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Author Topic: Hypocycloid Gear  (Read 30586 times)
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ArtF
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« Reply #15 on: October 30, 2011, 12:58:58 PM »

Dan:

   I suspect this is the differenc e between theory and practice in math. There is no roughness in terms of the gear since simulatio n shows it never conflicts with the pins. ( You cant get smoother than no conflict. .)
BUT, in practice leaving some backlash, and removing material that really isnt required can make an exact model of the gear look different . Take for example the case of non-internals.. the sharp tips are not really required, BUT they do allow teeth furhter away to also have some holding power.. so the perfect implement ation of the model dictates the sharp teeth, but a practical implement ation wouldl clip the teeth
to a maximum diameter and perhaps allow some backlash. The gear woudl look different as a result.
  All of my models I try to put in as perfect math models, thinking they could then be modified in one way or another as Im shown the limiation s of the theoretic al model vs the real world applicati on.
   As to the speed reducer, its a very similar tooth shape, BUT changed as a result dictated by the desired end result. That reducer is a kinda differenc e engine as I see it so far.... As I said earlier, the ratio is actually 60:59 or so in the concept of using such a gear, but the next two levels of it are calculati ng the differenc e in ratios and turning the output shaft at that rate, ( hence a 60:1 reduction ). ( Im making up the ratios, just wanted to show the ratio changes they are producein g). 

  Im still analysing that gear though, so I may "change my mind". It IS a facinatin g way to get a large scale reduction with very little friction. .
Mayeb we need a way to make such things.. lol
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Dan
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« Reply #16 on: October 30, 2011, 01:04:52 PM »

Art,

Thanks for the explanati on. I will try to output some Gcode and machine those and see if they work as a speed reducer. Will post the results.

Dan
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John S
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« Reply #17 on: October 30, 2011, 01:28:36 PM »

Andy Payne from Cambam had two of these on his stand at Harrogate show this year.
One was a 10:1 reduction and the other was 100:1 consistin g of two 10:1 stages.
Cut in acrylic they worked very well.

Andy has done a plug in for Cambam to generate these hypercycl oids.
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John S.
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« Reply #18 on: October 30, 2011, 01:30:55 PM »

Thanks, I missed that.

Kirk

Kirk:

You get those rounded teeth, ( which are epicycloi ds mixed with hypocyclo idals )
y selecting the cage gear as an planetary gear..jus t make the cage have more pins than the spur and the internal selection will light up for selection .

Art

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Mooselake
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« Reply #19 on: October 30, 2011, 02:32:19 PM »

Is the gear center distance how much the cage shaft has to be offset?  For 59 0.125" pins, 60 teeth, and a 15.0 DP it gets -0.0333 inches, which seems pretty small - I was expecting about half a pin or .06someth ing.

While John Sullivan could whip one off in about 15 seconds, I've never made an eccentric shaft.  I've got some 3/8" aluminum rod and a new/unused 4 jaw chuck for the 7x10 minilathe .  Is the correct procedure to offset the jaws by 33 thousandt hs (or whatever) and turning a 1/4" shaft on the end?

Kirk
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ArtF
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« Reply #20 on: October 30, 2011, 02:44:25 PM »

Kirk:

   Offset shaft distance is actually simple the differenc e between pitch diamters of that
DP of a gear. If it was allowed for the two gears to be the same diameter or number of teeth,
there woudl be no offset. SO you cant relate it to the pin size at all, change pin and the shaft offset stays the same..

Art
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ArtF
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« Reply #21 on: October 30, 2011, 08:14:02 PM »

John:

  Might have to try my hand at that as well on the laser to see how well they roll.
I checked CamBam's cycloidic s.. their made different ly from mine, you can see it the way the pin sets,
but mine follow the pin more accuratel y at the cycloidic inflectio n point , so the pin sits completel y in the recess,
where CamBams has the pins sitting with only one point touching. . Neither is wrong I think, but Im curious about the
efficienc y of the two methods in practice. .

