Antikythera Fragment #2 – Ancient Tool Technology – The Original Dividing Plate?


G’day Chris here, and welcome back to Clickspring. There’s some impressive engineering evidenced
within the wreckage of the Antikythera Mechanism. Not the least of which is the accurate division
of circles for both filing the gear teeth, and drilling
holes. Its even more impressive when you consider
that the average module of the device is a little less than 0.5. The tips of the gear teeth are separated by
about 1.5 mm, and the holes in the calendar ring groove
are separated less than a millimetre. The current assumption is that division was
achieved, using a set of dividers and other basic scribing
tools. For non prime numbers, a large factor of a
given tooth count can be marked out, and further subdivided for the final tooth
division. In this case the tooth count I’m dividing
is 64 and the initial factor that I’ve selected is 16. Starting from a fixed position on the perimeter, the first interval is determined by trial
and error, by walking the dividers around the wheel. Once a uniform division has been determined, the dividers are then used to mark out that
coarse division. The final tooth divisions are then placed
within each of those coarse divisions. Either by again walking the segment with dividers,
or simply splitting it by eye. A similar approach can be applied to prime
numbers. It is more time consuming , given that it
requires dealing with fractional counts instead of integers, but it’s doable. Although by no means would I describe any
of this as easy. In fact its quite a challenge to manage the
errors. Modern precision dividers and vision magnification
are essentially a requirement for success. If I remove those modern advantages, as would
have been the case in the ancient world, then something becomes immediately apparent: The smaller the module of the wheel, the more
impractical this method becomes. Or put another way, if I were to scale everything
up, the job would become much easier and potentially
much more accurate. Working with only the naked eye and simple
dividers, this fact would not have been lost on the
original maker. OK, now set that to one side for the moment, there’s something else about this method that’s
worth noting: It doesn’t do anything to assist with the
many repeated tooth counts within the mechanism. There are 7 wheels with 60 teeth, 4 with 50,
3 with 53 and so on. Of particular note is the high probability
that 2 wheels have the large prime number of 223 teeth. That’s a lot of task repetition, that any
maker no matter what era they might be from, would have wanted to avoid. Certainly a ‘master’ version of each count
could have been made to transfer the divisions to subsequent wheels. But this would at the very least have required
a simple platform to register the blanks with the master wheel. And having tried it, its not particularly
easy to transfer the markings, without introducing an unacceptable error. If such time saving concepts were considered
at all, then surely the issues discussed so far would have drawn the maker to at least consider
the possibility, of simply scaling up the divisions, on a jig
designed for repeated use. It could have been constructed from a flat
piece of wood, using only basic tools, and would have required
no more than a few days to complete. The easiest non prime numbers could be marked
out first. I started with 60 divisions, using the larger
factor of 10, and then further subdividing into intervals
of 6. Each step up in value leverages the factors
of the adjacent counts, speeding up the task significantly. And again, the prime numbers are a little
more work, but because the diameter of the circle being
divided is so much larger, the intervals are also much larger. So the scribing error is proportionally reduced. By moving the divisions out to a much larger
diameter than the wheels, the resolution is effectively increased beyond
what it would be if stepping off the divisions directly onto
the wheel surface as before. Its much easier to minimise the angular error, particularly when restricted to only non precision
tools and no magnification. A pin in the center, is all that’s required
to register each of the wheels on the platform. And a simple bushing means the pin can rotate
freely without wearing out the hole. In use, the wheel would be placed upon the
central pin, with a simple adhesive to lock it in place. In this case, I’m using shellac resin. There are a several ways to mark off the intervals. One way is to use dividers to scribe a small
arc on the perimeter, whilst stepping around the divisions. But an alternative is to use a simple straight
edge. I made a riser that will lift it up parallel
to the top surface of the wheels. I also made a small pin to fit to the straight
edge, to help locate it in the division markings. And as a convenience when using it, I’ve put
in a set of markings down one side, to make it easy to confirm that the pin is
engaged in the correct division circle. Once in use, the advantage of a jig like this,
becomes clear. The guesswork of stepping the intervals off
around the actual work piece is replaced with the relative confidence of
knowing that the hard part of the job has already been completed. Errors have been checked, and counts confirmed, all on the larger and more accurate scale
of the jig. And this is the key point that I’d like to
make: This looks like a more complex approach, but in reality it uses only tools known to
have existed at the time of the mechanisms creation. Most importantly, no vision magnification
is required to achieve a consistent successful result. Compared side by side the accuracy of each
method is about the same, which says a lot for the second method given
that no magnification was used. But when it comes to time to completion, there’s
no contest. Minutes for the second method versus potentially
hours for the first, especially for the larger tooth counts. Which brings me to the second big payoff of
the jig: Dealing with repeated tooth counts. The 60 division ring for example provides
the markings for 15 different wheels and pinions, generating
a massive time saving just on its own. Its also worth pointing out the 2 largest
wheels in the mechanism. One of them, E3, is required to have 223 teeth
to perform its role within the mechanism. B1 also most likely had 223 teeth. But that number plays no apparent role in
the mechanisms calculations. It could easily have been any number between,
say, 200 and 280. So if it was indeed 223, then that choice
is interesting. There are few reasons to select that more
difficult prime number, over more easily divided alternatives. Unless of course, it already existed on a
jig, making it an entirely logical choice. Now you’ve probably recognised that what I’ve
made is essentially a classic manual dividing plate. And I understand completely that I’m suggesting
something more than a little bit radical. That perhaps the Ancient Greeks had a manual
dividing plate a very long time before such a thing is generally
accepted to have existed. But just to be clear before I wrap this up, I’m proposing this method as an addition to
the manual division technique, not as a substitute. If it existed at all, and its a big if, then I would expect both methods existed side
by side, and were simply applied as the circumstances
required. For a higher module device with relatively
few wheels, like for example the Byzantine Sundial Calendar, manually stepping off the teeth would have
been accurate enough. So its easy to imagine the worker just not
bothering with the time investment of a jig. But I think once the module gets below 0.5
and if there are multiple repeated tooth counts, then the motivation to come up with a solution
like a dividing plate gets stronger. As to whether it actually existed? Well who knows. Maybe the Ancient Greeks just had really good
eyesight! For now it’s a bit of fun speculation, and
I share it with you only because it’s something that the process of reconstructing the mechanism
has led me to consider. I’ll continue to use both methods throughout
the build and see what turns up. Thanks for watching, I’ll see you later. Now if building geared mechanisms like this
is your thing, and you’d like to help me make these videos, then I’ve got just the thing for you: A modern reproduction of the 2nd oldest geared mechanism from antiquity. The device known as The Byzantine Sundial
Calendar, and also known as the London Sundial Calendar. I’m giving it the full reproduction treatment, but more from the perspective of how an 18th
century clockmaker might have tackled the project. So you’ll see all of the techniques and materials
that I’ve started to explore with the skeleton clock project, but developed further to work on this much
more condensed scale. Patrons get the same deal as for the first
patron series project. Exclusive access to the build videos, free plans for the patron series projects, and of course the added bonus that one lucky
patron will get to keep the finished project at the
end of the build. Visit Patreon.com/clickspring to find out
more. Thanks again for watching, I’ll catch you
on the next video.

