Jovilabe

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Jovilabe

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  • #258609
    Neil Wyatt
    Moderator
      @neilwyatt

      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).

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      #3738
      Neil Wyatt
      Moderator
        @neilwyatt
        #258611
        SillyOldDuffer
        Moderator
          @sillyoldduffer

          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

          #258613
          Cobbs Cobbledick
          Participant
            @cobbscobbledick49618

            Respect!

            #258615
            Neil Wyatt
            Moderator
              @neilwyatt
              Any ideas about how long your Jovilabe might take to construct?

              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.

              #258623
              Neil Wyatt
              Moderator
                @neilwyatt

                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.

                jovilabe.jpg

                #258638
                Neil Wyatt
                Moderator
                  @neilwyatt

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

                  jovilabe model.jpg

                  #258649
                  Neil Wyatt
                  Moderator
                    @neilwyatt

                    I'm talking to myself here…

                    The earth/sun gears work as well

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

                    jovilabe model 2.jpg

                    #258673
                    Enough!
                    Participant
                      @enough

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

                      #258684
                      Neil Wyatt
                      Moderator
                        @neilwyatt

                        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.

                        #258749
                        SillyOldDuffer
                        Moderator
                          @sillyoldduffer
                          Posted by Neil Wyatt on 30/09/2016 21:04:01:

                          I'm talking to myself here…

                          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

                          #258755
                          Neil Wyatt
                          Moderator
                            @neilwyatt

                            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

                            #258778
                            Enough!
                            Participant
                              @enough

                              Arthur C. might turn over.

                              #258781
                              MW
                              Participant
                                @mw27036

                                What will you make the jupiter globe out of?

                                Michael W

                                #258803
                                Neil Wyatt
                                Moderator
                                  @neilwyatt
                                  Posted by Michael Walters on 01/10/2016 23:47:48:

                                  What will you make the jupiter globe out of?

                                  Michael W

                                  Hydrogen, helium and methane

                                  #258804
                                  Neil Wyatt
                                  Moderator
                                    @neilwyatt
                                    Posted by Michael Walters on 01/10/2016 23:47:48:

                                    What will you make the jupiter globe out of?

                                    Michael W

                                    Hydrogen, helium and methane

                                    #258805
                                    Neil Wyatt
                                    Moderator
                                      @neilwyatt

                                      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

                                      #258822
                                      Michael Gilligan
                                      Participant
                                        @michaelgilligan61133

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

                                        MichaelG.

                                        #258828
                                        MW
                                        Participant
                                          @mw27036
                                          Posted by Neil Wyatt on 02/10/2016 08:27:22:

                                          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

                                          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

                                          #258847
                                          Neil Wyatt
                                          Moderator
                                            @neilwyatt
                                            Posted by Michael Walters on 02/10/2016 11:57:39:

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

                                            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…

                                            #258849
                                            SillyOldDuffer
                                            Moderator
                                              @sillyoldduffer
                                              Posted by Neil Wyatt on 02/10/2016 15:12:00:

                                              Posted by Michael Walters on 02/10/2016 11:57:39:

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

                                              The combination of a a rack-form hob and power feed makes it very easy to do these small ones.

                                              Is the rack-form hob home-made Neil?

                                              Regards,

                                              Dave

                                              #258861
                                              Enough!
                                              Participant
                                                @enough
                                                Posted by Michael Gilligan on 02/10/2016 11:00:24:

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

                                                Maybe **LINK**

                                                or: **LINK**

                                                #258863
                                                Michael Gilligan
                                                Participant
                                                  @michaelgilligan61133

                                                  Well-found, Bandersnatch yes

                                                  I had not seen those before.

                                                  MichaelG.

                                                  #258865
                                                  Neil Wyatt
                                                  Moderator
                                                    @neilwyatt
                                                    Posted by SillyOldDuffer on 02/10/2016 15:44:15:

                                                    Is the rack-form hob home-made Neil?

                                                    Regards,

                                                    Dave

                                                    Yep, I'll post a photo in a bit. Made out of silver steel using a simple cutter ground to the right angle on the end and then reduced to give the right shape, then cut a series of grooves.

                                                    Making a gears is just – set a tooth near centre of cutter to rotary table centre height (no great accuracy required, do by eye against tailstock).

                                                    Turn a blank or blanks, move to mandrel in chuck on rotary table. Set cutter to just 'kiss' blank, then move to side and apply 1.50mm in-feed (to allow 0.01mm for the kiss..)

                                                    I have a spreadsheet that gives me how many times I need to pass zero and then a reading 0.0 – 5.9 to set the dial for each tooth.

                                                    I have given up with multiple passes at different settings, at 0.7 mod anything down to 20 teeth looks fine with a single pass, smaller gears look a bit 'peg like' as do ones cut on blanks about 1 tooth too small, but they all seems to run together. No doubt there will be backlash but I'm banking on the fact that the pipe-in-pipe arrangement will generate enough friction to stop things waving about.

                                                    #258873
                                                    SillyOldDuffer
                                                    Moderator
                                                      @sillyoldduffer

                                                      Posted by Neil Wyatt on 01/10/2016 19:59:08:

                                                      I might add a Latin motto:

                                                      "Omnia enim vestra sunt Europa, quam"

                                                      Might be a good choice

                                                      Neil

                                                      Unlike "Omnia enim vestra sunt Ganymede, quam", which might be considered unsuitable for children.

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