The Split-Ring Compound Planetary - My Highest Reduction Yet

The technical name for the mechanism I designed is a split ring compound planetary gear set. So it is kind of a planetary gear set, but the way it does what it does is so different from a normal planetary gear set that the comparison isn't really useful. So instead I'll be comparing this mechanism, the split ring compound planetary gear set, to the harmonic drive because they operate more similarly. But of course they do have some very notable differences, namely the fact that this new mechanism doesn't bend at all and that it can produce reduction ratios up to an order of magnitude higher than your standard harmonic drive in the same volume, if not a smaller volume. This new mechanism is so good at packing a really high reduction ratio into a tiny volume that it's the highest reduction ratio of any mechanism I've ever designed by a landslide. Before we get too far into the mechanism, I need to mention that today's video is sponsored by PCBWay. Yeah, seriously, it's sponsored and by PCBWay of all companies. You may know that PCBWay is a circuit board manufacturer, they make custom PCBs that are super high quality for really low cost. But you might not know that in addition to doing custom circuit board manufacture and assembly, PCBWay also offers a whole host of other manufacturing services. PCBWay can do 3D printing of every kind, they can do CNCing in 3-axis and 5-axis, can even do sheet metal fabrication and injection molding. So not only can PCBWay make the circuit board for your new project, but they can offer all the services needed to make an entire product. Thank you again to PCBWay for sponsoring this video, and I look forward to working with them further in the future. Now back to the video. This project started with me trying to explain an idea I had to some people on my Discord server, which, by the way, you can join, there will be a link for that in the description. I was having a conversation with someone, trying to explain an idea I had while they were making suggestions, and eventually someone on my Discord server linked me to a Wikipedia page. And apparently this mechanism that I had been dreaming up, that I thought was new, was already established, and had existed for decades. So it does certainly exist, but it's surprisingly uncommon it seems. This is the Wikipedia page for epicyclic gearing. As far as Wikipedia pages goes, it is decently long, with quite a bit of math. Towards the bottom, there's a section on compound planetary gears. And in this section, kind of as a footnote, there's one paragraph that coincidentally explains the mechanism I'm trying to make exactly. It reads, During World War II, a special variation of epicyclic gearing was developed for portable radar gear, where a very high reduction ratio in a small package was needed. This had two outer ring gears, each half the thickness of the other gears. One of these two ring gears was held fixed, and had one tooth fewer than did the other. Therefore, several turns on the sun gear made the planet gears complete a single revolution, which in turn made the rotating ring gear rotate by a single tooth, like a cycloidal drive. And that describes the mechanism that I designed exactly. But that's the only mention of it here, and the mention is not even cited. So again, it exists, but it doesn't seem to be very common. Now if this explanation wasn't quite enough for you to fully understand this mechanism, don't worry, because I'll give my own in-depth explanation. I want to compare this mechanism to the harmonic drive, so I'll start by giving you a refresher on those. In a harmonic drive, the flex spline, in red, is bent and forced to engage with the ring gear, in blue. As the green input turns, the teeth on the ring gear and flex splines are forced to engage. But since they have different numbers of teeth, there will be a relative rotation on the flex spline. For each full revolution on the input, the flex spline will shift over by two teeth. This is because there's a two tooth difference between the flex spline and circular gear. Thus you can have a small tooth difference and get a really high reduction ratio. In order to understand how I designed this mechanism, it's also going to be useful to understand reference circles and modules. The reference circle, or pitch circle of a gear, is a circle that cuts approximately through the center of the gear's teeth. The reference circle is important because the teeth can only mesh if the reference circles of two gears are tangent to each other. The module of a gear represents the size of the gear's teeth. It's usually used in metric gears and it's measured in millimeters of reference circle diameter per tooth. Module is extremely important because two gears can also only mesh if they share the same module. Okay, now for the actual mechanism. So this is the design for the split ring compound planetary gear set. It's clever how it works, but it's still pretty simple. You get this name from the fact that it does have a split ring gear, so there's a bottom ring gear and a top ring gear. The bottom has 50 teeth and the top has 49 teeth, so one tooth offset. The input pinion gear is down there and engages with the bottom of