Nutation Wobbling Gears - Why Nobody Talks About This?
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- Опубліковано 22 лис 2024
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Pericyclic or nutational gears/transmissions typically consist of 4 bevel gears and thanks to their nutational motion, they provide extremely high gear ratios while also ensuring a high tooth contact ratio. This allows them to transfer high torques smoothly, making them competitive compared to other traditional gears. In this video, I discussed 3D printed pericyclic/nutational gears, their designs, working principles, and issues.
STL files: www.thingivers...
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I've seen high torque gearboxes before, and now I've seen a high twerk gearbox.
Work it baby, work, work, work.
that was my nickname in highschool
That joke really *grinds* my *gears*…
out
The issue you noticed on the end is related to a tiny flaw on the design, you should use tapered roller bearings on the ends! There is force being applied axially as well as radially, thus it requires tapered roller bearings instead of just standard radial ball bearings.
Might as well make the gear teeth like the cycloidal gears as well.
Didnt know tapered roller bearings were for multi directional loads, explains why you see them in automotive drivetrain applications. Good to know thanks for the info
Slab bearings. Barrel shaped like old right axles on Mercedes swing axle
@@jasonwhite2028 yes but they have a large nut or snap ring to hold it in place, so it's not the bearing on its own, and it's only in certain cars, possibly just trucks, I believe. The hubs of most cars are just a large straight bearing that gets pressed into the knuckle. While trucks and anything larger has tapered bearings that are made to come apart so you can pack grease into it and then pop it back together and fasten it down
I hear mention of tapered roller bearings mentioned around machinist lathes. Depending on what angle you’re cutting the load could be axial, radial or a mix of both.
i think this was genuinly one of the least annoying sponsor presentation ive seen,nice job bro
If you want it to operate smoothly, three things are to take into account :
1) the distance of each nutation gear to the nutation point depends on several factors such as tha nutation ratio and the difference in tooth count in each gear mesh, if not followed, the gears don't mesh perfectly
2) 3d printed gears need to be work smoothed by runing them with an abrasive to eliminate surface artifacts
3) greasing the gears is key in smooth and qiet operation.
Back to the first point, all herringbone gears have an average contact point wich describes a circle, the center of the fear being the center of this circle. With a nutation angle α, and an offset of a nutation gear from the nutation point (where the oblique and straigt axes cross) δ, and a meshing gear of radius r1 the nutation gear average radius needs to be r1/cos(α) + δ*tan(α),
if you trace the simple meshing on a piece of paper to find the proper dimensions, you will find this formula with simple trigonometry. On a side note, having the same nutation gears and meshing gears will simplify the design as the nutation gears will bea simetrical to the nutation point
So it’s possible to avoid the pulsing entirely if you design the gears to meet the constraints you described? I wonder if it would be zero-backlash like harmonic drives?
I don't know if it's useful, but it is hardly unnecessary. It may lead to a more advanced design. Try it with beveled helical gears and increase the gear contact by increasing the length of the gear teeth. You have a rather large gap between the teeth and shaft. More contact may increase stability.
Recreate this with magnets. No friction.
I don't quite understand what you mean. Can you make a model in your workshop to illustrate the principle, and then upload a video showing how it works?
@@ParaBellum2024 That's a weird way to troll. 🤔🤨
@@mspeir i just looked at your channel bc i was interested if you had a workshop due to parabellums comment , you earned a new sub.
@@sayorancode I haven't posted in years, but thank you.
The most useful aspect about it is making interesting UA-cam content like your video. Which I appreciate seeing stuff like this.
Overall though it’s noisy, vibrates (even when compensated for), inefficient due to friction and overly complex thus expensive. Its the answer to a question no one ask.
However like mentioned I really enjoy seeing stuff like this. Just because it’s impractical doesn’t mean it isn’t fun.
Looks like a neat variant of the harmonic drive that doesn't involve deformation
Why do you say this doesn't involve deformation? The end plates appear to deform (this is most visible in the thumbnail design - the orange plates are clearly shifting, especially the output side).
