Oddball Planetary Gearset

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deraudrl
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Oddball Planetary Gearset

Post by deraudrl »

I saw something a couple weeks ago, but my google-fu is weak and I don't remember where, possibly here.

It was a animation of a planetary set with different-sized planet gears, arranged as follows: 37-tooth ring, 11-tooth sun, three planets of 7, 13, and 19 teeth. I was able to cut the gears on the laser and sort of got them to mesh/move, but obviously the exact orientation of the gears is critical, possibly unique. It would really help if I could find the original animation again, or even better, some guidance on where to find the maths defining such a widget.

(And yes, I realize the practical applications are limited or nonexistent, but it would make a cool demo piece.  8))
BobL
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Re: Oddball Planetary Gearset

Post by BobL »

Hi Deraudrl;

Not sure if this helps any, but found these links to perhaps be something along the lines of what you're looking for? I'm unable to offer wisdom here, but have heard that Gearotic CAD gear calculator and gear train does help in figuring things out.


http://gearotic.com/ESW/FavIcons/index.php?topic=1969.0

http://gearotic.com/ESW/FavIcons/index.php?topic=650.0


Cheers
Bob
:)


Gearotic Motion
Bob
deraudrl
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Re: Oddball Planetary Gearset

Post by deraudrl »

Those look like somewhat related problems...similar but not quite.

Some further insight:

Given the ring gear and four spur gears I described above, I really "only" need the angles that describe the triangle connecting the planets. Only two unknowns...simple, right? Oh if only...

Consider the problem of determining the center/radius of a circle (ring) that encloses, and is tangent to, three arbitrary circles (planets). As far as I've been able to determine, such a circle is unique (if one exists) but I'm not finding a closed-form algebraic equation describing it. It looks like a question of finding the intersection of the three hyperbolas that run equidistant from each pair of planets. I could probably cobble up a search optimization program (call it 'FindRing'), but it would be ugly and have unknown run-time.

I would then have to run FindRing over the set of planet positions constrained by the size of the sun gear until I got a solution that has the correct radius for the ring gear. (I'm taking a leap of faith that I'd then have a configuration that would mesh and rotate, but at least I've seen it work for this set of gear sizes.) This is the kind of thing that gives "brute force" a bad name.

I'm not sure Gearotic will help, since the sun gear doesn't have a fixed shaft position, but if someone can prove otherwise, all the better. It sounds like maybe a job for Mathematica, but I really don't have the level of spare time required to learn that from scratch.

Any thoughts?

deraudrl
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Re: Oddball Planetary Gearset

Post by deraudrl »

Just in case anyone believes I'm crazy, this is the closest I've been able to render it in CorelDraw:
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Planetary 37-11-19-13-7.jpg
BobL
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Re: Oddball Planetary Gearset

Post by BobL »

Hi Deraudrl;

I personally have no feedback to offer you, however Art may when he returns in a few weeks.


Cheers
Bob
:)
Gearotic Motion
Bob
deraudrl
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Re: Oddball Planetary Gearset

Post by deraudrl »

Thanks, no particular hurry.

I used to be able to handle complex maths...
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ArtF
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Re: Oddball Planetary Gearset

Post by ArtF »

Hi:

  The secret to your question is the equivalent circles created by offset gears.
TO get proper measurements, you need a proper reference point at center of the
sun. Considering any two gears, one can create a rolling replacement gear on
the central axis. The pitch radius of that gears will be the measurements
required to calculate either of the two gears numbers.
  Ill be slow to get to doing this math to give you a formula, but I LIKE the way
you have formulated this question. I think perhaps I may do this as the next
module of Ticker, so one can design planetaries based on number of gears
with offset correction.  Ill give this a lot of thought in the next few weeks, this
sounds like a very nice module to have. Ellipticals was going to be next, but I
suspect planetary would be more useful.

