Laser cutter experiments

I recently joined the Cambridge makespace. It is a very well equipped workshop with a good community of members. Most of the machines require a specific training and last week I did the one for the laser cutter. This is not the first time I have used a laser cutter. I made a few small pieces using the one in the Google LA office back in late 2019 or early 2020. I think it was an Epilog. Makespace has a larger cutter, a LaserScript LS 6090. The Epilog was a little easier to use, for example it has auto focus, and to send a job to it you used a custom printer driver. The LaserScript (usually referred to at the Makespace as HPC) requires loading up a DXF into software called LaserCut, mucking around with it in various ways, and finally downloading a file to the cutter and running it. The software and workflow feel very last century, but it works.

The goal I am working towards is to create a back panel for the functional reproduction of the Antikythera Mechanism which I have described in several previous posts. I stalled out for a while, and recently started working on it again. As well as figuring out the back panel, I've been redesigning some of the mechanism to make it more stable.

The back panel is believed to have looked something like this:

(Attribution: By Tony Freeth - Original publication: The Antikythera Mechanism Research ProjectImmediate The Antikythera Mechanism Research Project, Fair use, https://en.wikipedia.org/w/index.php?curid=36445604).

I wanted to make it transparent to show some of the internal workings. The two large spirals, called the Metonic and Saros outputs) each have a groove in which a pin runs. The pin is mounted on the radial arms and slides along them. When it reaches the end, you have to lift it out of the groove and reset its position.

Cutting this will be a large and difficult project, and so I started with a few test pieces to learn more about what works and what doesn't, and to reinforce the things I learned in the training. Here they are:

At the top is a simple square, with a square line on it, used to get the basic settings right. The material is clear 3mm acrylic. I'll record the power settings here for my own reference. The cut was speed 10, power 100. I later changed the speed to 9. The line was speed 30, power 50. It is very shallow, less than 0.5mm at a guess. The cut only just goes through the material and some of the bottom edges feel a bit rough. Either more power or a slower speed might work better. There vertical edges slope slightly (I think this is called kerf), so that the top edges are about 0.4mm shorter than the bottom ones. In terms of absolute dimensions, the top edges are about 0.6 to 0.8mm smaller than the design (30mm), while the inner line is about 0.2mm smaller than designed (12mm).

The second piece has grooves of width 5mm, 2mm and 1mm. The circles are for M2, M3 and M4 diameters for tapping and clearance, the exact size, and the text and remaining two circles are lines just to see how they looked. One issue I had with this is the material between the grooves warped. I guess it must have softened a bit and sagged. The hole for the exact size test are about 0.4 to 0.5mm larger than they should be, and the other holes are similarly oversized. The holes for tapping took the thread OK, but were a bit loose. I can't say how much this is due to the holes being oversized and how much to my lack of skill in tapping them. I'm used to the dimensions being slightly off from 3D printing and will make adjustments for future work.

My design workflow for this and the final piece was the create a sketch in Fusion and export it as a DXF. In Inkscape, I then ungrouped objects and converted them to paths before saving them as a new DXF. The DXF directly exported from Fusion does not work in LaserCut: some or all of the lines are missing. I also tried using the free ShaperOrigin plug in for Fusion. It saves sketches as SVGs, and these can again be loaded in Inkscape, manipulated and output for the cutter. For reasons I don't recall, I think the second method worked a bit better.

The final piece is a test run for the backplate spirals. It has a smaller radius than I will need (50mm inner radius instead of 75mm or so) and the groove makes only two complete revolutions. The result is very flimsy and pulls itself out of shape. You can see this by looking at the two radial lines at the 3 o'clock position. They should line up. I've yet to try a pin in the groove. I'm not optimistic that it will work well.

This leads to a few ideas for improvements. First, I could leave some tabs in place in the grove, then glue a support piece to the back and cut through the tabs. Other reconstructions definitely use support pieces; for example you can see them in the Chronova Engineering video. I don't know if the slot, currently 1mm, will be wide enough and it would certainly need to be polished for smooth running. Another option is to drop the pin-in-groove idea and use the spiral pointer adopted by Spencer Connor. It's less authentic, and require a 5:1 bevel gear which is rather large, but works nicely.

