky not steadily, but with variable angular velocity, which is faster when the Moon is near its perigee.

Therefore, the Draconic pointer should also have a variable velocity. In the suggested model by [12], a kind of pin & slot gear design and additional gears should be added in the suggested gearing, in order to represent this Draconic pointer with variable velocity, as the ancient craftsman designed the preserved pin & slot (gears e5/e6/k1/k2) in order to represent the variable motion of the Moon in the sky (Anomalistic cycle).

-

Fourth argument against the planet gearing hypothesis: The mechanical remains in gear b1 can be related to necessary operation(s) of the Mechanism which are currently missing and without using the hypothesis of the planet indication gearing. The analysis and discussion are presented in the next two sections.

2.3. Remains of Mechanical Parts on the Gear b1

Gear b1 is the largest gear of the Mechanism and was designed as a combination of a ring with four radial arms distributed by 90°, further increasing the time and the effort for this construction (instead of a simple full metal disc as is the e3 gear), as shown in Figure 5. Therefore, it seems that it was constructed by scrap parts which were leftover in a craftsman’s machine shop. Even today metal recycling is a common practice by craftsmen (M. Wright constructed the middle plate of his model using a bronze recycled scrap plate that was the name plate from an office door and a pub door kicking plate ([46] p. 199). The large, deep engraved letters on the middle plate are visible; see at 09:00 and 11:10 https://www.youtube.com/watch?v=eC54F4vv_8E (accessed on 1 February 2026).

Since bronze was too expensive in that era (and also today), it is possible that the ancient craftsman might have attempted to save on this material. For example, the Middle Plate of the Mechanism has much shorter dimensions than the Front/Back Plates, as it was not necessary and did not have mechanical parts.

The four arms are stabilized on the ring by the design of a “dove tail” shape, offering very good stability. Today, the “dove tail” male/female shape design is used for many optomechanical systems’ safe stabilization (telescopes on their mounts, optical benches, microscope tables, guide sliding tables in woodworking, etc.).

On the b1 gear there are some preserved remains of mechanical parts, shown in Figure 3, Figure 5 and Figure 6, which constitute evidence for the existence a number of missing mechanical parts. These remains imply the existence of additional calculation processes performed by the Mechanism that are not preserved. One of these parts, the long pillar, can be directly related to the Cover Disc of gear b1 and the remaining three long pillars should have existed, since their imprints and holes are preserved symmetrically distributed by 90° around the gear’s perimeter. In

Table 3. The remains (or their imprints) of the mechanical parts and their positions on the gear b1 are presented. A mechanical description and their (probable) operation according to the Personal Constructional Characteristics of the ancient craftsman (see Section 3.1) are presented.

Mechanical Part on the b1 Gear	Description	Setting 0° at −7° to the Middle-Perpendicular of b1 Gear	Comments	Operation
1	Long pillar (preserved)	90°	Height ≈ 27 mm Figure 3	1st of 4 pillars for the b1 Cover Disc bearing
2	Long pillar (non-preserved)	0°	The imprint of its base is visible Figure 5	2nd of 4 pillars for the b1 Cover Disc bearing
3	Long pillar (non-preserved)	−90°	The imprint of its base is visible Figure 5	3rd of 4 pillars for the b1 Cover Disc bearing
4	Long pillar (non-preserved)	180°	The imprint of its base is visible Figure 5	4th of 4 pillars for the b1 Cover Disc bearing
5	Short pillar-1 (preserved) Figure 3	+120°	Height ≈ 19 mm Figure 13	For the Thin Sheet Strip-II stabilization
6	Short pillar-2 (preserved) Figure 3	+135°	Height ≈ 19 mm Figure 13	For the Thin Sheet Strip-II stabilization
7	(Twin) Oblong spacer-1 (preserved) Figure 6	+40°	Stabilized on the gear perimeter Figure 6	Spacer for the edge of the Thin Sheet Strip-I bearing
8	(Twin) Oblong spacer-2 (not preserved). Same part as the part No 7	+50°	Spacer’s imprint in Rehm and Svoronos photograph, Figure 6	Spacer for the edge of the Thin Sheet Strip-I bearing
9	Small oblong part with a hole for a pin adaptation Figure 3A–D	−45°	Figures 3, 5 and 11–13	For the Thin Sheet Strip-II edge immobilization See analysis in Section 3.1 and its reconstruction in Section 3.2
10	Hole in b1 arm Figures 3D and 5 and 6F,G,	45°	For a small pillar adaptation Figures 12 and 13A,B	For the Thin Sheet Strip-I edge immobilization Section 3.1 and its reconstruction in Section 3.2
11	The dug pothole (pit) in b1 arm	45°	Origin from scrap material, before the parts process (?) Figure 6F	Non-related to mechanical parts
12	Edge of a flexible Thin Sheet Strip-I	−135°	It is stabilized with pins on the b1 gear Figure 3E	See its reconstruction in Section 3.2, Figures 12 and 13A,B

