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播放视频

折纸工艺在工程中的应用

Engineering with Origami

[Music playing]
[音乐播放中]
Engineers are turning to origami for inspiration
工程师们正开始从折纸工艺中
for all types of applications
寻找各类应用的灵感
from medical devices to space applications
其中包括医疗设备 空间应用
and even stopping bullets.
甚至是防弹装置
But why is it that this ancient art of paper folding
但为何古老的折纸艺术
is so useful for modern engineering?
能对现代工程如此有用?
Origami, literally “folding paper”,
折纸工艺 就是字面意思上“折纸”的意思
dates back at least 400 years in Japan.
在日本至少有400年历史
But the number of designs was limited.
但那时的设计数量有限
There were only a handful of patterns,
只有少数的几个图案
maybe 100, 200 total in Japan.
可能在日本一共也只有一两百种
Nowadays there are tens of thousands that have been documented
而如今已有数以万计的图案记录在册
and most of that change happened in the 20th century.
大部分的转变都发生在20世纪
There were a handful of Japanese origami masters.
那时 日本有一些折纸大师
And by far the most successful of them
而目前为止 他们当中最成功的
was a man named Akira Yoshizawa
要数一个叫做吉泽章的男人
who created thousands of new designs and
他创造出来几千种新设计
wrote many many books of his works.
并为这些作品写了很多很多书
And his work inspired a worldwide renaissance of origami creativity.
他的作品推动了全世界折纸创作的复兴
Well, I wanted to fold a cactus.
我想折一只仙人掌
The first thing one needed to do
首先要做的是
is figure out how do I get spines on a cactus.
想办法做出仙人掌上的刺
So you can imagine if I can make two spines here,
你想 既然我可以在这儿做出两个刺
I could do the same thing to make a whole row,
那我也可以用同样的方法做一整行
then I can go back and do a complete design.
然后我可以返回去做一个完整的设计
-That’s, what this is. -Wow!
-这就是 -哇
– [Laughter] -And.
-[笑声] -并且
And this is actually the cactus and the pot
事实上 这就是仙人掌和花盆
are from a single sheet of paper.
仅用一张纸折成
Paper’s green on one side, red on the other.
纸的一面是绿色的 另一面是红色的
-That whole thing is a single sheet of paper. -So this is… this is…
-整个仙人掌盆栽就是一张纸 -这是……
One uncut square of paper.
是一张未剪的正方形纸
-How big was that piece of paper? -And this is about a one meter square.
-这张纸有多大? -大约有一平方米
So there is a huge amount of size reduction to
所以从一米缩减到这样
go from a meter down to here.
经过了大量的尺寸裁剪
But you need that to get all of the spines.
但是你得这样 才能制作出所有的刺
-And how long did that take to make? -That took about seven years from start to finish.
-制作花费了多长时间? -一共花了大概七年
-Wow! Why is origami this thing that
-哇 为什么折纸工艺这种
was created for aesthetics mainly…
主要为美学而创造的东西……
Why is it so useful?
能如此实用?
I guess is the question for,
我想这个问题 是针对
for like, you know, structural things or
比如 你知道的 结构之类 或者
for mechanical engineering or for space applications.
机械工程或空间应用而言的
Like, why does it find itself in so many of these applications?
比如 为何在那么多应用中都能见到它?
Why is it so useful?
为何它如此有用?
Well, the thing that makes origami useful
折纸工艺有用 是因为
is it is a way of transforming a flat sheet
它能用相对简易的加工方式
into some other shape with relatively little processing.
将一张平整的纸变成一些其它形状
This is a folded pattern.
这是一种折叠模型
It’s called a triangulated cylinder.
它叫做三角圆柱
It is bi-stable, meaning it’s stable in two positions.
它是双稳态的 意思是它在两个位置稳定
This is one and then if i give it a twist.
这是一个稳态 然后如果我扭动它
This is the other.
这是另一稳态
This really has a bunch of bi-stable mechanisms in it
的确有一堆的双稳态构造在其中
because I can…
因为我可以……
You can see how it sort of pops into place.
你可以看见它是如何突然出现的
But if you combine the two mechanisms
但是如果你把两个稳态机构结合
going in different directions.
向不同方向扭动
-Then you get the sort of magical color change effect.
-然后你就能得到神奇的变色效果
-Yeah that’s impressive. So you look at this
-那很难忘 看这儿
and you say: okay that is a cute paper toy.
你会说:那是一个有趣的纸质玩具
Is it anything more than that? and the answer is yes.
仅仅是这样吗?不仅限于此