these planets. These planets are divided into a top and bottom section, which both engage with the top and bottom parts of the ring gear. Looking at just the bottom section, it is a normal planetary gear set. This is a 3.5 to 1 gear reduction, so 3.5 rotations on the input pinion will rotate a planet around one full rotation. There's nothing special here until we get to the top gear set. The top and bottom sections of the planets both have 15 teeth. Now this ends up working similarly to a harmonic drive or a cycloidal drive. As each planet makes one full rotation, it will align the top and bottom teeth to itself, and the result of that forced alignment is that each time the planet makes one full rotation, the top gear will be offset by one tooth. So since it's offset by one tooth per rotation and it has 49 teeth, that's an additional 49 to 1 reduction. But remember the 49 to 1 is not the only reduction here, we still have that input planetary gear set. So if you multiply the 3.5 to 1 reduction on the input and the 49 to 1 reduction on the output, you get 171.5 to 1. That's the highest reduction ratio of anything I've ever designed by a landslide. Now 171.5 sounds like a big number alone, but it's even more impressive when you compare it to the harmonic drive, or a theoretical harmonic drive of a similar size. If I were to design a harmonic drive using the same gear tooth numbers in the same volume, it would be only a 24 to 1 reduction. I say that because if I used a 50 tooth gear on the circular spline, the flex spline would most likely have 48 teeth. So this mechanism is producing a reduction ratio over 7 times higher than a similarly sized harmonic drive. And earlier I said that you could produce reduction ratios up to an order of magnitude higher, and I'm not just pulling that out of nowhere, you can do the math for it. The minimum tooth difference on a harmonic drive is 2 teeth. This is because both gears have to have an even or odd number of teeth, otherwise they just won't mesh. With this though, you can get away with a tooth difference of only 1, because it's not a single gear that's engaging on all sides, they're all separate gears. So that's already a 2x betterment for this mechanism over the harmonic drive. But of course, this one has that input reduction of the planetary gear set on the bottom. And planetary gear sets usually max out around a 10 to 1 reduction ratio. So 10 times 2 is 20. So at most, this mechanism can produce a reduction ratio 20 times higher than a similarly sized harmonic drive. So looking at it from that perspective, this one is actually pretty tame. It's not unreasonable that something in a similar package could get up to something like a 500 to 1 reduction. I've said before that I'm not a huge fan of harmonic drives, so this kind of feels like a win for me. Secure, which is an online electronics store, sent me a few of these NEMA 23 stepper motors. But these aren't just your average run-of-the-mill stepper motors, because they have an integrated servo conversion on the back. What that means is the driver is built into it, and the driver also knows the position of the rotor at any given point. And that allows these motors to use something called FOC, or field-oriented control. Now we could spend a long time talking about everything that goes into field-oriented control, but we don't need to know all that. All we need to know for now is that it means that the driver recognizes the mechanical orientation of the rotor, and it then controls the orientation of the magnetic field and its amplitude to be able to control the output exactly. FOC allows you to do some really cool stuff, namely arbitrarily precise positioning. So you can move the rotor to any position, you're not just limited to the 200 steps per revolution that a stepper motor normally is. These drivers are also really cool because they are driven in the same way that normal stepper motor drivers are driven, that is, just via a step pin. So if you have any kind of CNC machine, you could swap these out, and you wouldn't even have to change the electronics. Before we build the mechanism on this, I want to demonstrate some of the really cool stuff we can do with it. The first thing we need to do with this is to calibrate it. I'm going to turn off control mode, and then turn on the automatic calibration mode. In the calibration step, it's going to move the rotor around full 360 degrees in one direction, and then back in the opposite direction, and it's taking positional data at every point. I can turn the calibration off, and the control mode back on. So now I can turn it with my potentiometer. So one of the first things you might notice is that it's super quiet. It's so quiet because the FOC is approximating sine waves to drive this, which is the most efficient way you can drive a brushless motor. So what it's really doing is it's just driving it smoother than you would normally be able to drive the motor, so you don't get that clicking noise. So what makes this whole system so cool is its ability to automatically control torque to maintain a speed. Right now the motor isn't turning at all, and you can see it's drawing 100 milliamps. Now if I go and try and turn it, you can see that it takes more current. The driver