Dr.-Ing. Th. SARTOROS

 

Where does a Diopfantine equation with 2 unknowns come from and what does it express?

 

 

In this text the question is addressed to everyone (Greeks and foreigners)

to explain to me, why the ancient Greek mathematicians studied so intensely

to find a method for calculating the greatest common divisor (GCD).

 

Of course, there was already the practical necessity and not just the theoretical question.

But the connection with practice was not clear from our Ancient Ancestors revealed.

 

What was the practical necessity for the theoretical solution of the problem?

 

Many modern Greek mathematicians (even university lecturers) repeat

what foreign authors have written and pride themselves on the authenticity

of their publications. Sore!!

 

When looking at the bibliography of hundreds of foreign authors on subjects

"Archaeological excavations", I note again and again, the heartfelt commitment

of Time and money for the localization of old and destroyed (buried)

Architectures, but nowhere can I find an image or an explanation

 

   Where does the Diophantine equation with two unknowns come from

     and what does it express?

 Which was the practical need for solving the linear equations with two Unknowns?

 

Concretely:

 

After solving the following Diophantine equation with the

         two unknowns X and Y, explain what it expresses.

 

                                           45 x + 51 y = 600

 

The solution is: X = 2 and Y = 10

 

After inserting the solution values in the equation and after simplifying

(Division of all terms by 3) we find:

 

                                  15 * 2 + 17 * 10 = 200

 

The above equation can be rewritten as      2/17 + 10/15 = 40/51

 

What does the result   40/51   express?

 

Who thinks they have found the correct answer to the above two questions

should please write me his solution briefly.

 

In my unpublished book entitled "The Hidden Mathematical and Technological

Treasure of the Ancient Greeks in the Antikythera Mechanism"

the solution is revealed.

 

What is proposed (by Greeks or foreigners) and the practical necessity of ancient Greeks

concern, shall be published under the name of the sender in the book above.

 

So, I wait with interest.

 

Dr. Theodor A. Sartoros

1. Designation:
                                   Antikythera Mechanism with Planetarium, Calendar
                        and driven by hydraulic or electric power Clock

 

                                             2. Object of the Invention.

 

The production of a functioning device in order to faithfully simulate all display indications of the Antikythera Mechanism, as rotation of the celestial globe, Astronomical time, Synodic and Sidereal months, lunar phases, solar and lunar eclipses, Saros cycle, Metonic Calendar with 235 Months of the 19 years cycle, Old Egyptian Calendar of 365 days, position of the Sun in the Zodiac.

 

                                3. Introduction: Actual level of the technique

 

The fragments of a Mechanism recovered in 1902 from a shipwreck at a depth of about 42 m. near the Greek island of Antikythera, in the Aegean Sea, south of the Peloponnese, showing some gears, since then known as the Antikythera Mechanism, proved to be more complicated and are still the subject of extensive studies and publications by several amateurs and scientists; here some Names: Svoronos, Stais, Rediadis, Theophanidis, Rehm, Price, Karakalos, Bromley, Wright, Tatjana van Vark and a team of scientists from the Universities of Athens and Thessaloniki (GR) and Cardiff (UK), (Freeth, Jones, Steele, Bitzakis, Seiradakis, Zafeiropoulou, Mangou, Moussas, Athanasiou, Edmunds, and others under the auspices of the Ar-cheological Museum of Athens (abbreviated: AMA), with the help of high specialized, internationally named Companies, as HP (with Mr. Malzbender and others) and X-Raytec (with Mr. Handland) dealing since 2006 with the enigmatic ruins furnished 3D Photos of previously 2160 letters from the PARAPIGMA (= Instructions) and about precisely identifiable fractions of gears with triangular teeth. There are read some astronomical and geographical terms imprinted on the fragments as complete words for example, ΕΓΛΕΙΠΤΙΚΗΣ, ΝΕΜΕΑ, ΙΣΘΜΙΑ, ΟΛYΜΠΙΑ, ΕΛΙΚΙ, ΑΡΗΣ, ΑΦΡΟΔΙΤΗ, ΓΝΩΜΩΝ, ΑΕΤΟΣ, ΛΥΡΑ, ΥΑΔΕΣ, ΠΛΕΙΑΔΕΣ, ΤΑΥΡΟΣ, ΔΙΔΥΜΟΙ, ΑΡΚΤΟΥΡΟΣ (ecliptic, Nemea, Isthmia, Olympia, Eagle, Lyra/Leier, Hiades, Pleiades, Taurus, Gemini, Arctur).

 

Theophanidis was the first man, who recognized (1934) the five (5) grooves of the upper half of the back side of Mechanism, where the pins supported two pointers, and also the four (4) grooves in the lower half of the back side of the fragments. On the front side Theophanidis recognized the names of months of the old Egyptian Calendar, which later (1974) Price confirmed.
He read the names (in Greek letters) of two (2) Zodiacs in a quarter of a annular disk with angle-indication of a goniometer in a another fragment.

 

Price stated (1974) the grooves as the furrows separating five (5) rotating circular disks on the upper half of the back side, and as furrows between four (4) rotating circular disks in the lower half of the backside; but his conjecture has proved later (2006) to be incorrect.

 

Price (with the help of the watchmaker John Gleave) presented in 1974 as first a model of the Antikythera Mechanism on the basis of his conjecture ( with the circular rings in the backside etc) and with reference to the number of teeth, determined on the basis of radiographs of the Greek nuclear physicist Karakalos, which sometimes willfully refused, in order to become a satisfying result.

 

The thus presented model showed a hand crank operated mechanism with a planetary gear. Unfortunately the teeth numbers used by Price led to confusion and complicated the identification of a correct solution. The model of Price showed and included more astronomical and design problems than ever solved and thus incited the researcher for further intensive investigations.

There followed the models of Bromley (1986-1991); M. Wright (2002-2008), Tatjana van Vark (2007), Edmunds (2008).These have repealed no significant deficiencies in the Price model but changed numbers of teeth and design of planetary gear and take off thus leaving more of the functions of the mechanism, so they are here little taken into account, especially since modelers took over the shares subscripted by Price crank drive as motion input, or the input of the drive in planet carrier of the planetary gear offset, which led to misleading results; However, the function of the hand crank ist quite another.

 

In 2008 M. Wright realized that the grooves at the back were actually spiral- shaped curves and not circles. In 2008 the team of the AMA confirmed that the grooves were spiral in both upper and in the lower half of the backside and identified the name of few months of the Corinthian-Calendar in the upper half of the backside, which caused a sensation regarding the origin of the device.

 

The team of the AMA completed and published (2008) the upper half of the back-side of the mechanism with the calendar of the 19 years cycle of the Greek astron-omer Meton, introduced in whole Greece at 432 and valid until 46 before our Time (B.o.T.) and explained the lower half of the backside as "display for eclipse pre-diction". However it has not explained how the mechanism works.

 

Despite the partial success of the above mentioned Researchers achieved in de-coding the CT-pictures, there are has been no models either as drawing or as functioning equipment, which the functions of the mysterious Antikythera mechanism fully explain.

 

There are neither the number of gears nor the number of teeth of each gear, given by the model builders.

 

There is a table with the number of teeth of the gears so far identified from four (4) principal researchers: Karakalos, Price, Wright, team of the AMA, which apart drift and often due to the different internal flow patterns of the drive chains and of the planetary gear are very inconsistent.

 

For some gear wheels in order to achieve a better result " possible teeth Numbers" was indicated a wide range of 2 to 6 teeth and often used in different kinematic chains.

 

Which drive-chains and where was the entrance into the device, and what function full filed each gear has so far remained unclear. Each modeler was trying to achieve empirically a plausible (astronomical interpreted) result using random teeth numbers. In the inventive device are exactly indicated both i.e. the numbers of teeth of each gear with the obtained results, their position in the flow schemata and the function of each gear-chain.

 

Among the Researcher, there is also disagreement about whether the Antikythera Mechanism ever a planetary gear was included, and of what type it might be, and with how many (4 or 5) gears, and with which number of teeth
was manufactured each gear.

 

There are researchers (Wright, Freeth, Edmunds) which in their publications, both versions (i.e. with and without of planetary gears) represented. In the models or drawing (see M. Wright) one sees pointers for 7 Planets at the front of the device, and in a later model (of M. Wright) are the hands of only two Planets (Sun, Moon) on the front side attached and visible. But none of them corresponds to the func-tions of the original Antikythera Mechanism.

 

The graphic representation of the research team of the AMA (published in journal NATURE, 2006) indeed provides a planetary gear with 4 wheels inside the mecha-nism, however, show the formula of the modern theory of planetary gear of the local inventor a useless result and indicate a nonsensical construction, which is unconceivable for the old Greek designers of the Antikythera Mechanism.

 

It has been found common ground that it is a Greek device with advanced technol-ogy, and that the rescued fragments were part of a more sophisticated and complex mechanism, which executed several operations, therefore, by some researchers called as "the oldest rack-computer in the world". Some other named the mecha-nism as "analog computer". Price calls it "a calendar computer from 80 b.C.; other (Theophanidis, Kritzas) dated the fragments from the time of 120 – 140 B.o.T Publi-cations in the Newspapers and magazines (such NATURE, Der Spiegel, GEO, P.M. and others) focus on the difficulties of the scientists to decipher the mechanism.

 

4. Description of the two sides of the model according to the invention

                          of the mechanism of Antikythera.
               The device according to the invention has the dimensions: 167*306*125 mm (W * H * D)

 

                                               4.1.1 Description of the front side (Fig. 1)

 

An observer who is facing the front of the device, see the following (on the front):

A clock is located at the upper right corner (which at the time of construction of the original mechanism, was driven by hydraulic power, as a watermeter) with indication of the 24-ISIMERIA-hours (just like today´s hours in modern clocks) with a day-hand.

 

ISIMERIA-hours are mentioned by Homer, and Pytheas (330 B.o.T.) described the daily-length also in ISIMERIA-hours for the places situated at the 66o degree north latitude near the mysterious island THULI. So the day-hand took place exactly a clockwise rotation in 24 hours.

 

The Babylonian had divided the circle in 360o degrees and the round trip time of day and night in 24 hours and it had been taken over by the Greek astronomers and ap-plied in the Antikythera Mechanism.

 

The Water Clocks of Ktisibios (Ktesibius, contemporary of Archimedes) were with gears been equipped and described 200 years later by Vitruvius, with great admira-tion for the precision. Here the Clock is powered by electrical energy from a battery.

 

In addition to the clock with Isimeria-hours, in the middle of the upper half of the front
there is a small window, where appears the image of a god or a planet (ΚΡΟΝΟΣ, ΗΛΙΟΣ, ΣΕΛΗΝΗ, ΑΡΗΣ, ΕΡΜΗΣ, ΔΙΑΣ, ΑΦΡΟΔΙΤΗ), i.e. was then alternately see-ing Saturn, Sun, Moon, Mars, Mercury, Zeus, Venus, valid for Saturday, Sunday, Monday, Tuesday, Wednesday, Thursday, and Friday) the same law as the names of the 7 days of the week. Thus, the rotating disc behind the pane took exactly 1 turn in 7 days. The pulley for the days of the week got its rotation from the Clock i.e. from the gear of the day-hand of the clock.

 

The Anaphoric clock was located at the upper left corner of the front side with the Gnomon (it is not further described herein, because it makes no part of the invention).

 

In the middle of the front side (Center B) four (4) concentric discs/rings can be seen.

 

From the inside to the outside of the regarded surface with center B, the observer sees follows:

 

The innermost concentric annular disc HG is rotatable about its center and represents the picture of the sky with stars, visible in a area of 36o (Lindos, Rhodos)- 37o Syracusa, 38o Athens/Corinth, North Latitude. From the north half of sky are listed in Parapigma the stars (Arctur, Eagle, Hiades, and Pleiades etc).

 

The left-handed figure HG of the sky rotates around the Polar star (Stella Polaris) and makes one revolution in 53 hours, 56 minutes, and 3,46 seconds and simulate the astronomical 365,24667 days of the tropical year, i.e. represents the revolution of the celestial globe with the fixed stars, according to the Pythagorean astronomy, which is also accepted from Ipparchos (Hipparchus).

Since the 6th century B.o.T. (=before our Time) had the Greek astronomers found that the sky with the fixed stars rotates around the Pole-Star.

 

This had been embodied in the Antikythera Mechanism. This has also been imple-mented faithfully in the invented device, according with the known fragments. The fact that the inner disk, HG, with the picture of the sky rotates in less than 24 hours and is driven by gear train, shall further be explained bellow, forming a patentable detail.

 

This is followed by a fixed annular disc, ZK, whereupon the Greek names of the 12 zodiac signs are engraved. Slightly recessed from the surface in a circle in the fixed plate, FP, 365 small holes are created where a pin with the simulated image of the Sun, SS, plugged in and however added daily at a little hole anti-clockwise by hand.

Why must the sun symbol SS in left-handed rotation daily into the 365 holes re-placed, is related with each different duration of the astronomical (sidereal) and the tropical year and was well known to the Greek Astronomers since the time of Pythagoras (595 -511 B.o.T.). Pythagoras had declared that the sun in comparison to the fixed stars rotates backwards and Plato (420 B.o.T.) required by the astronomers „ΣΩΖΕΙΝ ΤΑ ΦΑΙΝΟΜΕΝΑ", i.e. in all models of the astronomical phenomena must exactly as they are seen also shown and explained.

 

The next, on a circle gap for the 365 holes of the sun symbol SS, rotating at right-rotating direction a concentric annulus, JR, (ÄK) with engraved names of the 12 Egyptian months (in force of that time, about 120 years B.o.T.) with 365 equal-length small-arcs, and with radial small strokes marked subdivisions, for the 365–day Egyptian specific calendar. The Egyptian calendar had 360 days and a further 5 days, known as "Epagomenen" for a total of 365 days. The number of arcs (365) thus corresponds to the calendar days.

 

On a line on the fixed plate, FP, just above the Meridians (vertical axis of the concen-tric rings) the user could see and read the Egyptian month and day in which he lived. The Egyptian Calendar was much simpler than the ancient Greek astronomer Meton´s calendar (named after the Athenian Astronomer Meton, lived about 480 – 410 B.o.T.) with the 19 years cycle, and the 6940 days in 235 (synodic) months.

 

The Annulus JR (ÄK) makes one (1) revolution in 365,24667 days (deviation less than 0,56´´/year) according to the known data of the Greek Astronomer Ipparchos (lived about 195 – 125 B.o.T.). Note that the Number 365,24667 here is rounded up.

 

This ring JR (ÄK) simulated also the right-handed circular rotation of the Planet "Sun" according to the geocentric System and became the movement from the Clock with the ISIMERIA-hours; the corresponding kinematic gear train shall be bellow explained.

It is to be noted that the periodic orbital of 365,24667 days of the Sun around the Earth is known as the period of a lost clock made by Ipparchos. The kinematic gear chain for the movement of the Sun is starting by the Clock (day-hand) with the Isimeria-hours and includes till the central wheel B1 totally 8 gears.

The prerequisite for the precision of all followed movements is the accuracy that the central Gear B1 for the simulation of the celestial body makes one rotation in 365.24667 days in the tropic year.

 

From the Clock with the Isimeria-hours and from the following 7 wheels nothing has been saved. Only the last wheel B1, named Wheel of the Sun, is available as a complete fragment and seen in all publications.

 

The number of teeth of the big wheel B1 is controversial among researchers.

Here is named as the single correct number of teeth (223) and protected.

