Flexure Lecture – by Amy Makes Stuff
Below is the full transcript of the recording:
All right. Hello, everyone, and welcome to my presentation about 3D printed flexures. My name is Akaki and I don’t want to be on camera today, so I’m going to put my camera down onto my work bench. Today, I will come to you as a pair of talking hands if that’s okay with you. I’m going to tell you very briefly what flexures are and show you a ton of examples of these.
I have a box full of interesting trinkets you might like, and I’m going to ask the question if you can 3D print these. Spoiler alert, it’s not the perfect technology for 3D printing, so I’m going to show you why not. But there are ways around it. I, at the end, will show you a few of the learnings and tricks that I have that will let you use this flexure technology as it applies to 3D printing. All right.
My name is Akaki. I have a few 3D printers at home. Originally studied computer science and engineering, so I have a little bit of CAD experience, but mostly I’m self-taught. I like flight simulators, especially Condor 2 for gliders, if you want to play with me one day. I love building different sort of controllers and control interfaces. You might have seen my 3D printed controller designs that use flexures. Just this joystick online. All right. Let’s get started. Thank you for coming, and here’s my presentation. Okay. It starts with this.
To get a little taste of what flexures are as it comes to comparing them to older, more traditional technologies, take a look at this, this design I’ve found on Prusa printers. I will have the link to whoever made this. I’m sorry. I forget the name, but it’s a pen holder for your printer. You can attach a pen to your printer, put a piece of paper down on the print bed and suddenly your Prusa Mini here is a pen plotter. I’ve printed a copy of this attachment here. This is the files that you get. This would, with the round hole there, screw onto your print head, and here you have a linear rail.
Because once you have a pen on here, like so, you want to give it some room to slide up, in case the printer pushes too hard down on that paper. To give the slider a little bit of positive loading, you add a rubber band around it. Now, you have a linear rail and a elastic, a spring, and this completes your pen plotter. If my hand was the print bed, sorry, if my hand was the print head, you could make it, raw plots like this, without scratching the print surface.
Now, I’ve made my own version of this design. Sorry, I don’t want to put down the original designer, but I’ve designed the same mechanism using flexures. Finally, we’re getting to the meat of today’s presentation. Here is a flexure pen holder for your printer. It’s a bit larger, but it does the same function. Here’s the screw hole. You would screw it onto your print head like that, move it around, and your pen clips on here. It’s a flexure that replicates the functions of a linear rail and a rubber band elastic spring at the same time. See? All right. Sorry to whoever designed this design. I don’t want to put you down. All right. That’s the warmup.
What is a flexure? Very briefly. It’s a related term to compliant design. Now, compliant design is opposed to the traditional mechanism design. A mechanism is a collection of rigid parts. You have your bolts, your arms. Then to make a moving mechanism, you add axles, so pins and screws and bolts that your parts might turn around, rotate around. Here is my one-handed controller and it has hinges. Do not confuse this. These are not flexures yet. I’ll get to flexures later. This is the traditional design that you might be used to. Now, compliant design, finally, we’re getting some examples. Here is something I found online.
It’s a compliant grabber mechanism. If you push and pull here, these two jaws, they close in, because of all these bendy bits. This mechanism doesn’t use only rigid parts, and it doesn’t use any fittings or axles or bolts. Everything is one piece, but it embraces the flexibility of the material. In traditional design, you will try and minimize bend. You add material, you add infill in your 3D print, and you add more steel and wood in your traditional sort of design, until you get it completely rigid so you can understand and design it better. But in compliant design, you design around the idea of embracing this flexibility.
Flexure, very related to compliant design. It’s a subset of what compliant design is. It’s one element of compliant design. It stands for flexible structure. It’s a part that’s designed to flex, but also work as a structure. More rigidly, it flexures in one axis, but is rigid in another. My little pen holder here flexes in this axis. In fact, it moves linearly in this axis, but you won’t be able to twist it or bend it any other way. It’s giving structure.
It’s limiting the movement depending on this one axis, but giving it freedom in another. That’s a flexure. Often they manifest themselves in these flat flaps, like this Tic Tac box lid here. You’ve seen this. It will open and close because of that living hinge. It’s a thin piece of plastic that opens and closes. Here’s another example of a flexure, a very old car suspension. Those leaf springs are designed not to move sideways, but bend under the load in one direction only.
