This is a great video. Further to your last point on this video, the two gear sets can't have the same module because the 12/60 and 15/60 gear pairs have to have the same pitch diameters (e.g. share axles). The calculation isn't difficult but it stretched me to derive it! Sum the tooth counts of the first sun and planet gears (12+60), multiply by their module, then divide by the sum of the tooth count of the second sun and planet gears (15+60), to give the module of the second gear set. The tooth counts of the ring gears is S+2*P (12+60+60 and 15+60+60).
This was super great, I haven't seen this mechanism before and really like how compact it is for such a huge gearing ratio - also well explained. Thanks for sharing :)
Thank You so very much. Exactly the video I was looking for after being inspired from guys like "Gear Down For What", "Skyentific", "James Bruton", "Levi Janssen". Glad that i finally got here....Yay!!!
Hi David, you might want to check the math on this again, I believe the ratio you have is actually 540:1. Here is the formula I've come up with for calculating the ratio for this design. (1/(s1/(s1+a1))) / ((a2-((a1/p1)*p2))/a2) There may be a simpler way, but this seems to work. Fun note from this formula if you're going for really high ratios, you could increase the ratio to 2025:1 just by changing p2 from 60 to 61. But you would not be able to keep the idler gear any more. Or -8040:1 if you also change a2 to 134, and if you're ok with the output going the opposite direction of the input. Still no idler though.
@@Save_the_manual Can someone please explain how it is being calculated? I can't make it out. Is the ring fixed and planets the output? What is the logic for the calculation here?
Hey! For anyone interested, I updated the gear calculator spreadsheet for making these, and also i uploaded a set of 3d models for printing the gear box shown in this video: github.com/IdeaPropulsionSystems/CoolEpicyclicGearing
This is how a winch gear is setup, but it has just one set of planet gears (same teeth, not different like yours) that spin on both rings, the top ring turning really slow. Monster torque from a small motor, but the gears are super loud.
Nice work. Check out US patent 5762162. I "invented" this type of gear reduction for power steering in 1996-ish. I'm not sure if the novelty was the gear arrangement or the automotive application of it. Back then, 3D printing wasn't advanced enough. I made spreadsheet models to design the ratios and I verified it with ADAMS mechanism modeling. It's good to see a the physical model replicates the math model. By the way, you can play around with which element you want to drive with similar results. For offset axis applications the planet can be driven (input carrier is held to ground) and for concentric applications the ring gear can be driven.
Some thoughts, one year late: This mechanism might be printed with planet rings having a larger hole or internal diameter. This would speed up the printing a bit, nothing is gained from that extra material. Also, large holes might be printed in the top cover, to allow us to see what's happening inside. Finally, a really good thought (you're welcome) would be to print alignment marks on the gears, to ease initial positioning of the gears prior to assembly.
Great comment, dude. Since this type of planetary gives balance force to a gear (by having gears on the other side of the sun gear) could the outer gear drive the inner gear? This would be unique and very valuable, because if you have a 100 to 1 reduction, you can easily turn the little gear. But you can't use the big gear to drive the little gear- far too much friction and you can't overcome this with so little torque.
I was looking at your spreadsheet and I was wondering for Na2, does it need to be +P? Or is that arbitrary as long as it is inequal to 0? I cant seem to understand where you got the +P from. I'm guessing it has to do with keeping the planet gears on the same shaft, but I don't see how this is accomplished
Around 2015-2017 I experimented with something pretty similar, making simple gears but with two hollow gears off by a multiple of the number of planets. Here's my video on it: ua-cam.com/video/alwwyWFQwuM/v-deo.html I'm still not sure whether I'm just getting away with a slightly mismatched tooth profile / altered pressure angle for the second ring, but it worked surprisingly well. I very much enjoy seeing how different yet functionally equivalent from the outside our concepts are. Props for sharing it! (I had it on private until this year and it seems youtube overwrites the uploaded date with the current date when you decide to publish it, so I now look like an idiot claiming the earlier date. Ah well, as long as people can use the conecept for something cool, I don't care anymore).
In your spreadsheet, you state that both the sun gear 1 tooth count (Ns1) AND the annulus gear 1 tooth count (Na1) must each be evenly divisible by P (i.e. Ns1/P = integer and Na1/P = integer). I can basically understand how you would come to that conclusion (although I haven’t done the calculations). Doing it that way will ensure that your planet gears are perfectly “in-sync” (meaning if one planet gear meshes with the annulus/ring gear at 90 degrees, all of the of the other planets will each have one tooth that also meshes with the annulus gear at 90 degrees at the same time). Okay. In standard planetary gears, if the planet gears need to be spaced evenly, only the SUM of the sun gear 1 tooth count (Ns1) and the annulus gear 1 tooth count (Na1) need to be evenly divisible by P: (Na1 + Ns1)/P = integer. Your case is a special subset of this (having the gears in-sync). In the general case, as long as (Na1 + Ns1)/P = integer, then the gears will mesh perfectly, just they won’t necessarily be in-sync (i.e. if one gear from one planet meshes at 90 degrees, “none” of the other teeth from any of the other planet gears will also mesh at 90 degrees at the same time). The only exception is the special case you give (I think). I have a couple of questions. One is, is it necessary for (Ns1/P AND Na1/P) to each be integers in split ring compound planet gears (as you have in your spreadsheet), or is it also okay to use (Na1 + Ns1)/P = integer as well? My other question is do you know if there are any efficiency issues with the teeth being out of sync (i.e. (Na1 + Ns1)/P = integer)?
I actually don't know; I have seen it used in avionics motors from the 1950s. It is also sometimes used in the drive motors behind car rear view mirrors. It is pretty cool because of how high the ratio can be for a single stage of gearing.. :-D
It's called a "Wolfrom Gear", and there's even some variants with straight, i.e. not stepped, planet gears. i.imgur.com/r0ifQwG.png i.imgur.com/ICiAa1W.png
I actually have! I have a small growing family of types of printable stepper motors; may be a good subject for a new e-book :-) Thanks for reading/watching!