 

The Number of teeth of the others 7 gears of the kinematic chain from the pointer to the gear B1 to achieve the simulation of a revolution of the Sun in 365.24667 days will not disclosed here.

 

After the great circle concentric ring JR (ÄK) with the Egyptian calendar follows the fixed plate FP front, enclosing the previously described four (4) concentric rings.

 

Slightly below the large concentric ring with the Egyptian calendar JR (ÄK) and to the fixed plate FP, there is again a window and behind it, turn right a circular disc VK, which simulates the rotation of the Moon and of the 4 Phases of the Moon.

These disc of the Moon takes 13.36842105 revolutions in the above 365.24667 days of the year and simulates the 13.36842105 sidereal (astronomical) months of the year. The eight (8) digits after the decimal point are known as measured values since the 3rd century B.o.T. The values are derived from precisely calculated number of teeth for the gears, which also faithfully fulfill the known axis distances completely.

 

There is no doubt that the ancient Greeks the "13 books of arithmetic" of the ancient Greek mathematician DIOPHANTOS used, in order to calculate the numbers of teeth of gears mechanism; so is obviously the above numerical accuracy.

The kinematic chain with the number of teeth of the gears to simulate the exact lunar months (the sidereal month) will be further explained below.

 

The lower quarter of the front side is used as PARAPIGMA i.e. it includes instructions for the user and explanations about the rising and setting stars with full words engraved on the bronze plate of the front side. This information was very useful to the navigators in middle sea.

 

                              4.2 Description of the rear panel (back side of the device)

                      4.2.1 Description of the upper half of the back side

 

In the upper half of the back of the mechanism, as already said, are the 5 small spiral grooves constructed on the surface of the fixed plate.

Around the center N of the 5 spiral grooves rotates a pointer, supported by a pin which glides into the grooves.
The pointer N (ZN) makes exactly 5 rotation on 19 years.

 

In the upper half of back side are also engraved the 235 divisions around the 5 grooves which correspond to the 235 synodic months in the 19 years of the Greek calendar.

 

The kinematic gear chain for the rotation of the pointer N along the grooves on the upper half started with the gear B2 with the 64 teeth, which is fitted on the shaft of the great Sun wheel B1 with the 223 teeth, so that the Gear B1 which makes one revolution in 365.24667 days drive the pointer N of the Meton´s calendar.

 

In the Meton´s calendar with the 19 years cycle fit much better the time simulation on Earth with the revolution of the Sun- and of Moon-cycles and consequently could start the Olympic games almost the same day of the summer. This calendar is pan-hellenic in July 432 B.o.T. introduced.

 

The number 19 was written with golden color and designated as a golden number. After 19 years the heavenly bodies were almost to the same starting position.

 

Each of the five rings of the spiral 360o is divided into 47 equal length arcs (an-gles) with radial strokes, and in each sheet (sector) on the fixed plate is engraved the Corinthian name of the month of the used Metonic calendar.

 

The Corinthian month names have been discovered only recently with the CT pictures. Altogether 235 Months seen in figures of the 5 spirals of the upper half of the back side; the Number 235 corresponds to the synodic months of the Greek astronomers. So only and exclusively in the upper half of the backside are read the 235 synodic months.

 

In the Metonic calendar of the 19 years cycle, the years and the months were not all of equal length. There were years with 12 months and another year of 13 months; there were also months with 29 days (named hollow or lean) and there were 30-days months (named full or fat). (See Book of the ancient Greek astronomer Geminus "Introduction to the phenomena") this has been realized in the Antikythera mechanism.

 

The pointer discovered by Theophanidis at the upper half of back side with the pin in the separating gap of the spiral grooves has been confirmed be the AMA team.

 

But it was necessary to explain in the Antikythera Mechanism which days were "ΕΞΑΙΡΕΣΙΜΟΙ" i.e. shuld be excluded in the hollow months, so that the month has only 29 days. The designers of the Antikythera Mechanism have engraved in each sheet (sector) under the name of the month, which day was excluded. The discovery of the Word ""ΕΞΑΙΡΕΣΙΜΟΙ" owes to the CT-pictures, shown by the AMA-team in the years 2006-2008.

 

It is to note that the kinematic gear chain for the movement of the pointer N in the Metonic calendar, remained hidden (unrevealed) from the other researchers and that this chain had two functions was overlooked i.e. the second was to point simultaneously (the Olympic games in Olympia, Nemea, Isthmia, Naa)

 

The above mentioned kinematic chain branched and drove a second little pointer Zo in a small circle inside the large circle of the first spiral in the upper half of the back side.

So completes the little pointer Zo, one revolution every four (4) years, because every four years the games took place in Olympia.

 

There is also a further detail indication, by means of a rotating pointer in a small circle, which showed the 4 periods of the Kalippos-calendars; the Kalippos-Calendar yielded a higher accuracy in the simulation and consisted of four periods of the metonic calendar, i.e. it had a cyclic period of 4 * 19 = 76 years

 

                   4.2.2. Description of the lower half of the back side

 

The lower half of the back side with the four (4) spiral grooves or 4 spiral-like rings was used to predict the eclipses (Sun- and Moon-eclipses) according to the Chaldean cycle also called Saros-cycle.

 

The Chaldean (today, Iraq) had established in Niniveh (North Iraq) as a statistical office and registered since 750 B.o.T. for about 250 years long the sun- and moon- eclipses, and fixed (found) that the eclipses repeated after almost 18 years in the almost in the same days. That result had taken over the Greek Astronomers. The 18 years of the Saros cycle contained a total of 223 synodic months.

 

The four spiral rings of the lower half of the back side were therefore divided into 223 equal-length arcs with radial short lines and thus corresponds to the 223 synodic months of the Saros cycle. A few notes from the "PARAPIGMA" and identified in the four spiral rings allow this reconstruction.

 

It was known to the Greek Astronomers, and particularly from the time of Ipparchos that the Sun-Moon-eclipses occur in pairs every 6 months (Sun-eclipces approximately 2,3 times per year, lunar eclipses about 1,5 times per year) namely, solar eclipses at new moon and lunar eclipses at full moon. The designer of the Mechanism engraved for every six months the predicted eclipses in the arcs of the lower half of the Antikythera Mechanism. This can be seen in the CT Photos.

Here is to be noted, that within the central solid disk of the lower half of the back side two pointers can be seen in the pivot points I and G, whose functions and speeds have been detected by others researcher in error. It is also to be noted, that the gear train, which leads to the indicator G and I of the lower half of the back, gets the motion from the smaller gear E3 of the planet carrier of the com-pound planetary gear transmission.

 

The smaller pointer with the center of rotation I, is used to count the 18 years of the Saros cycle, that is, the smaller hand makes one revolution per year, and thus shows the orbital time period of each of 12.36842105 synodic months, but the larger pointer with pivot of rotation G, takes four (4) revolutions in 18 years.

It has been taken in consideration by the designers of the particular direction of rotation of the pointer and of the axis distances i.e. for the observer the back side, end all kinematic gear chains with a clockwise motion.

 

    5. Description of the inner gear chains of the Antikythera Mechanism (Fig. 2)

 

5.1 Gear chain to simulate the annual revolution of the Sun in 365,24667 days                          and the old Egyptian  calendar of 365 days/year.

 

The first gear train begins as already mentioned with a gear fitted on the shaft of the day-hand ) of the clock with the ISIMERIA –hours and from there with further gear pairs transmits the rotational movement to the central great Sun wheel B1 with the 223 teeth.

 

It is absolutely essential that the central wheel B1, has 223 teeth and through the over transmission chain, the wheel B1 executes exactly a revolution in 365.24667 days.

This is in the invented device achieved with four pairs of toothed wheels (8 toothed wheels including the wheel B1).

 

The central wheel B1 with the 223 teeth is the heart of the simulation of the solar movement or of the tropical year with the 365.24667 days (The word "year" is al-ways to be understood as "Tropical year"). This expressed in astronomical values (1 (one) turn in 365.24667 days); is only with the above mentioned number of 223 teeth to realize and have been used in the invented device.

 

Above the wheel B1 is a twin wheel B1a with the same number of teeth (223) and the same tooth module. Both wheels B1 and B1a with the 223 teeth are parallel superposed and interlocked with the gear crown showed A.

 

The twin wheel B1a and the gear crown A are required because the direction of the rotation of B1 is defined as clockwise (positive) for the observer standing at the back side, while for the observer standing in front of the front side is negative (i.e. anticlockwise). By means of the crown gear A, changes the direction of rotation of twin wheel B1a, and so the observer of the front side sees a clockwise rotation for the ring JR which carries the names of the 12 months of the Egyptian calendars with the 365 divisions (days). This Egyptian calendar ring has now (for the observer standing at the front of device) a clockwise rotation and makes exactly 1 revolution in 365.24667 days, as the great wheel of the sun, B1.

 

The crown gear is disconnectable in the device, according to the invention with an on/out hand crank AK. The hand crank AK is used to transfer the gears and the pointers back to the start position after the pointers has arrived the end of the grooves or in cases of repair of the device.

 

The hand crank AK does not serve therefore as constant drive and this is a serious error of the nearly all researchers.

The number of teeth of crown gears A does not matter, because the crown gear serves only to change the direction of rotation of the connected parts.

The number of teeth can be arbitrarily fixed (between 48-54) and respects only conditions for better mesh (engage) of the wheels B1 and B1a.

 

      5.2 The kinematic gear-chains of the compound Epicyclic transmission set

 

The biggest surprise in the Antikythera Mechanism is the "compound Epicyclic transmission set", where the integrated simple planetary gear consisted of 5 gears with 3 rotating spindles and has a speed-ratio of io = -1.

 

Not only the complicated definition, but also the design of a such composite Epicyclic transmission prepares to the specialized engineers many difficulties, therefore such transmissions are always avoided.

 

It is evident that the laws of design and of function of the "compound Epicyclic transmission" has been well known to the ancient Greeks and they used the properties of this unique and difficult construction in the Antikythera Mechanism.

 

The compound planetary transmission set of the Antikythera Mechanism had the duty to "calculate the half of the number of the synodic months of the year"

 

The ancient Greek astronomers and engineers knew that the composite Epicyclic transmission, as above shortly defined, was the unique mechanism in the world, capable to make algebraic operations (Addition and Division) and they took advantage of this property with virtuosity.

 

The compound Epicyclic transmission executes the algebraic addition of the in-coming two different rotations, i.e. the transmission took account of the direction of the rotation, and when both positive (also both clockwise direction) does the addition, but when the two introduced rotations have different directions (one clockwise and the other anticlockwise) then does the subtraction and the result lead out with the shaft of the planet carrier.

 

It should be noted, that none Patent application is till known, with a compound Epicyclic transmission, which has integrated one simple planet gear set with 3 rotatable shafts, with 5 toothed wheels and with speed-ratio io = -1.

The construction of the ancient Greeks is till today a world unique device.

 

The planet gear systems has appeared in the time of Archimedes and Ktisibios (Ktesibius), to this why the Mechanism of Antikythera with the complicated Compound Epicyclic transmission is probably of a newer Date, also after Archimedes.
The graphologists confirm that the handwriting is coming from 2d century B.o.T.

 

                               5.2.1 Short description of the compound Epicyclic transmission set
                                                   and explanation of the operation

 

To show the error of thought of the other researchers, which go out from a simple Differential planetary set as used in the rear axis of automobiles and the existing, are many technical explanations required, in order to better understand the invention.

In a differential planetary gear, like the one used in the rear axis of automobiles, the planet carrier is driven i.e. it introduces the power. This evenly distributes the power in the two axle halves. The wheels of the two axle halves rotate with the same (identical) speed when the automobile traveling on strait way. Shuts down the car a curve, then the wheels turns slower with the smaller radius of curvature and the externally situated wheels with the greater radius of curvature turns faster.

Thus the differential allows to transfer a part of the incoming power from the smaller turned half axle to the faster turning half axle and to compensate temporarily the different distance which must run the internal and external wheels. However the differential planetary gear as described cannot count.

 

     The differential planetary gear of automobile as described above has no resemblance to the composite  

                  Epicyclic transmission of the invention, which shall be soon explained.

 

Each gear (pair) transmission is symbolized by a circle and three radial lines for the three shafts shown. One for the power input, the second for the power output and the third coincides with the stationary housing of the (gear pair) transmission.

In order to make a planetary gear transmission, from the above gear pair transmis-sion, the third shaft must be made rotatable i.e. the housing is no more stationary and must rotate to; so the initial pair of gears mutate in planet wheels.
The third shaft carries now the planet wheels now called sun-wheels, which (are fitted on the so called Carrier of planet wheels and) and each sun wheel is con-nected correspondently one with the input and the other with the output shaft.

In simple industrial applications the shaft of a sun wheel is fixed, the other sun-wheel is used for power incoming and the shaft of the carrier for the power output.

The result is the simple planetary gear with 2 rotating shafts, regardless of the in-ner construction. A planetary gear with 2 rotating shafts cannot count. All power components are determined on the basis of the design features. The above men-tioned rule seems to be known almost to all the others researchers.

 

In a compound Epicyclic transmission set, the motion is starting from a common external shaft (denoted with T), with two internal different lines of kinematic gear chains, i.e. both kinematic gear chains, starts with the same speed of the external shaft T.

 

In each kinematic gear train are mounted one or a plurality of pairs of gears, de-pending on the calculation and design, in order to reduce the rotational speed which shall arrive the end of the line and shall introduced to the sun wheels of the simple planetary gear. It must therefore be connected each end (i.e. introduced the speed of each gear train) with the sun wheels, as in the invention of Antikythera mechanism.

 

In addition the simple planetary gear must have a basic ratio of io = -1.

 

From here on increase the difficulties for amateurs and professionals, because the simple planetary gears, have different properties depending on the model of gear.

The construction must be as in the invention of Antikythera Mechanism, i.e. each internal kinematic chain must be connected with one sun wheel of the simple planetary gear and the simple planetary gear must have a ratio io = -1.

This means that that when fixed the carrier and one sun wheel will be rotated clockwise, the other sun wheel rotates in opposite direction (anticlockwise).

 

A other essential condition is that the simple planetary gear with io=-1, must also have totally 5 toothed wheels all meshed externally. Otherwise is the be-fore mentioned condition (by fixed carrier the one sun wheel turns in one direction and the other sun wheel in opposite direction) not realized.

Herein is nothing to be shaken and nothing to change.

The other researchers were not familiar with the properties of the compound Epicyclic transmission set, therefore, they could not find the correct number of teeth of any gear neither the functions of the modules and made the error to identify the compound Epicyclic transmission set with a simple differential planetary drive of automobiles

 

In the invented device the compound Epicyclic transmission set has integrated the unit with 5 toothed wheels and with ratiospeed io = -1.

 

In a compound Epicyclic transmission set as the Antikythera Mechanism must lead the shaft of carrier the result to the outside. The so subscribed and constructed compound Epicyclic transmission set adds algebraically the incoming two rotations and the result divided by two, leads to the shaft of planet carrier to the outside. The resulting speed can be zero, positive or negative (in accordance with the definition of the direction of rotation).

 

In the apparatus according to the invention, the gears of the two shafts of the sun wheels (of the simple planetary gear with the 3 rotating shafts and the 5 gears) have number of teeth calculated and applied according the laws of compound Epicyclic transmission.

 

Well, on the shaft of the big wheel B1 with the 223 teeth and slightly below this, are two small gears mounted/assembled. The one labeled B2 has 64 teeth and the underlying labeled B3 has 32 teeth. All three gears (B1, B2, B3) are mounted on the same shaft, so they have the same (initial) speed, i.e. they do only one revolution in 365.24667 days. This detail is very important for all pursuit movements.