– Does that turn into that? -That turns into that, yep.
-是刚才的玩具变成这样了吗? -是的 是它变成这样了
We’re working with a company
我们正和直觉外科公司合作
called Intuitive Surgical that does the Da Vinci surgical robot
研发达芬奇手术机器人
where they wanted to be able to insert
他们想要利用机器人
a flexible catheter with the robot.
插入一根柔性导管
But the flexible catheters tend to buckle and stuff.
但柔性导管往往会有变形等问题
So we had developed these origami bellows
所以我们开发了这种折纸波纹管
that if you look down there,
如果你往这儿看
there’s a hole that no matter how far we move this
无论我们拉的多长都会有一个洞
that stays the same size on the inside.
在内部保持着同样大小
And what that means is we could put the catheter in there.
这意味着 我们可以将导管放进里面
And as the catheter moves and it’s getting inserted into the body.
导管移动着植入人体
It still has supports along the way,
在进入过程中 它仍然是撑起的状态
or for another example.
另外一个例子是
Here I have a foldable bulletproof collapsible wall.
这里有一面可折叠可拆卸的防弹墙
It’s based on the Yoshimura crease pattern.
它是基于吉村式折痕模型制造的
and if I made this out of a bulletproof material
如果我用防弹材料来制作
it could be very compact in a police officer’s car
它可以收到很小 放在警车里
and deploy out and be bulletproof.
然后展开用以防弹
But would it actually work?
但它真的有用吗?
Well, they’ve put it to the test.
他们已经把它用于测试了
[The sound of a handgun]
[手枪的声音]
Using 12 layers of kevlar, it can
它由12层凯夫拉尔合成纤维制成
stop bullets from a handgun.
能抵挡手枪子弹
And a new design featuring interchangeable panels
而一个以可换金属板为特色的新款
should be able to stop rifle rounds.
则可以抵挡步枪子弹
Those in that vial that is, those are actually
瓶子里装的那些 其实是
bullets that have been stopped by origami.
被折纸挡下的子弹
An intrinsic benefit of origami is that
折纸工艺的一个内在好处是
the simple act of folding a material can
只需简单地折叠这种材料
make it more rigid.
就可以使它更加坚硬
– I was gonna ask you about this. -Yeah.
-对此我想问 -请
More origami?
这也是利用折纸工艺做的?
-But I was going to say it’s a way of
我想说 它能不用像薄金属这类材料
making the cans stronger without actually like thinner metal, right?
就将罐头变得更加坚固 是这样吗?
But for engineering applications the more common challenge
但在工程应用中 更常见的挑战
is how to fold thick, rigid materials.
是如何折叠又厚又坚硬的材料
This is… uh… polypropylene.
这是聚丙烯
Okay, very rigid.
非常坚硬
There’s no way that I’m going to be able to
我不可能
fold that into this vertex.
把它折到这个顶点
So this is an example that shows a couple things,
所以这个例子说明了一些问题
surrogate folds, we can use to replace the the creases
我们可以用代折代替折痕
and then also that piece of polypropylene folds up,
这样这块聚丙烯就可以折叠起来
and it also accommodates the thickness.
也能适应这种厚度
By cutting or scoring materials and adding hinges as necessary,
通过切割或刻划材料 必要时增加铰链
thick rigid materials can in effect be folded.
厚的刚性材料可以真正折叠起来
This is useful for example in deploying solar panels.
这在展开太阳能电池板的时候很有用
This pattern is perhaps the granddaddy
这个模型可能是一种非常古老的
of deployable structures, it’s called the Miura Ori.
折叠结构 它叫做三浦•奥利
It’s been used for solar arrays.
它被用于太阳电池阵列
In fact, it was one of the first patterns
事实上 它是最初
that flew on a space mission back in 1995.
在1995年执行太空任务时的模型之一
It was called the space flyer mission.
那次任务叫做太空飞行任务
As you see here,
如你所见
it all opens and closes in a single motion
它在一个动作中张合
and when it flattens, it’s very thin and compact.
当变为平面时 它又薄又小
It’s a fun pattern called the origami flasher and
这就叫做折纸闪光器 是个好玩的模型
get this kind of interesting flasher motion.
会做这种有趣的闪光运动
This has been proposed as a design for satellite solar arrays
它已被提议用于设计卫星太阳能电池阵列
increasing compactness for launch
以提升发射时的压缩程度
and reliability in deployment.
以及展开时的可靠性
[Music playing]
[音乐播放中]
A new area for origami research is
折纸工艺研究的一个新领域是
in improving the aerodynamics of freight locomotives.
改善货运汽车的空气动力
The thing with freight locomotives is
货运机车的情况……