For each of the two annuli, instead of having two sets of Planet Gears, you are using one set of Planet Gear each having two sets of teeth, infused one above the other. I can see that the diameter of the teeth set in the top arrangement in all the three Planet Gears are smaller than that of the bottom arrangement. So, the Circle Pitch (angular distance between adjacent teeth) in both the arrangements must be different. So does the Ring Gears and the Sun Gears. Am I right? Please clarify...
@@Gopinath2119 you are correct, the module of the gears on or touching the rotor are different from those on or touching the stator. The modules were chosen so that the axis of rotation of the small planet gears exactly lines up.. that way they can be stacked and connected as compound planets.
Hi David, my name is Layne and I am currently working on a project at work that could quite possibly deal with something like this. What equations did you use to determine what your gear ratio was? Any response or help would be much appreciated, I'm looking to achieve 100:1 reduction in a pretty small space.
Hello Layne, thanks for your interest. I made a spreadsheet and included the equations next to the columns to help decipher the process of designing these: github.com/IdeaPropulsionSystems/CoolEpicyclicGearing/tree/master/GearSpreadsheets Let me know if that helps. 100:1 is certainly achievable. I recommend using a carrier to keep the planets' axis all parallel. I discovered pretty quickly that, if you let the planets 'free orbit' like in this example, putting torque on the gear box makes them all 'tilt' and jam, limiting the effective torque you can get out of the box. If you have a carrier that holds their shafts parallel, that fixes the whole problem. Enjoy! I'd love to see what you're making!
@@davoriffic Thank you so much for the quick reply, and your charts were incredibly helpful. How would the R2 equations change if I were to bring a worm gear our from the first set of gears? I have to turn my gears 90 degrees and I'm thinking the simplest way to do so is a worm gear?
@@laynehelmuth4736 Interesting; not sure exactly where you mean. Worm gears certainly give you the 90˚ change in direction and will add another 10X or more to your ratio depending on the teeth~ also adds a lot of friction. It might also be the weak-point in terms of breaking gear teeth under lots of torque because there's a lot more teeth material engaged in the rest of the gear box than in a single stage of worm gear. hmmmm.... :-D
So, good question. It is relying on the difference in the number of teeth between the first and second internal ring gears to work, but here's the thing: in order to have planet gears that fit both of the ring gears and share the same axis of rotation yet have the same number of teeth (each planet is like basically one gear stacked on top of another gear) they need to have different pitches. So the different pitches is a result of having different tooth counts but keeping those planets on the same axis.. if that helps! :-)
But won't having different pitches have uneven wear? Or are you saying that stage 1 gears are all same pitch and stage 2 are all the same pitch? I guess if not 3d printing and buying it gears it would result in buying say Mod 1.5 gears for first stage and mod 2 for second. Would result in a massive difference between two ring diameters, so therefore less gear ratio?!
@@adamgibbons210 Yes, only gears of the same pitch are in contact with one another. It would be difficult to find commercially available gears I think with the correct pitches to make a box like this work. More likely, you could find half the gears and then print half the gears.
Hey man do you have any advice for coping up high loads on the gear teeth. I had r created a gear system of 1:200 multiplication factor, and am facing the problem of very less life expectancy.
Hello, and yes. This is certainly a problem with plastic printed gears. I would recommend using a good lubrication (silicone grease is good with ABS plastic) and you may consider infusing the plastic parts in a 2-part epoxy resin. Beyond that, using more gears to spread the load will increase life, and if there is a way to actually support the gears in a gear carrier, vs. having them freely orbit, it will increase the life because the teeth will not be handling radial torques caused by the two annulus layers basically applying force in opposite directions at opposite ends of each compound gear... a more force-balanced gear design would help.
I want to add a gear ratio formula, becouse when i needed one i couldnt find it. I searched for a calculator but i couldnt find one. So i made up my own formula, and it works great. Count the teeth of : S1 (sun 1) drive wheel P1 (planet 1) R1 (ring 1) P2 (planet of the second gearset) R2 (ring 2) output wheel Ratio is (1+R1/S1)/(1-(R1*P2/(R2*P1))) to one You can check this with known gears on thingiverse or other sources. I hope i helped a lot of people
BAD FIT means something is wrong with the number of teeth for the angles involved; the won't mesh because it is asking a tooth to be some fractional amount shifted, for instance. Experiment with slight offsets in tooth numbers until that warning goes away.
In theory yes, but friction is really REALLY stacked against you with split planet gears. It's like a worm gear in that sense, only worse because there is more tooth involvement.
Hi David, is that due to the way this is working? 'pushing' second ring around rather than a true involute gear relationship. Of course the ratio massively increases torque.
If the box is set up properly, there actually is a true involute gear relationship between all teeth, it is just that the ratio is so great that static friction plays a huge part in the ability to make it start moving.
Oh, yes... well the first thing i noticed with one of these gear boxes is how rock-solid the output gear is in its position. I can imagine how, in a friction-free simulation, this thing could step up the speed very rapidly, but things like friction and angle-influenced binding of parts pretty much means it's not going to happen with this kind of box. It's basically like trying to push a very fine-toothed worm gear backwards.
I have not, formally. It feels like very tight gearing, though there is some wobble when it runs. I think much of that has to do with imperfections in the 3d print and the fact that there is no gear carrier.. the gears just orbit freely.
This kind of gear box seems to turn up in aircraft avionics and in some things like auto-mirror adjusting motors. There are also some gearing arrangements like this made by the company Harmonic, which makes strain wave as well as conventional gearing machines. It is a little bit obscure, and quite interesting, though. I am putting together a better spreadsheet for calculating the formulas.