, the mechanical remains of the gear b1 are presented and described, as is their operation (where this is possible).

Even if there were no additional processes related to the b1 gear, these four pillars are needed for the b1 Cover Disc attachment (see next section).

At the 45° arm of gear b1, there is a pothole—a dug area. This pothole seems to be unrelated to a mechanical procedure. It could have been present in the initial scrap bronze material before its processing to form a gear arm. The attachment of a moving part or its base in this pothole by the use of glue is not in accordance to the Personal Constructional Characteristics of the ancient craftsman (see further below) and the use of glue for moving parts’ axes/shafts is mechanically risky and doubtful.

2.4. The b1 Cover Disc of the Antikythera Mechanism’s Front Face

In terms of engineering and manufacturing, the Antikythera Mechanism was created by a professional craftsman of that era. It should therefore be at the limit of further improvement, comprising every necessary procedure for its operation and presenting a constructional uniformity: parts used for the same tasks should have a similar design and assembly style. Additionally, every part must exhibit maximum design efficiency and there should not be any non-essential or unjustified parts.

The user of the Mechanism should not be concerned about the internal parts.

A cover should exist above the b1 gear, for protection (to prevent stray parts from entering inside) and also for aesthetic reasons (from now on we will call this cover the b1 Cover Disc). Additionally, the surface of the b1 Cover Disc offers a satisfactory space for measuring scale(s) or other information.

The b1 Cover Disc should follow the internal round shape of the Zodiac month ring. The Cover Disc can be stabilized on the four long pillars of the b1 gear. The height of the preserved long pillar is larger than the diameter of the crown gear a1, which is engaged to the b1 gear (see Figure 3) and therefore the b1 Cover Disc can be based on the four long pillars without a mechanical malfunction.

The b1 Cover Disc rotates with the same angular velocity as the b1 gear, i.e., one full turn/solar tropical year, and it is the only external part of the Mechanism with a period of one tropical year. Therefore the Golden Sphere–Sun should be directly fixed on the Cover Disc via a small pillar. This design is in agreement to the reconstructed phrase by the authors of the preserved description for the Golden Sphere–Sun:

…ΕΙΣ/(εἷς/one) ΓΝΩΜΩΝ ΚΕΙΤΑΙ. ΧΡΥΣΟΥΝ ΣΦΑΙΡΙΟΝ ΕΠΙ ΤΟΥ ΓΝΩΜΟΝΟΣ ΕΣΤΙΝ “… a pillar stands. A Golden Sphere is mounded on the pillar” (preserved letters in bold from [19] p. 233, lines 20–21 and reconstructed text from [37] https://arxiv.org/pdf/2207.12009 pp. 13, 31 (accessed on 1 February 2026).

The (lost) base of the Lunar Cylinder would be in contact with the b1 Cover Disc in order to have good stability during its rotation.