I'd be interested in a proper 3d model showing zero deformation necessary while maintaining constant output ratio & continual output torque - it's not obvious to me that such a design exists given the changing angle of the teeth.
@@TheLoneWolfling the plates are tilting not bending. If anything, the center tube is the one that should be deforming
@@wedmunds The outer plates cannot tilt relative to the center tube without deformation. And yet they clearly are tilting relative to the center tube. This implies deformation.
You are correct in that the center tube could be deforming instead of the end plates; either way this involves deformation (my point).
If the materials choices were better deformation would be reduced or eliminated.
Poor materials will cause deformation in any mechanical system, yet you seem to think it is a specific flaw to this drive? He even states in the video that as the materials are not solid it is deforming
I suspect you only have the most surface level understanding of mechanisms. AND skipped most of the video.
@@backtoearth1983 Kindly stop with the unwarranted assumptions.
The point of contact of the center cylinder with the outer plates shifts both axially and radially as the assembly rotates. And the gear extends a finite amount radially.
It's easier to envision the problem if instead of treating the contact as two crown gears interacting, you unfold it 90 degrees and envision it as two spur gears interacting, where one spur gear has both a non-central axis _and_ said axle isn't square with the gear.
This results in the contact point shifting both radially and axially. It shifting radially isn't the end of the world - non-circular gears do exist - however, it also shifting axially introduces an additional set of constraints between different planes of the gear. (Normally with a gear of finite width different planes of the gear are mostly independently constrained - see e.g. helical versus herringbone gears: you can effectively independently rotate each plane of the gear and still result in a valid (though potentially hilariously impractical) gear.)
Non-circular gears are normally already fairly constrained. It is _not_ obvious to me that there exists a solution to the further constrained system, although I'd love to be proven wrong.
Don't know why you think that nobody talks about this, because this is well known solution for high gear rations. Nevertheless that's good you brought it out
the fact that so many teeth engage at once makes it far more suitable for high torque 3D printed gears as demonstrated here!! typical configurations will result in the teeth breaking if they're a weaker material
It’s easy to see that for a continuous input you have a pulsing outout. Even In the double gearbox configuration. You can improve the smoothness of the output by offsetting the mirrored gearbox by 90 degree rotation.
I'm struggling to understand what you mean. Can you make this design in your workshop, and then upload a video showing how it works?
I am not sure how to explain it, referencing 8:32
But if you install the right side transmission to be 90 deg out of phase with the left side, that will it switch which side does the pushing. Essentially you can smoothen the output motion by making it so that the push (instead of being in sync) happens twice per rotation instead, right left right left…
@@ParaBellum2024 bot
@@sayorancode Wot?
@@marco_gallone I'm not sure if you are referring to the smoothness of the axial movements. But if you picture the circular motion, your suggested offset of 90 degrees or pi/2 is equivalent to the sum of a sine and a cosine, which results in a larger amplitude, which means more axial vibration in both directions. Mathematically, as you know, only a phase shift of 180 degrees or pi will cancel. Here are two examples in Desmos: 'qfcs5camdc' (180 degrees) and 'kkvv0zanus' (90 degrees).
You have amazing skills in explaining things clearly. Well done.
I’m very impressed by the finish on that clear cover! I used to work with acrylics and polycarbonate many years ago. That looks as good as an injection moulding. The gearbox is an impressive force multiplier! 👍🏻
as you mentioned, a solid casing made of thick steel plate, machined solid steel parts, some grease and this thing would genuinely be useful in a lot of industrial applications
Excellent work! I hope that students pursuing advanced degrees in mechanical engineering will consider focussing on this concept for their research thesis.
Very interesting and bizarre stuff, I think the biggest shortcoming it has, is that the output is basically getting 'twitched' between gear meshes as a means of moving. So your output side isn't able to deliver a consistent level of torque in a direction. Also I think this means that despite the 40:1 ratio or so, the mechanical advantage is actually lower, each time it steps back it is undoing the mechanical advantage, then the forward stroke has to put it back that much further, so that's a sort of continuous movement ineffeciency. So it's mechanical advantage factor would be measured in the forward-wobble and advancement region only, if that makes sense. Basically it will act like a 40:1, but the input torque used to move it, will take the effort of something more like a 30:1.