I gave the gear specifics in Diametral pitch, which you can convert to module. There is a design spreadsheet on my github for the project here: github.com/IdeaPropulsionSystems/CoolEpicyclicGearing
Yes, a good question; it is terrible for speed multiplying because of how much leverage the least bit of friction has. It is similar or worse than trying to use a worm gear to multiply speed.
David Hartkop I can visualize how the setup in this video would have difficulty with back driving. The torque input at the ring gear would cause the planets to twist and bind on the housing/sun gear in the other stage. If rigid carrier was added and some bearings I imagine it should back drive just fine. It doesn't seem like there is sliding component that you would see in a worm drive. That being said, you have done some great work explaining how the setup works! I may have made a fundamental error but it seems logical if I keep the planets from twisting and binding. I'm going to try it and report back.
I have made a spreadsheet for calculating the factors for gears in arrangements like the gear box in this video. The gear sizes are given in diametral pitch, but you can use that to calculate the module. You can download the spreadsheet here: github.com/IdeaPropulsionSystems/CoolEpicyclicGearing/tree/master/GearSpreadsheets
helo, was wondering what margins you put in for 3D printing to account for shrinking/expansion of the material during 3D printing? I'm having issues with the gears being 'stuck'. Calculation wise it all works out, it's just in the 3D printing stage I can't figure out what to adjust to account for the expansion/shrinking.
That's a good question; fortunately to make it fit you only really have to shrink the size of the two smallest gears in the very middle. Just make them 1/2mm smaller than the object's given dimensions and that should do it... The small gears can basically be printed inside of 20 minute so it should hopefully be smooth sailing!
@@davoriffic thank you for your quick reply. I've considered changing the size but that in turn will change its module no? and as a result, a different module would mean issues with meshing. I haven't experimented with it however so i'll give it a try. Thank you and keep it up!
@@ikkeennigij121 for printed plastic gears, it'll work fine.. just make them 'smaller' by a percent or so... also one approach I have taken for making printed gear boxes is to print them so the gears mesh just slightly TOO-tightly, and then run the entire system at high speed without any lubrication with a cordless drill... the friction generated will smooth and 'squish' the teeth into a perfectly meshed low-friction state in about 5 min of continuous running. You can then add silicone grease (which won't destroy ABS or PLA) and it will run smoothly with very little backlash. Have fun!
The key to understand with gearing like this is that the two halves have slightly different modules. This lets compound planets mesh with annulus gears that have different tooth counts. In the case presented here, they differ by 1 or 2 teeth, that way a full revolution of the planets only advances one annulus by 1 or 3 teeth. It provides a huge mechanical advantage in basically 1 step
How very true. I used an A4988 stepper driver chip with an arduino, and basically turned the current-limiter pot almost all the way down. The motor was low torque, but only got warm instead of plastic-melting hot!
In the demo I printed, there is a collar that goes over the whoe a1 and holds it to the body and a2 by its flange. In a real application, there would have to be some bearing or bearings that keep it in position and centered.
I made a spreadsheet here: github.com/IdeaPropulsionSystems/CoolEpicyclicGearing/blob/master/GearSpreadsheets/190120_Hartkop_CmpdEpiGears.xls for figuring out the gearing. The teeth are given in diametral pitch and not module, though. You can convert one to another here: www.engineersedge.com/gear_pitch_chart.htm. Hopefully that helps! An improved spreadsheet would have the module for the gears. Thanks!
Very clever idea. I can't help but wonder though, does this have any advantage over infinite screws. I'm not being sarcastic btw. In fact, it's more important for me that you know this than i know the answer.
If by infinite screws you’ll mean like worm gears, it really depends; work gears are definitely more simple and less trouble in terms of backlash. This split ring approach can achieve really high ratios, maybe 5 or 10 times higher than a work gear of the same diameter. But depends on the specifics. One other advantage I could see in this split ring approach is that there are at least 3 gears engaged at all times. In a worm gear, there’s just one contact point. For really high torque, this may make it less likely to have the teeth shear off ( because there’s more of them)
@@davoriffic then again worm gears, i think, work with a lot of friction inherently. under big loads, they might be a lot less efficient despite having fewer gears.
@@timucinbahsi445 True, they have a lot of friction, especially under big loads. The split planetary gearbox shown in this video also suffers from increased friction if you really load it because the gears try to 'tilt' in the casing, which cause them to bind up. Having a gear carrier for the planets and also possibly arranging to have balanced loading in some way could make it more practical.
Great, its a very nice work. I'm still trying to work out why One revolution of the planetary gears equals the second ring only turning round by the difference in teeth (of the two rings)?! So in that case I imagine if the second ring has a bigger difference in teeth it actually provides less gear ratio?. Also, does it rely on the compound planet having the same number of teeth on both sides?! Thank you!
I lasercut a setup with same pitch of all gears last weekend and it worked. It just relies on a different number of teeth between the two nested planets, and therefore corresponding rings.