100 thoughts on “Antikythera Fragment #2 – Ancient Tool Technology – The Original Dividing Plate?

  1. One thing about this machine that is truly surprising, is just how small the teeth are.

    There's a well established theory as to how the tooth divisions were marked out, but employing that process to mark out multiple wheels has forced me to question whether it can reasonably be applied to the Antikythera Mechanism.

    So in this video I propose an alternative process of wheel division, using only the non precision tools of the period.

    Please enjoy!

  2. just notcied something:
    There is an easier and specially far more precise way of dividing a circle.
    You can get a multiple of 3 just by using the initial radius and getting a multiple of 2 (like 64) is also easy as halfing angles is easy to do.
    For 64 you could start with 2 perpenticular lines dividing the circle into 4 segments, then divide the segments into 2 – 2 times. and you have your 64 segments. You could also just do this for 1 segment and then copy it around.

    But should be more precises than trying to eyeball it.

  3. Your voice, the content, the background music, the video quality. It's like a bedtime story for the modern man. Tell me another story Chris.

  4. The way i look at it the Antikythera device existed as complicated as it was, and in a time period when it was assumed they wouldn't have devices that complicated. So why couldn't a dividing plate?

  5. makes me wonder if there was a way the two were used together. to not only measure accurately but to cut accurately.

  6. I am a master machinist and I will tell you few people have earned my respect like you have – especially in the way you work with simple tools to achieve such results. And Thank for your passion!!!