About 25% of the 365 subdivisions (days) of the solar tropical year cycle are preserved on the Zodiac month ring [22]. The solar pointer ΗΛΙΟΥ ΑΚΤΙΝ/Sun ray [19] travels through the subdivisions. Based on the Personal Constructional Characteristic No 4 (each pointer is accompanied by its corresponding dial; see next section), the 29½ subdivisions for the lunar synodic cycle could be engraved in circular distribution on the b1 Cover Disc, in circular dimension, right after the Lunar Cylinder. Many old cathedral clocks present the Lunar Age dial: [48] see http://www.patrimoine-horloge.fr/as-padoue.html; http://www.patrimoine-horloge.fr/as-brescia.html; http://www.patrimoine-horloge.fr/as-clusone.html (accessed on 1 February 2026). This scale shows the age of the Moon, as the Lunar pointer travels along it. The description of lunar pointer is partially preserved in the BCI in Line 16: ΠΡΟΕΧΟΝ ΑΥΤΟΥ ΓΝΩΜΟΝΙΟΝ Σ[ΕΛΗΝΗΣ [a little (Lunar) pointer projected from it… (preserved letters in bold from [19] p. 232, lines 20–21 and reconstructed text from [37]).

Based on the preserved inscription ΚΡΟΝΟΥ ΦΑ]ΙΝΟΝΤΟΣ ΚΥΚΛΟΣ, Saturn orbit-circle, six concentric cycles, each for the rest of the planets, should follow right after the 29½ subdivisions (days), representing the orbits of Mercury, Venus, Sun, Mars, Jupiter, and Saturn (see the analysis and the tables in Contradiction argument I).

3. Results

3.1. The Personal Constructional Characteristics (PCC) of the Ancient Craftsman

Any creator designs and constructs his/her creation according to his/her experience, aesthetics, and manual dexterity. The combination of these personal constructional skills creates the constructional style of the creator, which is specific and personal. There is always a characteristic “imprint” of the creator in every construction. In many cases, it is possible to identify the creator by observing the construction style, similar to identifying a composer by the style of his musical composition (or the era of that composition) or a painter by the style of his paintings. In the same manner, the ancient craftsman constructed a device with a specific distinctive style of the parts’ design and the method of their stabilization, creating his Personal Constructional Characteristics (PCC). By studying the AMRP X-ray CTs of the fragments, we detected these Constructional Characteristics, which are the constructional imprint of the ancient craftsman.

3.1.1. PCC-1: The Stabilization of the Moving Parts

For the stabilization of the moving parts on their axes, i.e., gears and pointers, which are parts that have a torque/load, the ancient craftsman used stabilizing pins, attached perpendicularly to the parts’ axes as shown in Figure 7.

The craftsman could have used glue for bronze (an alloy of tin/lead) in order to stabilize the gears on their corresponding shafts. But this would be risky, since at any time it could come off, halting the Mechanism.

Eventually the ancient craftsman used the safest, for that era, method to stabilize the gears on their corresponding shafts by the use of a perpendicular pin, in contact with the upper surface of the gear. This also offers a practical way to remove and reposition the parts of the Mechanism.

3.1.2. PCC-2: The Ω-Plates and the Thin Sheet Strips

The craftsman of the Mechanism, in order to stabilize an axis (and a gear), when using a thin sheet/bar, made an oblong hole on the edge of the sheet, then made an oblong part of equal shape and dimensions as the oblong hole and finally fixed that part to its base, Figure 8 and Figure 9.

For the stabilization of the thin sheet, the craftsman adapted the thin sheet via its oblong hole on the oblong fixed part. Then he secured the thin sheet by using a pin perpendicular to the oblong part. In this design, the pin(s) are in a direction parallel to the base.

This style of stabilization is clearly detected on the Ω-plate for the restraint of the d-shaft. The Ω-plate is stabilized on the Middle Plate, via two oblong parts fixed on the Middle Plate and two pins, penetrating the oblong parts perpendicularly (Figure 8).

Also evident, although partially preserved, is the Ω-(“butterfly shape”) plate for the restraint of the gears e5/e6 and k1/k2 on their axes/shafts. This Ω-plate is stabilized on the e3 gear via two oblong parts (today only one is preserved) and two pins parallel to the gear’s surface, as shown in Figure 9 (see also Figures 12 and 13 in [43]).