is automatically recognizing that there's an external torque on the system that's moving the rotor, and it gives it more current to pull it back into position where it thinks it should be. Now when I bring it up to speed, it's drawing 190 milliamps. Now if I try and stop it, you can see it jumps up to 450 milliamps. So again, the driver is seeing that the rotor isn't turning as fast as it should be, and it's automatically compensating. That's the beauty of servo control, and this whole system, this secure stepper motor, makes it extraordinarily easy. I'm seriously in love with these motors, and I'm so excited to give them a purpose. Before I 3D print this mechanism, I'm in need of an upgrade. I recently realized that the printer I've used all these years is totally dimensionally inaccurate, off by like a millimeter, and there's no way to adjust it. So I got this new printer. It's the tried and true Ender i3 v2. You may have noticed a couple of inconsistencies in this video, and you may have noticed that this place that I'm recording in is not somewhere I've ever been before. I'm actually almost a thousand miles away from the location that every other one of my videos has been recorded. I'm originally from Des Moines, Iowa, but this summer I was offered an internship opportunity in Austin, Texas, so here I am for the next few months. So I recently moved across the country, and that's why this video has been taking quite a bit longer than it should have. Back in Iowa, I did all my projects on an 8 foot solid oak workbench, and this isn't quite that, but it still is pretty manageable. I don't have a ton of tools, but I do have most of my electronics equipment, so my making capabilities have been limited somewhat, but it will be manageable for the next few months. Anyways, let's actually make this mechanism. I designed the gears for this mechanism with zero backlash, which generally would be a bad idea when you're 3D printing and don't have high tolerances. But instead of adjusting things in the CAD model itself, I instead use one of the functionalities of Cura, and I just offset everything inwards on the planetary gear sets by like 0.1mm, so that they were a little bit undersized, and it ended up fitting really well. Oh, and I also designed a camera mount that attaches to the bed of my 3D printer, so that the 3D print is always central in the camera, it stays still. I think it's pretty cool, I probably could have used a more wide angle lens though, let me know what you think about these time lapses. This should be a pretty straightforward assembly, there's not too many parts here, so first I'll press on the pinion gear, there we go, pinion's on. I'll attach the lower ring gear with a few M5 screws. I'll put in the planet gears next, but I should mention first that there's something special about these. Remember that the bottom ring gear and the top ring gear are offset by one tooth? Well that means that only one tooth is going to line up, all the other ones are going to be slightly off. To adjust for that, every one of these planet gears is different. For the first one you can see that the top and bottom teeth line up vertically, now when we go to the second one, the top and bottom teeth are offset slightly, and that keeps on going down the line. So all the teeth are offset, and they have to be put into here in this specific order, otherwise things will not line up. We'll stick this guy in, then I'll just go down the line, trying to space them about evenly. There we go. So hopefully this should fit over really easily. And it does, look at that. I do need to press on the bearing first though, oh yeah, that is a really nice fit. Look at that, that's the mechanism. There is a little bit of backlash, but it's not much at all, and I think I could reduce it. Definitely not backdrivable, which is unsurprising. It's wired up, let's turn the power on, look at that! Look at that, that is awesome. It definitely makes a little bit of noise, and you can probably see the output is rotating really slowly. This is as fast as I'm able to make it go with this setup, and it's not going very fast. That output is just crawling along, but that's what you get with a 171.5 to 1 reduction. The way I've explained this mechanism so far kind of makes it seem like it beats the harmonic drive at its own game. It can produce reduction ratios an order of magnitude higher than the harmonic drive in potentially a smaller space. Harmonic drives are known for their high torque and a low volume, so why isn't this thing the standard? I mean, according to the 172 to 1 reduction and the torque of the motor I used, the actuator I made should have a max stall torque of around 150 foot pounds. I mean, that's the kind of torque that a car's engine produces. So the question is, why isn't this more popular? I think part of the answer is just that it's not super well known. I had never heard of it until I went and tried to reinvent it myself. But I think the bigger answer is really just that it can't necessarily handle those big torques. Obviously, my 3D printed mechanism isn't going to handle 150 foot pounds, but even if it was made of metal, it probably couldn't either. The thing with harmonic drives or cycloidal drives is that they usually have