Cool! send a link? I'd love to see it; I improved my calculator spreadsheet to include gear tooth pitches. You could use this to make a box with the slightly different pitches for the top and bottom halves. Having different pitches but same numbers of teeth on the planets will let you get ridiculously high ratios in just the two stages as shown. github.com/IdeaPropulsionSystems/CoolEpicyclicGearing
The motor pinion is 12 teeth and the ring gear 132 teeth so ratio is 11:1 If the second ring gear has three extra teeth to accommodate the three planets wouldn't the calculation be; 135/3 = 45, so ratio is 11:1 x 45:1 = 495:1 ? just asking
Thanks! And a very good question with a two-part answer - First, the 11:1 ratio you found would hold IF the planetary gear was holding still with respect to the sun gear; in this special case, it is actually orbiting around as it engages with the annulus. The sun gear's engagement with the annulus basically falls behind by one full rotation once the planet has finished an orbit, so the ratio is actually found like this: (AnnulusTeeth/SunTeeth)+1=12:1. Secondly, figuring out the ratio you get between the two annuluses (annuli?) you correctly divided the tooth count difference into the number of annulus teeth; I had been incorrect in my thinking as to which annulus should be divided into - it SHOULD be divided into the output shaft annulus, not the stationary one, so 45, whereas I had calculated 44 by dividing into the stationary annulus. The distinction is important because the 3 tooth difference is a difference of three output teeth, not three stationary teeth... Taken together, the correct gear ratio for the box pictured in this video is 45 x 12 = 540 I'm going back to double check some things, and will update my spreadsheet to reflect this distinction. Thank you for your keen spotting! :-)
@@davoriffic Thank you for the reply and apologies for the first ratio; I forgot to add the 1 for a planetary gearbox ratio. Thanks for the explanation.
@@davoriffic I'm glad I'm not crazy haha I was positive it should have been 540 instead of 528 given the 135 teeth output annulus but kept second guessing myself.
@@Tonescarp Interesting - Can you walk me through the steps that you took to figure that out? It is very likely that I messed up somewhere, and would love to update my calculator as necessary.
@@davoriffic Hi, I agree, 540:1 is correct. I have made an animation page and a calculator for such gears. Pasting '12 135 132' into the top right [I O B] field will show your gear, and also show that the ratio is 540:1. saugstad.net/gear-animation
www.thingiverse.com/thing:4114551 But how to calculate the gear ratio? I got it way wrong. In that spread sheet, what is n "2nd stage multiplier"? I use the same diametral pitch on all gears.The openSCAD project is intended to be a library. They get connected together in the next project.
i think i found the purpose of that device if Meshed gearswith an equal number of teeth will turn at the same speed. If they have an unequal number of teeth, the gear with the fewest teeth will turn faster. if.that's true i think i know what this is meant to do
Well, the numerical model that I made suggests that the ratio goes from being 540:1 to being -539:1. That is to say, the output shaft would revolve the other way, and something is now going in the same direction when it was opposite before, loosing one full revolution per turn. That 'seems' right but maybe you better simulate it for yourself ;-D
One way I can see is to stack two gear arrangements like this together. This would essentially multiply the ratios. If you did that with the box shown in the video that has 500 some to one, you could very quickly have 250,000:1
Interesting; My best guess is that the small idler gear and the gear for the motor's shaft are too small. I seem to remember having to play with the scale of these two parts in order to get the demonstration gearset working properly. Thank you for your interest! Let me know if that helps.@@RebellisSpiritus
Interesting video. I didn't know about the fancy name of it, I just went on and made one not having seen it before. However 3-D printing it is fine but how would you go about to machine it? I milled mine with an ordinary end mill. Also I have used it once in a project. Then I made the sun and the outer rings in hard anodized aluminium and the planets of POM. Worked just fine. ua-cam.com/video/g821BOC_oAQ/v-deo.html
This is a great video. Further to your last point on this video, the two gear sets can't have the same module because the 12/60 and 15/60 gear pairs have to have the same pitch diameters (e.g. share axles). The calculation isn't difficult but it stretched me to derive it! Sum the tooth counts of the first sun and planet gears (12+60), multiply by their module, then divide by the sum of the tooth count of the second sun and planet gears (15+60), to give the module of the second gear set. The tooth counts of the ring gears is S+2*P (12+60+60 and 15+60+60).
This was super great, I haven't seen this mechanism before and really like how compact it is for such a huge gearing ratio - also well explained. Thanks for sharing :)
Thank You so very much. Exactly the video I was looking for after being inspired from guys like "Gear Down For What", "Skyentific", "James Bruton", "Levi Janssen". Glad that i finally got here....Yay!!!
It's funny you mention telescope tracker. That is the exact project I wanted to build that lead me to this kind of gearbox.
Thankful for your help to a better world of designers and builders.
This video really helped me to figure all this out, thanks!
Hi David, you might want to check the math on this again, I believe the ratio you have is actually 540:1. Here is the formula I've come up with for calculating the ratio for this design.
(1/(s1/(s1+a1))) / ((a2-((a1/p1)*p2))/a2)
There may be a simpler way, but this seems to work. Fun note from this formula if you're going for really high ratios, you could increase the ratio to 2025:1 just by changing p2 from 60 to 61. But you would not be able to keep the idler gear any more. Or -8040:1 if you also change a2 to 134, and if you're ok with the output going the opposite direction of the input. Still no idler though.
If you want the 528:1 ratio, while sticking with 3 planets and an idler sun, you can use the following:
S1: 15
P1: 18
A1: 51
S2: 18
P2: 21
A2: 60
Yep, it's 540 👍🏻
@@Save_the_manual Can someone please explain how it is being calculated? I can't make it out.
Is the ring fixed and planets the output? What is the logic for the calculation here?
Hey! For anyone interested, I updated the gear calculator spreadsheet for making these, and also i uploaded a set of 3d models for printing the gear box shown in this video: github.com/IdeaPropulsionSystems/CoolEpicyclicGearing
What is tooth multiplier in your spreadsheet? I didn’t get exactly the significance of that value.
David,
Very Good, I have reproduced my self, and works perfect.
Thank You
neat! Post any pictures or video of it? It's always fun to see people's projects!
This is how a winch gear is setup, but it has just one set of planet gears (same teeth, not different like yours) that spin on both rings, the top ring turning really slow. Monster torque from a small motor, but the gears are super loud.
Nice work. Check out US patent 5762162. I "invented" this type of gear reduction for power steering in 1996-ish. I'm not sure if the novelty was the gear arrangement or the automotive application of it. Back then, 3D printing wasn't advanced enough. I made spreadsheet models to design the ratios and I verified it with ADAMS mechanism modeling. It's good to see a the physical model replicates the math model. By the way, you can play around with which element you want to drive with similar results. For offset axis applications the planet can be driven (input carrier is held to ground) and for concentric applications the ring gear can be driven.