It's very much like on a worm gear reduction, friction takes away quite a bit of the performance.
This was my initial impression but actually I don't think this is a fundamental problem of the mechanism, but the tolerances/manufacturing of the part.
Like, its not like contact is made to force the gear once per per rotation, the contact is made cyclically around every contacting gear tooth in rapid succession.
I think that there are also ways to optimize the tooth design. Before involute gear tooth, the same (or similar) criticism could be made for simple gears!
@@MatrixRay19I am unsure of this. I think at first glance you'd assume something similar of cycloidal gearboxes
I was thinking the same thing with the engage and disengage being horribly indirect compared to planetary or worm etc, but it also looks like it could be constantly engaged with just a portion of the gear as it wobbles rotating the contact position? Not sure but the vibration alone makes this seem pretty unviable, still cool to learn about
Maybe. But the real show-stopper is friction. Properly designed gear trains have friction only in the bearings but never on the teeth (rolling motion via evolute geometry). Here, there teeth are sliding into position. Big no-no in engineering and the reason why worm gears wear out so quickly.
6:12 FWIW, the teeth on *BOTH* sides of the center gear are engaged, so the total force is _really_ spread out.
Looks useful for high torque applications, such as driving a winch and spool.
Neat fact related to your use of 4 degrees, that's also the same degree that water will travel uphill against gravity due to capillary action.
In practical sense, all tork is on one/ two teeth , balance can be mitigated, nice work thanks for knowledge
I would love to see a really high load on this gearbox. Maybe test its limits with what 3D printing material and precision you have, until a gearbox of a certain size fails. I bet if you optimize it as much as you can, it may be capable of producing much more torque for its size and mass than other more commonly used gearboxes.
It is not suited for high load. With a 45 degree tooth angle, the output force is equal to the bending force on the inner gear.
@@renedekker9806 because of the amount of surface area in contact between the gears, the load distribution on them is completely different than other gearboxes. That means that the gears can handle many times the force before failure. This thing is only made of plastic, imagine one made of metal. Optimizing this box would be a really fun project for me, if I had the means to do it
@@christiangray7826 _"because of the amount of surface area in contact between the gears"_ - the real contact is still only 1 or 2 gear teeth, the force concentrates on those teeth. Because the gear teeth have an angle, that force also tries the gear teeth to disengage. In a normal gear box, that force is towards the centre of the gear, which is easily withstood by the gear. In this gearbox, that force is perpendicular to the gear itself, causing the gear and its axle to bend.
I would not put large loads on it.
@@renedekker9806 We disagree on its function, but doesn’t that make it even more interesting to see it tested to failure? Whether it performs well or not, it would be very fun to learn more about. Maybe it has no potential. Maybe it has plenty. Only one way to find out, and that’s optimizing it
Interesting variation of the harmonic drive. 👍👍
You can make the gearing ratio even slower if you have 1 tooth difference between the two yellow gears, and each orange gear having 1 tooth more than its yellow mate.
Exactly, the ratio increases as the number of teeth get closer together.
this would've been a great example for my machine design course
They are very interesting and you have great physics and cad skills
Thank you for sharing your knowledge on the gearing
Sort of like a harmonic drive that doesn't require the fragile circular spline element. Cool!
I think even though it looks like there's a lot of teeth engaging it's still only one at a time. The teeth in front of and behind the one in contact are about to touch but aren't touching yet.
This broke my mind a bit but it is awesome
cool idea. maybe the center gear could be balanced by modulating the infill percentage at least a bit.
Excellent job on making this video and explanation. Thank you for sharing with us.
I think there may be less friction losses in comparison to worm gears. I think it might be used to aim anti missile batteries. Real slick!
Very cool! I have never heard of pericyclic transmissions before
Usefull in the circumstances you don't have access to flexible material for an harmonic drive. Harmonic drive don't have the wobbling of middle gear, much greater ratio and tooth engagement.
