Topopath by Voxatile by Palak J

Research Cluster 4 Gilles Retsin Manuel Jimenez Garcia Palak Jhunjhunwala, Efstratios Georgiou, Juan Rico, Yiheng Ye

The Bartlett School of Architecture UCL

CONTENTS

01 INTRODUCTION

1.1 Research context

Architecture in the digital age

1.2 Research context

8 10

Preceding research and development of 3D printing

1.3 Project overview

02 TILE DESIGN

2.1 Tile combinatorics 2.2 Tile design tests 2.3 Tile as body plan

03 VOXATILE DESIGN

3.1 Voxatile development 3.2 System Hierarchy 3.3 Voxatile design tests 3.4 Toolpath development

18 20 26

30 34 44 48

04 MATERIAL REALIZATION 4.1 Material testing 4.2 Multi-materiality

68 70

05 END EFFECTOR

5.1 Tool comparison 5.2 Pellet extruder design

78 80

06 TOOLPATH DEVELOPMENT 6.1 Toolpath combinatorics 6.2 Topological deformation 6.3 Optimization strategy 6.4 Toolpath automation 6.5 Discretization of flowfield

104 112 114 116 122

07 ARCHITECTURAL DEVELOPMENT 7.1 Meta-Voxatile 7.2 Meta-Tile

144 156

Introduction

Research Context Architecture in the Digital Age

Voxatile formations situates itself in between continuity and discreteness in the digital age of architectural explorations. There are many references in architecture history, ranging from old techniques such as the Chinese Dou Gong to more recent ones, such as Konrad Wachsmannâ&#x20AC;&#x2122;s space frames and Soviet Mass housing programmes. All of these explorations were dealing with part to whole relationships, where the parts of a system come together in a larger context to form the whole. Currently there are many attempts to scale-up digital fabrication techniques for architectural applications. Continuous ones, such as 3d printing, seem to be misused in scaled-up applications, as they need extensive infrastructure and support such as rails and cranes. The important question however is determining the point at which continuity stops and discreteness begins and the scale of the printed geometry. Applications of 3D printing today, involve the printing of the complete geometry of the structure or the problematic subdividing of a pre-designed top down form. Another application of digital fabrication methods is that of robotic assembly. Robotic assembly is more often used in problematic ways to achieve repetitive outcomes that are homogeneous. The potentiality of heterogeneity and mutli-scale building elements is not explored in the process. The difference between continuous printing processes that have previously been adopted for architecture and the system adopted by the project is that the image shows that though a robot is used for fabrication, the system is analog in nature and can be viewed as a parallel to pouring of concrete or laying bricks layer by layer for instance.

Voxatile formations on the other hand, uses aerial printing as opposed to layer by layer printing and creates forms that have spatial properties. Spatial printing allows for deposition of material as required saving material cost and the time for fabricatio. The process has far more architectural emobodiment as compared to layer by layer printing using large 3D printing setups, as done in some parts of China. Vo(x)atile formations aims to bridge the gap between continuity and discreteness in architecture. The project deploys discrete and continuous fabrication methods in combination to merge them into a single process that can take advantage of the fluidity of continuous fabrication and practicality of discrete assembly. Crucial to the project formation is the digital material theory that is evolved by Neil Gershenfeld. Gershenfeld argues that todayâ&#x20AC;&#x2122;s digital methods are not in reality digital but analogue. In his research, he investigates the possibility of creating a reconfigurable 3d printing method with digital material. Digital material thus becomes elemental in that process. The digital particle/body is capable of connecting to neighbouring ones in various combinations, forming wholes. They can also detach one from another, reconfiguring the existing structure or forming new ones. For that reason, the mathematical and computational tools referenced for the research project are derived from combinatorial systems. Combinatorics is the branch of mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints.