The Antikythera Mechanism 8: That's all for now

I've wrapped up work on the 3D printed Antikythera Mechanism for now. There are a few parts that are incomplete, and I would like to come back to it in future and redesign it. For now, I am out of patience and energy. So let's take a look at what worked and what didn't.

Some things which worked

Overall: the mechanism runs fairly smoothly and without excessive friction. Win!

Frame design: the skeletonized and split frame works well. It is rigid enough and has the right geometry, but without taking an excessive time to print, and it can easily be split into pieces which fit on the print bed.

The splits for the frame and the large gears are also good. Using M3 screws to hold the parts together makes them rigid enough, and adding 2mm dowels as alignment pins also helps. Some of the fixings are a little ugly, especially the brackets to hold the halves of b1 together.

Thin supports for the larger gears where they wobbled on their axes: this eliminated most cases where the mechanism was seizing. I also tried supports for b3/b4, but later found I didn't need them.

Press fit hex fixings for joining gears on the same axis.

Push-on shaft collars for gears where the axle was held only at one end. These worked quite well, I saw them slip off occasionally, and for long term use they should be glued in place. The shaft collars worked particularly well in the cases where I could bury them within the hub of a gear, saving vertical space. Similarly the fixing holes consisting of a hole and a slot worked well. It is possible to get pins into them without excessive force, while having a firm fit which won't work loose.

Most of the axles and pins are standard lengths. In past projects, I've often cut them to length. It's easy with brass and a harder with steel. Standard lengths, by which I mean ones I can easily buy, are better.

The gear sizes are mostly right. I discussed the choice of modules and the exact separation in an earlier post, especially as they deviate from the ones in the HAM.

Some things which didn't

Gear sizes for output: the modules I chose for the output gears meant that they had to sit quite far from the center. It pushed the spirals out while still not leaving much space for the Games, Callippic and Exeligmos dials. With a smaller module they could be moved further in, freeing up space. This is not hard to do but requires reworking the backplate geometry, and I ran out of enthusiasm to do it. Similarly, I never completed the output spirals and a change to the geometry to allow more space for them would make them easier to design.

Some of the shaft collars are not tight enough and slip off. It might work to make them longer where there is enough space. Otherwise, the only solution is to glue them onto the pins.

The planets stages use more vertical space than I would like. I tried thinner gears (doesn't save much, makes the mechanism more unstable), and I looked to see if I could interleave the gears in some way, but didn't find any arrangement that worked.

Finally, as I previous described, the a1 support isn't very stable and could do with a redesign, as part of generally redesigning the mid and back frames.

The Antikythera Mechanism 7: Input and Output

 

The mechanism up to this episode is working, with the only remaining elements being the input and output. The input comes from a gear known as a1, which drives the large b1 gear. a1 is at right angles to b1, but because of the difference in sizes (48 teeth for a1, 223 for b1), a bevel gear doesn't work very well. Instead, I made b1 as a regular flat gear, and then added a flat 48 tooth gear for a1. A set of bevel gears is mounted on top of a1. This assembly was a bit of an afterthought, and so I had to make a bracket which extends the existing back and mid planes. I decided I preferred a simple knob rather than a crank. The result looks like this:

It's a little wobbly but works well enough.

The planets output consists of pointers attached to the nested brass tubes. Most reconstructions use concentric rings. Freeth points out that this is better as it avoids parallax when reading the positions, and also allows the rings to be annotated with synodic events such as opposition and conjunction. By this stage in the project, I was cutting some corners and so went with the simpler scheme. Spencer Connor's version takes a similar approach. The upper output stage also accommodates a bevel gear set driving the moon phase output.

Instead of a 3-D printed dial, I printed the dial onto card. Here it is before mounting on the frame. I again followed Spencer Connor's version by using English month names, with displays for the zodiac and the actual spans of the constellations. The actual Antikythera Mechanism appears to have had a more complex output including an outer calendar ring which could be moved. The diagram was constructed as an SVG using a Python program.