With just a pair of metal worm/gears in series like the ones you showed at the start, you'd get 1600:1. Metal, simpler, stronger, quieter, cheaper, so, ...! Great to explore this kind of stuff, though!
Its a matter of use cases. Most of the time you don't need a planetary gear, but when you do its very useful to have.
Same thing here, a worm drive is fine if you have the space. But if you are limited in space a design like this is nice to have.
Neat. It's a shame that UA-cam is working hard to commit hara-kiri because I'm really going to miss channels like this one.
You're right something has changed, it is increasingly turning into brain rot, I assume that's what tiktok is like (I wouldn't know)?
@@Mike-jm5wttried tik tok once, it's still 100 times worse, not even joking. Tho youtube is getting worse and worse and content farms are also responsible for that
Hopefully they move to one of the pop up competitors like odysee or something
Fascinating. I think that, with a different way of meshing the teeth, the engagement could be gentler, like helical gears, though the vibration will remain an issue.
Maybe good for solar panel tracking because of the slow movement required. Could probably have the gearbox sealed and filled with oil for low maintenance since solar arrays are pretty remote sometimes
Idk about the torque situation - I'd say it's only actually engaging on or two teeth at a time, a lot of other teeth are really close, especially the closer they are to the contact point but unless the gears are flexing, no additional teeth are actually making proper contact. I'd think a next step could be to compare and contrast the design to a planetary configuration to see if there are any benefits but it's definitely interesting either way.
Just a different form of what I know as a harmonic drive, only a lot worse performance. Harmonic drives have high gear reduction, they're relatively compact, have close t0 0 backlash, run smooth/quiet, and are robust. They are commonly used on CNC machine centers to drive automatic tool changers. We have a bunch of Toyoda's that use them, a few machines are over 30 years old, never had to touch the harmonic drive sections.
Thanks I will look those up
Great work. If you use a much finer gear pitch, the distance of nutation can be reduced greatly, reducing imbalance forces.
If you casually look at a harmonic drive, the gear pitch more closely resembles a straight knurl rather than gear teeth.
I like this. Still not sure about it vs worm drive but either way I will take the extra arrow for my quiver. The one thing I can say is worm drive vs this has a perpendicular input naturally so this might have some advantage for situations.
Very inspiring! Ever considered to make a calender clock this way?
seems like a good application for differential gear
A match made in heaven. 3D printing and ball bearings. My first prints way back when had them at the get go. I see no reason for KUKA to not incorporate this design in their actuators.
Superb! I wonder how well this would work in low speed conditions like bicycle gearing? I’m looking forward to see more. Thanks
Interesting idea, my only concern would be high vibration, possibly having the gearbox on a floating platform and a lovejoy style coupling to absorb vibration going to the motor. The torque output has to be insane though
Cool, another gearbox that acts like a cycloidal gearbox. I already have a functioning print of a harmonic drive and a cycloidal drive.
This is more like a split ring planetary
These would be great to have in the hubs of each wheel on a vehicle with the proper gear ratio
in praxis you can make the wobblator and its shaft out of 1 part, id opt for a much larger shaft thoug, id go so far to increase its diameter to the point where its just a bit smaller than the inner diameter of the ring. stator
@7:05 the screws start to loosen. And that, ladies and gentlemen, is how Harley Davidsons are made.
Since the input and output are co-axial I think you could make a cool clock design with this, with a 1rpm input that gives you your minute hand with the input shaft going all the way through to the front and then with a design with a 1:60 reduction then the output wraps around the minute hand and gives you the hour hand and the low speed means that the noise and balance is not so much of an issue
Now we need a competition with 3D Printing Academy
What an interesting little gearbox. Im sure theres a few applications for it
There should be a counter balance weight installed to keep the center of mass around the center of rotation.
It’s an interesting concept. Have you done a comparison with a traditional gear with the same ratio for friction? I have a feeling the friction may be too high for practical purposes. Adding bearings to the shaft to reduce the friction there was a great idea, but as you mentioned in the video, there are multiple teeth meshing simultaneously instead of just one and that means more friction.
