FEATURE THEME | 主题专栏
建结 Knot Making 廖智威 ｜ Liao Zhiwei
Abstract This article tries to explore the digital fabrication by addressing the disparity between the computational form and the physical realization. The proposition of fabricating a knot is explored at three scales: fabric, hand-held and room-sized. Each scale uses a distinct material and fabrication method. It also explores the conception of parametric material to overcome the limitation on the materials and improve assembly precision, in particular for the room/sized knot. Keywords Digital fabrication, Knot (mathematics), Parametric material 摘要 本文尝试探讨数字建造中数字模型和物理现实之间的差异。在大、中、小三种尺度的实验中，分别运用独特的材料和方法来进行结的建 造。这组实验同时也提出参数化材料概念，探讨如何在大型结的建造中克服材料局限性和提高组装精确性。 关键词 数字化建造 结 参数化材料
The emerging techniques for digital modeling, programming and fabrication ease
新兴数字化建模、编程技术和相应的制造工艺的发展简
the process from data to artifact and vice versa. Today, the robotic arms and 3D
化了从数字化信息到人工制品的演变过程，当今，机器手和
printers are programmed to build things and to replace human hands to create its
三维打印被程序化后代替了人工固体砌筑（Stereotomics）的
mechanized stereotomics forms, whereas CNC machines incorporate new script-
方式，而数控机床（CNC）则被看作提升装配构筑（Tecton-
ing software enhance the potential of the tectonics assemblies. Paralleling these
ics）的潜力 [1]。除了这些大尺度的建造，本文关注数字化建造
macroscopic possibilities, it is essential to investigate the fabrication process by
领域中材料的研究，希望形成一种对更小尺度的建筑构造的
microscopic thinking[1]. This paper seeks to explore in this regard building material
思考。
within the digital fabrication realm.
受埃尔温 · 豪尔在 20 世纪 50 年代设计的墙的启发（图
Inspired by Erwin Hauer`s elegant screen wall built in the 1950s (figure 1), the ex-
1），本文提出三种不同规模的结（knot）的建造试验，分
periment proposed the design and fabrication of three different scales of knot.
别为织物、装配结和混凝土结。结，被定义为一个封闭的、
The knot is defined as a closed, non-self-intersecting curve which is embedded in
非自相交的曲线，它被嵌入在三维空间中，并且不能解开成
three dimensions and cannot be untangled to produce a simple loop.
一个简单的循环的环①。
①
The digital model of the knot as an exquisite virtual entity offers no
构建一个精致的虚拟实体，即对结进行数字建模并非难
resistance(figure 2), while fabricating the knot using physical material reveals nu-
事（图 2）。然而，结在建造过程中却受到了各种形式的制
merous forms of resistance. To bring this digital form into the physical realm, and
约。要把这个概念化或数字化的形式带到现实的物理材料世
still maintain its intrinsic character - a three-dimensional entity without beginning
界并保持其固有的特征，即营建一个无始无终的三维实体，
or end - challenges the fabrication methods. The 3D printer translates the digital
是一项非常艰巨的任务。在早期的尝试中，三维打印机将数
data into a physical entity(figure 3), whereas the handmade wooden knot is com-
字数据直接转换成实体（图 3），而纯手工的木制结则违反
posed by blocks with inevitable joints (figure 4).
了结的固有特征，产生了许多不可避免的缝（图4）。
3D prototype and the handcrafted model demonstrate the disparities between
三维打印技术和纯手工制作的模型显示了两者技术的
the two fabrication techniques. The fabric project and the hand-held knot are de-
巨大差距。织物和装配结的试验是为了进一步探索一种建造
veloped in order to discover a fabrication method to precisely present the topo-
方法去表达在数字领域中产生的这样一个复杂的拓扑形式
logical form generated in digital realm.
