Antikythera Mechanism Readme and Licensing Info

8/12/2019 Antikythera Mechanism Readme and Licensing Info

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CREATED BY

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These files were created by Kemal Tfeki in Slidwrks !"#$ d%rin& the mnth f December !"#$'

and released (an%ary !"#)*

+lease kee, this readme with the files*

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$D +R-.T-./0A1T2E.T-C-TY -.34

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-t isn5t ,erfect* There are a few iss%es that w%ld kee, if frm wrkin& if y% $D ,rinted this'

and a few mre iss%es that make it nt cm,letely a%thentic t the ri&inal 6echanism* 2ere are

the ,laces where the mdel differs frm the Antikythera 6echanism* Italicizediss%es kee, it frm

wrkin& well if it was $D ,rinted*

#7 All &ears e8ce,t fr the l%nar ,hase &eartrain are ass%med t ha9e a md%le f "*:* This is

act%ally the mean 9al%e f the md%les fr all &ears in the 6echanism* A mre acc%rate mdel

w%ld acc%nt fr 9ariatins in the &ears*In one instance, this creates a collision between a

gear and a support as it travels around. A few &ears sh%ld als be thicker(the main gear wouldhave to be thicker to support weight).

!7 - didn5t %se 9al%es fr the ,in ,lacement radii n the e,icycle &ears* These can be f%nd in

3reeth and (nes5 ;The Csms in the Antikythera 6echanism*;

$7 Tw indicatrs sh%ld slide nt the 6etnic and Sars ,inters' and track in the en&ra9ed

s,iral n the back face* Slidwrks had iss%es with a tan&ent relatinshi, t a s,iral' s these

are s%,,ressed in the mdel


2/17

ith the fllwin& e8ce,tins

#7 The files ;,late back*sld,rt; and ;a8le assembly a*sldasm; are frm the ed%catinal 9ersin f

Slidwrks and can nly be %sed fr ed%catinal ,%r,ses* - dn5t knw hw that ha,,ened' beca%se

- ha9e the cmmercial 9ersin f slidwrks* - m%st ha9e edited smethin& n my schl5s

cm,%ters*

!7 The files ;,late back lwer dial 9)*,n&; and ;,late back %,,er dial 9)*,n&; are taken frm

3reeth et al* ;Calendars with 4lym,iad and Ecli,se +redictin n the Antikythera 6echanism

S%,,lementary .tes;' and sli&htly edited by me* C,yri&ht beln&s t ri&inal wners' hwe9er

beca%se it is a ,%blished ,a,er all ed%catinal %ses are fair %se*

$7 The file ;,late frnt 9!*,n&; is taken frm this ima&e

0f%ll0AntikytheraF&ra,hicFbi&*G,&7' ri&inally made by

(* E9ans and A* Thrndike' and sli&htly edited by me* C,yri&ht beln&s t ri&inal wners*

The main reference for these columns is printed: the monograph, cited below, by the famous Yale

historian of science Derek De Solla Price (other printed references) !n the web one can find the

complete te"tof his #$%$ Scientific Americanarticle on the sub&ect ' eeman, *+, -Sdeli.ered lectures on the topic in #$$/ at the 0ni.ersity of Te"as, San 1ntonio and at Trinity

ollege, Dublin The 23 transparenciesfrom these lectures are on the web and it4s almost like

being there (see hispaperfor more detail) Di.ing+um 'nterprises has apagewith a photograph

of the curent installation in the 5ational 6useum of 1rchaeology, 1thens hris -orres4 pageSpheres and Planetariaon the Dre"el 0ni.ersity site has a nice photograph of Price himself -ob

S -ice of the 0ni.ersity of Pennsyl.ania has posted a .ery useful paperon the sub&ect, from a

#$$% 0S 5a.al 1cademy symposium on 5a.al 7istory 1 li.ely sketch of De Solla Price4sscientific and human personality can be found in the oreword, by -obert * 6erton and 'ugene

8arfield, to one of his books

1. The history of the Mechanism

The 1ntikythera 6echanism is the name gi.en to an astronomical calculating de.ice, measuring

about 32 by #9 by # cm, which was disco.ered in #$ in a sunken ship &ust off the coast of1ntikythera, an island between rete and the 8reek mainland Se.eral kinds of e.idence point

incontro.ertibly to around / + for the date of the shipwreck The de.ice, made of bron;e

