Jovilabe

I've completed the basic calculations for a Jovilabe (an orrery that shows the motion of Jupiter's moons). This is just for the four Galilean moons, plus the Earth and Sun (at a different scale of course...)

Starting with Jupiter rotating once every 9.925 hours, the first pair of gears will sort out Io with negligible error. This can be used to predict when the red spot will appear.

Although the three inner moons have a 1:2:4 ratio, in reality their pattern lags slightly as the 'perijove' of Io precesses around the planet, but i have solved this in two ways and get the same figure of 1:2.007 between each pair of moons. I've decided to accept an error of about 2% in the moon's positions over five years.

Calisto could be geared to the central Jupiter drive or from the Io pipe, I have a gearing for the latter with negligible error.

A bigger challenge was moving the Earth in relation to Jupiter as this determines the angle the moons are seen at. It get easier if you decide on a point to be the sun. The ratio is a massive 10477:1, and yes, 10477 is a prime! I found a simple train with five pairs of 5:1 ratio plus a single 57:17 gives 10477.9:1 so an error of less than 1 part in 10,000 every decade should be OK.

The ratio of Jupiter's year to the earthly year is incredibly close to 344:29.

A large stationary 344-tooth ring with a 29-tooth gear rolling around the outside of it at Jupiter's orbital speed will provide a pace for both the sun and the earth. Obviously this creates a 'joviocentric' perspective, I could fix the position of the sun, but I think that would look less interesting and take a lot more room for little benefit.

If I do embark on yet another unfinished project, this will require 28 gears, assuming the driving stepper motor is geared down once to give a smooth rotation to jupiter.

All this should fit into a 30cm diameter base, perhaps 10 cm thick.

Neil (boggled and buried under a large pile of scribbled-on A4).

Wow! My inferiority complex has just exploded.

Making it worse, I misread a sentence in the antepenultimate paragraph as 'If I do embark on yet another unfinished project, this will require 28 years...'

Which led me to a genuine query. When looking at plans and project descriptions I find it hard to estimate how much time they will take to build. Any ideas about how long your Jovilabe might take to construct?

Dave

Respect!

Good question. I have a suspicion it won't take a very long time for several reasons.

• All the gears are chosen so they can be 0.7 mod involute gears, so easy to make.
• Most of the gear pairs add up to 57+/- 1teeth, simplifying construction.
• It is all geared down, unlike a clock, so friction isn't a critical issue a stepper motor should have no trouble running it.
• No troublesome escapements or the like, all to be done in simple software - just set a pulse rate for the stepper.
• The concentric-pipe form of construction is well proven and easy to set out.

The challenging bits will be making a good job of the dial(s) and woodwork, I suspect.

And yes, it was the link posted by MichalG that inspired me to go back to this, combined with the original calculations I did a year ago turning up on Wednesday morning.

I have to go shopping for the pipes tomorrow. One advantage of this approach is I can start with a temporary frame and add bits.

These are the calculations. As you can see three spindles are needed for the moons, whilst the jupiter year train will be an over-under sequence and the earth/jupiter gears will be 'sun and planet' with the sun as the planet and jupiter as the sun, if that makes sense! With involute gears hobbed onto under/oversize blanks (by two teeth) I think I can get the gears to mesh OK.

Well, the moon gears look as though they will fit together without interference.

I'm talking to myself here...

The earth/sun gears work as well

Not quite the Antikythera mechanism, but very do-able, I reckon.

Wonder how much of this could be made, relatively quickly, using 3D printing .... as sort of a proof-of concept.

I've wondered that too. I think the weakness at the moment are my 50:10 gear pairs, I think 10-tooth gears will be challenging for hobbing involute gears so i may go up to something like 80:16.

The biggest challenge will be the big circular gear (which will can actually be the main base with some piercings instead of just a huge hole. Not least, cutting the teeth on something that big doh! - of course t a rotary table on the shaper will solve that. .Also, what to engrave on it; obviously degrees around the edge, but what to put in the void? Perhaps scales?

I think the sensible way to progress is to make the upper gears mechanism - the top picture, between simple steel frames. Assuming it works, it then becomes worth considering the extra effort to add the bottom train.

Of course the fun bit will be making & painting all the little planets and moons.

By the way proposed scales:

Jupiter globe & moon orbits 1mm = 10,000km (jupiter ~14mm diameter, largest (callisto) orbit radius 188mm, smallest (Io) orbit radius 42mm. Earth at this scale will be 1.2mm.

Scale for moons 1mm:1,000km which will make them ~3-5mm in diameter. A better scale for earth as it will be 1/2" across (12.7mm). In the unlikely event I add earth's moon it will be ~3.5mm across.

This keeps the overall size reasonable ~380mm biggest orbit over a 300mm base while the moons are large enough to see and a 1:10 exaggeration of their sizes is easy to understand. The base could have an oblate ring to show the size of jupiter at the same scale as the moons.

I'm reading the thread with interest Neil and would comment more if I had anything sensible to say.

It's good to see you moving forward from the calculations to a CAD drawing. I find that much easier to understand.

As you say the most obvious problem is putting teeth on the big wheel. I don't have a shaper and - if I were building one - might try having that particular part made by an Online 3D printing service. That would be a partial test of Bandersnatch's 3D suggestion too.

Dave

Telescoping tubing obtained & 14 and 28 tooth wheels done.

The big wheel will be a flat plate on top of the 'box' with all the gears inside, it should be easy to cut the teeth if I fit my rotary table to the shaper where the angle plate would normally fit. Just a long slow job!

I will have to get all the axle/pivot locations marked on the gear, most of them will fall on four arms at 90 degrees, but two of them can lie on a curve between the two arms.

I can also leave a ring at the right diameter to show the size of Jupiter at the same scale as the moons (142mm diameter).

Possibly I can engrave or etch various things onto the plate. One thought is etching little drawings of things like the Voyager probes, which might take a bit of ingenuity.

I might add a Latin motto:

"Omnia enim vestra sunt Europa, quam"

Might be a good choice

Neil

Arthur C. might turn over.

What will you make the jupiter globe out of?

Michael W

Hydrogen, helium and methane

Hydrogen, helium and methane

Seriously, something that takes paint well, so brass isn't a good choice. or I could use gold layered with platinum and a ruby embedded for the red spot

A glass marble would be an easy option ... 'though you could spend years finding one with a reasonably convincing pattern.

MichaelG.

Ha-ha, very drole. I'm thinking a good airbrush would give it a convincing look.

You could use acrylic but you'd need to overlay with varnish to make it last. I found also that a good acrylic paint that is truly matt is very hard to come by, but i know only of one brand that meets that criteria, the reflective bog standard stuff can ruin the illusion any shadows and highlighting.

But i'm rambling, you probably have something else in mind.

You could even use your lathe/mill or stepper RT to use as a turn table to achieve consistent lines all around it, it'll need to be very slow of course. 

Michael W  

Edited By Michael Walters on 02/10/2016 12:02:32

Me to spin it slowly and spray on very fine lines.

I'm churning through the gears like nobody's business. The combination of a a rack-form hob and power feed makes it very easy to do these small ones.

14T looks surprisingly good, the 12T one is a bit bit crude but works fine. I'm having to make some amendments to make sure i don't end up with bits of metal moving through each other though... my second version worked, but i would have had to levitate it on magnets...

Is the rack-form hob home-made Neil?

Regards,

Dave