（topological form）。
Fabric
织物
As the 3D printed prototype could be transformed precisely from computational
通过三维打印技术数字化的模型能被精确转化成物理实
data to physical entity, the fabric project is to further present the topological con-
体。织物的构建是为了进一步提出拓扑的概念，即“解开”
cept, in other words, the knots are "untangled" and "woven" completely in digital
和“结合”完全在数字空间中实现。8英寸（约203 mm）见
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城市建筑 2013.10 | URBANISM AND ARCHITECTURE Oct. 2013
1．埃尔温·豪尔设计的墙（图片来源： Erwin Hauer的《Erwin Hauer: ContinuaArchitectural Screen and Walls》）
2．数字模型
3．三维打印模型
5．织物：数字模型和三维打印模型
4．木制手工模型
6．模子的三维模型和三维打印模子组装的结
space. The 8 inches by 8 inches 3D printed fabric is consisted of 60 unitized in-
方的三维打印织物由 60 个单位化的结环环相扣，这是不可能
terlocking knots, which are unlikely achievable in the physical realm. The pure 3D-
在物理领域中实现的。纯三维打印技术能很好地诠释结的概
print has more to do with the knot concept but is less relevant to material reality
念特征，却与物质和建造不甚相关，因此可以认为它与物理
because it is not associated with the real world (figure 5).
材料世界并没有关联（图5）。
Assembly
装配结
Since the fabric project is limited in scale in material reality, the material of the
由于织物在材料现实中受到了三维打印机在尺度上的限
hand-held knot experiment is determined to be plaster. As the physical knot has
制，装配结选用了浇注石膏的方法。这个结实体在水平面上
only three points touching a supporting flat surface, most parts are supported by
存在 3 个支点，大部分都以拱状的形式悬挑。因此，石膏构
the arch-like shape. Hence, the plaster elements should be designed to address
件需进行结构考虑。这样的尺度限制了结的厚度和自身重量
those structural concerns. The scale determines the thickness of the knot which
不能过大，但同时要具有足够的强度。基于形式的对称性，
should be lightweight yet strong enough to span and retain its shape. The sym-
将结分为 6 个典型零件由模具灌注而生，而这个模具是通过
metrical form divides the knot into 6 typical parts which are reproduced by a 3D
三维打印机产生的。通过不锈钢紧固件连接，这些紧固件由
printed mold. They are connected by six stainless steel fasteners made by wire
放电加工机（electrical discharge machine）制作，以保证足
EDM (Electrical discharge machine), providing the required precision.
够的精度。
As precision reduces during the casting process, the 3D printed mold is designed
虽然铸造过程中精度会有所下降，但三维打印的模具保
digitally in order to maintain certain tolerance. For the purpose of assembling and
证了足够的精度。为了实现组合和拆卸的目的，模具由两个
striping, the mold is composed of two parts with flanges with 19 holes for bolts.
部分组成，带有 19 个螺栓孔，水平开口（考虑到石膏的流动
Considering the liquidity of the plaster, openings have to be horizontal. A recess
性）。凹槽是为了容纳连接两个单元的金属构件而设。虽然
accommodates the metal connector which clamps two parts together. While this
组装的方法运用了物理材料，但是同时结的特征却大打折扣
assembled knot has more to do with the material reality of plaster, the idea of the
（图6）。
knot is compromised(figure 6). 数字化的砌筑术
Digital Stereotomics
房间尺度的结由混凝土制成。模板需要精确装配，通过
The room-sized knot is made of concrete. The formwork parts are fabricated pre-
数字化形成的几何图案作为混凝土模板的图案，对胶合板进
cisely to conjoin. The patterns for the sides and bottom of the form-work are ex-
行分割、弯曲和夹紧形成所需形状。
tracted digitally from the rationalized knot geometry. The manufactured plywood
被特定加工后的胶合板，其固有特点发生了改变，增强
material is cut, bent and clamped in order to conform to the required shape.
