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.