The first three pictures are more common flexures, but when it comes to the study and research on flexures, often you’ll find the is sort of micro positioning. Or is it called nano positioning machines? In very microscopic equipment where you’re moving nanometers to position a needle inside a stem cell or whatever. Advantages of flexures. There’s no moving parts, and because of that, there’s no slop.
When you’re making a mechanism with multiple hinges, axes, and bolts, springs, all these parts out of the more traditional design regime, every single time you have parts rotating around each other, you’ll introduce a bit of slop. Because the tolerances, they can’t ever be perfect, can they? Relatedly, no wear. And because there’s less parts, there’s less assembly. This pin holder is print-in-place. You can take it off your print bed and it’s a ready mechanism where the previous version was two parts, plus the elastic. No assembly.
Disadvantages. They’re not easy to design, because our design principles, our CAD software and everything we learn about mechanisms and designing mechanical things is based on this older design, where you’re only using rigid objects. Your flexures and compliant design, you never can have a continuous rotation or a large displacement of movement. That’s why I have limited movement on there. Finally, you have something called creep. This is material fatigue. You can never have a plastic 3D printed part like this under constant deformation without it fatiguing over time. I’ll talk a bit more about that later.
Now, before you get bored, I’ll show you a bunch of these flexures that I’ve brought to you today. Some of these are mine and some of these are from different users online. I have no idea what this machine does, but it’s very satisfying. You can see that these thin pieces all over the design work as springs, but they also work as the linear motion for these little springs here that advance the gears. Very cool. You’ve seen the grippers. Pull here and the grippers grip very slightly. I think this design is designed for that sort of metal manufacturing, instead of 3D printing. Here, I love this.
If you didn’t know what was underneath this plate here, what would you guess? Would you think that there would be perhaps a spring that this rests on? Well, if it’s a spring, you’d think that you could then rotate this table. But it turns out it’s very free to move in X and Y directions, but you can’t actually rotate it very much. It’s very difficult to twist it. Well, could it then be two linear rails, so you have one linear rail this way and one the other way? Both with their centering springs? Perhaps you could have that, but the answer is a ton of flexures. Do you see? This is a model of those microscopic nano positioning mechanisms that you use in very accurate science. But it’s more of a desk toy that you can print.
Finally, we get to my own designs. I’m pretty proud of this one. Move the joystick around and watch closely. The joystick is on a ball joint sort of base there. This black member, this is rigid, but it’s mounted on two flexures, one on the Y axis and one on the X axis. That allow this black arm here to move in two axes, much in the same way as this platform is moving. Where it won’t twist around like this, but it’s free to move in X and Y, and that results in this end and this end performing the same motion. If I turn this joystick in a circle, the thumb stick moves in a circle.
I told you a lie. I told you that there was a ball joint under the joystick, but that’s not true. You actually have more flexures. See, how that part there is supported on these thin strips? That allows you to move it up and down. And further, this axis is the same. If you can see inside there, you have this crossing. Here is a whole bunch of flexures in my giant JoyCon. I call it the JoyiantCon. Can you guess what the mechanism inside might be? Look, it’s a centered spring, the spring-loaded buttons all over, and even the opening mechanism is a springy button.
Wow, this is just flexures galore, isn’t it? Let me take that off so you can see it better. Just to open it up. Here’s your first flexure, a very common clasp design. The button is also spring-loaded with a flexure. Not very visible. These shoulder buttons, that’s a flexure. Here are the large, perhaps five millimeter travel of the button. It’s translated to only half that because of this mechanical advantage. That end that is designed to push down on the same button on the real controller that mounts down here, that reduction in travel is achieved with this lever sort of flexure. And same on the other side.
Here, we go in even further where this stick, as it moves this black ring around, those motions are copied over to the stick on the real controller. Again, we can find the same mechanism there where you have these two parallel lines and these two parallel lines forming a X-Y flexure. Further, the shoulder buttons are also supported on these linear motion flexures, and they allow you to push down on the controller. Why I wanted to show you? Oh, more flexures. Look, these buttons also, they are held in place by their own springs. That’s what a flexure is. It’s a structure that’s also a spring.
Why I wanted to show you this? I don’t just want to brag about my cool designs. The reason I wanted to show you is because I have the same design before I learned to think with portals, to think with these flexures. I forgot how to open this. There we are. Oh, no. See? To make the same mechanism before I discovered the beauty of flexure design, I used, look, metallic springs, pins, and rigid mechanisms. More springs here. The stick centering was also a elastic band. Compare the simplicity here. See? I’m going to tell you … Oh, no. I’m never going to see that spring again. I’m going to tell you all about it. All right. That was the fun part. Now, let’s go back to the theory part.