The back outputs consist of the Metonic and Saros outputs and three smaller pointers. The Metonic and Saros should consist of a spiral groove which a pointer moves in, driven by the corresponding output gear. An alternative, with some advantages, is in the Spencer Connor video linked above. The spirals are large and my original plan was to laser cut them into pieces of acrylic or MDF. Unfortunately, my local makerspace (https://web.makespace.org/) has been closed to new members for some time and so I have had to defer this part of the work. I could have followed the model on cults by printing the panel in multiple separate parts. In the end I decided the shelve the back outputs for now. As we will see in the next installment, I've learned a lot by getting this far and may do a redesign for a new version.

The Antikythera Mechanism 6: Jupiter, and Beyond The Infinite

The mechanism is now really taking shape. I did more work to stabilize the back gear. One change was to add a rim on the top of the midplate which the b1 gear can rest on. This made a lot of difference and once I had done it, the mechanism began to move more smoothly. Both the inferior planets and the superior planets have a gear that must be fixed and so some work was needed to anchor them indirectly to the midplate and backplate. It's a bit hacky as present, as I hadn't thought ahead about how to do it, and so I used extra bits of framing that could be attached to the midplate. A redesign will follow.

I also made the decision to use brass tubes for the outputs instead of printing them. The thinnest tubes are the longest ones and so hard to print accurately as well as being fragile. The brass tubes I selected have diameters from 4mm to 11mm in 1mm steps, and they have walls 0.45mm thick. They are a snug fit but able to move freely. Some of the tubes came from K&S Metals, others from Albion Alloys, and I bought them from Macc Models in Macclesfield, England. Here's how they look (the middle 4mm one is not yet cut to size):

You can also see that the top frame had to be split into two to fit the printer. The superior plate is just underneath it, and with a bit of creative truncation it will just fit on the MK4 print bed.

Here is the mechanism running without and with the output pointers. You can see the retrograde motion.

The long "dragon" hand looks odd to me, and I'll check that later.

The next step will be to add the moon phase. At this point I can cut the 4mm brass tube and the (currently hidden) 3mm brass rod that connected with b3 to size. Freeth argues that the hands should have their tips in the same plane to avoid parallax; I might also do that later. The back pointers with the spiral Metonic and Saros dial are also still waiting.

The Antikythera Mechanism 5: Back Gears

The back gears lie between the large b1 gear and the outputs on the back, consisting of the Metonic and Saros spirals and the Callippic, Olympiad and Exeligmos dials. There are two slightly different versions of the configuration, from the Freeth 2012 and 2021 papers. I used the more recent one, which differs from the other only in swapping the position of the gears on the n-axis. The back gears are better supported than the planet gears, as most of them are on axles running between the midplate and the backplate. However, as we will see, there are some issue with the stability to deal with.

The following diagram, S20 from Freeth 2021's supplement, shows the arrangement of the gears.

Some co-axial sets of gears such as f1 and f2 can often be combined into a single printed object. The f-axis is also an example of an axis with no output. The diagram shows its axle as not extending to the backplate. By extending it and adding a spacer, we can make it more stable. Similar considerations apply to the h and p axes. The m axis can't be extended in this way as there isn't enough space around n3. Some axes extend through the midplate, for example d and m. For these, the gears are printed as separate objects, connected by a hexagonal extrusion on one which engages with a hexagonal socket on the other. I experiments with setting the size of the extrusion the same as the socket and 0.1mm smaller. Very close tolerance like this are a bit of a guess with 3D printing. Different printers, slicers and filament may end up with the fit being a bit different. If they don't fit, they can be sanded down until they do, and if they are too loose, they can be glued. I have this value set as a variable in Fusion, so it can be changed across all the parts that use it. I also noticed that the fit varies from one orientation to another. When I initially printed the m1 and m2/3 gears, they fit was quite loose, but rotating them 30 or 60 degrees relative to each other gave an adequately tight fit. In the end all the gears with hex joins seemed to work fairly well, but for the m and d axes, I allowed for a M3 screw to help hold them together, if it should be needed.

The axes which come through the backplate to form the output have a hex socket on the end, which a pointer will plug into. Most of these axes consist of two parts: the gear with an extended hub meeting up with the midplate, and an axle plugging into the gear and extending through the backplate. The n-axis is a bit different due to an extra gear, and the i-axis has the axle going to the midplate rather than the backplate due to the tight space. In some cases, I added a ring round the axle of hub to keep it stable. Here is an example of the entire n-axis in cross section to illustrate:

In this version, the hub of gear where it passes through the midplate is printed. In a later revision, I replaced this with a dowel pin.