It must be noted, that the named number of teeth are depending of each other and from the purpose of the structural Installation. It can be changed only the number of teeth of gear B2, if calculations permitted this.

Additional over checking must demonstrate that the change is possible. In this case the designated number of teeth has been established.

 

                  5.2.2 The kinematic gear chain to calculate the 13.36842105

                                       sidereal months per year

 

The first gear train (B2-C1-C2-D1-D2-B4, in the drawings with dense hatch from top left to the bottom right) of the compound Epicyclic transmission set, starts from the wheel B2 and ends to the wheel B4, supplies (with wheel B4) the 13.36842105 rev./year and thus simulate the sidereal months of the year. The wheel B4 is assembled on the end of the hollow shaft of the wheel B2. The shaft of wheel B4 is placed through the shaft of B2 and leads upwards, i.e. in direction front side and ends in the space between the Wheel B1 and the tin wheel B1a.

 

The speed of the wheel B4 is really given by: 1 * 64/38 * 48/24 * 137/32 = 13.36842105 rev./Year and has a negative sign of rotation, that means the B4 has the opposite direction of the wheel B2. The observer standing at the front side sees the rotation of B4 as clockwise (positive) but for the observer standing at the back side sees the rotation of B4 as negative (levorotatory).

 

After a change of the direction of B4 the rotation is introduced in the sun wheel E2i and E2ii of the simple planetary gear system. (constituted of: sun wheels E2i, and E2ii, idler wheel J, planet gears K1 and K2, and E5 sun wheel).

The planet gears K1 and K2 are mounted on a common shaft firmly connected with each other and therefore have the same speed.

The wheel E2i and E2ii are manufactured identically.

 

Some researchers (Freeth and others) have interpreted erroneously a connecting pin that holds the Planet gear wheels K1 and K2 and used the measured eccentriccity between the centers for calculate the anomaly of the moon movements.
The purpose of compound Epicyclic transmission set is so completely removed.

 

A second kinematic gear train (B3-E1-E5, drawn left of the central axis B) starts from the wheel B3 and performs one revolution per year, and is introduced with a negative sign in the shaft of the sun gear wheel E5 of the simple planetary gear system.

 

So in the simple -5wheels-3shafts planetary gears are introduced, according the invention, two speeds with opposite directions. The one with 13.36842105 revolution per year, and the other with only one revolution per year (i.e.by 1 turn in 365.24667 days).

 

The two introduced speeds are algebraically added and the result divided by two is lead from planet carrier to the outside. However the designer of Antikythera Mechanism have not used the shaft of the planet carrier, but the planet carrier itself, using the resulting speed of (+ 13.36842105 – 1) / 2 = + 6.184210525 revolution per year to move the other parts.

The high experience of many centuries is here evident and unmistakable.

 

The gears E3 and E4, manufactured at the periphery of planet carrier turn also with + 6.184210525 rev./year. They transmit this speed to two different gear trains which shall explained in following pages. Here with the gears E3 and E4, ends the compound Epicyclic transmission set.

 

              5.3. The previously identified two speeds (13.36842105

                             and 6.18421055 rev./Y.)
                                              are used at following manner:

 

The speed of 13.36842105 expressing the sidereal months of the year is, as said, for the observer standing at the backside, negative (but is positive for the observer standing at the front side) and is transmitted by a ratio of 1:1 upwards to the front side, and drives clockwise (observed from the front side) the disc V2 at a small window and simulates the 13.36842105 full moon of the tropical year. At the small hub at the window are also the colored four (4) moon phases to observe.

This information was necessary for the Greeks navigators in middle sea, because at new moon took place the sun and moon eclipses and some weather and wind conditions were to be expected.

 

The speed of 6.184210255 is completely transmitted from the gear E4 with the 223 teeth upwards to the front side, with a gear train so that the end speed in-creases to 366.24667 rev./Y. With this speed rotates the central disc HG with the image of the night sky. Here is striking the same direction of rotation of both, of the central disc HG in front side and of the planet carrier, i.e. of the gear E4 of the planet carrier. That means that the image of sky turns anticlockwise with 366.24667 rev./Y. for the observer standing at the front side.

 

The central ring disk HG, bears the image of northern stars sky and simulate both the duration of astronomical (sidereal) year of 366.24667 days, as well as duration of the astronomical day of 23 hours, 56 minutes and 3.46 seconds.

 

The astronomical time of the ancient Greeks has been banned in astronomical clocks in the middle Ages from the Catholic Church, because supposedly would be a divine creation and man was not permitted to sully that.

 

The other (smaller) gear E3 at the periphery of planet carrier has exactly 192 teeth and is not allowed to have different number of teeth. From the toothed wheel E3 starts a another gear train (E3-F1-F2-G1) with the original speed of 6.184210255 and with the help of the used gears teeth is increasing to the double i.e. 12.36842105 and thus results against the number of the synodic months of a year. This is, however, used as intermediate result. Then with the continuous gear train G1-G2-I1 is transmitted to the small hand with pivot point "I" and brings the pointer to make only 1 revolution per year.

 

The construction of the invention, provides the carry back of the one rev./Y. from the axle "I" , by the same axes (I-G), by means a new gear train and transmit it to the big hand pivoted at G at the center of the lower half of back side, so that the pointer G makes four (4) turns in 18 years, and so realize the Saros cycle.

 

It is emphasized that the dimensions of the gears and the axle distances measured in the original fragments, have been applied faithfully in the invented device, and it was found that the accuracy of the axis distances often lies in the range of 1/10 mm.

 

                      6. The gear trains for the pointer of the upper half of the back side

 

It remains to explain two further gear trains for the pointer of the upper half of the back side.

 

The gear train B2-L1-L2-M1-O2-O2-N1 starts with gear B2, which as stated, turns with 1 revolution in 365.24667 days.

 

The striking detail here is that the designers of Antikythera Mechanism equipped the train L1, L2, M1 with gears and suitable number of teeth and diameters so that a rotation of only one revolution results to a point (M) and from there (M) introduced the rotation (of one rev./Y.) in two branched and different gear trains till the pointers of the upper half of back side.

 

This beautiful design solution in conjunction with the compound Epicyclic transmission set and the water clock, reveal a centuries-old tradition with gear mechanism. Unfortunately this solution also the compound Epicyclic transmission set have not recognized from all previous researcher, which adopted many faulty assumptions.

 

The continuing gear train M2-O1-O2-N and the used gears with appropriate number of teeth, allow the clockwise rotation of the large pointer N i.e. ZN at the upper half of back side; the pin which supports the pointer N slides into the spiral-like five (5) small gaps (grooves) of the surface of the Greek calendar of the Metonic-Circle with the 19 years cycle. So the pointer N does in 19 years exactly 5 revolutions. After 19 years the pointer N must be brought back to the start position (by help of the hand crank).

 

The other kinematic gear train which also use the 1 revolution of the shaft M, equipped with the gears M-N-Λ drives the pointer Zo internally of the small circle with name of (Greek) places (ΟΛΥΜΠΙΑ, ΝΕΜΕΑ, ΙΣΘΜΙΑ, ΝΑΑ ,Olympia, Nemea, Isthmia, Naa) where took place the Olympic games. The pointer Zo makes also 1 revolution in four (4) years, because the Olympic games took place every forth year.

 

                                     7. The projection of the Sun on the Zodiac circle and
                   the interpretation of the 365 small holes for the Sun symbol

 

Finally remains to explain the purpose and function of the 365 small holes for the pin with the Image of the Sun Ss and the levorotary daily displacement in the gap, between the clockwise rotating ring disk with the names of the 12 Egyptian months and the fix ring disk with the names of the 12 constellations (Zodiac signs).

 

The Greek astronomers had observed and measured that the celestial globe exe-cute one complete revolution in less than 24 hours (that is 23 hours, 56 minutes and 3.46 seconds).

The difference (3 Min, 56.54 seconds) make exactly one day per year.

This additional day needed the sun to return to the initial position.

In addition, they observed and measured that the Sun compared to the same fixed stars was somewhat retarded in daily movement. The slower rotation of the Sun interpreted Greek astronomers as rearward rotation movement of the sun in comparison to the Constellations of the Zodiak circle.

 

The everyday situation of the sun was so projected and (the user) knew in which star sign the Sun was.

 

For the designers of the Antikythera Mechanism, it was therefore necessary to in-form the user of the device, according to the astronomical theory, in which Zodiac the Sun was. The 12 Zodiak signs were engraved to the fixed disk.

 

They have solved the Problem very elegantly; they produced 365 small holes for the pin with the image of the Sun, in a slightly recessed and fixed plate, and left it to the User to turn the pin daily and put it into the next left hole. Thus passed the pin with the image of the sun (current daily from one hole to the next) all zodiac signs in a year and arrived after 365 tropical days the initial position, just as the celestial body.

 

It was a mistake of the previous researchers to assume that the number of the holes were 366. Thus, the sun would be after 30 years retarded of a constellation width projected to the fixed stars. Known, that the fragments of Antikythera Mech-anism also a Kalippos-calendar revealed, that means that the device was de-signed for 76 years; After 76 years the solar image of the pin would be nearly 2,5 width (approximately 76o) retarded in comparison to the true position in the sky. That would be a gross mistake of the Engineers of the profession "S P H Ä R O P O I I A = Celestial Globe Builder) which, given the precision and know-how, which the fragments of the device emits, is not conceivable.

 

Finally, it should be noted, that the ancient Greek designers of the Antikythera Mechanism selected the distance between the center point (pivot) B (for the wheels B1, B1a, B2, B3, B4, B6) and the center point (pivot) E for the rotating shafts (E1, E2i, E2ii, E5) in that manner, that this corresponds to the distance between the Polar star and the Pole of the Ekleiptik, when the celestial sphere and the circle of the Ekleiptik shall be projected stereographic from the south sky pole on the celestial Equator.

 

The stereographic projection of the celestial globe and of the Ekleiptik on the celestial Equator was an invention of Ipparchos. The graphic design of Antikythera Mechanism complies with the invention of the Greek astronomer Ipparchos and these have been used in the device according to the invention.

 

                                                        Abridgement/Resumé

 

With the invented device, driven by a clock with hydraulic or electrical or mechani-cal energy, became for the first time possible to show all the adds and functions hidden in the Fragment of Antikythera Mechanism, and simulate on the front side some of them:

1a The annual revolution of the sun in exactly 365.24667 days according to the teaching of the ancient Greeks astronomy of the 2d century B.o.T., by means of a clockwise rotating disc on the front side of the machine.
1b the daily position of the sun projected in the zodiac during its circulation
1c The left-leaning daily rotation of the image of the sky around the Polar star (as center) in 23 hours, 56 minutes and 3,46 seconds) i.e. Simulation of the Astronomical day);
1.d The 13.36842105 sidereal months of tropical year (i.e. simulation of the Astro-nomical Month)
1.e The 13 full moons per year and the four (4) phases of the Moon
1.f The seven days a week in a continuous sequence
1.g The right-handed rotation of the ancient Egyptian calendar with the 12 names of months and the 365 days/year.
2. It is also for the first time became possible, with a clock, powered by hydraulic, electrical, or mechanical energy, to demonstrate the building and the functions of the ancient Greek Metons-calendar and of connected transmissions i.e.
2.a The 6940 days in the 235 synodic months of the 19 years cycle of the methonic-calendar and show the pointer which makes exactly 5 revolution in 19 years realizing the Meton´s-calendar-cycle.
2.b the pointer of the four (4) years cycle of the Olympic games, which makes only one revolution every 4 years
2.c the pointer which makes only one revolution every 76 years in the Kalippos-calendar (of a duration of 76 years).
2.d The Saros cycle of the 18 years for the purpose of prediction of the Sun and moon Eclipses, appear approximately every 6 months.
2.e realize the show of the 12.36842105 Synodic months of the tropical year, also the duration of the single synodic month, by means of a pointer which makes one revolution in 365.24667 days.

3. It is also for the first time became possible to show all the internal flow sche-mata, the gears of all kinematic chains, and the precise number of teeth of every gear, so that:
3.a to show how is transmitted to the great Wheel B1, with the 223 teeth, the daily rotation of a gear, assembled on the shaft of a clock, driven by hydraulic or electric or mechanical energy, and how to bring it (B1) to make one revolution in 365.24667 days. Also demonstrated that all other internal kinematic gear chains and the rotation of the Pointer or disc or rings at end of every chain are synchronized on the movement of the great wheel B1 and show in that man-ner, the relationship of the celestial phenomena with the Metonic-calendar of 19 years cycle and the old Egyptian calendar, which was used about 120 B.o.T.
3.b to show the structure, demonstrate mathematically the function and explain a complicated compound Epicyclic transmission set (world unique)
3.c to reveal that the distance of the pivots B and E (i.e. the center of Rotation of the wheels B1 etc and the center of rotation of the Wheels E1 etc, corresponds to the distance of Polar star from the center of the Ecliptic circle, when the celestial globe will be projected from the south celestial pole to the plane of the celestial equator.
The stereographic projection of the celestial globe and of the Ecliptic on the celestial Equator was an invention of Ipparchos. The graphic design of Antikythera Mechanism complies with the invention of the Greek astronomer Ipparchos and these have been used in the device according to the invention.

 

                                                                            CLAIMS

 

The invented device is based on the well-known Fragments of Antikythera Mechanism and has following characteristics:

1.1. On the Front side of the device can be observed following astronomical phenomena:
1.1.1 The clockwise rotation of a disc, which simulates the annual movement of the Sun in a year of duration of 365.24667 days, according to the teaching of Greek astronomer Ipparchos.
1.1.2 The position of a pin with the image of the sun, which simulate the daily position of the Sun, during its orbit, projected in the Zodiac circle: the pin is in anticlockwise transported by hand (of the user) from one small hole to next one, so that it runs in 365 days the 365 holes manufactured in a fixed plate.
1.1.3 The daily left-wing rotation of the picture of north sky around the Polar star, in 23 hours, 56 minutes and 3.46 seconds.
1.1.4 The 13.36842105 sidereal (astronomical) months of the tropical year.
1.1.5 At a window the 13 full moons per year and the four phases of moon
1.1.6 In another window the seven days a week in a continuous sequence
1.1.7 In a clockwise rotatable ring with 365 divisions (for the 360 days of the 12 months of the ancient Egyptian calendar and the 5 days so-called "Epagomenen"

1.2 On the back side of the invented device are following components or astronomical phenomena and calendar data, visible or readable:
1.2.1 The 6940 days distributed in the 235 synodic months of the 19 years cycle, of the old Greek Metonic-calendar, observed by a pointer which makes exactly five (5) revolutions in 19 years.
1.2.2 A pointer which executes one revolution in four (4) years and simulates the four years cycle of the Olympic games in Ancient Greece.
1.2.3 A pointer which executes one revolution in (76) years and simulates the Cycle of 76 years of Kalippos-calendar.
1.2.4 A pointer which executes four (4) revolutions in 18 years and simulates the 223 Months of the Saros cycle and so predict the Moon and Sun-Eclipses which took place approximately every 6 months.
1.2.5 The 12.36842105 synodic months of the tropical year and also observe at the posi-tion of a rotating pointer the duration of each synodic month. The pointer rotates in a circle divided in 12.36842105 arcs and makes 1 revolution in 365,24667 days.