gears fitted in a wooden case, was crushed in the wreck, and parts of the faces were lost, ? Transactions of the 1merican PhilosophicalSociety (@olume 9?, part >)
http://www.math.sunysb.edu/~tony/whatsnew/column/antikytheraI-0400/kyth4.htmlhttp://www.giant.net.au/users/rupert/kythera/kythera3.htmhttp://www.math.utsa.edu/ecz/ak_m.htmlhttp://www.math.sunysb.edu/~tony/whatsnew/column/antikytheraI-0400/kyth4.htmlhttp://www.geocities.com/Yosemite/9610/antikytheracomputer.htmhttp://www.mcs.drexel.edu/~crorres/Archimedes/Sphere/SphereIntro.htmlhttp://www.mcs.drexel.edu/~crorres/Archimedes/Sphere/SphereIntro.htmlhttp://ccat.sas.upenn.edu/rrice/usna_pap.htmlhttp://www.garfield.library.upenn.edu/lilscibi.htmlhttp://www.giant.net.au/users/rupert/kythera/kythera3.htmhttp://www.math.utsa.edu/ecz/ak_m.htmlhttp://www.math.sunysb.edu/~tony/whatsnew/column/antikytheraI-0400/kyth4.htmlhttp://www.geocities.com/Yosemite/9610/antikytheracomputer.htmhttp://www.mcs.drexel.edu/~crorres/Archimedes/Sphere/SphereIntro.htmlhttp://ccat.sas.upenn.edu/rrice/usna_pap.htmlhttp://www.garfield.library.upenn.edu/lilscibi.htmlhttp://www.math.sunysb.edu/~tony/whatsnew/column/antikytheraI-0400/kyth4.html


3/17

General plan of all gearing, composite diagram

from De Solla Price, Transactions of the 1merican Philosophical

Society @ol 9? 5o > (#$>?) -eproduced with permission

At is hard to e"aggerate the

singularity of this de.ice, or

its importance in forcing acomplete reBe.aluation of

what had been belie.ed about

technology in the ancientworld or this bo" contained

some 32 gears, assembled

into a mechanism thataccurately reproduced the

motion of the sun and the

moon against the background

of fi"ed stars, with adifferential gi.ing their

relati.e position and hence

the phases of the moon At is

enough to know that there isno trace of anything like it

until around # 1D, andthat when it was first

published there were serious

suggestions that it had beendropped into the wreck at a

much later date or e.en that it

was the work of alien

astronauts

The general plan of the

gearing could only be drawnafter #$># when, on De SollaPrice4s instigation, the

remnants of the mechanism

were .iewed with gammarays, which could penetrate

the calcareous block in which

the gears were embeddedThen careful counting of

teeth, and e"amination of the

way the gears meshed,

showed that


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This is the first of two

columns on the 1ntikythera6echanism An each we will

e"amine one part of the

mechanism that has special

mathematical interest Thismonth it is the SunB6oon

assembly, ne"t month: the

Differential 8ear

BBTony Phillips

SUNY at Stony Brook

2. Pictures of a Mechanism

7ere are three significant illustrations from Derek de Solla Price4s monograph on the 1ntikythera6echanism They are reproduced from the Transactions of the 1merican Philosophical Scoiety,

with permission


5/17

These two images are of the same fragment (


6/17


7/17

3. The Sun-Moon Assembly

Amages by +ill asselman

These two images gi.e a schematic .ersion of De Solla Price4s general gear planC on the right thecolor picks out the subBassembly connecting the sun4s motion to that of the moon

The sun marker and the moon marker were dri.en by the two central gears (the moon a"isthreaded through the sun4s), e"actly like the hour and minute hands on a modern clock The trainof gears linking the sun4s motion to that of the moon can be described by the meshing pattern and

the numbers of teeth

The sun gear has 9? teeth At meshes with the smaller of a3/,?/ gear pair The ?/ meshes with the smaller of a 2?,#2>

gear pair The #2> meshes with the 32 teeth of the moon

gear The ratio of angular speeds can then be calculated as>) )@ #!? !:)

HH I HH I HHH = HHH = #$*$>@)!** $@ !) $! #

which is an e"cellent appro"imation of the astronomicalratio #339/29>

Since the sunBmoon linkage in.ol.es an odd number of meshings, the two gears will turn in

opposite directions or the display to be realistic the sun and the moon must mo.e the sameway An the de.ice this was accomplished by a .ertical


8/17

This image can be

&a.aBanimated At

shows the operationof the SunB6oon

assembly, with a

somewhat fancifulsimulation of the

display An the actual

de.ice, the ;odiacconstellations were

represented by their

8reek names (


9/17

# = #$ L HHHHHHHHHHHHHHHHHHHHHHHH #

!L HHHHHHHHHHHHHHHHHHHHH #

#L HHHHHHHHHHHHHHHHHH # !L HHHHHHHHHHHHHHH # #L HHHHHHHHHHHH # #L HHHHHHHH # #?L HHHH etc

Stopping the process after the last had been a #, then 2%?F#$ would still be a continuant, but the denominator of the ne"t

continuant would only be 3 The other side of the same analysis then guarantees an error of at

least//

References

I 1llan +romley, 5otes on the 1ntikythera 6echanism, enta"r"s2(#$/9) pp %B2>

+romley proposes a plausible gearing plan, different in some important details fromPrice4s The differences do not in.ol.e either of the gear assemblys e"amined here

I Derek de Solla Price, 8ears from the 8reeks B The 1ntikythera 6echanism, 1 alendaromputer from ca / +, Transactions of the American Philosophical Society!4, part

> #$>?