There’s tons of resources out there for flexures and compliant design out there, but can I use these designs in 3D printing? Unfortunately, the answer is kind of. I have bad news for you, which is, our household FDM 3D printers and our plastics that we use, they don’t make very good flexures. PLA, the plastic that we use, and other common plastics that are in use, they yield too easily. What is yielding? Here’s a piece of our common PLA filament. You know that you can bend it around up to a certain degree. That’s fine. But at one point, some of these plastics, they start getting white. You’ve seen this, right? See? That has yielded. You’ve bent it too far and now, it doesn’t spring back anymore.
Next, and this is perhaps even worse. Our 3D printed plastics, they experience creep. Here’s my test specimen that I’ve made. I make this for different materials. This is made out of PLA+ and this dial indicator here, you choose your favorite angle here. You choose how far to push it. I’ve left it bent like this since this morning and now, we can see where it likes to rest. I’m going to take this off. Look, it started straight and now, it’s been left at this position and it only comes back so far. This is the largest problem that we have. Yielding and creeping are the biggest problems with our 3D printed plastics. Here’s a torsional spring, a little catapult you can make. You can’t leave this loaded for a long time, but it’s fine as a nice desk toy that only gets loaded before it’s used. That’s fine, but not leaving it loaded.
Finally, this is a bit more complex of an issue. Our 3D printed parts are not isomorphic. I’ve learned that word recently and it means that they have grain, basically. If you’re printing a flexure, let’s say it’s one of these flexures where it thins down, like here or like in this toggle switch where the more thick piece gets thinned down to a very thin spot. Well, if you’re cutting this out of aluminum or if you’re cutting it out of Delrins, then this whole part will be quite isomorphic. The grains and the fibers or whatever it’s made out of will be in all directions, and it’ll be equally strong no matter where you look.
As you make it thinner, you can trust it to be quite strong here, then less strong, less strong, more easily bendable here, and then stronger again, as a function of the thickness of this part. But now, if you’re 3D printing it, you have to make it out of sausages. You’ll have the surface sausage here. You’ll have another surface sausage there. What happens inside here? Well, you’ll get a surface sausage up to here, but then that sausage has to turn around and it’ll make up something like this. Leave a gap there. All right.
You’ll start to see where this area of the flexure might be as strong as two strands of filament, whatever that means. But here, it’s no longer a linear or I should say no longer a continuous function of strength as you go up the neck of this flexure, because the number of sausages changes, but in steps. And it’s even more complicated because of the different ways the infill might go. For this reason, it’s very difficult to predict or simulate. But those are the challenges that we have for FDM printing flexures. But I do think there are ways around those. I think there’s a few reasons why limited as they are, flexures with 3D printing are also a good match, and here they are.
First, 3D printed mechanisms are quite often ephemeral. That’s a word I learned recently. It means short-lived. We can all admit it. We’re making trinkets often, or we are making toys for our game consoles. Maybe Sony wouldn’t make their official joystick attachments with flexures, because you’ll never know how long these are going to last, or the quality issues might be difficult. But for us hobbyists, making little one-off toys, little one-off trinkets, little patches and hacks, I think flexures are a perfect fit because they don’t have to be so long-lived and reliable.
Next row there is an answer to the difficulty in analysis and design. Well, this whole field of tech 3D printing is all about rapid prototyping. I think we can overcome the challenges in difficulty of design of flexures, because we can turn over prototype, over prototype, very fast, so we can do trial and error design. Down there, the next row is what actually gives you a bit of a bonus when doing flexures over more traditional, rigid mechanism design. Because 3D printing can produce very complex shapes that wouldn’t be possible when carving or injection molding, you can suddenly make flexures in one piece that would be multiple pieces if you tried to make the same mechanism out of discrete parts.
Now finally, everything built in one part, there is no imprecision there, because there’s no need for tolerance. There’s no slop because it’s one piece. The last slide on this slide. Hopefully, they might cancel each other out, don’t you think? Here. Finally, we get to what I’ve learned over about a year of tinkering with 3D printing flexure designs. This is my flexure primitive and all these designs are built out of this. It’s a 40 miller, sorry, 40-millimeter long wall printed horizontally. So like this on your print bed instead of this.