Art


Art



deraudrl
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Re: Oddball Planetary Gearset

Post by deraudrl »

Art -

Thanks. I'm not entirely certain I understand your explanation, but whatever you come up with should be fun to play with in any case.  ;D

The thing that's kicking my butt at the moment is that I can (1) generate the gears (Gearotic/Gearify/GearGenerator/whatever), (2) import them into CorelDraw and arrange them so they mesh nicely, (3) cut them on the laser, and (4) arrange the physical gears so they mesh. And the drawing doesn't quite match the thing lying on my desk. The planet spacings along the ring on the physical set are like a third of a tooth off, so of course the planet-to-planet distances are different. I could measure them and try to cut a carrier, but I have no confidence that will work without adding a lot of slop to the gear cuts...the "brute force and massive ignorance" approach. I've tried working backwards from physical to drawing, and I can see tooth interference on the drawing when it's arranged the way it actually "works".

My gut says this arrangement is unique (given that the tooth counts are all prime), but I'm starting to wonder.
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ArtF
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Re: Oddball Planetary Gearset

Post by ArtF »

I suspect that certain integer multiplication rules for tooth counts  will apply.

By equivalent circles I just mean that if you consider only the motion of the shaft of a particular gear, and referance that to center,
thats an equivalent gear for that motion in a different reference, the pitch radius of that gear is likely important to the calculation.

  Sorry, I can see it in my head, but its a poor explanation..

Art
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Re: Oddball Planetary Gearset

Post by deraudrl »

After staring at (and tweaking)  the drawing for a couple of hours, I noticed a couple of things. I'm calling the gears R37, P19, P13, P7, and S11, if that makes sense. It also helped that I made each gear's effective radius equal to 1/10 of its tooth count. (E.g. S11 is 2.2" in diameter.)

Within the limits of how precisely I can manipulate the drawing without knowing actual coordinates, it looks like the distance between P19 and P13 is the same as the distance between P13 and and P7, and that distance is 3.9", equal to the sum of the three radii: 7 + 13 + 19. The third leg of that triangle, between P7 and P19, is 4.4"...44 = 7 + 11 + 19. I may try cutting a planet carrier tomorrow with those dimensions and see if it's really as close as it looks on the screen.

Then again, 44 is also the sum of 7 and 37, and the caliber of Dirty Harry's gun...I'm really not sure how much numerology can, or should, apply to gear design. All of these might just be coincidences, me trying to read patterns into imprecise data, who knows. All things considered, learning Mathematica might be less harmful to my sanity.  :P
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ArtF
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Re: Oddball Planetary Gearset

Post by ArtF »

It sounds to me like you have a good grasp on it. I didn't crunch numbers or anything, but
your logic seems sound. I find when I begin to explore such things for a module I rediscover
all kinds of secrets again, sometimes for the 100th time. Once the module is done I promptly
forget the process again.
  This is why I write modules, because I know I will futz about forever to do it manually when those
occasions arise. Im pretty sure I'll now have to add a planetary module, but Ill do it after I
officially release the newest Ticker, in a month or so...


Thanks for the imagination ,

Art
deraudrl
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Re: Oddball Planetary Gearset

Post by deraudrl »

A quick wrap-up...

Just for the record, I didn't use Gearotic to draw the gears, I used Mathias Wandel's GearGenerator3. I redid the gears this morning and re-imported them into CorelDraw, made up a planetary carrier, and cut everything again in 1/4" MDF. Everything lines up, and it meshes and turns...stupidly tight, since I only have the laser's 0.005" kerf for slop. So the numbers I was seeing are correct: in "half-tooth units", D(P19,P13) = D(P13,P7) = 39, D(P19,P7) = 44. Turns out D(R37,S11) = 13, which, except for being prime, has no relation to the others that I can see. FWIW, I've attached a 1:1 scale vector PDF of the drawing (Corel imports DXF fine, but doesn't export it worth a damn), but with the spacings known, you can probably just recreate it faster using Gearotic/Vexx.

I'd love to know the math behind arbitrary-sized planetaries, but I guess that will have to wait.
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[The extension pdf has been deactivated and can no longer be displayed.]

Last edited by deraudrl on Wed Jun 02, 2021 10:34 am, edited 1 time in total.
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