1.3. With the determined internal flow schemata, the calculated gear numbers of the kin-ematic chains and the exact number of teeth of any gear, is obtained following:
1.3.1 From a small gear fixed on the spindle of a hand of a clock, the rotation of the Hand (pointer) is transmitted to the central great gear B1 (so-called. "Gear of the Sun").
This central gear B1 synchronize all other internal kinematic gear trains. At the end of any kinematic gear train, are assembled the rotatable disc or rings or pointer, which are visible at the front side or at back side of the device and so simulate the celestial phenomena and the calendar data of ancient Greek Metonic calendar of 19 years cycle and of the old Egyptian calendar.
1.3.2 There are revealed all the secrets of a complicated compound Epicyclic transmission set and it was possible to describe and calculate it exactly.
1.3.3 It was possible to choose the distance between the pivot B (of the gears B1, B1a, B2,B3, B4, B6 ) and the pivot E (of gears E1, E2i, E2ii, E5) so that this corresponds to the design distance of Pole of Ecliptic from the Polar star, if the celestial globe be projected from the south Pole of Globe on the plane of the celestial equator.

2. Apparatus according to claim 1, characterized in that

a. In the upper half of the back of the invented device are produced or placed: 5 spiral-curved circumferential gaps (grooves) of 1.5 – 3.5 mm large, which separate 5 spiral formed rings of about 5.0 to 10.0 mm width (measured diametrically)
b. Around of the center N of the five spiral grooves, rotate clockwise a hand pointer,
supported by a pin, which slides in the helical grooves and so (the pointer) makes 5 revolution in 19 years.
c. After 5 turns the pointer and pin (and all other gears, rings, pointers) shall be returned to the initial position by means of the (dis)engangeable hand crank.
d. The 360o of each of the five spiral-rings are divided into 47 equiangular arcs.
In each arc and in continuous row is written the name of the month of the ancient Greek Metonic calendar. The name of the months could correspond to the Athenian
calendar or to the calendar of another Greek colony.
e. Within the circle, which forms the first spiral-ring but slightly to the right of the center N and displaceable to that, rotates a pointer Zo into a small circle, where at its periphery the names of Olympia, Nemea, Isthmia, Naa are engraved, and makes one revolution in four years. In the places Olympia, Nemea, Isthmia, Naa have taken place the ancient Greek Olympic games.

f. Within the circle, which forms the first spiral-ring but slightly to the left of the center N and displaceable to that, rotates a pointer into a small circle of Kalippos-calendar, which does one revolution in 76 years. The Circle is divided in four sectors meaning the four periods of the Metonic cycle.

3. Apparatus according to claim 1, characterized in that

a. At the lower half of the back side of the device are manufactured and arranged follow-ing:
Four (4) spiral-curved gaps of 1.5 to 3.5 mm large, which separate four spiral rings of 5-10 mm width (measured radial)
b. Around the center G of the 4 spiral gaps, rotate clockwise a pointer supported by a pin, which slides into the gaps, and so (the pointer) makes 4 (four) revolution in 18 years.
c. Within the circle, formed from the first spiral-curved gap, but slightly to the right and offset of the center G, there is a pointer I, which rotates into a small circle divided in 12,36842105 arcs and makes 1 Revolution in one year (of the 365.24667 days);
The above mentioned number of division of the circle simulates the duration of the synodic months.

4. Apparatus as claimed in claim 1, that

a. From a gear mounted on the shaft of a pointer of the clock, wherein the ISIMERIA-hours are showed, a gear train starts consisting of at least 8 gears, and the last and greatest gear, named B1, has 223 teeth. The number of teeth of the 8 gears are so selected that the last gear B1 rotates exactly only one revolution in 365.24667 days.
b. Above the gear B1 i.e. in direction of front side, there is a twin wheel B1a, with the same diameter and the same number of teeth (223) of the wheel B1 and disposed with its plane parallel to the B1.
c. The two gears i.e. B1 and the twin B1a are connected by means a crown gear A so that the rotation motion of the B1 via crown gear A to the twin gear B1a transmitted but with opposite turn direction, so that a observer standing before the front side sees the rotation of B1a as dextrorotary.
d. On the twin wheel B1a is mounted a ring HG which surface is visible on the front side, and makes one revolution clockwise in 365,24667 days; The periphery of the ring HG is subdivided in 365 small arcs; 12 large arcs carries each 30 divisions and bear the names of the 12 months of the Egyptian calendar. For the remaining (365-360) five (5) small arcs is used the name "Epagomenen".
e. On the shaft of the large gear B1 and slightly below it i.e. in direction back side, a smaller gear is assembled and makes the same one revolution of the gear B1 in 365.24667 days. The gear B2 has 64 teeth.
f. Also on the shaft of the large wheel B1 and slightly below the aforementioned gear B2 is manufactured and fixed a smaller gear B3. This makes as B1 and B2 exactly one revolution in 365.24667 days in the same rotational direction as B1 and B2.
The gear B3 has 32 teeth.

5. Device as claimed in claim 1, that
On the cylindrical gear grown A a hand crank AK is mounted. It is switched on and off.
During the operation of the device is the hand crank disconnected. It will be connected in case of repairs or to set back the pointers etc to the start position.

6. Device as claimed in claim 1, that
a. From the gear B2 with 64 teeth starts a gear train with 9 gears (B2-C1-C2-D1-D2-B4-B5-U1-V1) which transmits the one revolution of the gear B2 to the ring V2 and brings it to rotate clockwise (for a observer standing on the front side) with 13.36842105 revolution a year.
b. The gear B6 is located at the upper end of the shaft (i.e. towards the front side) and is located in the space between the large gear B1 and the twin gear B1a.

7. Apparatus according claim 1 characterized in that

a. From the gear B2 with the 64 teeth starts a gear train of 8 gears (B2-L1-L2-M1-M2-O1-O2-N1), which transmit the one revolution a year of the gear B2 to the pointer N and bring those to rotate clockwise with 5 rounds in 19 years (for a observer of the front side)

b. From the shaft M which also makes one revolution a year (of 365.24667 days) starts a gear train (M3-N1-N2-Zo), which transmit the 1 rev./year of the gear M3 to the Pointer ZN und brings it to make clockwise 1 revolution in four (4) years. (for a observer of the back side)

8. Device according claim 1, that
a. The invented device comprises a compound Epicyclic transmission set with 2 rotating shafts. This consist of a simple planetary gear transmission, with three rotating spindles and 5 gears i.e. the sun wheels E2i , E2ii and E5, the Planet gears K1 and K2, and the so called Idler gear J, situated between the E2ii and K1. The simple planetary gear transmission has the 5 gears externally meshed and has a basic speed-rotation io = -1. This means that the toothed wheels (sun and planet) on each side have the same number of teeth. In the present case the wheels E2i, E2ii, and K1 have each 32 teeth. The gears E5 and E6 and K1 of 48 teeth. The gear J (idler) can have any number of teeth, because it serves only to change the direction of the rotation. The number of teeth is defined here constructively 48-54.
b. The gear train which transmits the one revolution into the sun wheel E5 of the simple planetary transmission gear with the 3rotating spindles and the 5toothed wheels, contents the Wheels B3 and E1. Both gears (B3 and E1) have the same number of teeth 32.
c. The other gear train, which the 13.36842105 revolution per year into the sun wheel
E2i of the simple planetary transmission gear with the 3rotating spindles and the 5toothed wheels, contents the gears B2-C1-C2-D1-D2-B4-E2i and they have cor-respondently 64-38-48-24-127-32-32 teeth.
d. At the periphery of the two wheels of planet carrier, of the simple planetary transmis-sion gear with the 3rotating spindles and the 5toothed wheels, are manufactured two gears with respectively 192 and 223 gears.
The Gear E3 has 192 teeth and the Gear E4 has 223 teeth.
e. The planet carrier turns with 6.184210525 revolution a year (in 365.24667 days) From each gear E3 and E4 with the above mentioned teeth starts a gear train and introduce the 6.184210525 revolution/y. in two different branches.
f. The distance between the pivot B and the pivot E corresponds to the distance be-tween the Pole of ecliptic and the Polar star, when the globe will be projected from south pole to the plane of the celestial equator.

9. Device according claim 1, that

a. From the gear E4 of planet carrier starts a gear train with 7 gears (E4-Q1-Q2-R1-R2-B6) and transmit the 6,184210255 revolutions/year from the gear E4 to the circular disc HG to the front side, which as is said, ports the image of the night sky of north hemisphere and constrains it to make a turn anticlockwise (for the observer o f the front side) in 23 hours, 56 minutes and 3.46 seconds. That means, that the last gear B6 of the train and the circular disc HG at the front side, make exactly 366.24667 revolution a year (also in 365.24667 tropical days) in anticlockwise.
b. The gears B5, U1, V1 (and B6, R2) in aforementioned gear train are located in the space between the great gears B1 and B1a.

10. Device according claim 1, that
From the gear E3 with the 192 teeth of the planet carrier starts a gear train with 12 gears (E3-F1-F2-G2-G1-H1-H2-I1-I2-H3-H4-G3) and all the gears have number of teeth, so that the pointer "I" makes one rotation a year (in 365.24667 days) around its center and the pointer with center of rotation the pivot G makes four revolution in 18 years.
Both pointers "I" and "G" turn clockwise (for an observer standing on the back side)

11. Device according claim 1, that
a. There is on the surface of front side a gap of about 1.5 – 2.5 mm large between the fixed plate and the clockwise rotating circular ring with the names of the 12 months of the old Egyptian calendar. Slightly submerged below the surface of front side and in a circular ring on the fixed plate (visible through the slit) are manufactured 365 small holes .
b. Within this (365) circular holes a fine pin with the image of the sun SG is plugged in and shall be moved daily per hand (from User) from one hole to the next, but left-handed (for the observer on the front side)

12. Device according claim 1, that
On the circumference of the circular ring ZK on the surface of the front side are written the names of the 12 zodiac signs into 12 equal-length arcs and also engraved the pic-ture of the zodiac sign.
The circular ring ZK is located between the left-handed circular disc HG with the image of the heaven globus and the dextrorotatory ring JR with the names of the 12 months of the old Egyptians calendar.

13. Device according claim 1, that
The shaft of the gear B6 (for rotating the central disc HG with the image of the globe), the shaft of the gear B4 and B5 for rotating the circular disc VK to simulate the four phases of the moon, and the shaft of the gears B1, B2, B3, for rotating the circular ring JR(ÄK), are all coaxial and concentric.

14. Device according claim 1, that
In addition to the clock of the upper half of the front side, there is a small window, where appears a picture of the 7 gods engraved on the surface of the disc, which rotates behind the window; the picture of gods are synonymous with the name of the known seven planets, and synonymous of the days of the week; the disc receives its motion directly from the clock and make one revolution every 7 days. Every day appears a picture of God/planet Sun, Moon, Mars, Mercury, Jupiter, Venus, Saturn equivalent for Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.

Antikythera Mechanism by Dr.- Ing. Th Sartoros

Here is report from a device of the ancient Greeks , which should not exist according to many historians . It should not exist because it is associated with a science which had the ancient Greeks supposedly not developed. The ancient Greeks were well known, philosophy, astronomy , mathematics, geometry , theater, shipbuilding , mining, music, poetry , painting, sculpture , architecture , Olympic games , urban planning, medicine, pharmacy, botany , so all sorts of sciences, arts and commerce but apparently no gear technology and have developed no gear calculator. According to many historians, the ancient Greeks were brooders

and the Romans tinkerer . This widespread opinion may rebut a salvaged from the depths of the Aegean part .

After emerging from a depth of 42 m. in the Aegean Sea near the island of Antikythera recovered by sponge fishermen in 1900 AD from a Roman shipwreck , which was fully loaded with looted from Greek cities, cultural goods, the unit got the 1's name , " Bronze plates " and ended up in a wooden box ; after sorting the finds

in the Archaeological Museum of Athens ended up with the second name "lump " in a trash can .

The archaeologists were from the other finds ( bronze and marble statues etc. ) enthusiastic and none gave the "lump " attention. It is a godsend that the clumps survived the scrapping. The Greek Minister of Culture Valerio Stais happened to go past the camp of the Archaeological Museum and took the lump in his office with ; he discovered the lump some gears and the Greek letters and J. 1902 , the first message appeared in an Athens newspaper about a mysterious gear mechanism with Greek letters .

The Minister was risking not only his credibility but also his post ; he reaped from

the critics just spiteful laughter. Gears from the Greeks ? hardly anyone believed it.

By 1934, the country Greece experienced a series of local wars , the Balkan War , the 1s world war , a military defeat in 1923 , followed by military coups and dictatorships ;

the lump had been forgotten. Only in 1934 , the Greek admiral Theophanidis made ​​sketches of the gears and the words he could read , and provides a report in French about the finds in the sea of ​​Antikythera . A little later, the German archaeologist interested Rehm this, but the 2e World War brings everything back to a standstill.

Mid-50s interested in the lump a American scientist named Derek de Sola Price.

At the same time, also a Greek atomic physicist Charalampos Karakalos busy

with the lumps. The stroke of luck brings the two men to work together. Price published in 1974 , after almost 20 years of intensive work, the results of his investigations , with the provocative title "Gears from the Greeks " ie Gears from the Greeks and the device gets the name " Antikythera mechanism " by which it is world famous today. No one dares since then to assert that the ancient Greeks had no gear technology.

It is not a "lump " anymore, but it proved to be one of the most complicated and enigmatic gear mechanisms from the Ancient World to visit until today a world - unique, the AMA

= Archaeological Museum of Athens.

For 100 years, archaeologists , physicists, mathematicians , historians , engineers, watchmakers , and amateurs deal with the world - unique ; who built it ? what it was ? how it func -defined ? With what mathematics the ancient Greeks have solved such difficult problems of gear chains ? How many gears and with what number of teeth of the mechanism was fitted ? What machines and equipment which part of the ancient Greeks were the gears finished ?

Here are briefly the story of the rescue of the device , the name and attempts of previous researchers , and my results (see German Patent No. DE 10 2010 015 501 ) described

The device contains a series of inventions of the great ancient Greek pioneers namely:

> The engineer Archimedes with a compound planetary gear ,

> Astronomer Ipparchos with the stereographic projection of the sky and Ekleiptik ,

   and the measured values ​​of Ipparchos time for the rotation of the sun around the earth in

   365.246667 days , which is also measured by him Synodic duration of the months of

   29.5303030 days , the number of 13.36842105 sidereal ( astronomical ) months in a

    Year , the duration of the sidereal month , the duration of the astronomical day of 23 St. 46 min

    and 3.46 sec , etc.

> And finally the knowledge of the great mathematician Diophantus .

> The fourth name " Ktisibios " still hiding behind the fragments of the clock mechanism

My results are summarized major part in the patent

Now, a brief description :

On the front page: 7 rotating parts; namely the clock with the ISIMERIA hours at the upper left corner , the day of the week display of the 7 day week right next ; in the center of the large ring with the 12 month of the Egyptian calendar, the levorotatory large central disc with the picture of the northern sky , the ring of Zodiakkreises with the Greek names of the constellations and not visible because light absorbed 365 small holes for the positioning of a pin with a golden ball to simulate the sun; slightly below the small window on the right for the simulation of the four phases of the moon .

The rest of the free front surface has been used as Parapigma ie engrave for information on setting up and setting stars. At the top right of the probable position of the anaphoric

Clock with the gnomon .

On the back: on the upper half 5 spiral rings, separated by small channels , divided into 235 small arcs corresponding to the number of months in a Metonic calendar Synodic

with cycle of 19 years. The number 19 she was called golden number . The device was therefore inevitable for 19 years and realized one of the most difficult and complicated calendar of the Greeks.