  7. i think the ancient greeks might have done this by "simply" dividing the 360 degree angle of a circle by the number of segments required. still amazing though, no matter how they done it, simply the fact that it has been done never ceases to amaze me. most of the people today couldnt make this, even with all modern machines.

  8. Why not take this a step further? Surely it would not have been beyond ancient technology to manufacture and the imagination of Antikythera craftsmen to prepare a work holding fixture for filing that would have allowed rotation of the blank along with the dividing plate so that the marking step is totally side stepped and the filing could be more accurate?

  9. this is simply incredible, the effort you put into your projects. I sometimes wonder whether the internet is more education or distraction. your videos make me forget all the distracting stupid bs out there and make me really really glad to live right now and to have access to such incredible content.
    there are no words to express my gratefulness to you! thank you!

  10. also I think if you can come up with a mechanical computer like the antikythera mechanism, it wouldn't be surprising if the same person also came up with the idea of the dividing plate….

  11. Chris, it would make sense, to me, at least to think that the ancients would have used things like the dividing wheel you made and used here. If you think about it for a while, you can come up with a good deal of mechanical objects that would have benefited from ready made dividing wheels. Sundials, wagon wheels, pin driven wheels and torque producing items like a water wheel would be some uses. Also, division of circles are important for navigation and surveying equipment, too. In lieu of those things, among quite a few others, it may be possible that dividing rings or wheels were used to reduce vision errors in common construction. Maybe?

  12. One point you didn't mention about jigs, is that they come into their own when you need to make many copies of the same item. It is likely that if a mechanism is useful, then the maker won't simply be making one of them, but will be making many of them in a production line as a business. Once you are doing that, every jig that shortens the production time and increases quality will be a business asset. You make one-off items for amusement and diversion if you have free time and money to spare, but who in the ancient world was in that position? Far more likely were artisans and craftsmen looking to make a living.

  13. I worked with a man who was very near sighted. When he took off his glasses he would look at things from about 3 or 4 inches. He didn't need magnifier glasses to do small work.

  14. Just a thought. A project of the complexity of this mechanism. It seems that they wouldn't just suddenly decide to make this incredibly complex machine. They made others, a lot of others, of similar and less complexity. This just seems logical.
    So if they made others, they wouldn't have started making each wheel from scratch. Each dividing layout. They had dividing layouts on wood at the least, that were used in other mechanisms.
    So it is a logical progression. Simple machines, a 'dividing head', more complex machines, more capable dividing mechanism and so on.
    It seems that by the time they progressed to the Antikythera mechanism they would have had very complex and capable dividing heads. So take that a step further. They were sophisticated enough to build the antikythera mechanism, making a sophisticated dividing head would have been simplicity,
    This make sense? For that matter, it is only a small step from making a dividing head to building a manual mill, files in guide slots, to work with the dividing head.

  15. What impresses me even more than your already very impressive skills, is your patience. I don't think i can even begin to fathom the amount of patience one would need to do what you do, and as is with your skills, i also lack the patience to do anything like this which is why your videos are so interesting, they allow me to share the experience without sacrificing the countless hours to do it. Thank you for sharing this with us.

  16. Now that I subscribed ti this channel every time I hear the jingle bells at the beginning of the videos I start salivating like one of Pavlov's dogs.

  17. Ancient greeks had same eyesight as us, perhaps even poorer, but they were just as smart. They definitely used a jig.

    Look up the video about the Parthenon build built and how they discovered a clever trick used by the ancient greeks to taper their columns (a visual refinement) by using a simple measuring tool. Absolutely amazing.

  18. it would have requiered a simple sort of lay-over example, based on the geometry extending from the vesica pisces, to divide the wheel accurately. Punch-marks on the intersections would do the trick?
    Excellent work, thank you for sharing!

  19. Excellent theory to bygone days engineering problem solving. A history class and an engineering master class in one channel. Very interesting content.

  20. Slate. A sheet of slate for the jig. Nice and flat and could be marked out easily. And stable with temperature and humidity variations as well. That's what I would have used !

  21. The Ancient Greeks were many things, but stupid was not one of them. They were easily clever enough to come up with a simple but accurate and time saving device such as this type of dividing plate.