you know they’re just like bricks going down the tracks.
你知道的 它们就像是铁轨上的砖块
So their aerodynamics are horrible.
所以空气动力比较糟糕
Ideally you’d like to have a nose cone
理想情况下应有个前锥体
on the front of a freight locomotive
在货运机车的前部
to improve the aerodynamics.
来提高空气动力
But you can’t because they’re like lego blocks,
但是你不能这样做 因为货箱就像是乐高积木
they’re hooked up anywhere along the train.
沿着列车一个个挂着
You don’t know if it’s the first one or the second one or the third one.
你不知道它是第一箱 第二箱还是第三箱
Here’s a scaled prototype
这是一个按比例缩小的原型
showing a pattern that we demonstrated on a freight locomotive.
展示了我们要在货运机车上证明的模型
It folds up to be very flat but then deploys out.
它可以折叠到很平整的位置然后展开
And it turns out our computer models and wind tunnel testing
我们的电脑模型和风洞测试结果
show that this will save this one company
表明这将为这个公司每年在柴油上的花销
multiple millions of dollars a year in diesel.
节约好几百万美元
[Music playing]
[音乐播放中]
This is a violinist.
这是一个小提琴手
It was one of my favorite mechanism designs,
我最喜欢的机构设计之一
because he fiddles if you pull his head.
因为你一拉他的头 他就会拉小提琴
Fantastic.
妙极了
Functional motions of origami are inspiring new designs for devices
折纸的功能性动作正为设备设计带来新的灵感
like compliant mechanisms that can complete full 360 degree rotations,
比如能完成360度旋转的柔性机构
unlike a traditional mechanisms with you know bearings or hinges.
这不像你所知道的带轴承或铰链的传统机构那样
I can hook on a motor and I can get continuous revolution.
我可以把它挂在马达 然后它就能连续旋转
I couldn’t do that with a compliant mechanism.
我不能用柔性机构来做这样的事
But it turns out no one bothered to tell the paper folders that and created a
但事实上 不用费心告诉折纸艺人 他们就创造了一种
[The sound of paper]
[纸的声音]
uh continuously revolving compliant mechanism
四面体连续机构
which is called a Kaleidocycle.
它是一种能不断旋转的柔性机械
Origami motions are also being used in medical devices.
折纸工艺也应用于医疗设备
These would be you know the creases in the paper.
这是你所知的 纸的折痕
Uh and we have here now uh forceps.
现在我们有钳子
And so what’s nice about this is
这样做的好处是
we could put this at a smaller scale right on the medical instrument
我们能将其以更小的尺寸放在医疗仪器上
to go into the body.
从而进入身体
But then can morph and become the gripper
但是之后 它们变形成为钳子
so it’ll be very small incision,
所以只需要很小的切口
but then go and do some more complex tasks inside the body.
就可以在人体内完成更复杂的任务
A variant of this mini gripper is now being used in robotic surgeries
现在 一种演变而来的迷你钳子正被用于机器人手术中
replacing the previous mechanism and reducing the number of parts by 75 percent.
替换了以前的机构 并减少了75%的零件数量
The origami inspired device is smaller but with a wider range of motion
由折纸艺术研发而来的设备更小 却有更大的动作范围
and functional origami can be miniaturized even further.
功能性的折纸工艺品甚至可以进一步缩小
This is the world’s smallest origami flapping bird.
这是世界上最小的纸鹤
[Laughter]
[笑声]
That sounds cool.
听起来很酷
This one was devoted to developing techniques to make
这件产品致力于提高技术以制造
microscopic, self-folding origami.
微观自折叠式折纸工艺品
And what you see here is a microscope photo of the finished bird.
你看到的就是完工纸鹤的显微照片
But what the bird actually looks like.
但纸鹤实际上长什么样呢
-Well. -I’ll need my micro lens.
-好吧 -我需要微透镜
You’ll probably need not just your micro lens.
可能不止需要微透镜
You’ll need your microscope
你需要显微镜
because it’s smaller than a grain of salt.
因为它比一颗盐还小
So it started out, it was a bit less than a millimeter square.
一开始 它略小于一平方毫米
But when it’s folded,
但当它折叠起来
it’s much much smaller. -Wow!
它要变小很多 -哇!
Now you might ask yourself what would anyone ever use
现在你可能在问自己
a microscopic flapping bird for?
微型纸鹤究竟是用来做什么的?
And the answer is well nothing for a flapping bird.
答案与纸鹤本身毫无关系
But there are medical devices, medical applications implants
但微型的医学设备 医学植入物
that are microscopic where you might want a little machine.
需要微小的机械