Both the midplate and the backplate are large, much bigger than will fit on my print bed. The design by FizzyChickens splits these into smaller pieces which are clipped together and glued. It's still a lot of material to print, and large flat pieces like this are prone to warping. I decided on a different design, where I made a skeleton with just the necessary fixing points and enough mechanical support to make them rigid. These still have to be printed in two large parts, plus a circular bracket on top and two smaller brackets. The result is quite robust and also takes a lot less print time. Here is what it looks like:

A few M3 screws hold it together. Alternatively, it could be glued, maybe using M3 screws temporarily to keep everything aligned until the glue takes effect. There are two small brackets, intended to go underneath the frame. I later got rid of these as I don't think they are needed and they take up valuable space. The external back panel will need to be made from a complete panel. Maybe laser cutting it would be best.

The e3 gear is too large to fit on the print bed. Initially, I intended to split it up the same way that I split the large gear in the Swingtime clock, by dividing it in half and gluing the parts together with metal pins to help the alignment. The e3 gear is attached to another large gear called e4, and this is small enough to print as a single piece. So I decided to split e3 in two and attach it to e4 with screws along the spokes, plus a few extra ones on a tab. I arranged the position of the split so that it does not divide the hub in two, which makes for smoother movement. The three pieces look like this:

In a later revision, I also added some horizontal pins to the halves of e3 for alignment and extra stability.

Did it work?

The prototype back gear assembly worked somewhat, but not very well, as you can see in this video:

The calendar and eclipse prediction gear trains work well individually. They are supposed to work together, connected via the e-axis gears, and driven from b2, which is attached to the back of b1. In the last segment of the video, you can see that the mechanism seizes up. This is caused by (I think) a combination of friction and the larger gears tilting. In particular the very large e3/e4 gear and the d2 and m1 gears tilt a lot. The friction can be reduced a bit by lightly sanding the gear teeth as well as the parts of the gears that run through the frame.

The gear tilting is the bigger problem. The historical Antikythera mechanism includes supports near the rim of these gear which help keep them level. Although this increases friction locally, the net effect is to keep everything in alignment. I decided to try this out in two ways. For e3/e4, I added small brackets to the frame which lightly hold the rim of the gear. For d2 and m1, I added a thin flange to the gears themselves. In the HAM, supports attached to the midplate are used for both. The results are a bit better:

It still has a way to go, but is getting closer.

More changes

I made most of the gears 3mm thick in this version with just a few either 4mm or 5mm. I think it's better to make more of them at least 4mm. For the gears with a hub through the midplate, but which do not have a gear on each side (for example the n-axis), I had made the hub 10mm in diameter. There isn't really a need to do this, and for the next iteration, I replaced the hub altogether with a 3mm dowel for most of these. The e3/e4 brackets in the video hold the gear on both sides, when one side will do.

I broke the b3 gear tube during testing. It will eventually be much longer and go all the way through the planet mechanism. I'm not even sure this can be printed reliably and so I will probably replace it with a brass or steel rod. Similarly, I might replace some of the printed tubes in the planet mechanism with brass tubing. I've not decided about this yet.

The Antikythera Mechanism 4: Superior Planets Prototype

The prototype for the superior planets (Saturn, Jupiter, Mars and the true sun) uses similar design principles to the inferior planets. It's hard to video it in operation as there are parts that won't stay in place until it is combined with the front plate and the inferior planets. You can see the pin for the Mars gear slipping out its slot. I'll use a longer one in the final version.

The video shows first the Saturn and Jupiter trains and then the Mars and true sun ones. In the assembled version they will be linked by the sp1 gear. The superior planet plate is truncated so it will fit on the print bed. For the final version, I'll need to either find a larger printer or split it into parts.

There is only one new design element here: the use of an axle to hold the pair of eccentric gears used for the epicyclic motion, for example like this in the Jupiter gear train with the axle highlighted:

The two circular hole are for screws to hold the axle to the superior plate, and the remaining hole is for a dowel pin on which the eccentric gear will run.