Also, the stabilization of the gear e4 on e3 gear is done with the use of the four small oblong perforated parts (today only one is well preserved) fixed on the gear e3, four oblong holes on gear e4, and four stabilizing pins, perpendicularly adapted on the oblong part and parallel to the gear’s surface, Figure 10.

The preserved small oblong part located on the b1 gear’s arm at −45° has a similar design to all the preserved small oblong parts, Figure 11. Therefore, the operation of the small oblong part of the b1 gear should be similar to the operation of the rest of the oblong parts (see Figure 9), i.e., a thin bronze sheet should be inserted into this oblong part and a pin should secure this strip.

3.1.3. PCC-3: Using Spacers for the Gears’ Support

The ancient craftsman used spacers to better stabilize the gears by increasing their bearing surface. In this way, a gear rotates on a constant plane: almost all of the Mechanism’s gears have been constructed by a simple bronze plate 2 mm–2.5 mm thick. Since all the gears are thin, they cannot remain totally perpendicular to their axes/shafts, and therefore deviate from perpendicularity to their corresponding axes/shafts [9,33,36] (Figure 12A).

The ancient craftsman inserted a number of spacers which acted as bases for the gears, improving their functionality. All the spacers are fixed somewhere (mostly to the Middle Plate), are non-rotating parts, do not suffer from the torque/load, and do not have tension or strain. Therefore, their stabilization can be done with pins or glue, suitable for bronze without affecting the mechanical motion of the system.

3.1.4. PCC-4: The Pointers Rotated on Their Calibrated Dial

The ancient craftsman paired every pointer with a corresponding dial: all of the Antikythera Mechanism pointers rotated on their corresponding calibrated dials. A pointer without its calibrated dial does not perform any measurement. All of the Mechanism’s dials are subdivided with a constant unit period (subdivisions per turn): equal subdivisions for the circular dials (one year/subdivision on the Games dial, one Saros/subdivision in the Exeligmos dial, and a gradually increasing dimension (but in constant period) for the cells of the two spiral dials Metonic and Saros (1 synodic cycle/cell).

Hence, the ratio Pointer’s Angle/Subdivision = constant number.

These four basic constructional characteristics signify the Personal Constructional Characteristics of the ancient craftsman of the Antikythera Mechanism.

We applied the four Personal Constructional Characteristics of the ancient craftsman in all of our functional models and in our suggested reconstructions (described below). Our constructional protocol forbids the stabilization of a gear or a moving part using modern stabilizing parts (e.g., screws, nuts, etc.) or glue. The study of the Constructional Characteristics of the ancient craftsman gave us the ability to see and to experience the way the ancient craftsman was thinking for the parts’ assembly and what problems he faced during the parts’ construction, their assembly, and the use of his creation. We have also detected the constructional and measurement limits of the Mechanism, which differ from the theoretical study or the 3D simulations [45].

3.2. Reconstructing Lost Mechanical Parts of the b1 Gear by Applying the Constructional Characteristics of the Ancient Craftsman

The remains on the b1 gear are poorly preserved, but by applying the four Constructional Characteristics of the ancient craftsman, the reconstruction of the lost parts of the b1 gear can be achieved, as some of the mechanical remains of gear b1 have similar or identical design characteristics to other parts, which are better preserved and whose operation we already know.

• The 1 + 3 long pillars can be related to the attachment/stabilization of the b1 Cover Disc, which is the outer central front face of the Mechanism, as shown in Figures 6 and 14.
• One preserved spacer is placed at 40° and the imprint of the second similar spacer at 50° (well visible in the [5] and in Rehm photographs [47]). We call these two similar spacers the twin spacers (see Figure 6). In the opposite position (−135°), there exists one edge of a thin flexible bronze sheet. The second (lost) edge of this sheet should be in contact with the twin spacers, and therefore the thin sheet extends to the whole diameter of the b1 gear, as shown in Figure 12. The stabilization of the Thin Sheet Strip-I can be done with a perpendicular pin, according to the Constructional Characteristic No 2.
• According to the Constructional Characteristic No 2, the small oblong part with a hole located at the −45° position on the b1 arm should be the stabilizer for the edge of a second flexible thin bronze sheet. The edge of the thin sheet is stabilized with the use of a perpendicular pin in the hole of the small oblong part.