It’s 0.75 millimeters thick and at least 10 millimeters wide as a band. That’s it. That’s my primitive. I’ll show you the process where I got to this, because this is the perfect length, thickness, and width that has been shown to work. It’s not very scientific, but as I said, as I told you, unfortunately, with FDM printed flexures, it’s not very easy to scientifically analyze. Okay. Here is the process that I used to arrive at my flexure primitive. Here, thickness. Let me show you different thicknesses.
Here is a thicc, with two Cs, flexure primitive. It’s the same dimensions in other dimensions, but it’s thicker. Then I have a very thin one as well, and the funny thing about the thin one is that it’s almost impossible to print. Here. Here is a 0.4 millimeter flexure and you can start to see why my primitive is the correct Goldilocks size, because the printer actually can’t print very much thinner. The thicker, here, you’re losing a lot of that bendiness. It might work if it’s longer and so on, but you also get back to that isomorphism issue.
So, why not one line? Well, this is what happens when you try to slice a one line flexure. The printer doesn’t know where to start that wall, so it started all over between these two boxes and you get this weak spot here where the line starts. Whereas, if you have two walls, especially with these fillets like this, the outer wall of this box blends into this flexure line and you don’t have a stop there, with at least 10 millimeters in my testing. Here is a five-millimeter wide flexure of the same dimensions, but see, you can twist it too easily. That’s the reason. It can be thicker as well, but at least 10 millimeters, please.
Length? Four millimeters. I found this to be the perfect length. If you make it shorter, it doesn’t want to bend in the center. It’ll concentrate on some weak spots on the length and you don’t get enough travel either, because PLA is too easy to yield. Four millimeters, I found it to be best. If you make it too long, now you run into the issue where if you have compression from two ends, you can get a buckling in the middle. That’s the reason.
Finally, this is a limitation too, you might think that you’ll be able to print flexures lying down like this, and this in fact, was printed on the print bed. But there’s no way to ensure that the print lines are longitudinal along this flexure, which is the strongest way to do it. Instead, this is now filled in like this, which is not perfect, and it isn’t as stiff either. Please, print your flexures standing up. It’ll be the cleanest and the strongest. It’s well-known that 3D printing, FDM prints are the strongest along these layers.
Here, we get to the fun part where we can start building up mechanisms from our primitive, our flexure primitive. To make a simple hinge, well, just use a single flexure. That’s already a hinge for you. It only bends perhaps 10 millimeters at the end, but that’s a hinge. If you want a more advanced hinge, use this X configuration. Look, this has the advantage that it’s almost equivalent to turning around a fixed point. Whereas the simple hinge, you can get some parallel movement like this. This is the twisting, but this is the parallel movement. Whereas with the X hinge, I’m trying to do it parallel like this, but you simply cannot get it to move. It’s totally solid, but it’s free to move rotationally. This is what I’ve used in the joystick. This is the base of the joystick, if you are interested to see this. There’s two of these X hinges.
Next. For linear movement, and I’ve used this a lot also, it’s just two parallel lines. You’ve seen it here. I have a specimen here. This stays put, but I can move the other end about five millimeters both ways. You can have a more linear motion with two of these stages. Here’s two parallel lines, as you’ve seen in the original. That’s the same piece there. They twist so, but these two other parallel lines are here to, let me turn it this way, are here to cancel the up and down movement. Now, as I move it backwards, back and forth, this shuttle, this moving piece, not only does it have double the horizontal movement, but it moves vertically no longer. The distance here is constant.
Combine these and you get the X-Y movement. I’ve used this in the joysticks a lot. There’s a parallel here that moves up and down, and this moves side to side. Here’s something that might confuse you a bit. It looks like a little tower. Here, the two flexures are no longer parallel. They are slightly at an angle. That means that as this mobile part moves left and right, it rotates, but it’s calculated this time. It’s calculated so that the end here, where these two parallel lines meet, this stays almost put. There’s a little bit of movement here, because the geometry isn’t perfect. But with this, you can get a rotation about a point that’s outside the hinge.
Do you see? Here is solid, but this piece remain in the same relation. You can’t push on here to turn the mobile pin. Instead, if you push here, it will yield to you. But if you push here, it’s totally solid. It’s really confusing to play with your hands. And this is used in the bottom of my joystick. This is not my design, but here is … I’m going to this next dimension where you are building up flexures with basically this sort of design here, but where the flexures were parallel before.