I Derek de Solla Price, 1n 1ncient 8reek omputer, Scientific AmericanEune #$%$ pp 9B9>
http://www.math.sunysb.edu/~tony/whatsnew/column/antikytheraI-0400/kyth4.htmlhttp://www.math.sunysb.edu/~tony/whatsnew/column/antikytheraI-0400/kyth4.html


10/17

I D !lds, ontin"ed Fractions, -andom 7ouse (5ew 6athematical ibrary) 5ew York

#$93 (The result =uoted is Theorem 3/ on p >?)

I ' eeman, 8ears from the 8reeks,Proceedings of the #oyal $nstit"tion(8+) "#

(#$/9) #3>B#%9

CAD files for the Antikythera Mechanism

Antikythera Mechanism,CAD,engineering,projects

By request, Im making the CAD files for the model of the Antikythera Mechanismthat I created freely

available. Click that link for an overvie! of the "ro#ect.$

Do!nload the Antikythera Mechanism from %oogle Drive here. &oull need 'olid!orks to o"en it.$

It isnt "erfect. (here are a fe! issues that !ould kee" it from !orking if you )D "rinted this, and a fe!

more issues that make it not com"letely authentic to the original Mechanism. *ere are the "laces !here

the model differs from the Antikythera Mechanism. Italicizedissues kee" it from !orking if it !as )D

"rinted. I estimate it !ould take me +- hours to fi/ them it !ould require a redo of a lot of "arts$, !hich
http://theshamblog.com/tag/antikythera-mechanism/http://theshamblog.com/tag/antikythera-mechanism/http://theshamblog.com/tag/cad/http://theshamblog.com/tag/cad/http://theshamblog.com/tag/cad/http://theshamblog.com/tag/engineering/http://theshamblog.com/tag/engineering/http://theshamblog.com/tag/engineering/http://theshamblog.com/tag/projects/http://theshamblog.com/tag/projects/http://theshamblog.com/2014/01/05/presenting-the-antikythera-mechanism/https://drive.google.com/file/d/0ByXtJ-o_8yW6OEVYOHk3b1hpYVE/edit?usp=sharinghttp://theshamblog.com/tag/antikythera-mechanism/http://theshamblog.com/tag/cad/http://theshamblog.com/tag/engineering/http://theshamblog.com/tag/projects/http://theshamblog.com/2014/01/05/presenting-the-antikythera-mechanism/https://drive.google.com/file/d/0ByXtJ-o_8yW6OEVYOHk3b1hpYVE/edit?usp=sharing


11/17

I dont really have time for right no!. But0 if someone had access to a )D "rinter and !ould "rint me a

co"y "ro bono, I might be motivated enough to clean it u".

# All gears e/ce"t for the lunar "hase geartrain are assumed to have a module of .. (his is

actually the mean value of the modules for all gears in the Mechanism. A more accurate model

!ould account for variations in the gears.In one instance, this creates a collision between a gear

and a support as it travels around.A fe! gears should also be thicker.

2 I didnt use values for the "in "lacement radii on the e"icycle gears. (hese can be found in 1reeth

and 2ones 3(he Cosmos in the Antikythera Mechanism.4

3 (!o indicators should slide onto the Metonic and 'aros "ointers, and track in the engraved s"iral

on the back face. 'olid!orks had issues !ith a tangent relationshi" to a s"iral, so these are

su""ressed in the model but are still there5$.

? (he Antikythera Mechanism used a combination of adhesives, "ins, and friction fits as fasteners.

The model uses no fasteners, and would need a few if printed.All the gears that need to have

locked rotations are keyed and s"aced out !ith s"acers, but some of the keys are really small

loose pieces and should be changed.

% There are no tolerances built into this model.

9 (he Antikythera Mechanism used triangular teeth. (he model uses involute "rofiles. Solidworks

was having issues creating these profiles in a couple cases, and a few gears dont mesh

correctly.

> (he !ooden frame, "ointers, and "osts are creative inter"retations. (he large "ointers should be

removable in the real model to allo! the indicators to reset.

/ (he "lanet "ositions are not 6eroed to any celestial day.


12/17

Des"ite these differences, the form, function, and essence of the Antikythera Mechanism remain intact.

Also, some licensing info5

I am releasing this to the "ublic under a Creative Commons ). Attribution 'harealike 7icence. (hat

means you are free to use, edit, and redistribute these files so long as you a$ credit me for originally

making them, and b$ a""ly the same license !henever you redistribute it. (his means they !ill be forever

free. 8ith the follo!ing e/ce"tions5

# (he files 3"late back.sld"rt4 and 3a/le assembly a.sldasm4 are from the educational version of

'olid!orks and can only be used for educational "ur"oses. I dont kno! ho! that ha""ened,

because I have the commercial version of 'olid!orks. I must have edited something on my

schools com"uters.

2 (he files 3"late back lo!er dial v+."ng4 and 3"late back u""er dial v+."ng4 are taken from 1reeth

et al. 3Calendars !ith 9lym"iad and :cli"se ;rediction on the Antikythera Mechanism

Documents

Antikythera Mechanism Readme and Licensing Info