Very cool, that sounds like a cool real world application for this.
Big thanks for the clear explaination
Excellent explanation. Thank You.
It’s not geeky…….its fun!
Backlash? Repeatability? I like it
Cool Gearset!
Damn, u were here before too lol...i found this video , finally.
Some thoughts, one year late: This mechanism might be printed with planet rings having a larger hole or internal diameter. This would speed up the printing a bit, nothing is gained from that extra material. Also, large holes might be printed in the top cover, to allow us to see what's happening inside. Finally, a really good thought (you're welcome) would be to print alignment marks on the gears, to ease initial positioning of the gears prior to assembly.
Great comment, dude.
Since this type of planetary gives balance force to a gear (by having gears on the other side of the sun gear) could the outer gear drive the inner gear? This would be unique and very valuable, because if you have a 100 to 1 reduction, you can easily turn the little gear. But you can't use the big gear to drive the little gear- far too much friction and you can't overcome this with so little torque.
I was looking at your spreadsheet and I was wondering for Na2, does it need to be +P? Or is that arbitrary as long as it is inequal to 0? I cant seem to understand where you got the +P from. I'm guessing it has to do with keeping the planet gears on the same shaft, but I don't see how this is accomplished
Around 2015-2017 I experimented with something pretty similar, making simple gears but with two hollow gears off by a multiple of the number of planets.
Here's my video on it: ua-cam.com/video/alwwyWFQwuM/v-deo.html
I'm still not sure whether I'm just getting away with a slightly mismatched tooth profile / altered pressure angle for the second ring, but it worked surprisingly well. I very much enjoy seeing how different yet functionally equivalent from the outside our concepts are. Props for sharing it!
(I had it on private until this year and it seems youtube overwrites the uploaded date with the current date when you decide to publish it, so I now look like an idiot claiming the earlier date. Ah well, as long as people can use the conecept for something cool, I don't care anymore).
absolutely brilliant! Thank you !!!
well, right-on! ;-D Enjoy
Merhaba David. Dosyaları indiremiyorum. Başka bir yolu deneyebilir miyiz lütfen.
In your spreadsheet, you state that both the sun gear 1 tooth count (Ns1) AND the annulus gear 1 tooth count (Na1) must each be evenly divisible by P (i.e. Ns1/P = integer and Na1/P = integer). I can basically understand how you would come to that conclusion (although I haven’t done the calculations). Doing it that way will ensure that your planet gears are perfectly “in-sync” (meaning if one planet gear meshes with the annulus/ring gear at 90 degrees, all of the of the other planets will each have one tooth that also meshes with the annulus gear at 90 degrees at the same time).
Okay. In standard planetary gears, if the planet gears need to be spaced evenly, only the SUM of the sun gear 1 tooth count (Ns1) and the annulus gear 1 tooth count (Na1) need to be evenly divisible by P: (Na1 + Ns1)/P = integer. Your case is a special subset of this (having the gears in-sync). In the general case, as long as (Na1 + Ns1)/P = integer, then the gears will mesh perfectly, just they won’t necessarily be in-sync (i.e. if one gear from one planet meshes at 90 degrees, “none” of the other teeth from any of the other planet gears will also mesh at 90 degrees at the same time). The only exception is the special case you give (I think).
I have a couple of questions. One is, is it necessary for (Ns1/P AND Na1/P) to each be integers in split ring compound planet gears (as you have in your spreadsheet), or is it also okay to use (Na1 + Ns1)/P = integer as well? My other question is do you know if there are any efficiency issues with the teeth being out of sync (i.e. (Na1 + Ns1)/P = integer)?
Love it! Great video, thx 👍🏻
Can this be used for a winch mechanism and can handle high out put torque?
the idea is great, but it is very difficult to manufacture. How can you make a metal gear with two set of teeths instead of 3d printing?
LOL this is awesome, let me pull it apart
Question. I have a ring gear. So sun or planets. How do I calculate the size of sun and planets. With right amount of teeth
Brilliant explanation, sir :-)
thanks! this video helped me a lot!
I came up with the same thing on my own recently and wondered if it had already been discovered. Do you know any of the history behind it?
I actually don't know; I have seen it used in avionics motors from the 1950s. It is also sometimes used in the drive motors behind car rear view mirrors. It is pretty cool because of how high the ratio can be for a single stage of gearing.. :-D
It's called a "Wolfrom Gear", and there's even some variants with straight, i.e. not stepped, planet gears.
i.imgur.com/r0ifQwG.png
i.imgur.com/ICiAa1W.png
it`s easy to calculate 1st Stage carrier output = 1+annulus tooth/sun tooth, but how to calculate the 2nd Stage??... I`m really curious
hi david excellent video! maybe have you kept working in the experimental 3d printable Nema 17 Stepper Motor?
I actually have! I have a small growing family of types of printable stepper motors; may be a good subject for a new e-book :-) Thanks for reading/watching!
For each of the two annuli, instead of having two sets of Planet Gears, you are using one set of Planet Gear each having two sets of teeth, infused one above the other. I can see that the diameter of the teeth set in the top arrangement in all the three Planet Gears are smaller than that of the bottom arrangement.
So, the Circle Pitch (angular distance between adjacent teeth) in both the arrangements must be different. So does the Ring Gears and the Sun Gears. Am I right? Please clarify...
@@Gopinath2119 you are correct, the module of the gears on or touching the rotor are different from those on or touching the stator. The modules were chosen so that the axis of rotation of the small planet gears exactly lines up.. that way they can be stacked and connected as compound planets.
@davoriffic Thanks for clarifying...
