@@bob2859 I always like it when the mathematics, or in this case the engineering, forces you into a part of the design space that you’d never think to go on your own. You end up with things that look really alien.
I love the way that a series of completely logical design decisions led from a version that looks very mechanical, to something that looks very organic.
To get a snug fit between 3D printed and metal parts, you can take advantage of the fact that the print is thermoplastic. Print the hole slightly undersized, and heat the metal part before pressing it in. Soldering irons work well as combined manipulator and heating element for this task.
Could you instead chill the bushings to get them to shrink, and then install them in the correct sized hole? Such that as the bushing warms it expands to press itself into place?
It looks like a bunch of dragon heads all folding together into an icosahedron! The very awesome design, the amount of thought that you put into it especially the clearances required for putting it together and the movements of the parts is super impressive!
We miss your models, it was always great when we got a new Segerman to print. Every now and then we still get one of the racks come through or the tilings and I love showing the new recuits the coolness.
I haven't put this one up because it requires special hardware and I don't think it would work on an FFF printer. I have some more accessible designs on the way though!
@@henryseg I work for Shapeways, so we have the full range of printers ;) Always enjoyed showing the newbies the triple gear when they came through and how to make sure they were loosened.
@ Ah sorry, I thought you were talking about a maker space or similar. Are you with the new iteration of Shapeways out of Eindhoven? If and when the marketplace comes back online I’ll consider putting my stuff back up.
So it's a lovely table centre piece who transform into a plate mat. As long as it's heat resistant to a safe point then you made something pretty good. Great work 👍
This feels like something that would deploy from an exploration spacecraft. Maybe for its journey it needs to be stored flat, and when deployed for its descent in to a gas giant it curls up in to a ball, protecting some instrument inside. Probably ten thousand ways to do that simpler but who cares, looks super cool. Maybe the opening credits of a movie
Now you have spent the time & effort creating this amazing thing mass produce it & sell it to schools & universities. These devices expand young minds.
A mechanized build like that would make an awesome game. It could roll itself into a ball, flatten out, and then roll up again in the opposite direction. This could even allow it to change its colors in a fun and dynamic way
Could try printing the holes slightly small, and cutting them to perfect size with a reamer. Reamers are sold with incredible resolution and precision, so if you had the exact right reamer for your rod stock, you could make your holes ~0.005-0.01mm smaller than the rod. Then when you insert your rod, it stretches the hole slightly, leaving you with zero play. Not as durable as the bushings, of course. But a little bit of friction could make the system feel more solid.
Have you tried printing channels through the parts and routing steel or some other low stretch cables through it? You could do away with the gears entirely if desired, and the double run of cables through the piece would tension it but themselves. Wear could become an issue unless bushings come into play tho
@henryseg they might be able to if they are run in pairs on either side of the hinges and trade sides every other segment so that as the cable on the outside of the hinge gets pulled as it bends, it switches places with the inner cable when it passes though the next segment, and it anchors to a point on the inside of the segment after that one where it will pull to force that hinge to close. It's sorta hard to describe, but it is kinda like the pulley equivalent to what you are already doing with the gears. You could get away with just two pairs running along each track of segments, each one fixed to alternating segments so that it's effectively multiple three-segment long linkages without the hassle of running them in pieces.
I tried to find a video of what l mean, but l couldn't. I guess it's sorta like the way cars have a tie rod linking the casters of the front wheels together so that they stay aligned, but instead this would be equivalent to the tie rod attaching to the rear of a caster instead of the front, so that the wheels would turn in opposite directions. The only difference with this is that you need twice as many cables since they can only act in tension unlike a tie rod linkage
While staggeringly beautiful, this could also work as a 1-DoF mechanical gripper! Perhaps a simpler platonic solid would be preferrable but I could totally see this having utility in robotic design :D
Yeah that would help it snap together, although there would then be a lot of force spread out around the mechanism stopping it from gracefully coming apart again. Unless they were electromagnets that could be turned on and off…
Functionally the diameter of the crucifix net of the cube may be better counted as 5 or maybe even 6, since minimising slop means that you’re interested in the chain of gears more than the chain of faces. So there are 2 sets of gears that transfer the angle from one edge of a square face to the opposite edge. The icosahedron doesn’t have this problem, obviously.