Discrete - material deposition as per structural requirement

- spatial possibilities

- faster process

Voxatile

spatial printing

layered continuous printing

-material deposition in continous layers, no spatial possibilities

-slow process

Continuous

Research Context Preceding research and development of 3D printing

Mesh Mould (Gramazio and Kohler Research), Filamentrics (Bartlett RC4 2013-2014) an Curvoxels (Bartlett RC4 2014-2015) are a few research projects that have used similar fabrication processes of aerial printing as that used here. Learning from preceding research in aerial printing, Voxatile formations develops strategies that equip the use of this fabrication method at the scale of architecture. Mesh mould, Filamentrics and Curvoxels use a plastic filament extruder to print aerially and fabricate the form produced in the digital environment. While mesh mould prints a single scale aggregation of serially repeated lines, filamentics adopts aerial printing of a customised line. Curvoxels on the other hand is able to produce serial repetition at multiple scales. Voxatile formations develops a discrete printable line that is capable of adapting to local conditions by deforming using the direction of the vector field. The project involves the production of a discrete logic is able to produced customised variation using a set of system rules. The fabrication tool used for production is a pellet extruder which enables large scale printing at low cost, creating architectural applications.

Mesh Mould

Filamentrics

Curvoxels

- Using both positive aspects of previous projects and resolving the negative ones. - Combinatoric strategy to solve the first level of adptation to extend conditions, and basic geometry such as a line. - Deformation of that essential unit to adapt further to conditions at the local level

Voxatile

Geometric Adaptation + Adaptation - purely formal - based on a surface

Deformation + Adaptation - Global application

Combinatorial + Local rules - closed system

Repetition

AND

Adaptation 11

Research Statement discrete logic - continuous fabrication - discrete assembly

Project Overview Spatial printing and robotic assembly

Discrete

Discretizing Continuity Research Statement discrete logic - continuous fabrication - discrete assembly

VoxaTile proposes to 3D-print materially efficient large-scale building blocks which can be robotically assembled. Through a combinatoric design method, part-to-whole relations are established which bridge between the micro-scale of robotic tool-path organisation to the macroscale of architectural part-to-whole relations. These serialised building blocks can be understood as lego-like pieces, but with the ability to deal with specific structural conditions. Voxatile formations explores reversible combinatorial systems by printing continuous voxel-tile aggregations as discrete mereological structures. These sub-systems take advantage of the fluidity of continuous printing and voxeltile mereology as a versatile geometrical strategy for robotic pick and place assembling and reassembling of larger systems.

Discrete

Discrete System Hierarchy SYSTEM HIERARCHY

Research Statement discrete logic - continuous fabrication - discrete assembly

Each discrete structure is fabricated by a robotcontrolled pellet extruder as a continuous multimaterial aggregation. These mereological arrays consist of meta-voxatiles, these of voxatiles, and these of tiles, the latter working as the basic geometrical units. The mereological hierarchy between these three levels enables the bridging between continuous fabrication and discrete assembly. Discarding serial repetition in printing, the project aims to enable dynamic geometrical variations in the structure by deforming its topological framework to local conditions. Using a constant body plan that deforms topologically based on its position and its local context provides countless unique iterations.

COMBINATORIAL LOGIC

SYSTEM HIERARCHY

Discrete SYSTEM HIERARCHY

COMBINATORIAL Combinational Logic

COMBINATORIAL LOGIC

COMPUTATION Computation

LOGIC

Continuous COMPUTATION

FABRICATION

RIAL

Continuous

COMPUTATION

Discrete

Continuousline Printable

Discrete

Production of architectural meta-tiles

FABRICATION Toolpath fragment

ASSEMBLY

Local adaptations

Fabrication

Robotic assembly of meta-tiles

Tile Design 15

Tiles aggregation

Tile Design Tile form and geometric properties

The tile forms the basic unit of combinations and development of the research. The tile is a digital brick that demonstrates a combinatoric relationship to other tiles and rotates in the digital space to form patterns that might be linear, planar, closed loops, etc. The basic form of the tile is extracted from the geomteric logic of combination of a square pyramid and a triangular pyramid. The fusing of the two pyramids produces the digital brick for our project, which consists of a sqaure base, two triangular sides and two rhomboid sides.

The tile form went through several iterations depending on the geomterical and combinatorial capabilities of the tile. The final form of the tile depicts high adaptable and versatile behavior. The tile is also capable of interesting aggregations if put together at different scales.