My husband would understand this. It is interesting. 😊😊👋👋❤❤
I'm sure the angle for the shaft needs to be big enough for the gear teeth to pass by each other as it spins, but reducing this angle as much as possible will reduce the vibrations as well.
Increadably high gear wear but good potential.
Regards from South Africa
That reminds me of how hydraulic pumps and motors work. Frankly, I'm thinking of all the times I wish I had known about this in my special project at work.
you could make it half the size and 3d print it in metal to get strength and precision . great work!
A former Czech friend many years ago came up with a compact compound planetary gearbox that was actually capable of infinity to zero gear ratios.
seems like a fun concept but must be one helluva thing to balance properly
Brilliant, thanks for sharing
Keep in mind, mirroring the gear boxes doubles the gear contact area. 2x the strength, or same strength, half the weight neaded in materials
Smart idea, but how strong is it? Will it be stronger than a worm gear set up, also what about long will it last under load?
Sürekli kendini geliştiriyorsun dostum tebrik eder başarılı işler dilerim.
Well, this is definitely interesting --- I like your presentation -- but what are the advantages?
I'm sure there's an application somewhere that's useful vs a worm drive. Maybe if you needed a large ratio like a two stage worm drive might be less desirable than this nutating layout esp considering the lower stress on teeth. Also mechanisms that might depend on specific gear ratios for timing, since your 1:409 ratio is super compact for that kind of specific extreme ratio
Some perhaps interesting ideas, a different tooth profile, like herringbone might be more forgiving and yield a more silent operation at a higher speed.
Alternatively, could you not just make the sides flat and simply surface the sides with a "sticky" material like an o-ring or silicon coating/layer? Are the gears even needed for it to nutate if there is sufficient compliance and friction in the surfaces?
This is great for high ratio needs.
3D printing is showing us so many new systems.
Amazing saw this first time. Can you build cyclodial gearbox.
It will be useful for many Robotics applications.
Definitely interesting, but I think the Split Ring Compound Planetary gearbox is a much more useful design. Equally compact, practicality unlimited ratio options, and balanced.
I spent a bit of time working on it but I could not justify the cost of adequate tapered bearings for my experiment. They seem to work best when the input speed is relatively low but provide great torque in a fairly compact package, printing them is a problem because all the tolerances compound and you get a lot of vibration out of it.
The issue you're going to run into is that the teeth are wedging across each others faces, that is not how reliable gears work. It may be a tolerance issue as in a few shots it seems as though they can roll across each other like they're supposed to. But yeah, as long as the inter-face....uh interface is sliding you're going to have forces trying to force the gears apart, ie that outward bending moment on the mounts, and the gears are going to wear down. And wear faster when experiencing more load.
....its almost like a century and some change of gear design was onto something....just sayin....
Are they neat? Yes, absolutely. Are they capable of extreme ratios? Again, abso-freaking-lutely. Are they going to replace standard gears, especially made out of FDM SLA plastic? Not a chance. Maybe if you cast them in a good resin (using a 3d printed gear as the molding part to create the casting tool), then machined the faces to the proper profile...possibly with some sort of additive in the casting material to prevent shear force fractures (like how fiber glass prevents the resin from fully crumbling by distributing forces to surrounding material). But I mean....at that point...just cut em out of metal....I wonder how difficult it would be to use a thick walled pipe, fill it with resin and cut the tooth profile into the pipe wall, that way youd have metal on metal which can be lubed and wont wear as much, and is far less likely to shear....but again at that point just make the whole thing metal....Then again, I wonder how hard it would be to, like, lay some thin plate in the tooth faces so the contact points are metal....nice and slidey and wont grind itself to bits....
I'm wondering about how it could be miniaturized - high torque, low part gearboxes with less tooth shearing could be quite useful in robotics.
Try swapping the incoming and outgoing rotation. In order not to slow down the final rotation, but rather to accelerate it.
Is it possible to create a propeller based on this transmission mechanism ?
For example, for "pedal catamarans".
I've been addicted to videos of all the various gearing and drive mechanisms , and this is the first of this kind that I've seen!