In the upper half of the back of a small clock is for the display of the Olympic Games

in Olympia, Nemea , Isthmia , Naa as well as a clock for the Kalippischen calendar of 76 years .

In the lower half of the back 4 Spiral rings are visible , divided into 223 small

Arcs for the realization of the Chaldean cycle of 18 years , also named Saros cycle ,

for the prediction of lunar and solar eclipses .

A small pointer in the lower half showed the duration or the end of each 12.36842105 Synodic month in a year, information necessary for the prediction of lunar and solar eclipses .

In summary :

It is a unique combined gear computer planetarium calendar.

Gears the Greeks had already 7s century BC and therefore this cycle of the calendar with the age of 8 used for the production of gear mechanisms to implement the simpler the calendar OKTAETIRIS ; Calendar valid in GR from about 540 v.u.Z. to 432 v.u.Z.

My model of the Antikythera mechanism consists of at least 50 gears whose manufacturing is very difficult because many numbers of teeth " primes " are ; Primes which divide numbers is called only by the unit and by itself ; So they have no other divisors.

As is known, prepare the primes of the gears also today's manufacturing engineers headache.

Prime numbers as numbers of teeth of gears are systematically avoided because today is very difficult to produce with conventional machines ; until a few years ago were still expensive part of equipment for the conventional milling machines also difficult to learn and to use. Indexing units are devices , with which the circle in an arbitrarily large number of small arcs ( angle) can be divided ; The indexing units are essential for the production of gears.

The ancient Greeks had already dividing heads since the time of Pythagoras (560 BC J. ) and

obviously had long since been overcome with primes in about 120 -140 BC , as the Antikythera mechanism has been built , the manufacturing difficulties of gears.

see GR-Bücher/Literatur

What has been said shows the Antikythera mechanism with multiple gears with prime numbers as numbers of teeth such as 223 , 127, 59, 61 , 37, 19, 17 , etc. without the exact dividing heads have the cylindricity between bronze discs can not be made ​​with these prime numbers as numbers of teeth.

It must also be emphasized that the gears can be produced only in milling machines,

and the Antikythera mechanism proves that the ancient Greeks in addition to the lathes had also milling machines. Homer mentions lathes than known machines and Plato repeatedly mentioned lathes , where the ball has been made ​​( ).

Archaeologists have discovered a Nekromanteion in northern Greece , locking wheels and flanges with slotted holes and can be seen in the Museum of Ioannina, which approximately from the 4th century BC come and have an identical form as machine parts from modern machine tools of 1960.

On the part of the critics have never considered this evidence of Greek technology.

The pictures are of the locking wheels a challenge to the critics .

Companies was the Antikythera mechanism from a Präzisionswasseruhr with ISIMERIA - hours (as in our modern watches). This may be an imitation of the famous water clock of Ktisibios suspect ( contemporary of Archimedes ) . The water clock of Ktisibios worked about 200 years and has been described by Vitruvius ( 200 years after the public statement of the clock ) with much admiration. My research dbzgl ongoing.

The ancient Greek astronomers used the ISIMERIA hours to describe the duration

the celestial phenomena , ( Astronomical day , round trip times , moon and solar eclipses etc ) during the Greek people have a preference for the sundial and the anaphoric clock had .

In my original model ( patent ) of the Antikythera mechanism is electrically operated .

The Antikythera mechanism includes a gear calculator ; with his co - compound planetary gear drive can also expect yet , add namely , subtract, and divide , and even with extreme precision of 8 decimal places , and that is what causes the admiration of the whole world.

A unique evidence of applied mathematics of the ancient Greeks in gear mechanisms for gear manufacturing , precision engineering , astronomical devices , watches , planetariums , etc.

The Antikythera mechanism also works as a planetarium ;

The left-rotating central disc on the front page with the picture of the northern sky is part of the planetarium and realizes 366.246667 days in a year; So it shows the daily rotation of the celestial sphere with the fixed stars in 23 St., 56 min , and 3.46 sec with a deviation of 0.64 sec ie he simulated the astronomical time , the astronomical day, and astronomical year.

He also allowed the prediction of lunar and solar eclipses with deviation of a few minutes.

He also simulated the exact orbital period of the Sun around the Earth in a geocentric system in 365.246667 days and realized that 12.36842105 synodic months in a year .

The fair values ​​for the duration of the astronomical day , for the tropical year and synodic months for the 8 places after the decimal point , are known from the ancient Greek literature and the Antikythera mechanism realizes time accuracies in three advertisements of less than 1 sec

The Notified details and time values ​​and the stereographic projection of the sky discovered in the Antikythera mechanism , allow me to conclude that the device comes from the school of Ipparchos ; the Greek astronomer Ipparchos lived about 180-120 BC So at the time of production of the Antikythera mechanism .

A big surprise was the discovery of the month name of a Corinthian calendar in

the upper half of the back, where the 19-year Metonic cycle of the calendar is visible ; the Metonic calendar was in GR from 432 to about 46 BC Z. ; Syracuse, where Archimedes lived , however, was a Corinthian colony. Could the device from Corinth or Syracuse originate ?

It is an alternative Coll examines whether the device is in Corinth by students of Ipparchos has been built.

Many American / French / English Studiosi have claimed that the complicated Metonic calendar (introduced in GR in the year 432 BC) with the 6940 days in a cycle of 19 years , where some years 13 months, and another year had only 12 months, and the months times 30 days times were 29 days long, was never built with gears .

A great mistake of the alleged Studiosi .

The Antikythera mechanism proves beyond doubt the high level of Sciences of the ancient Greeks .

                             Well, what has become of the knowledge of the ancient Greeks ?

Christianity destroyed about 11,000 ancient Greek temple.

The columns of less than 10 remaining but perfectly built ancient Greek temple

can be admired today in Greece and Sicily.

Marble columns of the other have been often used for the manufacture of asbestos.

The Byzantine emperor needed to about 1050 AD in order to enforce Zwangschristianisierung of the Greeks. They banned the Olympic Games and the ancient Greek religion and often ordered the transport of the pillars of the ancient Greek temple to Constantinople Opel , where they built churches. However, many customs of the ancient Greek religion still live in the subconscious of the Greek people .

A similar fate also experienced the machines , planetariums, watch the ancient Greeks ; they ended up largely in the furnaces for the production of new metal parts.

In the year 1204 besieged and conquered Constantinople , the crusaders of the Opel 4's Crusade , everything plundered from Constantinople Opel and brought everything to Western Europe ( Venice / Italy, Switzerland , France, England , Belgium, Germany ) . The Crusaders killed about 1 /4 of the population of Constantinople ; another ¼ of the population fled to the Greek sites along the Black Sea from Asia Minor . Many Greeks went ( as prisoners ) with the looted equipment to the west, where they showed the " franc = Φράγκους " the operation of the machines and equipment.

Some looted cultural objects (icons, statues , and equipment) are to be seen in EU museums.

Even in Catholic churches of the European Capital of Culture 2010, Essen , 's plundered

from Constantinople Opel .

The question I asked myself was, however, to find : whether other constructions of

planetariums or clocks in Western Europe realized after the Antikythera mechanism , where

the composite planetary gear drive of the ancient Greeks have been installed .

Become resourceful I am in the Astronomical clock of the Gothic Cathedral of Strasbourg / France , built by Dasypodius in the year 1574 , and in later globe constructions of Baldewein 1584 and Jost Bürgi and in a patent of the French Pequeur & Perellet from 1823 to simulate the circulation time of the moon or the Synodic month . So it took about 2000 years to the same humanity invented what the ancient Greeks in the years 120-140 BC have built.

 

 

 

Translation on English of the german patent application

 

1. Designation:
Antikythera Mechanism with Planetarium, Calendar
and driven by hydraulic or electric power Clock

2. Object of the Invention.

The production of a functioning device in order to faithfully simulate all display indications of the Antikythera Mechanism, as rotation of the celes-tial globe, Astronomical time, Synodic and Sidereal months, lunar phases, solar and lunar eclipses, Saros cycle, Metonic Calendar with 235 Months of the 19 years cycle, Old Egyptian Calendar of 365 days, position of the Sun in the Zodiac.

3. Introduction: Actual level of the technique

The fragments of a Mechanism recovered in 1902 from a shipwreck at a depth of about 42 m. near the Greek island of Antikythera, in the Aegean Sea, south of the Peloponnese, showing some gears, since then known as the Antikythera Mechanism, proved to be more complicated and are still the subject of extensive studies and publications by several amateurs and scientists; here some Names: Svoronos, Stais, Rediadis, Theophanidis, Rehm, Price, Karakalos, Bromley, Wright, Tatjana van Vark and a team of scientists from the Universities of Athens and Thessaloniki (GR) and Cardiff (UK), (Freeth, Jones, Steele, Bitzakis, Seiradakis, Zafeiropoulou, Mangou, Moussas, Athanasiou, Edmunds, and others under the auspices of the Ar-cheological Museum of Athens (abbreviated: AMA), with the help of high specialized, internationally named Companies, as HP (with Mr. Malzbender and others) and X-Raytec (with Mr. Handland) dealing since 2006 with the enigmatic ruins furnished 3D Photos of previously 2160 letters from the PARAPIGMA (= Instructions) and about precisely identifiable fractions of gears with triangular teeth. There are read some as-tronomical and geographical terms imprinted on the fragments as complete words for example, ΕΓΛΕΙΠΤΙΚΗΣ, ΝΕΜΕΑ, ΙΣΘΜΙΑ, ΟΛYΜΠΙΑ, ΕΛΙΚΙ, ΑΡΗΣ, ΑΦΡΟΔΙΤΗ, ΓΝΩΜΩΝ, ΑΕΤΟΣ, ΛΥΡΑ, ΥΑΔΕΣ, ΠΛΕΙΑΔΕΣ, ΤΑΥΡΟΣ, ΔΙΔΥΜΟΙ, ΑΡΚΤΟΥΡΟΣ (ecliptic, Nemea, Isthmia, Olympia, Eagle, Lyra/Leier, Hiades, Pleiades, Taurus, Gemini, Arctur).

Theophanidis was the first man, who recognized (1934) the five (5) grooves of the upper half of the back side of Mechanism, where the pins supported two pointers, and also the four (4) grooves in the lower half of the back side of the fragments. On the front side Theophanidis recognized the names of months of the old Egyptian Calendar, which later (1974) Price confirmed.
He read the names (in Greek letters) of two (2) Zodiacs in a quarter of a annular disk with angle-indication of a goniometer in a another fragment.

Price stated (1974) the grooves as the furrows separating five (5) rotating circular disks on the upper half of the back side, and as furrows between four (4) rotating circular disks in the lower half of the backside; but his conjecture has proved later (2006) to be incorrect.

Price (with the help of the watchmaker John Gleave) presented in 1974 as first a model of the Antikythera Mechanism on the basis of his conjecture ( with the circular rings in the backside etc) and with reference to the number of teeth, determined on the basis of radiographs of the Greek nuclear physicist Karakalos, which some-times willfully refused, in order to become a satisfying result.

The thus presented model showed a hand crank operated mechanism with a planetary gear. Unfortunately the teeth numbers used by Price led to confusion and complicated the identification of a correct solution. The model of Price showed and included more astronomical and design problems than ever solved and thus incited the researcher for further intensive investigations.

There followed the models of Bromley (1986-1991); M. Wright (2002-2008), Tatjana van Vark (2007), Edmunds (2008).These have repealed no significant deficiencies in the Price model but changed numbers of teeth and design of planetary gear and take off thus leaving more of the functions of the mechanism, so they are here little taken into account, especially since modelers took over the shares subscripted by Price crank drive as motion input, or the input of the drive in planet carrier of the planetary gear offset, which led to misleading results; However, the function of the hand crank ist quite another.

In 2008 M. Wright realized that the grooves at the back were actually spiral-shaped curves and not circles. In 2008 the team of the AMA confirmed that the grooves were spiral in both upper and in the lower half of the backside and identified the name of few months of the Corinthian-Calendar in the upper half of the backside, which caused a sensation regarding the origin of the device.

The team of the AMA completed and published (2008) the upper half of the back-side of the mechanism with the calendar of the 19 years cycle of the Greek as-tronomer Meton, introduced in whole Greece at 432 and valid until 46 before our Time (B.o.T.) and explained the lower half of the backside as "display for eclipse prediction". However it has not explained how the mechanism works.

Despite the partial success of the above mentioned Researchers achieved in decoding the CT-pictures, there are has been no models either as drawing or as functioning equipment, which the functions of the mysterious Antikythera mechanism fully explain.

There are neither the number of gears nor the number of teeth of each gear, given by the model builders.

There is a table with the number of teeth of the gears so far identified from four (4) principal researchers: Karakalos, Price, Wright, team of the AMA, which apart drift and often due to the different internal flow patterns of the drive chains and of the planetary gear are very inconsistent.

For some gear wheels in order to achieve a better result " possible teeth Numbers" was indicated a wide range of 2 to 6 teeth and often used in different kinematic chains.

Which drive-chains and where was the entrance into the device, and what function full filed each gear has so far remained unclear. Each modeler was trying to achieve empirically a plausible (astronomical interpreted) result using random teeth numbers. In the inventive device are exactly indicated both i.e. the numbers of teeth of each gear with the obtained results, their position in the flow schemata and the function of each gear-chain.

Among the Researcher, there is also disagreement about whether the Antikythera Mechanism ever a planetary gear was included, and of what type it might be, and with how many (4 or 5) gears, and with which number of teeth
was manufactured each gear.

There are researchers (Wright, Freeth, Edmunds) which in their publications, both versions (i.e. with and without of planetary gears) represented. In the models or drawing (see M. Wright) one sees pointers for 7 Planets at the front of the device, and in a later model (of M. Wright) are the hands of only two Planets (Sun, Moon) on the front side attached and visible. But none of them corresponds to the functions of the original Antikythera Mechanism.

The graphic representation of the research team of the AMA (published in journal NATURE, 2006) indeed provides a planetary gear with 4 wheels inside the mecha-nism, however, show the formula of the modern theory of planetary gear of the local inventor a useless result and indicate a nonsensical construction, which is uncon-ceivable for the old Greek designers of the Antikythera Mechanism.

It has been found common ground that it is a Greek device with advanced technology, and that the rescued fragments were part of a more sophisticated and complex mechanism, which executed several operations, therefore, by some researchers called as "the oldest rack-computer in the world". Some other named the mecha-nism as "analog computer". Price calls it "a calendar computer from 80 b.C.; other (Theophanidis, Kritzas) dated the fragments from the time of 120 – 140 B.o.T Publi-cations in the Newspapers and magazines (such NATURE, Der Spiegel, GEO, P.M. and others) focus on the difficulties of the scientists to decipher the mechanism.

4. Description of the two sides of the model according to the invention of the mechanism of Antikythera.
The device according to the invention has the dimensions:
167*306*125 mm (W * H * D)

4.1.1 Description of the front side (Fig. 1)

An observer who is facing the front of the device, see the following (on the front):

A clock is located at the upper right corner (which at the time of construction of the original mechanism, was driven by hydraulic power, as a watermeter) with indication of the 24-ISIMERIA-hours (just like today´s hours in modern clocks) with a day-hand.

ISIMERIA-hours are mentioned by Homer, and Pytheas (330 B.o.T.) described the daily-length also in ISIMERIA-hours for the places situated at the 66o degree north latitude near the mysterious island THULI. So the day-hand took place exactly a clockwise rotation in 24 hours.

The Babylonian had divided the circle in 360o degrees and the round trip time of day and night in 24 hours and it had been taken over by the Greek astronomers and ap-plied in the Antikythera Mechanism.