  22. At 5:27 I thought to myself "I'm going to need a few moments to reassure myself how that works in theory,
    but I know Chris will confirm that it works in practice, so I can already celebrate its brilliance !
    That's a phenomenally sweet, and also elegant, way to solve an apparently intractable problem.
    Kudos, kudos, and kudos.

  23. really enjoying your channel! Despite religiously watching about 15 channels yours is the first and only one I have decided to back on patreon! Thanks and keep up the great work!

  24. Mathematics are a wonderful tool. Maybe they got into linear algebra or calculus to figure out the 223 tooth count divisions? Is this clock from before that era?

  25. To say that I am impressed with your patience, your meticulous attention to detail, your ability to explain things and your skills would be a gross understatement.

  26. I think the dividing plate is a likely tool for someone to come up with in that time period. Who ever built the mechanism did this type of work daily and not as a one of for someone who asked for it. Working daily for years in any trade will inspire a craftsman to make tools to make his work easier,the same way it has forced you to consider alternative ways to approach a problem. Awesome work,I enjoy this series very much

  27. Mehkehnizm
    Haha. You say it soooooo much.
    I’m only takin the piss mate. I absolutely love this channel. You do a lot of fantastic work, and have a love if ancient tech like I do. I do very similar work. But I’m not making a mehkehnizm. 😉 cheers lad. Class stuff.

  28. Oh god just use chord length calculation and set the dividers to that length, would they have been able to do it that way?

  29. What method in ancient times was used for accurate grading/marking straight edges? Rules for example.

  30. You do a lot of lathe work in your videos. Can you explain how that may have been done in ancient times? I love your work btw. Very inspiring

  31. Do note that when marking divisions with a compass, anything divisible by 2, or 3 can be started using the radius of the circle as the starting point, pick any random point on the circle, center punch it, then use the compass to mark spots that are 1 radius away from that point, repeat until you have 6 points, they will be perfectly equidistant from the center and from each other, the pattern can be expanded, but this requires the original circle to be a fraction of what the outside one will be, so it might be easier to simply index on the first iteration of the pattern, and go from there. Hexagons are dope as hell.

  32. You sir, are a clever dude. I loved your original skeleton clock project, and continued content has earned you another subscriber. Your style, delivery and the quality of your work will eventually net you over a million subscribers, I’m sure. And you deserve many more than that. Great, great work fella and good luck.

  33. Where did you get/who makes the dividers you use? They appear to be much more beefy and sturdy than any of the commercially available ones I've used. Amazing work as always!

  34. This multi use dividing plate is an inspired idea, but it leads me to wonder would it not be possible to figure out the divider length through mathematics rather than trial and error?

    If you have a circle with radius R and a regular polygon with N sides inscribed inside the circle you can know the length L of its sides with
    L = 2 * R * sin(pi / N)
    set the divider length to L and bam! correct division length on the first try

    Even if it was only used to make the dividing plate in the first place it would certainly speed up getting the correct length from the divider and probably be more accurate than trial and error

  35. Clickspring, I've just recently discovered your channel, and I am enjoying it so much. I have always admired the antikythera mechanism and wanted to know more about it. Thank you so much for these videos!

  36. wonderful, simple and very logical approach. Ancient Greeks also had Heron's Pantograph, a device that used large scale templates to accurately copy/reproduce smaller duplicates.

  37. Someone linked me this when talking about ancient soldering and I've been hooked on watching you build this since.

    This video in particular really sticks out to me because I feel like this dividing plate jig is exactly what the maker of the Antikythera would've used. It just makes sense. The other tools and creations that we've been able to reproduce or were fortunate enough to be preserved allude that the Greeks were crazy smart, and a smart engineer will find the easiest solution to a problem because they're lazy. This is a motif that seems to span all manners of engineering. Look at any modern feat of engineering and it seems very complicated, but underneath it all is just very simple concepts.

    The 223 teeth being used twice makes perfect sense if paired with the assumption that the maker used a jig that already had the divisions. The division plate itself just feels very appropriate for what we know about ancient Greek culture. Personally I think that's exactly what would've been used. Maybe not precisely the same as you made it or what future incarnations of it looked like, but definitely similar in principle. It's a simple and easy solution.

  38. Seems like the method of manufacture was used to make future repairs easier without having to refabricate an entire gear. Especially if the parts were not interchangeable because of hand fitting.
    Like old flintlocks didn't interchange.