On the opposite side (at 120° and 135°), there are two short pillars. The second edge of the thin sheet is stabilized on the two short pillars via two perpendicular pins, as shown in Figure 13. This stabilization method is in perfect accordance to the Constructional Characteristics of the thin sheets of the Ω-plates.

According to our suggested reconstruction of the b1 gear’s lost parts, there are two different thin sheet strips in crossed directions, located at different heights/levels above b1 gear, Figure 14. The height of the twin spacers (≈ 6 mm) defines the height of the Thin Sheet Strip-I above the b1 gear surface and the height of the two short pillars (≈16 mm) defines the height of the Thin Sheet Strip-II.

The Cover Disc should be the place where the pointers and corresponding dials associated with additional necessary procedures were located (see next section).

3.2.1. Measuring Procedures That Must Have Been Present in the AM but Are Not Preserved

Two necessary measurement procedures which are not preserved today on the Mechanism emerged during the extended use of the functional models of the Antikythera Mechanism. The absence of these two procedures creates difficulties and doubts while using the Antikythera Mechanism: many times, the operation had to be stopped, to find the time instance corresponding to the pointers. The problem was even worse when only one user was handling the Mechanism. In order to avoid losing count during the Mechanism’s operation, we used some small sticky notes, attached to the Mechanism’s Front Plate.

It is evident that this is not a correct and proper way for operating the Antikythera Mechanism and makes its use problematic, irregular, and difficult. This practice negates the device’s independent and self-contained operation.

Both of the necessary—but missing from its current state—procedures are directly related to the Front Central Dial of the Mechanism and they can be introduced on the Mechanism via gearings, pointers, and scales, taking into account the existing holes and the mechanical remains of the b1 gear and the b1 Cover Disc.

3.2.2. First Necessary (Not Preserved) Measurement Process

The Front Central Face of the Mechanism (along with the two Parapegma plates [18] is dedicated to the solar tropical year: the Ecliptic sky–Zodiac month ring (Fragment C), in which the Golden Sphere–Sun and its pointer travel around the ring of the Zodiac constellations [22]. One full turn of the solar pointer (ΗΛΙΟΥ ΑΚΤΙΝ/Sun-ray) corresponds to one solar tropical year. The 19 solar tropical years of one Metonic cycle are equal to 19 full rotations of the Golden Sphere–Sun.

On the Back Plate of the Mechanism, the Metonic spiral consists of 235 cells/synodic months of the Metonic cycle. Each of the 19 unequal Metonic years is a repeated set of 13 or 12 months as Geminus mentions [21,49,50,51]. Therefore, 19 unequal Metonic years correspond to 19 equal solar tropical years; however, a time difference exists between the Υth Metonic year and the corresponding Υth tropical year, which resets at each 19 years.

The position of the Metonic pointer aiming at a specific cell of the Metonic spiral defines the current Metonic year: in the first month/cell (ΦΟΙΝΙΚΑΙΟΣ/Phoinikaios month) of each Metonic year, the ancient craftsman engraved successively the symbols LA, LB, LΓ … LΙΘ (Year 1, 2, 3, … 19), which correspond to the numbered Metonic years [35,52]. The Metonic years are in disharmony to the solar tropical years and each Metonic year precedes the solar tropical by about 3–28 days (i.e., max ≈ 95% of the Zodiac Sign).

When the user operates the Mechanism by turning the input–Lunar Cylinder [36,39], he/she has no information of how many turns the Golden Sphere–Sun has completed (one tropical year equals 13.368 full turns/Sidereal cycles of the Lunar Cylinder). Therefore, while operating the Mechanism, the user either should keep in mind the number of the Golden Sphere full rotations (but losing count on many occasions), keep notes (as the authors did), or he has to halt the operation of the Mechanism, turn it back to check the Metonic pointer position, and see at which Metonic month/cell of the spiral the pointer aims. Then he must find the first month Phoinikaios by following the order of months in reverse direction and read the engraved symbol L(+letter number). Afterwards, the user looks again on the front and continues the operation of the Mechanism.