@@olyve4167 Indeed, Alice in Wonderland was written by Lewis Carroll! There are many mathematical and logical references in the story based on Carroll's mathematics work
Rolling contact joints would be an interesting method of removing the play in the mechanism given its organic appearance, but may be tricky to assemble given the number of joints.
If CNCing the parts from metal is possible, you might be able to make the gears larger (reducing slop) by having separate gear pieces that screw onto the triangle pieces during assembly, avoiding the problem of needing to fit the gears past each other
A good point about not having too many different metal parts touching... if it gets used in outer space... you have to worry about metal on metal welding to each other. A thing that happens in a vacuum and solar radiation can be a catalyst. There have been several cases where low-pressure welding has occurred in various space missions.
@@nnotcircuit010 I design in Rhino3D with its visual programming language Grasshopper. You can add sliders for all the parameters of the design, and you can use any slider to make an animation. It just moves along the slider, putting screenshots into a folder, which can then be made into an animation.
I believe the proof for the diameter being minimized at 10 for an icosohedron is in the fact that the least faces you can go across without having an already visited face being adjacent and return to the original is 10. With a cube, its 4. Tetrahedron is 3. Octahedron is 6. Dodecahedron I think is also 6. If you visit a face where an adjacent face has already been visited, then you decrease the amount of branches it can have, so it has to avoid them.
11:05 I'm fairly sure that the minimum net diameter is related to the closed shape. Let me try to be slightly more formal, though... Starting from any face, mark all faces with how many edges you need to cross to get to that face. The highest marked number will be a 5 (the opposite face). From this, the minimum net diameter is twice the highest number marked (and for a non-regular polyhedron, it's twice the lowest possible highest number by picking your starting point optimally). Possible that the actual minimum is twice + 1 if there are more than one face with the same highest number.
Could you 3d print with two different materials that do not stick together in order to print it in place and remove the assembly issues? Similar practices exist already, but I've generally seen it used for printing easy to remove supports.
Parker: this us 1000% something we would find at like a yard sale or thrift store or randomly get as a present at age 9, and I mean that in the absolute best way
Best kind of chunky and complicated! I think I would next try _not_ doing the space-sharing gears in triangle corner, I'd have one plain and simple gear pair near a corner, and turn the other pair into a gear train instead: conical gears (printed as one piece with the face) somewhere sturdy in the midpoint of the edge, and an axle (separately printed, with conical gears on both ends) nestled inside the triangle face through which the rotation must be transmitted.
at 10:48 there's an academic pub shown that lists M. Parker as an author. Definitely went down a rabbit hole trying to figure out if it's Matt Parker from Stand-Up-Maths. (I don't think he worked/studied in Brussels in 1998, so probably not). But you got me curious.
“Can you prove there’s no net of diameter less than 10?” Tell me if I’m on the right track here, but what I’d do is start with the graph of the connected faces of an icosahedron, then you can create a net by cutting some number of connections while maintaining a connected graph (this won’t always produce a viable net, but it is a repeatable operation that affects the diameter) then the task of a proof is to show that no amount of cutting can decrease the diameter below 10 without disconnecting the graph. Are there better approaches here?
I think slapping triangular panels on is a bit of a cop-out. That said, I can't imagine the further engineering hurdles it would take to just aesthetically close the hole at 11:59 otherwise. Simple first thing I would try is just reduce the thickness of the triangles and possibly gears. The thickness was probably way over-corrected for the sufficient rigidity you need, especially if you 3d print with a more solid maybe metal material (or just machine it). Also awesome stuff. This is cool.