Art
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Dan
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« Reply #22 on: October 31, 2011, 01:37:03 PM »

Made a quick prototype to prove the concept. Made a two stage 60:1 reducer out of acrylic. The result is very good. Movement is very smooth. Backlash is evident, but then I intention ally put in large clearance s (0.1-0.2mm). Reducing clearance s backlash should theoretic ally approach zero since there are at least 2 teeth engaged from opposite sides at any given instance.

Dan


* CamDisk.jpg (55.54 KB, 697x509 - viewed 611 times.)

* InputRing.jpg (44.94 KB, 697x506 - viewed 608 times.)

* OutputRing.jpg (46.89 KB, 698x512 - viewed 560 times.)

* RetainingCover.jpg (50.2 KB, 697x513 - viewed 591 times.)
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Dan
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« Reply #23 on: October 31, 2011, 01:38:31 PM »

And two more:



* EccentricShaft.jpg (54.23 KB, 696x510 - viewed 562 times.)

* HC_Reducer.jpg (32.92 KB, 446x596 - viewed 560 times.)
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Dan
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« Reply #24 on: October 31, 2011, 02:46:17 PM »

Apparentl y my reduction ratio math is wrong. The reduction in two stages with this reducer doesn't work as I thought it did. My first input pin ring has 11 pins, then there is the 10 lobe disk. This should give 10:1 reduction and is obvious. Then there is the second cam disk with 6 lobes which meshes with the 7 pin output ring. I had thought this would give another 6:1 reduction . However, counting the number of revolutio ns I am getting 17.5:1 ratio. I can't explain it and figure the right formula for reduction ratio calculati on yet.  Huh

Dan
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ArtF
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« Reply #25 on: October 31, 2011, 03:18:40 PM »

Dan:

  Hmm, math seems right. I dont see any informati on on the multiplic ation of ratio's in such a unit though... .

I see now why my cycloids are different looking.. their correct, but there is an optimiisa tion of the pressure angle that can be done..
Im looking into it to see if it should be added. Whats there will work, but they claim the circling of the pins bottom when its in the
groove is wated and can create binding.. they reduce by an optimisat ion method..

 That looks pretty good what you have though.. must be somethign simple about the math we're missing.. I cant see 17:5 as a
magic number that points out what the math is top of head..

Art
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Dan
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« Reply #26 on: October 31, 2011, 03:56:10 PM »

Art,

Yes, I don't know where the 17.5:1 does come from either. Regarding the multiplic ation of ratios, I haven't found any info on this either, except for the link I posted in the first message in this thread (www.zincl and.com/hypocycloid). In his video it does look like a 100:1.

Please let me know if you shall find an explanati on.

Regarding the optimizat ion, I think that the sharp transitio n corners will be crushed by extensive operation under load. And this might be more so if you try to keep things tight to minimize backlash.

Dan
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ArtF
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« Reply #27 on: October 31, 2011, 03:59:47 PM »

Dan:

 Its possible, though it shouldnt. .Id think the forces involved are being tranmisst ed over a much larger area when your in the inflectio n point.. Im no expert though..

  Ill dwell on the 17.5:1 ..

Art
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Dan
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« Reply #28 on: November 01, 2011, 01:16:02 AM »

Art,

Found the answer:
http://forums.reprap.org/read.php?14,35968,71742#msg-71742

I will retype the formula he derived below in a more convenien t way:

I/O = (b+1) / (b-a) , where,

I - input speed
O - output speed
a - first (or input) stage ratio
b - second (or output) stage ratio

Substitut ing the numbers for my example:

I/O = (1/6 + 1) / (1/6 - 1/10) = 17.5

Makes sense... doesn't it Grin

Dan

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ArtF
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« Reply #29 on: November 01, 2011, 07:27:39 AM »

Dan:

 Perfect sense.. Thx for the update. Ill ask Bob to add this to a reference topic

Art
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