It is imperative for the Antikythera Mechanism’s user to know at any time, very fast and without any interruption, the number of turns completed by the Golden Sphere–Sun (i.e., how many tropical years passed after the initial starting date [24]. This procedure must be located at the Front Central Face of the Mechanism.

A measurement of the tropical solar years via a pointer and calibrated dial, counting the number of turns of the Golden Sphere–Sun around the Ecliptic, is missing from the Antikythera Mechanism Front Plate (as the Front Plate is dedicated to the solar tropical year). The 19-solar-tropical-year gearing can be fitted on the b1 gear, the Thin Sheet Strip-II and the Cover Disc.

The gearing must satisfy the condition for a full rotation of the b1 gear, the pointer rotates 1/19 of a turn on its dial.

Three pairs of gears must satisfy the ratios of the equation:

(1/2.5) × (1/2) × (5/19) = (1/19) or (1/2) × (1/3) × (6/19) = 1/19 or (1/2.5) × (1/2.8) × (7/19) = (1/19) or
(1/2.5) × (1/2.4) × (6/19) = (1/19)

(1)

(adopted in this work); see

Table 4. The teeth number of the six suggested gears (I–VI) for the 19-solar-tropical-year gearing.

The 19-Solar-Tropical-Year Gearing on the b1 Gear
Numbered gear (I–VI) and their teeth number	I: 24 teeth	III: 20	V: 18	=1/19
	II: 60 teeth	IV: 48	VI: 57
Ratio	1/2.5	1/2.4	6/19

.

The 19-solar-tropical-year scale is divided in 19 equal numbered sectors (Α, Β, Γ, …., ΙΘ) and it is engraved on the b1 Cover Disc, as shown in Figure 15.

3.2.3. Second Necessary (Not Preserved) Measurement Process

The solar tropical year lasts 365.25 days. The ancient craftsman divided the Zodiac ring into 365.25 subdivisions or more likely rounded to 365.0 [22]. The Egyptian calendar of 365.00 days is represented on the Mechanism by the Egyptian calendar ring divided into 365 subdivisions. Both rings are free to rotate [22]. Additionally, beneath the Egyptian calendar ring, he constructed a third ring with 365 holes of ≈0.8 mm diameter, in circular distribution. It is thus evident that the ancient craftsman wanted his sophisticated Mechanism to be very accurate and so he paid special attention to the Egyptian calendar measuring procedure.

For every four rotations of the Golden Sphere–Sun, the user must rotate the Egyptian ring by one subdivision CCW. In this way the Egyptian calendar precedes by one day every four tropical years.

During the use of our functional models, very often we forgot to rotate the Egyptian calendar ring CCW after four rotations of the Golden Sphere, or after losing count of the Golden Sphere rotations we were not sure if it was time to rotate the Egyptian calendar ring.

This problem was more pronounced if the Mechanism was not used for some days; it was nearly impossible to remember if the ring had been already turned or not. Before restarting the measuring procedure, we tried to calculate the Golden Sphere rotations, and measure the number of subdivisions on the Egyptian ring from the fiducial line mark [24], i.e., from the initial calibration date. Then we rotated (or not) the ring to its proper position, but having a doubt if it was the correct position.

We also tried to correct any counting error either by using small yellow sticky note pads or operating the Mechanism in pairs: one was “the Operator” and the other “the Observer/Counter” for the Golden Sphere rotation and the Egyptian ring rotation.

It is evident from the above that this is not a correct, regular, and continuous operational procedure for the Antikythera Mechanism.

Therefore, a pointer with a dial alerting the user when it is necessary to rotate the Egyptian calendar ring by one subdivision CCW is mandatory. The Egyptian-year-reminder scale can be engraved on the b1 Cover Disc, divided in four quadrants corresponding to the four tropical years, Figure 16.

The gearing should satisfy the ratios of the equation (1/2) × (1/2) = (1/4) or (1/2.5) × (1/1.6) = (1/4) (adopted in this work for reasons of gearing uniformity with the previous necessary procedure, see Equation (1)), so that the pointer rotates by one turn every four years; see

Table 5. The teeth number of the four suggested gears (VII–X) for the Egyptian-year-reminder gearing.