I'd like to see something like this, but instead of opening from just one point, it could open up from any vertex without ever coming apart and while retaining the gearing mechanism so that it all opens and closes together. Complicated request. Probably mostly impossible without substantial jank, but if I had talent and a 3D printer, I would give it a go
11:05 it's not a particularly rigorous proof, but I'd say the reason there can't be a path shorter than 10 is because that path of 10 triangles forms a direct line around the center of the polyhedron, like a great circle on a sphere. In order to take a 3D mesh and flatten it to 2D you'd have to cut that path somewhere, and cutting the entire mesh in half will leave that as the shortest possible path between two opposite sides.
If you reduce slop some more and make everything mesh all around, unfurling the icosahedron bends space itself (and magically adds an infinitude of ‘triangles’ to fill flat and hyperbolic space).
I've never attempted a proof before but here goes. Attempting to prove that 10 is the shortest diameter for the net of an icosahedron: 1. Icosahedron is defined as having 20 faces, equilateral triangles. 2. So the "middle" of the net will be the line that connects 2 faces. 3. In the example given in the video, it would appear like there are different branches or arms with differing number of faces. 4. however if considering the two faces that join at the "middle" as the starting point - the middle two faces of the net, 5. We can see there are 6 equal diameter "arms" of 3 faces protruding from the middle 2. 6. since 6x3 = 18, plus 2 makes twenty. 7. therefore any increase or decrease in the diameter of one of the 6 "arms" would not result in a decrease in diameter of the net. So I conclude that 10 is the shortest diameter for the net of an icosahedron. Readable?
Since gears often have some “slop” or “play” in them, could this design be constrained using a compliant mechanism approach? Alternatively, could miniature “cables” instead of gears be used? For example, metal wires or filament fishing line.
A proof that an icosahedron net must have a run of at least 10 triangles: Start with an icosahedron and select 11 edges to cut in order to unfold to a net. As 11 is an odd number, at least one of these edges must be opposite one of the 19 uncut edges. Call the triangles either side of this cut edge A and B, and call the uncut opposite edge E. The unfolded net must include paths from E to both A and B. For each of these paths there are 2 possible shortest choices (of 5 triangles each, including final triangle A or B itself) making a total of 10. Icosahedron nets with runs of more than 10 triangles may take more convoluted paths from E to A and B, but nets with a maximum run of only 10 triangles must include these two half paths of 5 triangles which each unfold to a trapezium. They can be linked to form a parallelogram of length 10, or a V with two arms of 5 each.
I know you wanted to use just mechanical means of connecting/rotating, but I think it's reasonable to use magnets here to help the ends "meet" eachother in a satisfying *click* like those connect-shape toys you can get. they don't have to be strong, in fact I think its best if they aren't.
The work on this is insane! Strangely both mechanical and organic, looks almost like an alien artifact.
It's because it shows superhuman design and attention to details!
@@bob2859 I always like it when the mathematics, or in this case the engineering, forces you into a part of the design space that you’d never think to go on your own. You end up with things that look really alien.
It's got a hard-to-place sci-fi look to it, love it.
it's an armored star fish
The ivory finish gives it a bio-punk (like the video game Scorn) aesthetic I feel, that may be what you are trying to touch on.
Reminds me of the Thargoids in Elite: Dangerous, also in the way it moves
Covenant from Halo
Looks like something out of Warframe
"through the bushings that we definitely remembered to insert earlier" the dreaded forgotten assembly step
8:51 the word "triangle" is putting in a lot of work here
I love he even addresses this at 11:37 😂
I love the way that a series of completely logical design decisions led from a version that looks very mechanical, to something that looks very organic.
To get a snug fit between 3D printed and metal parts, you can take advantage of the fact that the print is thermoplastic. Print the hole slightly undersized, and heat the metal part before pressing it in. Soldering irons work well as combined manipulator and heating element for this task.
