Nutation Wobbling Gears - Why Nobody Talks About This?
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- Опубліковано 11 жов 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...
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.
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.
i think this was genuinly one of the least annoying sponsor presentation ive seen,nice job bro
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.
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.
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! 👍🏻
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.
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).
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
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
6:12 FWIW, the teeth on *BOTH* sides of the center gear are engaged, so the total force is _really_ spread out.
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
You have amazing skills in explaining things clearly. Well done.
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
Certainly a nice gadget but not a solution for real-life problems: the 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.
That's wrong. Checkout the harmonic drive or the cycloidal drive. They are zero backlash drives and require friction on the gears.
Here's a good explanation of the harmonic drive:
ua-cam.com/video/7QidXf9pFYo/v-deo.html
That's not true. Involute gears have sliding and rolling contact. Pure rolling only happens at the pitch radius. Some sliding is a benefit in operation as it keeps the oil film from collapsing.
Even ideal evolute gears slide, this is plain wrong
Worm drives if properly designed with suitable materials and tribology do not wear out quickly. But it is so easy to make a badly designed worm gear.
@@zachary3777 Haha! Correct! Totally accept your response in the context of substantial forces & hardened steel surfaces. However, in the concept shown in the video, we are seeing a "dry" system built from a low-melting-point material. Here, we should aim at a system where we only see rolling motion & big radii if we want the system to survive for a reasonable time... self-lubricating materials would be a bonus too...
Similar to a strain wave gearbox, it should have extremely low backlash due to the large number of teeth engaged.
Yes, but this design is much more 3D printer friendly. James Bruton did some experiments with a printable hamonic/strain wave drive but ultimately settled on cycloidal drives for his projects because of issues he had.
ua-cam.com/video/QoBgSWkJyM4/v-deo.html
Maybe someone will see a solution to the balance issue other than using a second gearbox and a better system of bearing (or maybe even something like a delrin bushing) might further improve things.
Yeah, looks interesting
Unlike strain wave gearing, this only connects at one area, until another mirrored part got added. Very similar mechanism indeed.
Excellent work! I hope that students pursuing advanced degrees in mechanical engineering will consider focussing on this concept for their research thesis.
Looks useful for high torque applications, such as driving a winch and spool.
Sort of like a harmonic drive that doesn't require the fragile circular spline element. Cool!
They are very interesting and you have great physics and cad skills
this would've been a great example for my machine design course
This broke my mind a bit but it is awesome
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.
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.
@7:05 the screws start to loosen. And that, ladies and gentlemen, is how Harley Davidsons are made.
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
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
Interesting variation of the harmonic drive. 👍👍
Now we need a competition with 3D Printing Academy
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.
In practical sense, all tork is on one/ two teeth , balance can be mitigated, nice work thanks for knowledge
cool idea. maybe the center gear could be balanced by modulating the infill percentage at least a bit.
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.
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
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.
The main advantage of a pericyclic gearbox is vey high output torque because several gear teeth are in contact at the same time. Because of its inherent design, we have this vibration problem causing the gearbox to self destruct. The only way to cancel out the vibration is by adding a "mirror image" of the gearbox. But then the output is now in the center of the whole gearbox which leaves us no other option but to use a spur or helical gear which is quite counterintuitive.
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.
Thank you for sharing your knowledge on the gearing
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.
These would be great to have in the hubs of each wheel on a vehicle with the proper gear ratio
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.
seems like a good application for differential gear
There should be a counter balance weight installed to keep the center of mass around the center of rotation.
seems like a fun concept but must be one helluva thing to balance properly
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.
Keep in mind, mirroring the gear boxes doubles the gear contact area. 2x the strength, or same strength, half the weight neaded in materials
3D printing is showing us so many new systems.
Very cool! I have never heard of pericyclic transmissions before
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.
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!
If you can imagine it, it's probably already been done. Fascinating stuff, but he mentioned the practical, real world solution at the start of the video: the worm gear drive.