GREAT WORK
Very good Thanks
Great video!
Hi David, my name is Layne and I am currently working on a project at work that could quite possibly deal with something like this. What equations did you use to determine what your gear ratio was? Any response or help would be much appreciated, I'm looking to achieve 100:1 reduction in a pretty small space.
Hello Layne, thanks for your interest. I made a spreadsheet and included the equations next to the columns to help decipher the process of designing these: github.com/IdeaPropulsionSystems/CoolEpicyclicGearing/tree/master/GearSpreadsheets Let me know if that helps. 100:1 is certainly achievable. I recommend using a carrier to keep the planets' axis all parallel. I discovered pretty quickly that, if you let the planets 'free orbit' like in this example, putting torque on the gear box makes them all 'tilt' and jam, limiting the effective torque you can get out of the box. If you have a carrier that holds their shafts parallel, that fixes the whole problem. Enjoy! I'd love to see what you're making!
@@davoriffic Thank you so much for the quick reply, and your charts were incredibly helpful. How would the R2 equations change if I were to bring a worm gear our from the first set of gears? I have to turn my gears 90 degrees and I'm thinking the simplest way to do so is a worm gear?
@@laynehelmuth4736 Interesting; not sure exactly where you mean. Worm gears certainly give you the 90˚ change in direction and will add another 10X or more to your ratio depending on the teeth~ also adds a lot of friction. It might also be the weak-point in terms of breaking gear teeth under lots of torque because there's a lot more teeth material engaged in the rest of the gear box than in a single stage of worm gear. hmmmm.... :-D
Very good, Thank you!
Is it relying on a difference in pitch for the gear ratio or is it relying on a different number of teeth between first and second ring to work?
So, good question. It is relying on the difference in the number of teeth between the first and second internal ring gears to work, but here's the thing: in order to have planet gears that fit both of the ring gears and share the same axis of rotation yet have the same number of teeth (each planet is like basically one gear stacked on top of another gear) they need to have different pitches.
So the different pitches is a result of having different tooth counts but keeping those planets on the same axis.. if that helps! :-)
But won't having different pitches have uneven wear? Or are you saying that stage 1 gears are all same pitch and stage 2 are all the same pitch? I guess if not 3d printing and buying it gears it would result in buying say Mod 1.5 gears for first stage and mod 2 for second. Would result in a massive difference between two ring diameters, so therefore less gear ratio?!
@@adamgibbons210 Yes, only gears of the same pitch are in contact with one another. It would be difficult to find commercially available gears I think with the correct pitches to make a box like this work. More likely, you could find half the gears and then print half the gears.
Hey man do you have any advice for coping up high loads on the gear teeth. I had r created a gear system of 1:200 multiplication factor, and am facing the problem of very less life expectancy.
Planetary gears tend to melt after 1 hr run
Hello, and yes. This is certainly a problem with plastic printed gears. I would recommend using a good lubrication (silicone grease is good with ABS plastic) and you may consider infusing the plastic parts in a 2-part epoxy resin. Beyond that, using more gears to spread the load will increase life, and if there is a way to actually support the gears in a gear carrier, vs. having them freely orbit, it will increase the life because the teeth will not be handling radial torques caused by the two annulus layers basically applying force in opposite directions at opposite ends of each compound gear... a more force-balanced gear design would help.
I want to add a gear ratio formula, becouse when i needed one i couldnt find it. I searched for a calculator but i couldnt find one. So i made up my own formula, and it works great.
Count the teeth of :
S1 (sun 1) drive wheel
P1 (planet 1)
R1 (ring 1)
P2 (planet of the second gearset)
R2 (ring 2) output wheel
Ratio is (1+R1/S1)/(1-(R1*P2/(R2*P1))) to one
You can check this with known gears on thingiverse or other sources.
I hope i helped a lot of people
Hello,
What does BAD FIT means for the gears in the spreadsheet? Will it mesh?
BAD FIT means something is wrong with the number of teeth for the angles involved; the won't mesh because it is asking a tooth to be some fractional amount shifted, for instance. Experiment with slight offsets in tooth numbers until that warning goes away.
Hi David, I've found some formulas online and calculate your ratio at 540, where am I going wrong? Could you share your formula please?!
Hi Adam. I put up a spreadsheet with the formulas I used here: goo.gl/bLfA0a
David Hartkop do you think this system can be run in reverse?!
In theory yes, but friction is really REALLY stacked against you with split planet gears. It's like a worm gear in that sense, only worse because there is more tooth involvement.
Hi David, is that due to the way this is working? 'pushing' second ring around rather than a true involute gear relationship. Of course the ratio massively increases torque.
If the box is set up properly, there actually is a true involute gear relationship between all teeth, it is just that the ratio is so great that static friction plays a huge part in the ability to make it start moving.
have ever tried to run it backwards as a step up gear box with no external load or resistance???
Oh, yes... well the first thing i noticed with one of these gear boxes is how rock-solid the output gear is in its position. I can imagine how, in a friction-free simulation, this thing could step up the speed very rapidly, but things like friction and angle-influenced binding of parts pretty much means it's not going to happen with this kind of box. It's basically like trying to push a very fine-toothed worm gear backwards.
Very cool design! Have you done backlash and max. payload tests on this?
I have not, formally. It feels like very tight gearing, though there is some wobble when it runs. I think much of that has to do with imperfections in the 3d print and the fact that there is no gear carrier.. the gears just orbit freely.
Hi David, I'm really interested in this gear box, are there any resources that discuss this type of gear box in much more details?
This kind of gear box seems to turn up in aircraft avionics and in some things like auto-mirror adjusting motors. There are also some gearing arrangements like this made by the company Harmonic, which makes strain wave as well as conventional gearing machines.
It is a little bit obscure, and quite interesting, though. I am putting together a better spreadsheet for calculating the formulas.