了柔韧性。一般胶合板在超出其所能承受的物理极限的情况
The specific modification to the plywood shifts its characteristic and enhances its
下会对所受的弯曲产生抵抗，或者会产生撕裂。提前引入的
pliability. Beyond its physical limits, common plywood resists deformation and
凹缝产生了故意的不连续性，凹缝使3/4英寸（约19 mm）厚
will bend or tear. Hence, the intentional introduction of discontinuity, the kerfs,
的胶合板达到所需的曲率，这些凹缝的图案是通过特定的曲
into the smoothly continuous ¾ inch plywoods surface alleviated the material's
面由计算机生成的，带有这些凹缝的胶合板具有容易弯曲的
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FEATURE THEME | 主题专栏
7．三维曲面展平的示意图
10．数字模型
8．模板的底部
11．装配中的最终模板
9．3个模板的研究模型
12．拆卸模板
13．混凝土结
resistance to the required curvatures. The kerfs used to assist in
特性，同时具有足够强度支承相当大的混凝土混合物的重量及流体压力。一
shaping the plywood are translated from computer-generated
次浇注而成的混凝土消除了构造缝，充分体现了结最原初定义的诗意（图 7～
sub-divisional lines based on the required curved surface. As a
图13）。
result, the notched plywood becomes flexible, yet remains strong enough to support the considerable weight and fluid pressure of
结语
the concrete mixture. The concrete, cast in one pour, eliminates
本文旨在描述结的制造工艺，反思数字化设计和建造，探索材料的特征
the joint to represent the poetry of the primitive math-defined
和在曲面形式中所产生的建造局限以及所受到物体尺度的限制。这些探索包
knot(figure7-13).
括 ： ①三维打印的织物实现了从刚性材料演变成柔性物质 ； ②结的组装品是 通过精确的三维打印、石膏铸件和不锈钢紧固件实现的 ； ③通过评估模板的
Conclusion
研究模型，选择材料的依据不是材料的原始特征，而是其可被加工的潜力。[2]
This paper seeks to describe the fabrication process of making the
这些曲面制造进一步提出了参数化材料的概念 ，在微观尺度下 ，对材
knot and rethink digital design and physical fabrication. The explo-
料进行“数字化”定制加工而非传统意义的切割加工。例如，凹缝在模板上
ration investigates the material characteristics and constructability
的位置、密度和深度通过参数化方式修改产生，然后评估并输出至数控机床
associated with the curve form and the object scale, which include:
（CNC）进行切割。从理论上来说，通过参数化图案和数控机床（CNC）加
1) The configuration of 3D printed entity was transformed from
工产生的材料具有用于接合的外在轮廓以及利于弯曲的内在特性。随着阻力
rigid form to fabric. 2) The assembled knot is achieved by the pre-
的削减，胶合板成为了织物般的材料。材料的性能将能够精确地迎合建造的
cision of 3d printed mold, the components casted in plaster and
需要。■
the stainless steel fasteners. 3) Through evaluating the formwork mockups, the decision of selecting the material is driven not by
注释
the original material's pliability, but customized potential.
①数学结的定义详见：http://mathworld.wolfram.com/Knot.html.
The fabrication of the curve surface further addresses the notion of parametric material in a microscopic scale, changing the con-
参考文献
ventional material to customized material, e.g., parameter such as
[1] Frampton K. Rappel Al' ordre: the Case for the Tectonic[J]. Architectural
location, pattern density and depth of the kerfs on the formwork panels are generated and manipulated parametrically, then evaluated and exported to a CNC milling machine to cut the sheet material. Theoretically CNC cut material with parametric enhanced value will contain both an extrinsic profile for joining and an intrin-
Design, 1990 (3,4): 19-25. [2] Liao Z. Knot Making: Exploring the Boundary Between Digital Modeling and Physical Fabrication[D]. New York: State University of New York at Buffalo, 2005.
sic feature for bending. As the bending resistance being released,
作者简介：廖智威 10 DESIGN（拾稼设计）高级建筑设计师
the plywood turns into a fabric-like material. Hence, the performa-
曾在理查德·迈耶建筑师事务所（Richard Meier & Partners Architects），
tive characteristic of the material are precisely transformed to
盖里技术公司（Gehry Technologies）和Gensler工作
meet the particular fabrication need.
收稿日期：2013－09－23
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