The issue with heated inserts is avoiding deformation where not wanted. Pain in the ass, but heated inserts are my favorite with 3d printing
Could you instead chill the bushings to get them to shrink, and then install them in the correct sized hole? Such that as the bushing warms it expands to press itself into place?
Watching you guys come up with designs is like watching prebiotic molecular evolution. Pretty soon you'll be printing and folding proteins. :b
Imagine they're working with the thought emporium to do this in the future
looks like a cursed sea star. Really good
Add neomags to the non-geared edges, this would help align the edges when closing up the 3d shape
I would call this absolutely unhinged, but
Add a locking mechanism, rebalance the weights of each side a bit, and we'll get the best D20 ever
Rig the locking mechanism with some magnets and you could set up something like a Bakugan that explodes on rolling a 1.
10:49 Unforunatelly no. It's Monique Parker. I don't think Matt ever worked in Brussels.
Fantastic work. I am impressed with the amount of engineering you put into it.
it looks so organic. my mind is blown by the complex shapes! i'll follow to see more.
It looks like a bunch of dragon heads all folding together into an icosahedron! The very awesome design, the amount of thought that you put into it especially the clearances required for putting it together and the movements of the parts is super impressive!
It's a wonderful video, showing the whole thought process during designing this thing. I can feel experience in teaching.
All your videos leave me in awe!
I like the chonkiness! The twisted gears are beautiful. Sometimes form follows function, and I think it is always a good idea to see where that leads.
This is incredible. Thank you for sharing.
Also, all the movements look so very organic...
We miss your models, it was always great when we got a new Segerman to print. Every now and then we still get one of the racks come through or the tilings and I love showing the new recuits the coolness.
I haven't put this one up because it requires special hardware and I don't think it would work on an FFF printer. I have some more accessible designs on the way though!
@@henryseg I work for Shapeways, so we have the full range of printers ;) Always enjoyed showing the newbies the triple gear when they came through and how to make sure they were loosened.
@ Ah sorry, I thought you were talking about a maker space or similar. Are you with the new iteration of Shapeways out of Eindhoven? If and when the marketplace comes back online I’ll consider putting my stuff back up.
@@henrysegThanks for sharing Henry. I really hope you can please respond tp my email or other comments when you can. Thanks very much.
@@henryseg i just like modelling and playing with the models and using them as a jumping off point to iterate and integrate.
So it's a lovely table centre piece who transform into a plate mat.
As long as it's heat resistant to a safe point then you made something pretty good.
Great work 👍
This feels like something that would deploy from an exploration spacecraft. Maybe for its journey it needs to be stored flat, and when deployed for its descent in to a gas giant it curls up in to a ball, protecting some instrument inside.
Probably ten thousand ways to do that simpler but who cares, looks super cool. Maybe the opening credits of a movie
That is one of the most interesting devices I’ve seen all year
It looks like a giant starfish.
It's a very fun looking mechanism.
Now you have spent the time & effort creating this amazing thing mass produce it & sell it to schools & universities. These devices expand young minds.
that's one gnarly looking coaster
Dude, you never cease to amaze me!
so awesome, v interesting to hear about the major obstacles and innovations, I bet there many more that didn't make the cut!
The look of the final piece is out of this world, something you would see in a scifi movie.
Incredible work 😊😊
This thing almost looks like some lizard-like creature. Amazing stuff!
Very cool. It has a very biomechanical look to it!
I'd say this is just beautiful.
impressiv very well designed 👍 thank you for sharing this process
This is actually super fascinating.
Excellent video and project!
Wow, that's nice assemble. I would love to explore that thing physically
This is one of the most beautiful things I've ever saw.
Merry Christmas, Henry & entourage! :)
This is the stuff that i live for on the internet.
My gosh, Henry! ...I think you've lost your mind. 😃Keep up the great work!!