I’ve seen it referred to elsewhere as a Wolfrom drive. A bit of research shows that Ulrich Wolfrom held a patent for this design about 100 years ago.
what's the module of the planet gears selected for stage one and stage two ? please reply David.
I gave the gear specifics in Diametral pitch, which you can convert to module. There is a design spreadsheet on my github for the project here: github.com/IdeaPropulsionSystems/CoolEpicyclicGearing
@@davoriffic thanks david, with your help i have designed a new gearbox.
but made slight modifications in the design and completed it.
@@aravindputtah118 Please share a link! I'd love to see it.
How well would this work as a speed multiplier? For instance, in a generator concept where the input is high torque and low speed?
Yes, a good question; it is terrible for speed multiplying because of how much leverage the least bit of friction has. It is similar or worse than trying to use a worm gear to multiply speed.
David Hartkop I can visualize how the setup in this video would have difficulty with back driving. The torque input at the ring gear would cause the planets to twist and bind on the housing/sun gear in the other stage. If rigid carrier was added and some bearings I imagine it should back drive just fine. It doesn't seem like there is sliding component that you would see in a worm drive. That being said, you have done some great work explaining how the setup works! I may have made a fundamental error but it seems logical if I keep the planets from twisting and binding. I'm going to try it and report back.
We want a delete version button. Having a lot of versions accidently created casuses stresses.xc
what are the module of the gear selected for stage one and stage two ?
I have made a spreadsheet for calculating the factors for gears in arrangements like the gear box in this video. The gear sizes are given in diametral pitch, but you can use that to calculate the module. You can download the spreadsheet here: github.com/IdeaPropulsionSystems/CoolEpicyclicGearing/tree/master/GearSpreadsheets
thanks for the reply
helo, was wondering what margins you put in for 3D printing to account for shrinking/expansion of the material during 3D printing? I'm having issues with the gears being 'stuck'. Calculation wise it all works out, it's just in the 3D printing stage I can't figure out what to adjust to account for the expansion/shrinking.
That's a good question; fortunately to make it fit you only really have to shrink the size of the two smallest gears in the very middle. Just make them 1/2mm smaller than the object's given dimensions and that should do it... The small gears can basically be printed inside of 20 minute so it should hopefully be smooth sailing!
@@davoriffic thank you for your quick reply. I've considered changing the size but that in turn will change its module no? and as a result, a different module would mean issues with meshing. I haven't experimented with it however so i'll give it a try.
Thank you and keep it up!
@@ikkeennigij121 for printed plastic gears, it'll work fine.. just make them 'smaller' by a percent or so... also one approach I have taken for making printed gear boxes is to print them so the gears mesh just slightly TOO-tightly, and then run the entire system at high speed without any lubrication with a cordless drill... the friction generated will smooth and 'squish' the teeth into a perfectly meshed low-friction state in about 5 min of continuous running. You can then add silicone grease (which won't destroy ABS or PLA) and it will run smoothly with very little backlash. Have fun!
@@davoriffic that's an interesting approach, I'll give all of those options a go and see what suits me best. Thanks!!
Класс! Спасибо!
tres bon gearing !!
Thank you. Let me know what uses you might have for this kind of gearing.
v cool video
Hi, which module did you use ?
The key to understand with gearing like this is that the two halves have slightly different modules. This lets compound planets mesh with annulus gears that have different tooth counts. In the case presented here, they differ by 1 or 2 teeth, that way a full revolution of the planets only advances one annulus by 1 or 3 teeth. It provides a huge mechanical advantage in basically 1 step
i need help designing the gearing mechanism in this piece of artwork
Oh? Tell me about your art project. Do you have any links to share?
@@davoriffic I do, but its very provocative.
@@davoriffic I'm trying to build a room that has an ultimate gear ratio of 28 x10^17 and multiple transmissions within it.
@@NwoDispatcher hmmm.... counting down the seconds to the end of the universe? ;-D
@@NwoDispatcher I have corresponded with this gentleman, and he has some excellent super-ratio designs: ua-cam.com/video/kYmUJVE6Vo0/v-deo.html
Remember not to keep the motors idle for too long or they will get extremely hot. If you use PLA that will melt your 3D print.
How very true. I used an A4988 stepper driver chip with an arduino, and basically turned the current-limiter pot almost all the way down. The motor was low torque, but only got warm instead of plastic-melting hot!
"Ratio of 528:1" (c) ???
Ratio of 495:1 > 132/12=11 ; 135-132=3; 135:3=45; 11*45=495 !)
It's 4 x 132
By what means do you hold a1 on?
In the demo I printed, there is a collar that goes over the whoe a1 and holds it to the body and a2 by its flange. In a real application, there would have to be some bearing or bearings that keep it in position and centered.
whats the module of the gears
I made a spreadsheet here: github.com/IdeaPropulsionSystems/CoolEpicyclicGearing/blob/master/GearSpreadsheets/190120_Hartkop_CmpdEpiGears.xls
for figuring out the gearing. The teeth are given in diametral pitch and not module, though. You can convert one to another here: www.engineersedge.com/gear_pitch_chart.htm.
Hopefully that helps! An improved spreadsheet would have the module for the gears. Thanks!
Very clever idea. I can't help but wonder though, does this have any advantage over infinite screws. I'm not being sarcastic btw. In fact, it's more important for me that you know this than i know the answer.
If by infinite screws you’ll mean like worm gears, it really depends; work gears are definitely more simple and less trouble in terms of backlash. This split ring approach can achieve really high ratios, maybe 5 or 10 times higher than a work gear of the same diameter. But depends on the specifics. One other advantage I could see in this split ring approach is that there are at least 3 gears engaged at all times. In a worm gear, there’s just one contact point. For really high torque, this may make it less likely to have the teeth shear off ( because there’s more of them)
@@davoriffic then again worm gears, i think, work with a lot of friction inherently. under big loads, they might be a lot less efficient despite having fewer gears.