This is a nano injector
这是一个纳米注射器
used in gene therapy to deliver DNA to cells.
在基因疗法中用于向细胞输送DNA
It’s only four micrometers thick.
只有四微米厚
So 400 of them can fit onto a one centimeter wide computer chip.
所以一厘米宽的电脑芯片可以放得下400个
-There’s some things down there that kind of look a bit star wars to me -Yes.
-在我看来 那儿的东西有点像星球大战 -是的
This art called elliptic infinity
这件艺术品叫做椭圆无穷
and we wanted to do that in a material other than paper.
我们想用除纸以外的材料来做
You see this from flat
你可以看见它从平面
into that elliptic infinity shape.
变成椭圆无穷的形状
This is actually a lamp
这实际上是一个用一张纸
that’s made from a single sheet,
制成的灯
so it comes in an envelope like this.
它像这样包装起来
Put its cable in.
再把它的缆绳放进去
Fold it.
折起来
Add a clip.
加一个别针
Now this relies on a lot of math.
现在需要许多数学知识
The curvature of these lines affects links
这些线的曲率会影响连接
the bending and curvature here, to here, to here.
这些连接处的弯曲度和曲率
All of these are coupled.
所有这些都是耦合的
Pretty much the only way to design them
几乎唯一的设计手段
is by following mathematical methods
是依照数学方法
and get all the folds to play together.
让所有的褶皱合到一起
My professional background is
我的专业背景是
mathematics and physics.
数学和物理
I did laser physics for 15 years as a profession.
我专职研究激光物理15年
I got my PhD in Applied Physics
我获得了应用数学博士学位
and my kind of my job in many cases was
很多情况下我的工作都是
to figure out how to describe lasers mathematically.
弄清楚如何用数学方式来表示激光
And if I could put
如果我能
my problem into mathematical language,
把我的问题转化成数学语言
then I could rely on the tools of mathematics to
然后就能利用数学工具
solve those problems and to accomplish the goals.
解决那些问题并达到目标
But I also felt like
不过我觉得
origami would be amenable to that same approach.
折纸工艺也适用于同样的方法
So I started trying to figure out how to describe
所以我开始努力研究 如何利用数学工具
origami using the tools of mathematics, and that worked.
来描述折纸工艺 真给我找到了
I’m sort of fascinated about the math here like
我对其中的数学知识挺着迷
it’s hard for me to conceive of like, what does that math look like?
很难想象 其中的数学知识会是怎样的
The math comes down
这里的数学可以归结为
to a way of representing a design called crease pattern.
用折痕图来代表一个设计的方法
-Let me grab a couple of crease patterns. -Okay.
-让我找几张折痕图 -好的
So this is an origami crease pattern.
这就是一张折纸折痕图
It’s a plan for how to fold.
是一份折纸计划
In this case, how to fold a scorpion.
这个讲的是如何折一只蝎子
A really good way of designing something like this
设计类似的折痕图的一个很好的方法是
is to represent every feature claw, leg, tail
用一个圆形区域 一个圆的形状
by a circular region, a circular shape.
代表爪子 腿 尾巴这样的特征
It’s not circular folds.
不是说要按圆形折
It’s an abstract…
它是一种抽象的……
It’s an abstract concept that you represent the pattern by a circle,
它是一种用圆代表来代表图形的抽象概念
but then you find an arrangement of those circles on the square
再把这些圆安排在正方形纸的合适位置上
like packing balls into a box.
就像把球装进盒子里
So for the scorpion you’ve got a long tail.
所以 蝎子 它有的一条长长的尾巴
Imagine a big circle,
想象一个大圆
like a big tin can,
比如一个大罐头
and the legs are smaller circles, or circles of different sizes.
而腿就像更小的圆 或者不同尺寸的圆
So you’ve got different smaller cans.
也就是不同的更小的罐头
The claws are a couple more circles
爪子就是再多几个圆
and you’re going to put them into a square box
然后你用一种合适的方式
in such a way that they all fit.
把它们放进一个方框里
So you pack the circles into the box and
你把那些圆放进了方框里
the arrangement of those circles
那些圆的排列
tells you the the skeleton of the crease pattern.
正揭示着折痕图的框架结构
And from that you can geometrically construct all the crease patterns.
由此 你可以利用几何学构建出所有折痕图
You follow rules:
你按照规则做:
put a line between the center of every pair of circles,
用直线连接每对圆的圆心
um and then whenever any two lines meet in a v,
然后每当两条线相交成一个v形
you add a fold halfway in between, it’s called a ridge fold,
在中间加一条折痕 这叫做脊折线