The Egyptian-Year-Reminder Gearing on the b1 Gear
Numbered gear (VII–X) and their teeth number	VII: 24 teeth	IX: 30	=1/4
	VIII: 60 teeth	X: 48
Ratio	1/2.5	1/1.6

. When the pointer of this dial aims to the letter Δ (4), the user should rotate the Egyptian calendar ring by one day/subdivision.

4. Discussion

The hypothetical/suggested planet gearing indication on the Antikythera Mechanism requires the use of an extremely large number of hypothetical/non-preserved mechanical parts (about 60+): gears, axles, shafts, plates, bars, spacers, small and large diameter discs, bearing bases, tubes, large diameter rings, pointers, spheres, side supports, etc.

The adaptation of these hypothetical parts definitely increases to a large degree the static friction and the kinetic friction, the weight and the (irregular) center of gravity of this system, and the inertia. These hypothetical parts, apart from being too heavy to hold (about 1.5–2kg), are difficult to assemble, have increased inertia, are of doubtful functionality, and introduce mechanical problems and non-seamless motion. Of course, if modern design parts, like screws, specially designed gears, and other special materials are used for their reconstruction, then they can be functional (see below).

Some of the suggested/hypothetical parts are not in accordance to the Personal Constructional Characteristics of the ancient craftsman.

Moreover, there is no clear reference about planets, their spheres, and pointers in the Instruction Manual of the Mechanism.

The use of the modern mechanical assembly parts, such as screws and grub screws, nuts for the parts’ stabilization (instead of perpendicular pins that as are used by the ancient craftsman), polished iron/steel axes (instead of bronze), special alloys’ gear material (that are much harder than the typical bronze), thicker gears (the max thickness of the gears is ≈2.5 mm) or differently designed gears (the gear design is a simple disc plate, not a gear with a hub), and the modern involute tooth shape (instead of triangular tooth shape as with the original gears), improves the Mechanism’s models functionality. However, all these deviations constitute an unacceptable and incorrect practice for the Antikythera Mechanism’s research, because they change dramatically the mechanical status of the system, leading to different mechanical behaviors of the device than the original prototype, and leading to different and incorrect conclusions.

One of the most characteristic examples of a mechanical status change after adapting different parts is the almost fatal airplane disaster after the use of wrong-sized bolts (2.5 mm shorter than the proper size!) in the pilot’s window https://www.newscientist.com/article/mg13418180-300-wrong-bolts-sent-pilot-into-the-blue/ [53] (accessed on 1 February 2026).

Using 3D simulations can also be a helpful research tool for the study of the Mechanism, but it cannot substitute for a physical model. The 3D representations present an ideal and sterilized condition and mechanical behavior, without friction, inertia, constructional mismatches on the gears, periodic errors, non-perfect transmission of motion, etc.

Many times we use simple and straightforward ideas to design something based on thought, but as the “The devil is in the details”, real-world designs often display very different behaviors than the desired behavior.

An accepted—research grade—reconstruction model of the Antikythera Mechanism must be strictly constructed according to

Table 6. Protocol of Mandatory Parameters for a Research Grade Bronze reconstruction of the Antikythera Mechanism (revised from [22]).