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.
i don't know why, but I'm getting a constant velocity joint vibe from it.
But is it though? the output shaft literally moves forward and back, it jitters and isn't constant at all, much more obvious on the higher ratio box, fyi.
What an interesting little gearbox. Im sure theres a few applications for it
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.
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.
I think this kind of gearbox is used in some of the electric driven parking brakes in cars (usually at the rear wheels)
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
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. 🤔
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.
you could make it half the size and 3d print it in metal to get strength and precision . great work!
Very inspiring! Ever considered to make a calender clock this way?
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
Excellent job on making this video and explanation. Thank you for sharing with us.
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.
Superb! I wonder how well this would work in low speed conditions like bicycle gearing? I’m looking forward to see more. Thanks
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
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.
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".
This is great for high ratio needs.
There are a bunch of alternate gear box solutions, but they all have the same issue: More wear, and much harder to make.
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?
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)
i love energy converters, does it gets hot? i like my ECs cool and chill.
Excellent
Brilliant, thanks for sharing
Maybe use a counter weight like in car engines crank shaft to balance the gearbox without adding a mirrored gearbox?
here are planetary gears with high ratios: ---- Ratio: 5310.6 ---- sun1: 106, ring1: 158 diff1: 52, sun2: 110, ring2: 164 diff2: 54, max planets = 15 15, coherent planets: 10 halfDegAB = 17.72727 and 18.39416
---- Ratio: 3554.626 ---- sun1: 107, ring1: 159 diff1: 52, sun2: 111, ring2: 165 diff2: 54, max planets = 16 16, coherent planets: 10 halfDegAB = 17.59398 and 18.26087
---- Ratio: 5313.742 ---- sun1: 110, ring1: 164 diff1: 54, sun2: 106, ring2: 158 diff2: 52, max planets = 15 15, coherent planets: 10 halfDegAB = 18.39416 and 17.72727
---- Ratio: 3557.574 ---- sun1: 111, ring1: 165 diff1: 54, sun2: 107, ring2: 159 diff2: 52, max planets = 16 16, coherent planets: 10 halfDegAB = 18.26087 and 17.59398 i have a planet gear generator which materializes them out of thin air i am checking it it today adn uploading it to thingiverse zoon1234micron soon
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.
It appears you used involutes for the gears. Might a saw tooth or acme work better?
I have an idea for a clutch mechanism, that would require a lot of pressure but not a lot of parts.
Increadably high gear wear but good potential.
Regards from South Africa
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
what if those gear tooth are rounded , probably would be much smoother and wouldn't skip since many are engaged at the same time
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.
I want to see it in an enclosed case with gear oil to see if it quites down then put it to its limit!
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.
Sürekli kendini geliştiriyorsun dostum tebrik eder başarılı işler dilerim.
Something like this would be perfect for a home telescope.
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
Ultra-high gear ratios are not difficult.
Three worms, labeled A, B, C. Three 100-tooth gears, labeled 1, 2, 3.
Worm A drives gear 1, which is coupled to worm B. Worm B drives gear 2, which is coupled to worm C. Worm C drives gear 3.
1,000,000 to 1.
Very compact. Nothing wobbles. Off-the-shelf parts.
Most of modern engineering centers on minimizing slip and vibration.
Creating a box that both vibrates and slips wrecks that.
also, in order to 'balance' this you would need infinite gears because the angle of slip is a rather advanced calculus problem that centers itself on the fact that a circle has infinite angles.
All you did with 2 is make the reaction more violent against the bolts holding them in.
I give this a meh out of 10.
I feel like you could mechanically tether a counterweight to be driven by the same motor to oscillate at the same speed.
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.
I think this is useful. Perhaps we will see this in microscopic form. Nanogearing.
Well, this is definitely interesting --- I like your presentation -- but what are the advantages?
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.
My husband would understand this. It is interesting. 😊😊👋👋❤❤