A mechanized build like that would make an awesome game. It could roll itself into a ball, flatten out, and then roll up again in the opposite direction. This could even allow it to change its colors in a fun and dynamic way
Could try printing the holes slightly small, and cutting them to perfect size with a reamer. Reamers are sold with incredible resolution and precision, so if you had the exact right reamer for your rod stock, you could make your holes ~0.005-0.01mm smaller than the rod. Then when you insert your rod, it stretches the hole slightly, leaving you with zero play. Not as durable as the bushings, of course. But a little bit of friction could make the system feel more solid.
Have you tried printing channels through the parts and routing steel or some other low stretch cables through it? You could do away with the gears entirely if desired, and the double run of cables through the piece would tension it but themselves. Wear could become an issue unless bushings come into play tho
Cables would close everything up, but could they be used to force all the hinge angles to be the same?
@henryseg they might be able to if they are run in pairs on either side of the hinges and trade sides every other segment so that as the cable on the outside of the hinge gets pulled as it bends, it switches places with the inner cable when it passes though the next segment, and it anchors to a point on the inside of the segment after that one where it will pull to force that hinge to close.
It's sorta hard to describe, but it is kinda like the pulley equivalent to what you are already doing with the gears. You could get away with just two pairs running along each track of segments, each one fixed to alternating segments so that it's effectively multiple three-segment long linkages without the hassle of running them in pieces.
I tried to find a video of what l mean, but l couldn't. I guess it's sorta like the way cars have a tie rod linking the casters of the front wheels together so that they stay aligned, but instead this would be equivalent to the tie rod attaching to the rear of a caster instead of the front, so that the wheels would turn in opposite directions. The only difference with this is that you need twice as many cables since they can only act in tension unlike a tie rod linkage
While staggeringly beautiful, this could also work as a 1-DoF mechanical gripper! Perhaps a simpler platonic solid would be preferrable but I could totally see this having utility in robotic design :D
Really cool! How about strong magnets on the extreme ends of each appendage, so that they snap together a bit when it's going to sphere mode?
Yeah that would help it snap together, although there would then be a lot of force spread out around the mechanism stopping it from gracefully coming apart again. Unless they were electromagnets that could be turned on and off…
Great design!
Amazing work! 🤩👏👏👍
Ok I can't deny it anymore. I'm subscibing
Functionally the diameter of the crucifix net of the cube may be better counted as 5 or maybe even 6, since minimising slop means that you’re interested in the chain of gears more than the chain of faces. So there are 2 sets of gears that transfer the angle from one edge of a square face to the opposite edge. The icosahedron doesn’t have this problem, obviously.
Yes - I did think about bringing this up but I decided it was getting too far from the icosahedral focus of the video!
@ fair call!
How very appropriate that you talk about "going down a rabbit hole", a phrase invented by the mathematician Lewis Carroll!
isnt it a common phrase referencing the rabbit hole alice fell down in "alice in wonderland"?
@@olyve4167 Indeed, Alice in Wonderland was written by Lewis Carroll! There are many mathematical and logical references in the story based on Carroll's mathematics work
@@Ambidextroid oh my, i didnt know the author was a mathmatician, thats awesome
I've been dreaming for a while about making a 3D printed globe that unfolds into a butterfly map. Very nice inspiration!
Amazing!
Rolling contact joints would be an interesting method of removing the play in the mechanism given its organic appearance, but may be tricky to assemble given the number of joints.
I’d love to see a video series about the engineering challenges of the JWST, e. g. the mirror folding and alignment mechanism.
that first prototype looks like it could be useful for a swimming robot, like an eel or something
Great video
If CNCing the parts from metal is possible, you might be able to make the gears larger (reducing slop) by having separate gear pieces that screw onto the triangle pieces during assembly, avoiding the problem of needing to fit the gears past each other
A good point about not having too many different metal parts touching... if it gets used in outer space... you have to worry about metal on metal welding to each other. A thing that happens in a vacuum and solar radiation can be a catalyst. There have been several cases where low-pressure welding has occurred in various space missions.
I love your mechanism designs. Can I ask how you make the models, like those in your animations?
