engineers are turning to origami for
inspiration for all types of
applications from medical devices to
space applications and even stopping
bullets
but why is it that this ancient art of
paper folding is so useful for modern
engineering
origami literally folding paper dates
back at least 400 years in japan
but the number of designs was limited
there were only a handful of patterns
maybe 100 200 total in japan
nowadays there are tens of thousands
that have been documented and most of
that change happened in the 20th century
there were a handful of japanese origami
masters and by far the most successful
of them was a man named akira yoshizawa
who
created thousands of new designs wrote
many many books of his works
and his work inspired a worldwide
renaissance of origami creativity well i
wanted to fold a cactus
the first thing one needed to do
is figure out how do i get spines on a
cactus so you can imagine if i can make
two spines here
i could do the same thing to make a
whole row
then i can go back do a complete design
that's what this is
[Laughter]
and
and this is actually the cactus and the
pot
are from a single sheet of paper
the paper's green on one side red on the
other that whole thing is this thing so
this is
one uncut square of paper
how big was that piece of paper and this
is about a one meter square
so
there is a huge amount of size reduction
to go from a meter down to here but you
need that to get all of the spines and
how long did that take to make
that
took about seven years
from start to finish
wow
why is origami this
thing that was created for aesthetics
mainly why is it so useful i guess is
the question for for like you know
structural things that were for
mechanical engineering or for space
applications like why does it find
itself in so many of these applications
why is it so useful
well the thing that makes origami
useful
is it is a way
of transforming a flat sheet
into some other shape with relatively
little processing
this is a folded pattern
it's called a triangulated cylinder it
is by stable meaning it's stable in two
positions this is one and then if i give
it a twist
this is the other this really has a
bunch of bi-stable mechanisms in it
because i can
you can see how it sort of pops into
place
but if you combine the two mechanisms
going in different directions then you
get the sort of magical color change
effect yeah that's impressive so you
look at this and you say okay that is a
cute paper toy
is it anything more than that and the
answer is yes
does that turn into that
turns into that yep we're working with a
company called two against surgical that
does the da vinci surgical robot
where they wanted to be able to insert a
flexible catheter with uh with the robot
but the flexible catheters tend to
buckle and stuff so we had
developed these
origami bellows
that if you look down there there's uh
a hole that no matter how far we move
this that that stays the same size
on the inside and what that means is we
can put the catheter in there
and as the catheter moves and it's
getting inserted into the body it still
has supports along the way
or for another example
here i have a foldable
bulletproof
collapsible wall
it's based on the yoshimura crease
pattern meanings might make this out of
a bulletproof material can be very
compact being a police officer's car
and deploy out and be bulletproof
but would it actually work
well they've put it to the test
using 12 layers of kevlar it can stop
bullets from a handgun and a new design
featuring interchangeable panels should
be able to stop rifle rounds
those and that vial that is those are
actually
bullets that have been stopped by
origami
an intrinsic benefit of origami is that
the simple act of folding a material can
make it more rigid
i was going to ask you about this
yeah more origami
but i was going to say it's a way of
making the can stronger without actually
like thinner metal right
but for engineering applications the
more common challenge is how to fold
thick rigid materials this is uh
polypropylene okay very rigid there's no
way that i'm going to be able to to fold
that into
this vertex so this is an example it
shows a couple things surrogate folds we
can use to replace the the creases and
then also
that piece of polypropylene folds up and
it also accommodates the thickness
by cutting or scoring materials and
adding hinges as necessary thick rigid
materials can in effect be folded
this is useful for example in deploying
solar panels
this pattern is perhaps the granddaddy
of deployable structures it's called the
miura ori it's been used for solar
arrays in fact it was one of the first
patterns that flew on a space mission
back in 1995
it was called the space flyer mission as
you see here
it all
opens and closes in a single motion and
when it flattens it's it's very thin and
compact it's a fun pattern called the
origami flasher and
you get
this kind of interesting
flasher motion
this has been proposed as a design for
satellite solar arrays increasing
compactness for launch and reliability
in deployment
[Music]
a new area for origami research is in
improving the aerodynamics of freight
locomotives the thing with freight
locomotives is you know they're just
like bricks going down the tracks so
their aerodynamics are horrible ideally
i'd like to have a nose cone on the
front of a freight locomotive to improve
the aerodynamics but you can't because
they're like lego blocks they're hooked
up anywhere along the train you don't
know if it's the first one or the second
one or the third one here's a
scaled prototype showing a pattern that
we demonstrated on a freight locomotive
it folds up to be
very flat
but then deploys out and it turns out
our
computer models and wind tunnel testing
show that this will save this one
company multiple millions of dollars a
year in diesel
[Music]
this is a violinist it was one of my
favorite mechanism designs because
he fiddles if you pull his head
fantastic
functional motions of origami are
inspiring new designs for devices
like compliant mechanisms that can
complete full 360 degree rotations
unlike a traditional mechanisms with you
know bearings or hinges i can hook on a
motor and i can get continuous
revolution
i couldn't do that with a compliant
mechanism but it turns out no one
bothered to tell the paper folders that
and
created
a
uh continuously revolving compliant
mechanism
which is called a kalita cycle
origami motions are also being used in
medical devices these would be
you know the creases in the paper
uh
and we have here now uh forceps