The Water Clocks of Ktisibios (Ktesibius, contemporary of Archimedes) were with gears been equipped and described 200 years later by Vitruvius, with great admira-tion for the precision. Here the Clock is powered by electrical energy from a battery.

In addition to the clock with Isimeria-hours, in the middle of the upper half of the front
there is a small window, where appears the image of a god or a planet (ΚΡΟΝΟΣ, ΗΛΙΟΣ, ΣΕΛΗΝΗ, ΑΡΗΣ, ΕΡΜΗΣ, ΔΙΑΣ, ΑΦΡΟΔΙΤΗ), i.e. was then alternately see-ing Saturn, Sun, Moon, Mars, Mercury, Zeus, Venus, valid for Saturday, Sunday, Monday, Tuesday, Wednesday, Thursday, and Friday) the same law as the names of the 7 days of the week. Thus, the rotating disc behind the pane took exactly 1 turn in 7 days. The pulley for the days of the week got its rotation from the Clock i.e. from the gear of the day-hand of the clock.

The Anaphoric clock was located at the upper left corner of the front side with the Gnomon (it is not further described herein, because it makes no part of the inven-tion).

In the middle of the front side (Center B) four (4) concentric discs/rings can be seen.

From the inside to the outside of the regarded surface with center B, the observer sees follows:

The innermost concentric annular disc HG is rotatable about its center and represents the picture of the sky with stars, visible in a area of 36o (Lindos, Rhodos)- 37o Syra-cusa, 38o Athens/Corinth, North Latitude. From the north half of sky are listed in Parapigma the stars (Arctur, Eagle, Hiades, and Pleiades etc).

The left-handed figure HG of the sky rotates around the Polar star (Stella Polaris)
and makes one revolution in 53 hours, 56 minutes, and 3,46 seconds and simulate the astronomical 365,24667 days of the tropical year, i.e. represents the revolution of the celestial globe with the fixed stars, according to the Pythagorean astronomy, which is also accepted from Ipparchos (Hipparchus).
Since the 6th century B.o.T. (=before our Time) had the Greek astronomers found that the sky with the fixed stars rotates around the Pole-Star.

This had been embodied in the Antikythera Mechanism. This has also been imple-mented faithfully in the invented device, according with the known fragments. The fact that the inner disk, HG, with the picture of the sky rotates in less than 24 hours and is driven by gear train, shall further be explained bellow, forming a patentable detail.

This is followed by a fixed annular disc, ZK, whereupon the Greek names of the 12 zodiac signs are engraved. Slightly recessed from the surface in a circle in the fixed plate, FP, 365 small holes are created where a pin with the simulated image of the
Sun, SS, plugged in and however added daily at a little hole anti-clockwise by hand.
Why must the sun symbol SS in left-handed rotation daily into the 365 holes replaced, is related with each different duration of the astronomical (sidereal) and the tropical year and was well known to the Greek Astronomers since the time of Pythagoras (595 -511 B.o.T.). Pythagoras had declared that the sun in comparison to the fixed stars rotates backwards and Plato (420 B.o.T.) required by the astronomers „ΣΩΖΕΙΝ ΤΑ ΦΑΙΝΟΜΕΝΑ", i.e. in all models of the astronomical phenomena must exactly as they are seen also shown and explained.

The next, on a circle gap for the 365 holes of the sun symbol SS, rotating at right-rotating direction a concentric annulus, JR, (ÄK) with engraved names of the 12 Egyptian months (in force of that time, about 120 years B.o.T.) with 365 equal-length small-arcs, and with radial small strokes marked subdivisions, for the 365–day Egyptian specific calendar. The Egyptian calendar had 360 days and a further 5 days, known as "Epagomenen" for a total of 365 days. The number of arcs (365) thus corresponds to the calendar days.

On a line on the fixed plate, FP, just above the Meridians (vertical axis of the concentric rings) the user could see and read the Egyptian month and day in which he lived. The Egyptian Calendar was much simpler than the ancient Greek astronomer Meton´s calendar (named after the Athenian Astronomer Meton, lived about 480 – 410 B.o.T.) with the 19 years cycle, and the 6940 days in 235 (synodic) months.

The Annulus JR (ÄK) makes one (1) revolution in 365,24667 days (deviation less than 0,56´´/year) according to the known data of the Greek Astronomer Ipparchos (lived about 195 – 125 B.o.T.). Note that the Number 365,24667 here is rounded up.

This ring JR (ÄK) simulated also the right-handed circular rotation of the Planet "Sun" according to the geocentric System and became the movement from the Clock with the ISIMERIA-hours; the corresponding kinematic gear train shall be bellow explained.
It is to be noted that the periodic orbital of 365,24667 days of the Sun around the Earth is known as the period of a lost clock made by Ipparchos. The kinematic gear chain for the movement of the Sun is starting by the Clock (day-hand) with the Isimeria-hours and includes till the central wheel B1 totally 8 gears.
The prerequisite for the precision of all followed movements is the accuracy that the central Gear B1 for the simulation of the celestial body makes one rotation in 365.24667 days in the tropic year.

From the Clock with the Isimeria-hours and from the following 7 wheels nothing has been saved. Only the last wheel B1, named Wheel of the Sun, is available as a complete fragment and seen in all publications.

The number of teeth of the big wheel B1 is controversial among researchers.
Here is named as the single correct number of teeth (223) and protected.

The Number of teeth of the others 7 gears of the kinematic chain from the pointer to the gear B1 to achieve the simulation of a revolution of the Sun in 365.24667 days will not disclosed here.

After the great circle concentric ring JR (ÄK) with the Egyptian calendar follows the fixed plate FP front, enclosing the previously described four (4) concentric rings.

Slightly below the large concentric ring with the Egyptian calendar JR (ÄK) and to the fixed plate FP, there is again a window and behind it, turn right a circular disc VK, which simulates the rotation of the Moon and of the 4 Phases of the Moon.

These disc of the Moon takes 13.36842105 revolutions in the above 365.24667 days of the year and simulates the 13.36842105 sidereal (astronomical) months of the year. The eight (8) digits after the decimal point are known as measured values since the 3rd century B.o.T. The values are derived from precisely calculated number of teeth for the gears, which also faithfully fulfill the known axis distances completely.

There is no doubt that the ancient Greeks the "13 books of arithmetic" of the ancient Greek mathematician DIOPHANTOS used, in order to calculate the numbers of teeth of gears mechanism; so is obviously the above numerical accuracy.

The kinematic chain with the number of teeth of the gears to simulate the exact lunar months (the sidereal month) will be further explained below.

The lower quarter of the front side is used as PARAPIGMA i.e. it includes instructions for the user and explanations about the rising and setting stars with full words engraved on the bronze plate of the front side. This information was very useful to the navigators in middle sea.

4.2 Description of the rear panel (back side of the device)

4.2.1 Description of the upper half of the back side

In the upper half of the back of the mechanism, as already said, are the 5 small spiral grooves constructed on the surface of the fixed plate.
Around the center N of the 5 spiral grooves rotates a pointer, supported by a pin which glides into the grooves.
The pointer N (ZN) makes exactly 5 rotation on 19 years.

In the upper half of back side are also engraved the 235 divisions around the 5 grooves which correspond to the 235 synodic months in the 19 years of the Greek calendar.

The kinematic gear chain for the rotation of the pointer N along the grooves on the upper half started with the gear B2 with the 64 teeth, which is fitted on the shaft of the great Sun wheel B1 with the 223 teeth, so that the Gear B1 which makes one revolution in 365.24667 days drive the pointer N of the Meton´s calendar.

In the Meton´s calendar with the 19 years cycle fit much better the time simulation on Earth with the revolution of the Sun- and of Moon-cycles and consequently could start the Olympic games almost the same day of the summer. This calendar is pan-hellenic in July 432 B.o.T. introduced.

The number 19 was written with golden color and designated as a golden number. After 19 years the heavenly bodies were almost to the same starting position.

Each of the five rings of the spiral 360o is divided into 47 equal length arcs (angles) with radial strokes, and in each sheet (sector) on the fixed plate is engraved the Corinthian name of the month of the used Metonic calendar.

The Corinthian month names have been discovered only recently with the CT pictures. Altogether 235 Months seen in figures of the 5 spirals of the upper half of the back side; the Number 235 corresponds to the synodic months of the Greek astronomers. So only and exclusively in the upper half of the backside are read the 235 synodic months.

In the Metonic calendar of the 19 years cycle, the years and the months were not all of equal length. There were years with 12 months and another year of 13 months; there were also months with 29 days (named hollow or lean) and there were 30-days months (named full or fat). (See Book of the ancient Greek astronomer Geminus "Introduction to the phenomena") this has been realized in the Antikythera mechanism.

The pointer discovered by Theophanidis at the upper half of back side with the pin in the separating gap of the spiral grooves has been confirmed be the AMA team.

But it was necessary to explain in the Antikythera Mechanism which days were "ΕΞΑΙΡΕΣΙΜΟΙ" i.e. shuld be excluded in the hollow months, so that the month has only 29 days. The designers of the Antikythera Mechanism have engraved in each sheet (sector) under the name of the month, which day was excluded. The discovery of the Word ""ΕΞΑΙΡΕΣΙΜΟΙ" owes to the CT-pictures, shown by the AMA-team in the years 2006-2008.

It is to note that the kinematic gear chain for the movement of the pointer N in the Metonic calendar, remained hidden (unrevealed) from the other researchers and that this chain had two functions was overlooked i.e. the second was to point si-multaneously (the Olympic games in Olympia, Nemea, Isthmia, Naa)

The above mentioned kinematic chain branched and drove a second little pointer Zo in a small circle inside the large circle of the first spiral in the upper half of the back side.
So completes the little pointer Zo, one revolution every four (4) years, because every four years the games took place in Olympia.

There is also a further detail indication, by means of a rotating pointer in a small circle, which showed the 4 periods of the Kalippos-calendars; the Kalippos-Calendar yielded a higher accuracy in the simulation and consisted of four periods of the metonic calendar, i.e. it had a cyclic period of 4 * 19 = 76 years

4.2.2. Description of the lower half of the back side

The lower half of the back side with the four (4) spiral grooves or 4 spiral-like rings was used to predict the eclipses (Sun- and Moon-eclipses) according to the Chaldean cycle also called Saros-cycle.

The Chaldean (today, Iraq) had established in Niniveh (North Iraq) as a statistical office and registered since 750 B.o.T. for about 250 years long the sun- and moon-eclipses, and fixed (found) that the eclipses repeated after almost 18 years in the almost in the same days. That result had taken over the Greek Astronomers. The 18 years of the Saros cycle contained a total of 223 synodic months.

The four spiral rings of the lower half of the back side were therefore divided into 223 equal-length arcs with radial short lines and thus corresponds to the 223 synodic months of the Saros cycle. A few notes from the "PARAPIGMA" and identi-fied in the four spiral rings allow this reconstruction.

It was known to the Greek Astronomers, and particularly from the time of Ipparchos that the Sun-Moon-eclipses occur in pairs every 6 months (Sun-eclipces approximately 2,3 times per year, lunar eclipses about 1,5 times per year) namely, solar eclipses at new moon and lunar eclipses at full moon. The designer of the Mechanism engraved for every six months the predicted eclipses in the arcs of the lower half of the Antikythera Mechanism. This can be seen in the CT Photos.

Here is to be noted, that within the central solid disk of the lower half of the back side two pointers can be seen in the pivot points I and G, whose functions and speeds have been detected by others researcher in error. It is also to be noted, that the gear train, which leads to the indicator G and I of the lower half of the back, gets the motion from the smaller gear E3 of the planet carrier of the com-pound planetary gear transmission.

The smaller pointer with the center of rotation I, is used to count the 18 years of the Saros cycle, that is, the smaller hand makes one revolution per year, and thus shows the orbital time period of each of 12.36842105 synodic months, but the larger pointer with pivot of rotation G, takes four (4) revolutions in 18 years.

It has been taken in consideration by the designers of the particular direction of ro-tation of the pointer and of the axis distances i.e. for the observer the back side, end all kinematic gear chains with a clockwise motion.

5. Description of the inner gear chains of the Antikythera Mechanism (Fig. 2)

5.1 Gear chain to simulate the annual revolution of the Sun in 365,24667 days and the old Egyptian calendar of 365 days/year.

The first gear train begins as already mentioned with a gear fitted on the shaft of the day-hand ) of the clock with the ISIMERIA–hours and from there with further gear pairs transmits the rotational movement to the central great Sun wheel B1 with the 223 teeth.

It is absolutely essential that the central wheel B1, has 223 teeth and through the over transmission chain, the wheel B1 executes exactly a revolution in 365.24667 days.
This is in the invented device achieved with four pairs of toothed wheels (8 toothed wheels including the wheel B1).

The central wheel B1 with the 223 teeth is the heart of the simulation of the solar movement or of the tropical year with the 365.24667 days (The word "year" is always to be understood as "Tropical year"). This expressed in astronomical values (1 (one) turn in 365.24667 days); is only with the above mentioned number of 223 teeth to realize and have been used in the invented device.

Above the wheel B1 is a twin wheel B1a with the same number of teeth (223) and the same tooth module. Both wheels B1 and B1a with the 223 teeth are parallel superposed and interlocked with the gear crown showed A.

The twin wheel B1a and the gear crown A are required because the direction of the rotation of B1 is defined as clockwise (positive) for the observer standing at the back side, while for the observer standing in front of the front side is negative (i.e. anticlockwise). By means of the crown gear A, changes the direction of rotation of twin wheel B1a, and so the observer of the front side sees a clockwise rotation for the ring JR which carries the names of the 12 months of the Egyptian calendars with the 365 divisions (days). This Egyptian calendar ring has now (for the observer standing at the front of device) a clockwise rotation and makes exactly 1 revolution in 365.24667 days, as the great wheel of the sun, B1.

The crown gear is disconnectable in the device, according to the invention with an on/out hand crank AK. The hand crank AK is used to transfer the gears and the pointers back to the start position after the pointers has arrived the end of the grooves or in cases of repair of the device.

The hand crank AK does not serve therefore as constant drive and this is a serious error of the nearly all researchers.

The number of teeth of crown gears A does not matter, because the crown gear serves only to change the direction of rotation of the connected parts.
The number of teeth can be arbitrarily fixed (between 48-54) and respects only conditions for better mesh (engage) of the wheels B1 and B1a.

5.2 The kinematic gear-chains of the compound Epicyclic transmission set

The biggest surprise in the Antikythera Mechanism is the "compound Epicyclic transmission set", where the integrated simple planetary gear consisted of 5 gears with 3 rotating spindles and has a speed-ratio of io = -1.

Not only the complicated definition, but also the design of a such composite Epicyclic transmission prepares to the specialized engineers many difficulties, therefore such transmissions are always avoided.

It is evident that the laws of design and of function of the "compound Epicyclic transmission" has been well known to the ancient Greeks and they used the properties of this unique and difficult construction in the Antikythera Mechanism.

The compound planetary transmission set of the Antikythera Mechanism had the duty to "calculate the half of the number of the synodic months of the year"

The ancient Greek astronomers and engineers knew that the composite Epicyclic transmission, as above shortly defined, was the unique mechanism in the world, capable to make algebraic operations (Addition and Division) and they took advantage of this property with virtuosity.

The compound Epicyclic transmission executes the algebraic addition of the in-coming two different rotations, i.e. the transmission took account of the direction of the rotation, and when both positive (also both clockwise direction) does the addition, but when the two introduced rotations have different directions (one clockwise and the other anticlockwise) then does the subtraction and the result lead out with the shaft of the planet carrier.