something with the tooth geometry that allows it to take a greater load. Often the teeth are a lot wider and shallower so they can take extra force. With this mechanism though, they're just normal old envelope gear teeth. So this mechanism makes a lot of promises about high torque, but it can't really keep them because at the end of the day, those normal old envelope gear teeth, they're long and they're thin and they kind of have to be. They're just weak relative to other gear options. So yes, this is a really high reduction ratio in a really compact space, but it being so compact means that it will break at those higher torques. So my expectation is that when you try to approach those values that you can calculate theoretically, is that the teeth on the gears are just going to shear off. Your gears are going to turn into wheels and your mechanism will fail. Well that's what I hypothesize is going to happen, I suppose the next step is to go ahead and test it out. I've attached this 3D printed lever arm so I should be ready to do some torque tests. This actuator should theoretically be able to handle torque significantly higher than anything I'd be able to apply to it. So I'm not expecting the motor to be the one to give up here. If anything fails, it should be the mechanism itself. It should be the gear's teeth shearing off or something like that. So my goal here is to test to complete failure. Alright, here goes. Testing to failure. The actuator is holding a stall torque right now. I should note, there is a little bit of backlash as you can see here. But it's not too much and I think I can get rid of it. I have some ideas on how to get rid of it. Stall torque is being held. My first weight is a water bottle. This is two pounds full. Two pounds. The whole bench is shaking but it can lift it without any problem. The current doesn't even go up. It doesn't care about that weight whatsoever. Now I've got five pounds. Here goes five pounds. Nothing shearing yet. Lifts it like a champ. No problem whatsoever. And the stall torque current has gone up by twenty milliamps. That's it. We're doubling our weight and we're going to ten pounds this time. Here we go. It's staying. The stall torque is only up thirty milliamps. Oh! Yep. I'd call that a failure. So I think what happened here is the teeth themselves didn't actually break. But instead the individual planet gears all bent inwards which then disengaged the teeth. Since there isn't a sun gear on the top layer there to push them outwards they're free to bend in which is how it failed. And then in addition to that some of the teeth got shaved down a little bit. I'm going to call that a pretty successful test. Of course it didn't end up being a hundred and fifty foot pounds of torque but that was pretty obvious. That was ten pounds at a hundred and fifty millimeters. So that's about five foot pounds and I'll put the newton meters of torque on screen. And that's pretty respectable. That's nothing to shake a stick at. And I do also have some ideas on how I can potentially increase that torque. But for now I'm pretty happy with ten pounds. And as an added benefit the mechanism does actually still work. There's a lot more backlash than there was before but it still works as a whole. Well there you have it. That was the split ring compound planetary gear set. I'll remind you that this was a hundred and seventy one point five to one reduction which is by far the highest reduction I've ever made. I don't necessarily think that this is going to be great for all of your really high torque applications because again those teeth are probably going to shear at those higher loads. But if you have an application where you want a really high reduction ratio, you want something to be compact, you want something to be precise, you want something to be slow, then this mechanism could definitely be a strong contender. This actuator was a lot of fun to make. It was surprisingly simple and straightforward which is kind of new for me. I do also have two more of these motors and I've got some ideas on how to make this handle higher torque and on how to get rid of some of that backlash. I'm thinking it probably wouldn't be too difficult to throw together a relatively simple robotic arm using these motors and this mechanism. Let me know if that's something you'd like to see. I know I've talked about making a robotic arm for a while but this one I feel like I could just throw it together and it'd work great. Thank you again to PCBWay for sponsoring this video, for being my very first sponsor. Thank you to Secure for sending me these beautiful motors. If you enjoyed this video and you want to support my work or if you want to get some of these files and make this mechanism yourself, you can do so via my Patreon. There will be a link for that in the description. There's also going to be a link in the description for my Discord server. You can come on there, show off your projects, talk to like-minded individuals about engineering things. There's also going to be a link to my Instagram on there for updates on my projects. So I hope you enjoyed this video. I felt like there was a lot of learning to be had in this one which is always a blast for me. But that's all I have for now so bye.