@@nnotcircuit010 I design in Rhino3D with its visual programming language Grasshopper. You can add sliders for all the parameters of the design, and you can use any slider to make an animation. It just moves along the slider, putting screenshots into a folder, which can then be made into an animation.
I really want to see a sintered metal version of this; maybe some of the more sensitive surfaces could be machined.
Talk about a challenge....
For one, how would you support and constrain the part dringend machining?
I believe the proof for the diameter being minimized at 10 for an icosohedron is in the fact that the least faces you can go across without having an already visited face being adjacent and return to the original is 10. With a cube, its 4. Tetrahedron is 3. Octahedron is 6. Dodecahedron I think is also 6. If you visit a face where an adjacent face has already been visited, then you decrease the amount of branches it can have, so it has to avoid them.
It feels like some mechanical protein. Amazing.
11:05 I'm fairly sure that the minimum net diameter is related to the closed shape. Let me try to be slightly more formal, though...
Starting from any face, mark all faces with how many edges you need to cross to get to that face. The highest marked number will be a 5 (the opposite face). From this, the minimum net diameter is twice the highest number marked (and for a non-regular polyhedron, it's twice the lowest possible highest number by picking your starting point optimally). Possible that the actual minimum is twice + 1 if there are more than one face with the same highest number.
I just wanna see lazer pointers attached in the center of each one.
To see if they line up like the death star beam.
Could you 3d print with two different materials that do not stick together in order to print it in place and remove the assembly issues?
Similar practices exist already, but I've generally seen it used for printing easy to remove supports.
I’d be surprised if they wouldn’t stick and also would have low friction between them.
Maybe, but even if that's somewhat the case if it works it's cutting out what appears to be your largest continuing hurdle with this type of project
Parker: this us 1000% something we would find at like a yard sale or thrift store or randomly get as a present at age 9, and I mean that in the absolute best way
Cutest evil 3d print I have ever seen!
another great one! cool !!
Awesome!
Very nice work
Best kind of chunky and complicated!
I think I would next try _not_ doing the space-sharing gears in triangle corner, I'd have one plain and simple gear pair near a corner, and turn the other pair into a gear train instead: conical gears (printed as one piece with the face) somewhere sturdy in the midpoint of the edge, and an axle (separately printed, with conical gears on both ends) nestled inside the triangle face through which the rotation must be transmitted.
Interesting... of course more parts (the separate axle) means more slop. But it does sound like it could be easier to design and construct.
at 10:48 there's an academic pub shown that lists M. Parker as an author. Definitely went down a rabbit hole trying to figure out if it's Matt Parker from Stand-Up-Maths. (I don't think he worked/studied in Brussels in 1998, so probably not). But you got me curious.
Holy $#!t... just saw that @Henry also put a "
imagine all of the parts can attach or detach from each other; the pieces actually implement any of the icosahedron nets
“Can you prove there’s no net of diameter less than 10?”
Tell me if I’m on the right track here, but what I’d do is start with the graph of the connected faces of an icosahedron, then you can create a net by cutting some number of connections while maintaining a connected graph (this won’t always produce a viable net, but it is a repeatable operation that affects the diameter) then the task of a proof is to show that no amount of cutting can decrease the diameter below 10 without disconnecting the graph. Are there better approaches here?
Very cool
I think slapping triangular panels on is a bit of a cop-out. That said, I can't imagine the further engineering hurdles it would take to just aesthetically close the hole at 11:59 otherwise.
Simple first thing I would try is just reduce the thickness of the triangles and possibly gears. The thickness was probably way over-corrected for the sufficient rigidity you need, especially if you 3d print with a more solid maybe metal material (or just machine it).
Also awesome stuff. This is cool.
A dragon head design for the tips would look amazing, it already looks a bit like dragons head
Looks insane, though I wonder how it would look with a layer of straight edged triangles on top of the main structure
I'd recommend moving away from a geared system, to aim towards these as compliant mechanisms.