and so what's nice about this is we
could put this at a smaller scale right
on the medical instrument to go into the
body
but then can morph
and become the gripper so it'll be very
small incision but then go in and do
some more complex tasks inside the body
a variant of this mini gripper is now
being used in robotic surgeries
replacing the previous mechanism and
reducing the number of parts by 75
percent
the origami inspired device is smaller
but with a wider range of motion
and functional origami can be
miniaturized even further this is the
world's smallest origami flapping bird
that sounds cool this one was devoted
to developing
techniques to make
microscopic self-folding origami and
what you see here is a microscope photo
of the finished bird
but
what the bird actually looks like
well
i'll need my micro lens you'll probably
need
not just your macro lens you'll need
your microscope
because it's smaller than a grain of
salt so it started out it was a bit less
than a millimeter square
but when it's folded
it's much much smaller wow
now
you might ask yourself
what would anyone ever use
a microscopic flapping bird for and the
answer is well nothing for a flapping
bird
but
there are
medical devices medical applications
implants that are microscopic where you
might want a little machine
this is a nano injector
used in gene therapy to deliver dna to
cells
it's only four micrometers thick
so 400 of them can fit onto a one
centimeter wide computer chip
there's some things down there that kind
of look about star wars to me yes this
art called elliptic infinity
and we wanted to do that in a material
other than paper
you see this
from flat
into that elliptic infinity shape this
is actually a lamp
that's made from a single sheet so it
comes in an envelope like this put its
cable in
fold it
add a clip
now this relies on
a lot of math the curvature of these
lines affects links
the bending and curvature here to here
to here all of these are coupled and
pretty much the only way to design them
and get all the folds to play together
is by following mathematical methods my
professional background is mathematics
and physics i i did laser physics for 15
years as a profession i got my phd in
applied physics
and my kind of my job in many cases was
to figure out how to describe
lasers mathematically and if i could put
my problem in the mathematical language
then i could rely on the tools of
mathematics
to solve those problems and to
accomplish the goals but
i also felt like
origami would be amenable to that same
approach
so i started trying to figure out how to
describe origami using the tools of
mathematics and that worked i'm sort of
fascinated about the math here
like
it's hard for me to conceive of like
what does that math look like the math
comes down
to uh a way of representing a design
called a crease pattern let me grab a
couple of crease patterns okay
so this is an origami crease pattern
it's a plan
for how to fold in this case how to fold
a scorpion a really good way
of designing something like this is to
represent
every feature
claw leg tail
by a circular
region a circular shape
it's not circular folds it's an abstract
it's an abstract concept that you
represent the pattern by a circle but
then you find an arrangement of those
circles on the square
like
packing
balls into a box
so
for the scorpion you've got a long tail
imagine a big circle like a big tin can
and the legs are smaller circles or
circles of different sizes so you've got
different smaller cans and the claws are
a couple more circles and you're going
to put them into a square box
in such a way that they all fit
so you pack the circles
into the box and
the arrangement of those circles
tells you the
the skeleton of the crease pattern and
and from that you can geometrically
construct all the crease patterns you
follow rules
put a line between the center of every
pair of circles
um
and then whenever any two lines meet in
a v
you add a fold halfway in between it's
called a ridge fold
and there's similar more complicated
rules for adding more and more lines but
the thing is it's all step by step it
says it
if you find this geometric pattern that
tells you where to add the next line and
you go through that process until you've
constructed all the lines and when
you're done you can take away the
circles
they were the scaffolding for your
pattern and the pattern of lines that's
left
is the are the folds you need to create
the shape and that's what's shown here
and this was probably the biggest
revolution
in
the world of origami design was if you
followed that systematic process
the fold pattern
would give you
the exact shape that you set out to fold
to begin with the circle packing method
that i described this works for anything
that can be represented
as a stick figure like a scorpion you
could draw this as a stick figure with a
line for the body and tail
lines for each of the legs lines for the
claws and from that stick figure
from any stick figure you can use circle
packing and get a shape that folds it
but suppose the thing you're folding is
not
a stick figure suppose it's something
that's more like a surface
like a sphere
or you know or a cloud or or just in
animal terms a big blobby body like an
elephant
stick figure algorithm is not going to
work but there are other algorithms for
that about 10 years ago a japanese
mathematician named
tomohiro tachi
developed
an algorithm that works for any surface
you give it a triangulated surface as a
mathematical description and he will
give you or his algorithm will give you
the folding pattern that folds into that
surface it's now quite famous and it's
called origamizer
and that is a way you could make
a sheet of anything
and take on any three-dimensional shape
so origami is useful in engineering
because it provides a method of taking a
flat sheet of material and forming it
into virtually any shape by folding
or if the end product is flat origami
offers a way to reduce its dimensions
while still deploying easily
the simple act of folding can increase
rigidity
or origami can take advantage of the
flexibility of materials to create
specific motions
and its principles are scalable enabling
the miniaturization of devices
perhaps most of all origami allows
engineers to piggyback on the bright
ideas people have had over the centuries
while experimenting with folding paper
but translating these ideas into
practical solutions requires a lot of
math modeling and experimentation
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