What I mean is that these lines, these walls, they were vertical always. This time, they aren’t vertical. They’re actually meeting at a point here, which means that if you keep this point solid, the end of that pen won’t move, because all these flexures are meeting at a point at the end here. This is a bit outside of the scope. I actually don’t know how to design this, but I wanted to show you that if you have one primitive flexure, which I have here, you can build up from there and make many different ones.
All these designs that I’ve shown you were that I’ve designed. The JoyiantCon and the joystick, they’re using just these built up hinges, or mechanisms I should say, based on my flexure primitive. There is an X hinge, there is an outside hinge, and there is an X-Y mechanism here. For the pin holder, all you have is one parallel linear movement using the doubly linear parallel flexure joint. For the JoyiantCon, again, it’s a X-Y joint and then some parallel movements. That’s it. All of these are made with the primitive and these intermediate built up phases. Okay. Some extra tips.
As I’ve told you, 3D printed flexures, they yield easily. How to stop that? Well, build in some end-stops. You can see this member down here that’s dangling down, it hits those two ends and it’s designed so that the flexures never go close to where they would start to yield. I have as my rule of thumb, five millimeters of displacement at the end of the flexure. Same thing right here. These jumpers at the end, when they jump down, they stop the flexure from moving. And these half-circles, if you’re compressing it, those will meet. They aren’t meeting at normal use. They only meet when you compress it, and that stops the user from flexing those flexures too far. With that, you can have very long-living flexures.
Here is another maxim, another rule of thumb that I have, which is never to leave these flexures under tension. In this mechanism here where you have the rubber band or in real world, you often have springs that are loading apart, perhaps I should use the trebuchet here as an example. Don’t let the user, or don’t let your design be under tension like this for long. Flexure springs should only be used for temporary loads. For easier printing.
You might have been wondering what these notches are on all my designs. I called the these seam attractors. You can see in the screenshot, if you have these sort of notches on the inside of this parallel mechanism, many of the slicers that you might use here, I’m using Prusa Slicer, it will start the parameter lines on this sharp corner, instead of starting them near where the flexure wall starts, as you saw earlier. This flexure doesn’t have these seam attractors and it doesn’t have the little fillet. That is also important. And the line has started near the flexure.
It starts because that’s a natural place for the slicer to start its line, because it thinks that’s going to be a hidden place. Well, it’s going to be a soft spot for the plastic to start yield from. Always use this field, sorry, seam attractors and the fillets, if you can. And further, even better. If you can, instead of starting the flexure out of a wall like this suddenly, make half of it follow another line like this. That’s what I mean, extend from a parallel wall if possible. This way, the outside line is here. These lines are drawn from this end to this end and they’re going to be very strong.
Oh, here. Look. How can you have two flexures on top of each other like this? Well, it turns out you can bridge these very easily. Nothing specially you have to do. No supports. You can have two flexures across each other if you’re thinking in three dimensions. The first line, as you can see, might be a little bit rough. But after a few lines, the flexure print lines, they stabilize and you can print flexures in thin air, as long as you print them vertically as I’ve told you. If you must print them horizontally, so laying flat, make sure that you use some sort of slicer trick or something and make them longitudinal, like that.
I think you can turn the direction of infill in most slicers. I think that would be the only trick. In my very nonclinical tests, I’ve only used the very common materials that you can buy on Amazon. Well, PLA+ has been the most useful. Many people say that PTG should be better for this sort of bending and fatiguing designs and devices. But in my experience, the difference hasn’t been big. And if anything, PTG has less springiness. It’s more sloppy, so your spring force is not as strong. It’s not even as useful as a flexure as PLA parts, which are more stiff, would be.
Here, that’s my tips and my different designs. I hope you could gleam some out of that. To learn a bit more, there are universities around the world that do research on this sort of topic, but the one with the best publications is here. It’s Brigham Young University. They have a whole department for this sort of stuff, and they have great gifts and videos and even principle SDL files that you can find. My next step to learn an intuition of how these different flexure mechanisms work, I say this unironically, you can search for flexures on Pinterest. Just make sure you don’t subscribe because they’ll send you spam mails every day.
Oh, here’s one video that I found very useful, by Amy Makes Stuff. She made 10 cool flexure examples and went into the science behind, and the calculations behind flexure bending. Right. I’ll leave a list of downloadable files for most of what you’ve seen. To summarize, use my primitive size flexure primitive and build up your own designs from there. It’s only a subset of what compliant design and flexures are, but I think if you follow these rules of thumbs, you can get started on designing flexure for your 3D printing projects quite soon. All right. See you again. Goodbye.