Protocol of Mandatory Parameters for a Research Grade Bronze Reconstruction of Antikythera Mechanism
1	CT Scans and Photographic Documentation: The reconstruction must be based on detailed CT scans and visual photographs of the fragments.
2	Preservation of Dimensions and Positioning: The preserved parts must not undergo any arbitrary/unjustified changes in dimension or position. The symmetry of the design should be introduced, considering the deformation and displacement of some of the parts in the original artifact.
3	No Arbitrary Alterations/Modifications: No holes should be made where they do not exist in the original prototype.
4	Hypothetical Additions: Hypothetical components cannot be introduced in places where no clear indication of a missing part exists in the original artifact.
5	Respect for the Ancient Craftsman’s Techniques: The reconstruction should preserve the Personal Constructional Characteristics of the ancient craftsman (analyzed and presented in this work)
6	No Use of Modern Mechanical Parts: Modern components such as screws, bolts, grub screws, or other mechanical fasteners or bearings must not be used in the reconstruction.
7	Gear Thickness, Design and Stabilization: The gears should have a uniform thickness of approximately 2–2.5 mm, without any central thickening (hub). The gears should be secured to their shafts using a perpendicular pin.
8	Gear Teeth Shape: The teeth of the gears must be triangular in shape, similar to the original, not following the modern involute design used in contemporary gear systems.
9	Material Specifications: All gears, shafts, and axles should be made from a simple bronze alloy (bronze gears, bronze shafts, and bronze axles), rather than special alloys, steel, or other ferrous materials.
10	Minimal Hypothetical Additions: The addition of hypothetical components should be kept to a minimum, ensuring that the reconstruction remains as close to the original as possible.
Scientific Methodology
I	Hypothetical Considerations: Any hypothetical considerations (e.g., units of a lost scale) must be accepted only after their consequences, impacts, and functionality are tested directly. These should be validated through the construction and use of a Research Grade functional model.
II	Experimental Validation: Any proposed hypothetical function of the Antikythera Mechanism must be supported by experimental evidence or a functional bronze reconstruction. Theoretical speculation alone is insufficient.
III	Experimental Disagreement: If a hypothesis contradicts experimental results, it must be considered incorrect.
IV	Theoretical Approaches: Theories that have not been experimentally validated cannot be accepted as definitive and they cannot be used to reject hypotheses that are backed by experimental evidence.
V	Measurement Precision: It is strongly recommended to use traditional simple measuring tools, such as a compass and ruler, rather than relying on modern electronic digital display calipers.
Note: Any deviation from the aforementioned parameters can significantly alter the mechanical status of the system/Antikythera Mechanism, potentially leading to the following: - Changes in mechanical behavior, - Different results and conclusions, and ultimately - Flawed interpretations.

.

5. Conclusions

In this work we analyzed and presented a probable reconstruction of the mechanical remains located on the b1 gear and the b1 Cover Disc of the Antikythera Mechanism. The mechanical remains can be related to the two missing but necessary procedures of the Mechanism, in order to be considered as a complete and independent time-measuring device. The two procedures we suggest, the 19-solar-tropicalyear Dial and the Egyptian-year-reminder Dial are closely related to the solar tropical year, which is presented by the ancient craftsman on the Front Central area of his creation. According to our experiments and following the use of our models and the problems in the measurements that arose, these two suggested procedures are necessary for the orderly/non-stop operation of the Antikythera Mechanism, as shown in Figure 17.

The existence of the mechanical remains on the b1 gear is not a proof for the hypothetical planet indication gearing and is not the only available suggestion.

The experience we had during the study of the fragments and their CT scans, the design, the construction, and the extended use of our Antikythera Mechanism functional models has revealed the characteristics of this remarkable machine, the possible problems faced by the ancient craftsman during the parts’ construction and assembly, and the mechanical limits of this geared system. These limits have an impact on the calculations made by the gears [45].

As many parts and information are missing from this device, the safest way to learn more about the additional procedures of the Mechanism would be to find additional lost fragments.

Someone may think that the Antikythera Mechanism seems incomplete or that it lacks completeness without the planets and by only presenting the Sun and the Moon on its central front face. The answer is presented in Figure 18: many clocks in southwestern Europe (also in the volvelles of the Medieval era [54,55]) present on their face the Sun and the Moon, without planets and they bear a striking resemblance to the Mechanism’s design, which has resulted from the research presented in this paper.

After a very long time spent in designing, constructing, assembling, handling, testing, studying, and interacting with our functional reconstruction models of the Antikythera Mechanism, our experience, and the new observations of the present work, we can conclude that the Antikythera Mechanism was a mechanical geared calculator for calendrical/astronomical/time-measuring procedures, based on the relative timed positions of the Moon and the Sun, constructed around 180 BC; and it must have been constructed for use by an authority for the management of time in that era. The integrated mechanical scheme of the Antikythera Mechanism is presented in Figure 19.