Little, to no-assembly 🤓💗💗
I agree with this in general but this geared system is too cool not to try.
I'd like to see something like this, but instead of opening from just one point, it could open up from any vertex without ever coming apart and while retaining the gearing mechanism so that it all opens and closes together. Complicated request. Probably mostly impossible without substantial jank, but if I had talent and a 3D printer, I would give it a go
I’ve thought about trying to make a mechanism like that, but it seems hard to do, even for a cube!
I dont know how to make a rigorous proof of 10 being the minimum diameter but i would bet itd have to do with the icosahedron's anti-prisim band
now .im curious about a geared dodecahedron net
I think it might be easier, since there are only three pentagons around each vertex. So there’s no need for fancy nested axles.
11:05 it's not a particularly rigorous proof, but I'd say the reason there can't be a path shorter than 10 is because that path of 10 triangles forms a direct line around the center of the polyhedron, like a great circle on a sphere. In order to take a 3D mesh and flatten it to 2D you'd have to cut that path somewhere, and cutting the entire mesh in half will leave that as the shortest possible path between two opposite sides.
Yo this pokeball looks sick!
could some of the edges be living hinges?
So cool
If you reduce slop some more and make everything mesh all around, unfurling the icosahedron bends space itself (and magically adds an infinitude of ‘triangles’ to fill flat and hyperbolic space).
this goes hard as a dnd monster
An Icosaholder ?
Or a Gassporehedron ?
I've never attempted a proof before but here goes.
Attempting to prove that 10 is the shortest diameter for the net of an icosahedron:
1. Icosahedron is defined as having 20 faces, equilateral triangles.
2. So the "middle" of the net will be the line that connects 2 faces.
3. In the example given in the video, it would appear like there are different branches or arms with differing number of faces.
4. however if considering the two faces that join at the "middle" as the starting point - the middle two faces of the net,
5. We can see there are 6 equal diameter "arms" of 3 faces protruding from the middle 2.
6. since 6x3 = 18, plus 2 makes twenty.
7. therefore any increase or decrease in the diameter of one of the 6 "arms" would not result in a decrease in diameter of the net.
So I conclude that 10 is the shortest diameter for the net of an icosahedron.
Readable?
JLC offer metal 3d printing. You could design the holes slightly undersize and then ream them out for a perfect fit.
11:39
It's clearly a "seraphim", because of the six wings :)
well it can really be a great start for a nano robot that deliver drug in its ball shape
kinda crazy how advanced engineering like this ends up looking eerily organic. It looks like some kind of alien parasite
Since gears often have some “slop” or “play” in them, could this design be constrained using a compliant mechanism approach? Alternatively, could miniature “cables” instead of gears be used? For example, metal wires or filament fishing line.
A proof that an icosahedron net must have a run of at least 10 triangles: Start with an icosahedron and select 11 edges to cut in order to unfold to a net. As 11 is an odd number, at least one of these edges must be opposite one of the 19 uncut edges. Call the triangles either side of this cut edge A and B, and call the uncut opposite edge E. The unfolded net must include paths from E to both A and B. For each of these paths there are 2 possible shortest choices (of 5 triangles each, including final triangle A or B itself) making a total of 10.
Icosahedron nets with runs of more than 10 triangles may take more convoluted paths from E to A and B, but nets with a maximum run of only 10 triangles must include these two half paths of 5 triangles which each unfold to a trapezium. They can be linked to form a parallelogram of length 10, or a V with two arms of 5 each.
I know you wanted to use just mechanical means of connecting/rotating, but I think it's reasonable to use magnets here to help the ends "meet" eachother in a satisfying *click* like those connect-shape toys you can get. they don't have to be strong, in fact I think its best if they aren't.
I've seen one where a string is ran through it where when you pull the string it assembles the icosohedron
I d love to turn it into a worldmap
It'd be great to see wht an artist with some paint could do with this!
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