@@timucinbahsi445 True, they have a lot of friction, especially under big loads. The split planetary gearbox shown in this video also suffers from increased friction if you really load it because the gears try to 'tilt' in the casing, which cause them to bind up. Having a gear carrier for the planets and also possibly arranging to have balanced loading in some way could make it more practical.
@@davoriffic also this one can be mostly cured by decreasing play with bearings.
are your second stage gears all at the same pitch?
Yes; the first stage gears are all the same pitch, and then the second gears are all the same slightly different pitch.
Great, its a very nice work. I'm still trying to work out why One revolution of the planetary gears equals the second ring only turning round by the difference in teeth (of the two rings)?! So in that case I imagine if the second ring has a bigger difference in teeth it actually provides less gear ratio?. Also, does it rely on the compound planet having the same number of teeth on both sides?! Thank you!
I lasercut a setup with same pitch of all gears last weekend and it worked. It just relies on a different number of teeth between the two nested planets, and therefore corresponding rings.
Cool! send a link? I'd love to see it; I improved my calculator spreadsheet to include gear tooth pitches. You could use this to make a box with the slightly different pitches for the top and bottom halves. Having different pitches but same numbers of teeth on the planets will let you get ridiculously high ratios in just the two stages as shown. github.com/IdeaPropulsionSystems/CoolEpicyclicGearing
The motor pinion is 12 teeth and the ring gear 132 teeth so ratio is 11:1
If the second ring gear has three extra teeth to accommodate the three planets wouldn't the calculation be;
135/3 = 45, so ratio is 11:1 x 45:1 = 495:1 ? just asking
Thanks! And a very good question with a two-part answer -
First, the 11:1 ratio you found would hold IF the planetary gear was holding still with respect to the sun gear; in this special case, it is actually orbiting around as it engages with the annulus. The sun gear's engagement with the annulus basically falls behind by one full rotation once the planet has finished an orbit, so the ratio is actually found like this: (AnnulusTeeth/SunTeeth)+1=12:1.
Secondly, figuring out the ratio you get between the two annuluses (annuli?) you correctly divided the tooth count difference into the number of annulus teeth; I had been incorrect in my thinking as to which annulus should be divided into - it SHOULD be divided into the output shaft annulus, not the stationary one, so 45, whereas I had calculated 44 by dividing into the stationary annulus. The distinction is important because the 3 tooth difference is a difference of three output teeth, not three stationary teeth...
Taken together, the correct gear ratio for the box pictured in this video is 45 x 12 = 540
I'm going back to double check some things, and will update my spreadsheet to reflect this distinction. Thank you for your keen spotting! :-)
@@davoriffic Thank you for the reply and apologies for the first ratio; I forgot to add the 1 for a planetary gearbox ratio.
Thanks for the explanation.
@@davoriffic I'm glad I'm not crazy haha I was positive it should have been 540 instead of 528 given the 135 teeth output annulus but kept second guessing myself.
@@Tonescarp Interesting - Can you walk me through the steps that you took to figure that out? It is very likely that I messed up somewhere, and would love to update my calculator as necessary.
@@davoriffic Hi, I agree, 540:1 is correct. I have made an animation page and a calculator for such gears. Pasting '12 135 132' into the top right [I O B] field will show your gear, and also show that the ratio is 540:1.
saugstad.net/gear-animation
hello everyone, could you please help me to get 18:1 gear ratio with this technology. My requirement of Sun gear 1 PCD is 32 to 34 mm. Please help me.
how to calculate the gear ratio?
check out the spreadsheet for the project, published on my Github; check the links under the video for links to it to download and play with.
www.thingiverse.com/thing:4114551
But how to calculate the gear ratio? I got it way wrong.
In that spread sheet, what is n "2nd stage multiplier"?
I use the same diametral pitch on all gears.The openSCAD project is intended to be a library. They get connected together in the next project.
i think i found the purpose of that device if
Meshed gearswith an equal number of teeth will turn at the same speed. If they have an unequal number of teeth, the gear with the fewest teeth will turn faster.
if.that's true i think i know what this is meant to do
what if the top had.135
amd the bottom had 132
Well, the numerical model that I made suggests that the ratio goes from being 540:1 to being -539:1. That is to say, the output shaft would revolve the other way, and something is now going in the same direction when it was opposite before, loosing one full revolution per turn. That 'seems' right but maybe you better simulate it for yourself ;-D
Please tell me how to get several hundred thousands to one, thank you so kindly
One way I can see is to stack two gear arrangements like this together. This would essentially multiply the ratios. If you did that with the box shown in the video that has 500 some to one, you could very quickly have 250,000:1
@@davoriffic
Thank you so much I really like what you did
Really incredible
@@jamesmatheson5813 awesome, thanks!
Printed base that is on github and it is too big - planets do not reach it...
Interesting. I wonder if the small central gears are not scaled correctly. Do planet gears mesh with the annulus teeth?
@@davoriffic Base, rotor and seal do mesh together. So are only planet gears scaled incorrectly? Any idea figuring which part is wrong?
Interesting; My best guess is that the small idler gear and the gear for the motor's shaft are too small. I seem to remember having to play with the scale of these two parts in order to get the demonstration gearset working properly. Thank you for your interest! Let me know if that helps.@@RebellisSpiritus
Interesting video. I didn't know about the fancy name of it, I just went on and made one not having seen it before. However 3-D printing it is fine but how would you go about to machine it? I milled mine with an ordinary end mill. Also I have used it once in a project. Then I made the sun and the outer rings in hard anodized aluminium and the planets of POM. Worked just fine.
ua-cam.com/video/g821BOC_oAQ/v-deo.html
Rong gear ration dear sir
Please explain?
can i get your email?