I wonder if these are used in any real products? The geometry doesn't even seem too hard to machine with standard lathes and mills. 🤔
just a tought , dunno if this would work at all, but instead of adding a second gearbox if you make the two outer gears each half the weigth of the diddle gear , and then give them an oposite inclination to the middle on so when the midlle one force is maximum at one point the two other max out in the other direction ?, would put more strain on the shaft but i think its doable
I think this kind of gearbox is used in some of the electric driven parking brakes in cars (usually at the rear wheels)
I wonder how well this kind of gearing would work for wind/hydro setups 🤔
Maybe Hydro would be more applicable with high flow streams to spin a generator. This would come into play when a load is applied to the generator. Granted, the generator would need to still spin at high rpm (not slow like the outputs shown here) but maybe something that'd be doable.
I had a winch that used a planetary drive but it was unusual, It had the motor connected to the planet gears and no sun gear. It drove between 2 ring gears which had a different number of teeth. One was mounted to the housing the other to the drum.
Excellent
i love energy converters, does it gets hot? i like my ECs cool and chill.
I could really see this in some super low speed application that needs only torque. So you could stick a smaller motor on it and call it good. That 400-1 is crazy! and could be useful, just needs some optimization
That is interesting. In a sense , it looks like a mechanical relative of the planetary gear, or even the differential, If the output is the center and you hold one shaft while spinning the other. Perhaps counterweights in the nutating gear would cure the problem of being out of balance.
I saw a generator that operated on gravity. Just like a pendulum clock, the weight is hoisted up in the day. And at night as (the weight) "slowly" descends, A high gear ratio generator makes power from the potential energy of the big (weight). Only trouble was, no gear could hold all that weight on one tooth. It looks like your gear has solved that problem.
ur oh, maybe not. I remember you say your gear, jams up if you try to "back drive" it. And that is exactly what that gravity generator project needs. A slow (rpm) into a fast (rpm)
Would it be possible to play with the weight distribution of the wobbling gear to make it stable? I guess that might be more dependent on manufacturing quality compared to adding a mirrored gear, but at least it would only be one unit
Pretty damn cool, but I have to imagine that this would be pretty high wear, no matter how refined it gets. But if it's made with easy to change setup, might be a pretty nice alternative
I think that this should technically be backdriveable. The fact that it isn't I think implies that there are inneficiencies in the gear tooth designs.
Reminds me a lot of cycloidal gears! I think this idea is very cool and potentially practical!
In theory all gearboxes should be backdrivaeble 😂
@tymoteuszkazubski2755 eh, if you assume that friction doesn't exist in theory.
Maybe I should have said that I think this is feasibly backdrivable. I don't see why it couldnt be if cycloidal gearboxes are.
It appears you used involutes for the gears. Might a saw tooth or acme work better?
Maybe use a counter weight like in car engines crank shaft to balance the gearbox without adding a mirrored gearbox?
I wonder if you can scale that down to be used in something like a model train locomotive? It could give it true scale speed operation smoothly.
You should be able to machine it with a bit of cleverness. It consists of 3 cylinder parts where the middle one is tilted. You just have to tilt it in the mill to make it work. One edge part can be machined in the tilted angle, but big enough to encompass the final result. Then you can machine it down again to the correct size.
Unusual, but use only for decreasing speed (for what?). If we will use that for increasing torque we also need to increase the shaft diameter proportional. High torque will break geer teeth.
Plus vibration and axial load.
Nice video, thanks :)
Very interesting.
Question: What is the benefit of this design?
Steel gears with tapered bearings, immersed in a gearbox full of heavy oil would probably solve most of your issues. No more flex, significantly less noise/vibration/wear.
instead of other gear to oposite the angular momentum, why dont you use a metal ring attatched with the first yellow gear but with the oposite angle for balance the wheght, adjusting its centr of mass to reduce vibration
Hallo, sehr interessant vielen Dank 👍 wünschen dir eine schöne neue Woche ❤ danke für gegenseitige Unterstützung 🔔 Siggi & Anne 👍