  39. Not just a question of really good eyesight but also of lighting. Doing this outdoors in full sun could be a real problem. Indoors by the light of a oil lamp, I have my doubts. The maker, or the makers workshop must of had some sort of filtering system to allow enough natural light to illuminate the work space yet avoid the glare that working in full sun could have caused. It could be as simple as a sunshade made of a reasonably translucent cloth. Maybe he pinched the wife's best nightgown. The maker, whoever he was, was truly one of the most talented craftsman of his age, or any other. Did he work alone? Did he have assistants similar to the apprentice system of the Middle Ages? Was he a free man? A slave? Did he design the device or was it commissioned by some genius who worked out all of the principles first? Did the maker produce multiple machines?

    Alas we will never know. If we have sculpture dedicated to other giants of that time there should be one dedicated to the maker.

  40. I think that with the knowledge of mathematics of the time, your method of using dividers for the odd tooth gears was too time consuming. The trial and error method with dividers I don't believe would have been used by someone that had the creativity to create the mechanism and the knowledge of mathematics of the day. I have a theory of how they were able to achieve the accuracy. I would like to hear your thoughts on idea and can be contacted at [email protected]

  41. how would someone make the tiny gears that would have been in pocket watches useing the tools available in early 1600s ?

  42. I scrolled the comments, but is there any chance they used a pantograph to draw the gear large and then reduce it onto the smaller gear?

  43. Chris if you say something wasn't easy, like manually marking a wheel, it must mean it's fiendishly difficult for a mere mortal such as I

  44. Wait. My math classes have indicated that there weren’t locking or fixed compasses in ancient times. To what extent would that affect the processes used by the original makers?

  45. there is the Bion-Rinaldini method (or general geometric method) to divide the circunference in N sides. only straight edge and compass method. Might worth a research

  46. Could you please provide link to Shellac resin used? Can't find it on amazon or ebay. Amazing video as usually! Thank you

  47. thank you very much for your videos are great! I wanted to ask you please, if you can subtitle them to Spanish

  48. Thanks for this wonderful series. Your dedication to your craft is an inspiration to us all.
    One clarification from an astronomer: the large prime number 223 is the number of synodic months (eg. full moons) in one Saros cycle, after which the Earth Sun and Moon return to the same configuration. At 7:50 you suggest that while this number of teeth was needed for wheel E3, the appearance of 223 teeth on wheel B1 is arbitrary, and perhaps due to the proposed use of a jig. But is it not also plausible, or indeed likely that the B1 wheel did indeed require 223 teeth for an eclipse-related purpose, perhaps not known to us? Could it have actuated gears not currently known, for example?
    To be clear, I do not wish to discourage your hypothesis of a jig, nor your other hypothesis of a "dividing plate" being invented by or known to the Antikythera Maker long before it is known elsewhere in history. Indeed, so much about this device pre-dates all known similar technology, that such hypotheses are by no means radical.

  49. Man. You are just, amazing. My brain can't even comprehend that fine of a level of detail. Excellent excellent work! I like that your fastidiousness also shows in your video editing.. it really makes your work "pop"! Cheers

  50. Sir, you are an artisan in your hobby, so satisfying to watch you work and a joy to listen to your narration, newly subscribed I'm happy to learn more at my age from such a person.

    Thank you for your efforts and showing me what can be done in a simple way.

  51. Chris, I very much like your videos but I very much dislike the jingle-jangle background music, if one can call it music. Please cut that out. Your English is fancy enough, at least to my ears. A fellow mechanician

  52. Hi Chris, these videos are amazing. I thought you might be interested in these two articles.
    1. Minoan artefact which shows many of the algorithms (orbital periods) used on the Antkythera mechanism are known from around 1700BCE on Crete. Also that rock crystal lens are known from at least 700BCE on the islands.
    https://www.quora.com/Do-you-think-the-2000-year-old-Greek-computer-was-actually-real/answer/Nick-Deakin-4?__filter__=&__nsrc__=2&__snid3__=5053402599&comment_id=105999925&comment_type=2
    2. This is produced around 1400BCE, it shows the use of a compass and a milling bit of around 30micron and placement precision of around 5 microns! Amazing.
    https://www.quora.com/What-do-you-think-is-the-greatest-thing-human-hands-have-created/answer/Nick-Deakin-4?__filter__=&__nsrc__=2&__snid3__=5036162251

Leave a Reply

Your email address will not be published. Required fields are marked *