and there’s similar, more complicated rules
还有类似的 更多复杂的规则
for adding more and more lines.
用以添加更多的线
But the thing is, it’s all step by step.
但问题是 都得一步一步来
It says if you find this geometric pattern, that tells you
就是说如果你发现了这种几何模型 它将会告诉你
where to add the next line and you go through that process
下一条线添在哪儿 你在整个过程中跟着它走
until you’ve constructed all the lines.
直到你构画出所有的线
And when you’re done you can take away the circles,
完成之后 你就可以去掉那些圆
they were the scaffolding for your pattern,
它们是你的模型的支架
and the pattern of lines that’s left,
留下来的那些线条图案
are the folds you need to create the shape,
就是你需要创作的图形的折痕
and that’s what’s shown here.
如图所示
And this was probably the biggest revolution
这可能是折纸工艺设计领域
in the world of origami design.
最大的革新
Was if you followed that systematic process,
如果你跟随着这个系统性的过程
the fold pattern would give you the exact shape
这种折纸模型会让你得到
that you set out to fold to begin with.
开始时需要折出的具体形状
The circle packing method that I described, this works for anything
我讲述的圆包装法适用于一切
that can be represented,
像蝎子这种
as a stick figure like a scorpion,
能用线条图像来代替的事物
you could draw this as a stick figure
你可以把这个画成线条图案
with a line for the body and tail,
用线条来代替身体和尾巴
lines for each of the legs, lines for the claws
用线条来代替每一条腿 每一个爪子
And from stick figure, from any stick figure,
线条图案 任何线条图案
you can use circle packing and get a shape that folds it.
都能让你用圆包装法找到一个可以折叠的形状
But suppose the thing you’re folding is not a stick figure,
假设你要折的东西不是一个线条图案
suppose it’s something that’s more like a surface,
假设它更像是一个面
like a sphere or you know or a cloud
比如你所知的球面或者一朵云
or just in animal terms, a big blobby body like an elephant.
或者就是以动物为例 像大象一样又大又圆的身体
Stick figure algorithm is not going to work,
线条图案的算法就无效了
but there are other algorithms for that.
但是针对这些也有其它的算法
About 10 years ago, a Japanese mathematician,
大约10年前 一个日本数学家
named Tomohiro Tachi, developed an algorithm that works for any surface.
叫馆知宏 开发了一种适用于任何面的算法
You give it a triangulated surface
你以数学描述的形式
as a mathematical description,
给出一个三角形的表面
and he will give you, or his algorithm will give you the folding pattern
他将会给你或者说他的算法将会给你
that folds into that surface.
折成相应的面所对应的折叠模型
It’s now quite famous and it’s called origamizer.
现在这个算法很出名 叫做origamizer
And that is a way you could make
这个方法 你可以用于任何平面材料
a sheet of anything and take on any three-dimensional shape.
也可以构建任何三维图形
So origami is useful in engineering
折纸工艺在工程领域也很有用
because it provides a method of taking a flat sheet of material,
因为它提供了一种能将平面材料
and forming it into virtually any shape by folding
通过折叠形成几乎任何形状的方法
or if the end product is flat,
或者如果最终产品是平的
origami offers a way to reduce its dimensions while still deploying easily.
折纸工艺在保持易展性的前提下 提供了一种降维方法
The simple act of folding can increase rigidity
简单的折叠就能提高硬度
or origami can take advantage of the flexibility of materials
折纸工艺可以利用材料的柔性
to create specific motions.
来创建特定的运动
And its principles are scalable, enabling the miniaturization of devices.
原则是可伸展性和使设备最小化
Perhaps most of all, origami allows engineers
可能在大多时候 折纸工艺只能让工程师
to piggyback on the bright ideas people have had
利用人们在过去的几个世纪
over the centuries while experimenting with folding paper.
在尝试折纸时产生的巧思
But translating these ideas into practical solutions
而要让这些想法变成实际解决方案
requires a lot of math, modeling and experimentation.
则需要很多数学 建模和实验
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视频概述

折纸是一种古老的东方艺术,同样也是一门新兴的前沿科学,应用于数学、机械、物理等多个基础学科的交叉领域。本视频中你可以了解到折纸工艺在工程中的各种应用。

听录译者

嘟嘟嘟噜啦啦

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审核员

审核员IBRT

视频来源

https://www.youtube.com/watch?v=ThwuT3_AG6w

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