It should be noted, that none Patent application is till known, with a compound Epicyclic transmission, which has integrated one simple planet gear set with 3 rotatable shafts, with 5 toothed wheels and with speed-ratio io = -1.
The construction of the ancient Greeks is till today a world unique device.

The planet gear systems has appeared in the time of Archimedes and Ktisibios (Ktesibius), to this why the Mechanism of Antikythera with the complicated Compound Epicyclic transmission is probably of a newer Date, also after Archimedes.
The graphologists confirm that the handwriting is coming from 2d century B.o.T.

5.2.1 Short description of the compound Epicyclic transmission set
and explanation of the operation

To show the error of thought of the other researchers, which go out from a simple Differential planetary set as used in the rear axis of automobiles and the existing, are many technical explanations required, in order to better understand the invention.
In a differential planetary gear, like the one used in the rear axis of automobiles, the planet carrier is driven i.e. it introduces the power. This evenly distributes the power in the two axle halves. The wheels of the two axle halves rotate with the same (identical) speed when the automobile traveling on strait way. Shuts down the car a curve, then the wheels turns slower with the smaller radius of curvature and the externally situated wheels with the greater radius of curvature turns faster.

Thus the differential allows to transfer a part of the incoming power from the smaller turned half axle to the faster turning half axle and to compensate temporarily the different distance which must run the internal and external
wheels. However the differential planetary gear as described cannot count.

The differential planetary gear of automobile as described above has no resemblance to the composite Epicyclic transmission of the invention, which shall be soon explained.

Each gear (pair) transmission is symbolized by a circle and three radial lines for the three shafts shown. One for the power input, the second for the power out-put and the third coincides with the stationary housing of the (gear pair) transmission.

In order to make a planetary gear transmission, from the above gear pair transmission, the third shaft must be made rotatable i.e. the housing is no more stationary and must rotate to; so the initial pair of gears mutate in planet wheels.
The third shaft carries now the planet wheels now called sun-wheels, which (are fitted on the so called Carrier of planet wheels and) and each sun wheel is connected correspondently one with the input and the other with the output shaft.

In simple industrial applications the shaft of a sun wheel is fixed, the other sun-wheel is used for power incoming and the shaft of the carrier for the power output.
The result is the simple planetary gear with 2 rotating shafts, regardless of the in-ner construction. A planetary gear with 2 rotating shafts cannot count. All power components are determined on the basis of the design features. The above mentioned rule seems to be known almost to all the others researchers.

In a compound Epicyclic transmission set, the motion is starting from a common external shaft (denoted with T), with two internal different lines of kinematic gear chains, i.e. both kinematic gear chains, starts with the same speed of the external shaft T.

In each kinematic gear train are mounted one or a plurality of pairs of gears, de-pending on the calculation and design, in order to reduce the rotational speed which shall arrive the end of the line and shall introduced to the sun wheels of the simple planetary gear. It must therefore be connected each end (i.e. introduced the speed of each gear train) with the sun wheels, as in the invention of Antikythera mechanism.

In addition the simple planetary gear must have a basic ratio of io = -1.

From here on increase the difficulties for amateurs and professionals, because the simple planetary gears, have different properties depending on the model of gear.
The construction must be as in the invention of Antikythera Mechanism, i.e. each internal kinematic chain must be connected with one sun wheel of the simple planetary gear and the simple planetary gear must have a ratio io = -1.
This means that that when fixed the carrier and one sun wheel will be rotated clockwise, the other sun wheel rotates in opposite direction (anticlockwise).

A other essential condition is that the simple planetary gear with io=-1, must
also have totally 5 toothed wheels all meshed externally. Otherwise is the before mentioned condition (by fixed carrier the one sun wheel turns in one direction and the other sun wheel in opposite direction) not realized.
Herein is nothing to be shaken and nothing to change.
The other researchers were not familiar with the properties of the compound Epicyclic transmission set, therefore, they could not find the correct number of teeth of any gear neither the functions of the modules and made the error to identify the compound Epicyclic transmission set with a simple differential planetary drive of automobiles

In the invented device the compound Epicyclic transmission set has integrated the unit with 5 toothed wheels and with ratio-speed io = -1.

In a compound Epicyclic transmission set as the Antikythera Mechanism must lead the shaft of carrier the result to the outside. The so subscribed and constructed compound Epicyclic transmission set adds algebraically the incoming two rotations and the result divided by two, leads to the shaft of planet carrier to the outside. The resulting speed can be zero, positive or negative (in accordance with the definition of the direction of rotation).

In the apparatus according to the invention, the gears of the two shafts of the sun wheels (of the simple planetary gear with the 3 rotating shafts and the 5 gears) have number of teeth calculated and applied according the laws of compound Epicyclic transmission.

Well, on the shaft of the big wheel B1 with the 223 teeth and slightly below this, are two small gears mounted/assembled. The one labeled B2 has 64 teeth and the underlying labeled B3 has 32 teeth. All three gears (B1, B2, B3) are mounted on the same shaft, so they have the same (initial) speed, i.e. they do only one revolution in 365.24667 days. This detail is very important for all pursuit movements.
It must be noted, that the named number of teeth are depending of each other and from the purpose of the structural Installation. It can be changed only the number of teeth of gear B2, if calculations permitted this.
Additional over checking must demonstrate that the change is possible. In this case the designated number of teeth has been established.

5.2.2 The kinematic gear chain to calculate the 13.36842105 sidereal months per year

The first gear train (B2-C1-C2-D1-D2-B4, in the drawings with dense hatch from top left to the bottom right) of the compound Epicyclic transmission set, starts from the wheel B2 and ends to the wheel B4, supplies (with wheel B4) the 13.36842105 rev./year and thus simulate the sidereal months of the year. The wheel B4 is assembled on the end of the hollow shaft of the wheel B2. The shaft of wheel B4 is placed through the shaft of B2 and leads upwards, i.e. in direction front side and ends in the space between the Wheel B1 and the tin wheel B1a.

The speed of the wheel B4 is really given by: 1 * 64/38 * 48/24 * 137/32 = 13.36842105 rev./Year and has a negative sign of rotation, that means the B4 has the opposite direction of the wheel B2. The observer standing at the front side sees the rotation of B4 as clockwise (positive) but for the observer standing at the back side sees the rotation of B4 as negative (levorotatory).

After a change of the direction of B4 the rotation is introduced in the sun wheel E2i and E2ii of the simple planetary gear system. (constituted of: sun wheels E2i, and E2ii, idler wheel J, planet gears K1 and K2, and E5 sun wheel).
The planet gears K1 and K2 are mounted on a common shaft firmly connected with each other and therefore have the same speed.
The wheel E2i and E2ii are manufactured identically.

Some researchers (Freeth and others) have interpreted erroneously a connecting pin that holds the Planet gear wheels K1 and K2 and used the measured eccentriccity between the centers for calculate the anomaly of the moon movements.
The purpose of compound Epicyclic transmission set is so completely removed.

A second kinematic gear train (B3-E1-E5, drawn left of the central axis B) starts from the wheel B3 and performs one revolution per year, and is introduced with a negative sign in the shaft of the sun gear wheel E5 of the simple planetary gear system.

So in the simple -5wheels-3shafts planetary gears are introduced, according the invention, two speeds with opposite directions. The one with 13.36842105 revolution per year, and the other with only one revolution per year (i.e.by 1 turn in 365.24667 days).

The two introduced speeds are algebraically added and the result divided by two is lead from planet carrier to the outside. However the designer of Antikythera Mechanism have not used the shaft of the planet carrier, but the planet carrier itself, using the resulting speed of (+ 13.36842105 – 1) / 2 = + 6.184210525 revolu-tion per year to move the other parts.

The high experience of many centuries is here evident and unmistakable.

The gears E3 and E4, manufactured at the periphery of planet carrier turn also with + 6.184210525 rev./year. They transmit this speed to two different gear trains which shall explained in following pages. Here with the gears E3 and E4, ends the compound Epicyclic transmission set.

5.3. The previously identified two speeds (13.36842105 and 6.18421055 rev./Y.)
are used at following manner:

The speed of 13.36842105 expressing the sidereal months of the year is, as said, for the observer standing at the backside, negative (but is positive for the observer standing at the front side) and is transmitted by a ratio of 1:1 upwards to the front side, and drives clockwise (observed from the front side) the disc V2 at a small window and simulates the 13.36842105 full moon of the tropical year. At the small hub at the window are also the colored four (4) moon phases to observe.
This information was necessary for the Greeks navigators in middle sea, because at new moon took place the sun and moon eclipses and some weather and wind conditions were to be expected.

The speed of 6.184210255 is completely transmitted from the gear E4 with the 223 teeth upwards to the front side, with a gear train so that the end speed increases to 366.24667 rev./Y. With this speed rotates the central disc HG with the image of the night sky. Here is striking the same direction of rotation of both, of the central disc HG in front side and of the planet carrier, i.e. of the gear E4 of the planet carrier. That means that the image of sky turns anticlockwise with 366.24667 rev./Y. for the observer standing at the front side.

The central ring disk HG, bears the image of northern stars sky and simulate both the duration of astronomical (sidereal) year of 366.24667 days, as well as duration of the astronomical day of 23 hours, 56 minutes and 3.46 seconds.

The astronomical time of the ancient Greeks has been banned in astronomical clocks in the middle Ages from the Catholic Church, because supposedly would be a divine creation and man was not permitted to sully that.

The other (smaller) gear E3 at the periphery of planet carrier has exactly 192 teeth and is not allowed to have different number of teeth. From the toothed wheel E3 starts a another gear train (E3-F1-F2-G1) with the original speed of 6.184210255 and with the help of the used gears teeth is increasing to the double i.e. 12.36842105 and thus results against the number of the synodic months of a year. This is, however, used as intermediate result. Then with the continuous gear train G1-G2-I1 is transmitted to the small hand with pivot point "I" and brings the pointer to make only 1 revolution per year.

The construction of the invention, provides the carry back of the one rev./Y. from the axle "I" , by the same axes (I-G), by means a new gear train and transmit it to the big hand pivoted at G at the center of the lower half of back side, so that the pointer G makes four (4) turns in 18 years, and so realize the Saros cycle.

It is emphasized that the dimensions of the gears and the axle distances measured in the original fragments, have been applied faithfully in the invented device, and it was found that the accuracy of the axis distances often lies in the range of 1/10 mm.

6. The gear trains for the pointer of the upper half of the back side

It remains to explain two further gear trains for the pointer of the upper half of the back side.

The gear train B2-L1-L2-M1-O2-O2-N1 starts with gear B2, which as stated, turns with 1 revolution in 365.24667 days.

The striking detail here is that the designers of Antikythera Mechanism equipped the train L1, L2, M1 with gears and suitable number of teeth and diameters so that a rotation of only one revolution results to a point (M) and from there (M) introduced the rotation (of one rev./Y.) in two branched and different gear trains till the pointers of the upper half of back side.

This beautiful design solution in conjunction with the compound Epicyclic transmis-sion set and the water clock, reveal a centuries-old tradition with gear mechanism. Unfortunately this solution also the compound Epicyclic transmission set have not recognized from all previous researcher, which adopted many faulty assumptions.

The continuing gear train M2-O1-O2-N and the used gears with appropriate number of teeth, allow the clockwise rotation of the large pointer N i.e. ZN at the upper half of back side; the pin which supports the pointer N slides into the spiral-like five (5) small gaps (grooves) of the surface of the Greek calendar of the Metonic-Circle with the 19 years cycle. So the pointer N does in 19 years exactly 5 revolutions. Af-ter 19 years the pointer N must be brought back to the start position (by help of the hand crank).

The other kinematic gear train which also use the 1 revolution of the shaft M, equipped with the gears M-N-Λ drives the pointer Zo internally of the small circle with name of (Greek) places (ΟΛΥΜΠΙΑ, ΝΕΜΕΑ, ΙΣΘΜΙΑ, ΝΑΑ ,Olympia, Nemea, Isthmia, Naa) where took place the Olympic games. The pointer Zo makes also 1 revolution in four (4) years, because the Olympic games took place every forth year.

7. The projection of the Sun on the Zodiac circle and
the interpretation of the 365 small holes for the Sun symbol

Finally remains to explain the purpose and function of the 365 small holes for the pin with the Image of the Sun Ss and the levorotary daily displacement in the gap, between the clockwise rotating ring disk with the names of the 12 Egyptian months and the fix ring disk with the names of the 12 constellations (Zodiac signs).

The Greek astronomers had observed and measured that the celestial globe exe-cute one complete revolution in less than 24 hours (that is 23 hours, 56 minutes and 3.46 seconds).
The difference (3 Min, 56.54 seconds) make exactly one day per year.
This additional day needed the sun to return to the initial position.
In addition, they observed and measured that the Sun compared to the same fixed stars was somewhat retarded in daily movement. The slower rotation of the Sun interpreted Greek astronomers as rearward rotation movement of the sun in com-parison to the Constellations of the Zodiak circle.

The everyday situation of the sun was so projected and (the user) knew in which star sign the Sun was.

For the designers of the Antikythera Mechanism, it was therefore necessary to inform the user of the device, according to the astronomical theory, in which Zodiac the Sun was. The 12 Zodiak signs were engraved to the fixed disk.

They have solved the Problem very elegantly; they produced 365 small holes for the pin with the image of the Sun, in a slightly recessed and fixed plate, and left it to the User to turn the pin daily and put it into the next left hole. Thus passed the pin with the image of the sun (current daily from one hole to the next) all zodiac signs in a year and arrived after 365 tropical days the initial position, just as the celestial body.

It was a mistake of the previous researchers to assume that the number of the holes were 366. Thus, the sun would be after 30 years retarded of a constellation width projected to the fixed stars. Known, that the fragments of Antikythera Mechanism also a Kalippos-calendar revealed, that means that the device was designed for 76 years; After 76 years the solar image of the pin would be nearly 2,5 width (approximately 76o) retarded in comparison to the true position in the sky. That would be a gross mistake of the Engineers of the profession
"S P H Ä R O P O I I A = Celestial Globe Builder) which, given the precision and know-how, which the fragments of the device emits, is not conceivable.

Finally, it should be noted, that the ancient Greek designers of the Antikythera Mechanism selected the distance between the center point (pivot) B (for the wheels B1, B1a, B2, B3, B4, B6) and the center point (pivot) E for the rotating shafts (E1, E2i, E2ii, E5) in that manner, that this corresponds to the distance be-tween the Polar star and the Pole of the Ekleiptik, when the celestial sphere and the circle of the Ecliptic shall be projected stereographic from the south sky pole on the celestial Equator.

The stereographic projection of the celestial globe and of the Ekleiptik on the ce-lestial Equator was an invention of Ipparchos. The graphic design of Antikythera Mechanism complies with the invention of the Greek astronomer Ipparchos and these have been used in the device according to the invention.