I used black non-silk PLA for some parts of the prototype. Getting the dowels pin in is much harder with this filament, probably due to slight differences in how much the filament expands or squishes when printing and because it is less slippery than silk PLA. I filed out the holes in some cases to make pins fit more easily.

Next, to the back gears, a larger and more complex part of the mechanism.

The Antikythera Mechanism 3: Inferior Planets Prototype

The inferior planets mechanism is a part of the Antikythera mechanism which models the motion of Mercury and Venus as seen from Earth, as well as the mean position of the sun and part of the information about the phase of the moon. This part of the mechanism was not found amongst the recovered fragments and so has to be hypothesised from the required motion and some hints provided by fixings on the parts that were recovered. There are several versions, with the most recent one in Freeth's 2021 paper. The previous version was also proposed by Freeth, in a 2012 paper.

I decided the make the inferior planets mechanism as a prototype for the design. I cut some corners, in particular only printing part of the large b1 gear and printing short versions of the tubes which will ultimately carry the output pointers. Here is a very shaky video:

It moves fairly smoothly, so the dimensions and tolerances are about right. Some things I want to change or experiment with:

• the two dark coloured gears in the middle are wrong. After printing them and the b1 fragment, I noticed that they should have a tube which runs through b1 and is fixed to a (not yet implemented) back plane. See Freeth 2021 supplement section 6.2.6 for details.
• the idler gears attached to the "strap" (upper plate) wobble too much.
• co-axial gears such as the purple and grey mercury gears (called mer1 and mer2, following Andronis) can be joined in a simpler way.
• some of gears can probably be made thinner. My version is scaled from the original by roughly a factor of 2 in the XY plane, but I needed to almost triple the Z direction size. Freeth reports the strap and b1 as an estimated 16.2mm apart while my version has them 41mm apart. I'd like the reduce this.
• there are a few places where the mechanism is sticky. I need to see if this is due to printing or a design issue. I have done very little to clean up the parts and reduce their friction, so it's more likely the former. A couple of places where there really was interference have already been corrected.

Reducing wobble

As you can see in the video, some of the gears wobble a lot. They skew away from the vertical, sometime causing the mechanism to bind. This happens when either the arbor passes loosely through a thin component - in this model either the gear itself or the strap. In addition, you also need something to stop the arbor just dropping out of the loose hole. In the video you may be able to see some shaft collars on top of the strap to do this. You can improve this a bit by making sure the hole is just large enough for the arbor to run smoothly and not more. Thickening the part or adding a hub/bush also helps when the spacing allows it. The idea is really to have the arbor anchored securely at each end. The geometry does not always allow this. Some earlier versions (like Freeth 2012) has arbors with a bracket to hold them steady, but Freeth 2021 largely does away with this.

I tried a redesign with a larger diameter arbor, 5mm instead of 3mm, and found it didn't make a lot of difference. Another thought I had was the have the arbor contain a bearing like a miniature ball bearing. It might help if the arbor is tight in the bearing, and the bearing is tight in its mount (for example the strap), though you might still need a shaft collar.

One other experiment I did was to use print-in-place bearings, for example in the middle item here:

In this case, the arbor sits tightly in circular bearing in the middle, which then rotates freely in the plate. There is about 0.2mm or 0.3mm spacing between them. The bearing widens up inside like this:

With a good enough printer, this prints quite well and you can move the bearing easily once you have broken it free by turning it a few times. It still does not work very well for preventing wobble, so I won't push this any further.

Gear wobble or tilt is an issue which came several times in the prototype of other sections, and I will come back to it with further solution later on.

Second prototype

For the second prototype I changed the gear heights to be 3mm apart from a few which are deeper for clearance purposes. All arbors are now rigidly fixed in either b1 or the strap and the gears run loosely on them. As a consequence, the arbors now also need a shaft collar or some other way of stopping the gears from falling off the shafts. I wasn't very happy about this at first as it costs vertical space. However, I found a nice solution, which is to hollow out the gear hubs and embed the shaft collar into the gear. You can see this on the video at the 15 second mark, for example. For the tall gears such as mer1/mer2, I printed them with a hexagonal piece on one which fits into a recess on the other. It holds together well with just a friction fit, but could be glued for extra strength.

Here is a view of the shaft collar, and of the space it fits into. The angle of the top of the recess means that the part can be printed without support.