Abridgement/Resumé

With the invented device, driven by a clock with hydraulic or electrical or mechani-cal energy, became for the first time possible to show all the adds and functions hidden in the Fragment of Antikythera Mechanism, and simulate on the front side some of them:

1a The annual revolution of the sun in exactly 365.24667 days according to the teaching of the ancient Greeks astronomy of the 2d century B.o.T., by means of a clockwise rotating disc on the front side of the machine.
1b the daily position of the sun projected in the zodiac during its circulation
1c The left-leaning daily rotation of the image of the sky around the Polar star (as center) in 23 hours, 56 minutes and 3,46 seconds) i.e. Simulation of the Astronomical day);
1.d The 13.36842105 sidereal months of tropical year (i.e. simulation of the Astro-nomical Month)
1.e The 13 full moons per year and the four (4) phases of the Moon
1.f The seven days a week in a continuous sequence
1.g The right-handed rotation of the ancient Egyptian calendar with the 12 names of months and the 365 days/year.
2. It is also for the first time became possible, with a clock, powered by hydraulic, electrical, or mechanical energy, to demonstrate the building and the functions of the ancient Greek Metons-calendar and of connected transmissions i.e.
2.a The 6940 days in the 235 synodic months of the 19 years cycle of the methonic-calendar and show the pointer which makes exactly 5 revolution in 19 years realizing the Meton´s-calendar-cycle.
2.b the pointer of the four (4) years cycle of the Olympic games, which makes only one revolution every 4 years
2.c the pointer which makes only one revolution every 76 years in the Kalippos-calendar (of a duration of 76 years).
2.d The Saros cycle of the 18 years for the purpose of prediction of the Sun and moon Eclipses, appear approximately every 6 months.
2.e realize the show of the 12.36842105 Synodic months of the tropical year, also the duration of the single synodic month, by means of a pointer which makes one revolution in 365.24667 days.

3. It is also for the first time became possible to show all the internal flow sche-mata, the gears of all kinematic chains, and the precise number of teeth of every gear, so that:
3.a to show how is transmitted to the great Wheel B1, with the 223 teeth, the daily rotation of a gear, assembled on the shaft of a clock, driven by hydraulic or electric or mechanical energy, and how to bring it (B1) to make one revolution in 365.24667 days. Also demonstrated that all other internal kinematic gear chains and the rotation of the Pointer or disc or rings at end of every chain are synchronized on the movement of the great wheel B1 and show in that man-ner, the relationship of the celestial phenomena with the Metonic-calendar of 19 years cycle and the old Egyptian calendar, which was used about 120 B.o.T.
3.b to show the structure, demonstrate mathematically the function and explain a complicated compound Epicyclic transmission set (world unique)
3.c to reveal that the distance of the pivots B and E (i.e. the center of Rotation of the wheels B1 etc and the center of rotation of the Wheels E1 etc, corresponds to the distance of Polar star from the center of the Ecliptic circle, when the celestial globe will be projected from the south celestial pole to the plane of the celestial equator.
The stereographic projection of the celestial globe and of the Ecliptic on the celestial Equator was an invention of Ipparchos. The graphic design of Anti-kythera Mechanism complies with the invention of the Greek astronomer Ip-parchos and these have been used in the device according to the invention.

CLAIMS

The invented device is based on the well-known Fragments of Antikythera Mechanism and has following characteristics:

1.1. On the Front side of the device can be observed following astronomical phenomena:
1.1.1 The clockwise rotation of a disc, which simulates the annual movement of the Sun in a year of duration of 365.24667 days, according to the teaching of Greek astronomer Ipparchos.
1.1.2 The position of a pin with the image of the sun, which simulate the daily position of the Sun, during its orbit, projected in the Zodiac circle: the pin is in anticlockwise transported by hand (of the user) from one small hole to next one, so that it runs in 365 days the 365 holes manufactured in a fixed plate.
1.1.3 The daily left-wing rotation of the picture of north sky around the Polar star, in 23 hours, 56 minutes and 3.46 seconds.
1.1.4 The 13.36842105 sidereal (astronomical) months of the tropical year.
1.1.5 At a window the 13 full moons per year and the four phases of moon
1.1.6 In another window the seven days a week in a continuous sequence
1.1.7 In a clockwise rotatable ring with 365 divisions (for the 360 days of the 12 months of the ancient Egyptian calendar and the 5 days so-called "Epagomenen"

1.2 On the back side of the invented device are following components or astronomical phenomena and calendar data, visible or readable:
1.2.1 The 6940 days distributed in the 235 synodic months of the 19 years cycle, of the old Greek Metonic-calendar, observed by a pointer which makes exactly five (5) revolu-tions in 19 years.
1.2.2 A pointer which executes one revolution in four (4) years and simulates the four years cycle of the Olympic games in Ancient Greece.
1.2.3 A pointer which executes one revolution in (76) years and simulates the Cycle of 76 years of Kalippos-calendar.
1.2.4 A pointer which executes four (4) revolutions in 18 years and simulates the 223 Months of the Saros cycle and so predict the Moon and Sun-Eclipses which took place approximately every 6 months.
1.2.5 The 12.36842105 synodic months of the tropical year and also observe at the posi-tion of a rotating pointer the duration of each synodic month. The pointer rotates in a circle divided in 12.36842105 arcs and makes 1 revolution in 365,24667 days.

1.3. With the determined internal flow schemata, the calculated gear numbers of the ki-nematic chains and the exact number of teeth of any gear, is obtained following:
1.3.1 From a small gear fixed on the spindle of a hand of a clock, the rotation of the Hand (pointer) is transmitted to the central great gear B1 (so-called. "Gear of the Sun").
This central gear B1 synchronize all other internal kinematic gear trains. At the end of any kinematic gear train, are assembled the rotatable disc or rings or pointer, which are visible at the front side or at back side of the device and so simulate the celestial phenomena and the calendar data of ancient Greek Metonic calendar of 19 years cycle and of the old Egyptian calendar.
1.3.2 There are revealed all the secrets of a complicated compound Epicyclic transmission set and it was possible to describe and calculate it exactly.
1.3.3 It was possible to choose the distance between the pivot B (of the gears B1, B1a, B2,B3, B4, B6 ) and the pivot E (of gears E1, E2i, E2ii, E5) so that this corresponds to the design distance of Pole of Ecliptic from the Polar star, if the celestial globe be projected from the south Pole of Globe on the plane of the celestial equator.

2. Apparatus according to claim 1, characterized in that

a. In the upper half of the back of the invented device are produced or placed: 5 spiral-curved circumferential gaps (grooves) of 1.5 – 3.5 mm large, which separate 5 spiral formed rings of about 5.0 to 10.0 mm width (measured diametrically)
b. Around of the center N of the five spiral grooves, rotate clockwise a hand pointer,
supported by a pin, which slides in the helical grooves and so (the pointer) makes 5 revolution in 19 years.
c. After 5 turns the pointer and pin (and all other gears, rings, pointers) shall be returned to the initial position by means of the (dis)engangeable hand crank.
d. The 360o of each of the five spiral-rings are divided into 47 equiangular arcs.
In each arc and in continuous row is written the name of the month of the ancient Greek Metonic calendar. The name of the months could correspond to the Athenian
calendar or to the calendar of another Greek colony.
e. Within the circle, which forms the first spiral-ring but slightly to the right of the center N and displaceable to that, rotates a pointer Zo into a small circle, where at its periphery the names of Olympia, Nemea, Isthmia, Naa are engraved, and makes one revolution in four years. In the places Olympia, Nemea, Isthmia, Naa have taken place the ancient Greek Olympic games.

f. Within the circle, which forms the first spiral-ring but slightly to the left of the center N and displaceable to that, rotates a pointer into a small circle of Kalippos-calendar, which does one revolution in 76 years. The Circle is divided in four sectors meaning the four periods of the Metonic cycle.

3. Apparatus according to claim 1, characterized in that

a. At the lower half of the back side of the device are manufactured and arranged follow-ing:
Four (4) spiral-curved gaps of 1.5 to 3.5 mm large, which separate four spiral rings of 5-10 mm width (measured radial)
b. Around the center G of the 4 spiral gaps, rotate clockwise a pointer supported by a pin, which slides into the gaps, and so (the pointer) makes 4 (four) revolution in 18 years.
c. Within the circle, formed from the first spiral-curved gap, but slightly to the right and offset of the center G, there is a pointer I, which rotates into a small circle divided in 12,36842105 arcs and makes 1 Revolution in one year (of the 365.24667 days);
The above mentioned number of division of the circle simulates the duration of the synodic months.

4. Apparatus as claimed in claim 1, that

a. From a gear mounted on the shaft of a pointer of the clock, wherein the ISIMERIA-hours are showed, a gear train starts consisting of at least 8 gears, and the last and greatest gear, named B1, has 223 teeth. The number of teeth of the 8 gears are so selected that the last gear B1 rotates exactly only one revolution in 365.24667 days.
b. Above the gear B1 i.e. in direction of front side, there is a twin wheel B1a, with the same diameter and the same number of teeth (223) of the wheel B1 and disposed with its plane parallel to the B1.
c. The two gears i.e. B1 and the twin B1a are connected by means a crown gear A so that the rotation motion of the B1 via crown gear A to the twin gear B1a transmitted but with opposite turn direction, so that a observer standing before the front side sees the rotation of B1a as dextrorotary.
d. On the twin wheel B1a is mounted a ring HG which surface is visible on the front side, and makes one revolution clockwise in 365,24667 days; The periphery of the ring HG is subdivided in 365 small arcs; 12 large arcs carries each 30 divisions and bear the names of the 12 months of the Egyptian calendar. For the remaining (365-360) five (5) small arcs is used the name "Epagomenen".
e. On the shaft of the large gear B1 and slightly below it i.e. in direction back side, a smaller gear is assembled and makes the same one revolution of the gear B1 in 365.24667 days. The gear B2 has 64 teeth.
f. Also on the shaft of the large wheel B1 and slightly below the aforementioned gear B2 is manufactured and fixed a smaller gear B3. This makes as B1 and B2 exactly one revolution in 365.24667 days in the same rotational direction as B1 and B2.
The gear B3 has 32 teeth.

5. Device as claimed in claim 1, that
On the cylindrical gear grown A a hand crank AK is mounted. It is switched on and off.
During the operation of the device is the hand crank disconnected. It will be connected in case of repairs or to set back the pointers etc to the start position.

6. Device as claimed in claim 1, that
a. From the gear B2 with 64 teeth starts a gear train with 9 gears (B2-C1-C2-D1-D2-B4-B5-U1-V1) which transmits the one revolution of the gear B2 to the ring V2 and brings it to rotate clockwise (for a observer standing on the front side) with 13.36842105 revolution a year.
b. The gear B6 is located at the upper end of the shaft (i.e. towards the front side) and is located in the space between the large gear B1 and the twin gear B1a.

7. Apparatus according claim 1 characterized in that

a. From the gear B2 with the 64 teeth starts a gear train of 8 gears (B2-L1-L2-M1-M2-O1-O2-N1), which transmit the one revolution a year of the gear B2 to the pointer N and bring those to rotate clockwise with 5 rounds in 19 years (for a observer of the front side)

b. From the shaft M which also makes one revolution a year (of 365.24667 days) starts a gear train (M3-N1-N2-Zo), which transmit the 1 rev./year of the gear M3 to the Pointer ZN und brings it to make clockwise 1 revolution in four (4) years. (for a ob-server of the back side)

8. Device according claim 1, that
a. The invented device comprises a compound Epicyclic transmission set with 2 rotating shafts. This consist of a simple planetary gear transmission, with three rotating spin-dles and 5 gears i.e. the sun wheels E2i , E2ii and E5, the Planet gears K1 and K2, and the so called Idler gear J, situated between the E2ii and K1. The simple plane-tary gear transmission has the 5 gears externally meshed and has a basic speed-ratio io = -1. This means that the toothed wheels (sun and planet) on each side have the same number of teeth. In the present case the wheels E2i, E2ii, and K1 have each 32 teeth. The gears E5 and E6 and K1 of 48 teeth. The gear J (idler) can have any number of teeth, because it serves only to change the direction of the rotation. The number of teeth is defined here constructively 48-54.
b. The gear train which transmits the one revolution into the sun wheel E5 of the simple planetary transmission gear with the 3rotating spindles and the 5toothed wheels, contents the Wheels B3 and E1. Both gears (B3 and E1) have the same number of teeth 32.
c. The other gear train, which the 13.36842105 revolution per year into the sun wheel
E2i of the simple planetary transmission gear with the 3rotating spindles and the 5toothed wheels, contents the gears B2-C1-C2-D1-D2-B4-E2i and they have correspondently 64-38-48-24-127-32-32 teeth.
d. At the periphery of the two wheels of planet carrier, of the simple planetary transmis-sion gear with the 3rotating spindles and the 5toothed wheels, are manufactured two gears with respectively 192 and 223 gears.
The Gear E3 has 192 teeth and the Gear E4 has 223 teeth.
e. The planet carrier turns with 6.184210525 revolution a year (in 365.24667 days) From each gear E3 and E4 with the above mentioned teeth starts a gear train and intro-duce the 6.184210525 revolution/y. in two different branches.
f. The distance between the pivot B and the pivot E corresponds to the distance be-tween the Pole of ecliptic and the Polar star, when the globe will be projected from south pole to the plane of the celestial equator.

9. Device according claim 1, that

a. From the gear E4 of planet carrier starts a gear train with 7 gears (E4-Q1-Q2-R1-R2-B6) and transmit the 6,184210255 revolutions/year from the gear E4 to the circular disc HG to the front side, which as is said, ports the image of the night sky of north hemisphere and constrains it to make a turn anticlockwise (for the observer o f the front side) in 23 hours, 56 minutes and 3.46 seconds. That means, that the last gear B6 of the train and the circular disc HG at the front side, make exactly 366.24667 revolution a year (also in 365.24667 tropical days) in anticlockwise.
b. The gears B5, U1, V1 (and B6, R2) in aforementioned gear train are located in the space between the great gears B1 and B1a.

10. Device according claim 1, that
From the gear E3 with the 192 teeth of the planet carrier starts a gear train with 12 gears (E3-F1-F2-G2-G1-H1-H2-I1-I2-H3-H4-G3) and all the gears have number of teeth, so that the pointer "I" makes one rotation a year (in 365.24667 days) around its center and the pointer with center of rotation the pivot G makes four revolution in 18 years.
Both pointers "I" and "G" turn clockwise (for an observer standing on the back side)

11. Device according claim 1, that
a. There is on the surface of front side a gap of about 1.5 – 2.5 mm large between the fixed plate and the clockwise rotating circular ring with the names of the 12 months of the old Egyptian calendar. Slightly submerged below the surface of front side and in a circular ring on the fixed plate (visible through the slit) are manufactured 365 small holes .
b. Within this (365) circular holes a fine pin with the image of the sun SG is plugged in and shall be moved daily per hand (from User) from one hole to the next, but left-handed (for the observer on the front side)

12. Device according claim 1, that
On the circumference of the circular ring ZK on the surface of the front side are written the names of the 12 zodiac signs into 12 equal-length arcs and also engraved the pic-ture of the zodiac sign.
The circular ring ZK is located between the left-handed circular disc HG with the image of the heaven globus and the dextrorotatory ring JR with the names of the 12 months of the old Egyptians calendar.

13. Device according claim 1, that
The shaft of the gear B6 (for rotating the central disc HG with the image of the globe), the shaft of the gear B4 and B5 for rotating the circular disc VK to simulate the four phases of the moon, and the shaft of the gears B1, B2, B3, for rotating the circular ring JR(ÄK), are all coaxial and concentric.

14. Device according claim 1, that
In addition to the clock of the upper half of the front side, there is a small window, where appears a picture of the 7 gods engraved on the surface of the disc, which rotates be-hind the window; the picture of gods are synonymous with the name of the known seven planets, and synonymous of the days of the week; the disc receives its motion directly from the clock and make one revolution every 7 days. Every day appears a picture of God/planet Sun, Moon, Mars, Mercury, Jupiter, Venus, Saturn equivalent for Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.