Surface Surface

Loop Loop

square base triangle base square base pyramid + + triangle base pyramid= pyramid pyramid square base pyramid

triangle base pyramid

Liner Liner

Tile Combinatorics Combinatorial logic chart

All possible combinations of two tiles using the triangular, rhomboid and square faces

Tile Design Test Manually fabricated panton chair

The panton chair was constructed by manually aggregating 324 tiles from a digital model of the chair. During the construction process the structural skeleton of the chair consisting of the larger size tiles was constructed first. These tiles provided stability and a core to which the more intricately patterned edges were attached. The tiles were constructed as part wireframe and part solid units using laser cut cardboard pieces, to give variation in form and to reduce the weight of the chair. The chair produced clearly depicted two types of behaviors of tiles. One behavior which was more

individual tiles 20

homogenous and linear in nature based purely on the tile logic and ther other which was much more heterogenous and varied in nature or the voxel logic.Both behaviors however, help in aggregations and growth in a particular manner. For instance, the tile behavior is more suitable for linear growth whereas the voxel behavior helps in generating curves and change in direction. The back rest of the chair was based on the structural logic of a central spine of large tiles supported on the base tiles forming the seat of the chair and extending in a triangular formation to the floor. All other neighboring tiles were attached to the structural spine of the back rest.

aggregation of tiles

manual fabrication starting from structural spine

First manually fabricated chair using tile combinatorial principles

Tile Combinations and Behaviors Decoding of the manually fabricated panton chair

Chair spine Large scale

Linear aggregation of tiles Medium scale

Rotated varied orientations Small scale

Tile Design Test High resolution digital panton chair

High resolution panton chair constructed from 938 tiles with highlighted edge conditions

tile behaviour in the seat of the chair

voxel behaviour

tile and voxel behaviour transitions

Tile as a Body-Plan Tile as a container of information

The tile was tested in states that allowed for different levels of transparency. The use of the tile as a part wireframe in the manually fabricated chair allowed for less transparency as compared to the high resolution digital model which assumed the tiles to be complete wireframes. Further the high resolution chair considered some of the edges of the tile to be highlighted which produced heterogenous patterns in the chair whilst retaining the same set of combinatoric logics. For the development of the research towards 3D printing the tile is therefore considered as a body-plan for the generation of different sets of lines depending on the location and function of the tile. This is done retaining a common set of combinatorial rules for the structure to develope a discrete system with the line as the primal unit of printing. The tile starts dissolving in form in this way and becomes a container for information.

toolpath derivation using the body-plan of the tile

Voxatile Design 29

Voxatile Development Economies of scale

In computer-based modelling or graphic simulation, each of an array of elements of volume that constitute a notional three-dimensional space is called a voxel. A voxel could also be defined as each of an array of discrete elements into which a representation of a three-dimensional object is divided. In simple terms a voxel can be defined as three dimensional pixel The divisions of an object into voxels is most commonly done using cubes. However, other geometries which are completely packing like the metal organic polyhedron can be used. The tile or the digital brick occupies the voxel space such that the square face of the tile aligns with the square face of the voxel. Therefore the tile can exist in the voxel space in 6 positions or the voxel can be occupied by one to six tiles simultaneously to form a shape that resembles a metal-organic polyhedron with two holes. The variation of the number of tiles in the voxel space lead to the production of heterogenus aggregations that combine with each other in a controlled manner.

1 tile

2 tiles

2tiles

2 tiles

216 tiles = 36 voxels homogenous composition

3 tiles

4 tiles

174 tiles = 36 voxels heterogenous composition

5 tiles

6 tiles

= 1 voxel

6 tiles = 1 voxel

154 tiles = 36 voxels heterogenous composition

Voxatile Development Voxelization of the tile

Behaviours observed in the manually fabricated chair were used to voxelize the tile. A voxel is essentially a 3D pixel that exists in a spatial digital environment as opposed to a flat planar environment that houses the pixel. A cube is considered as the voxel space within which six tiles can be organised without overlapping to form a volume resembling a metal-organic polyhedron with two holes. The voxelization of the tile into voxatiles produces six types of voxatiles depending upon the number of tiles in the voxel space. The voxatile with six tiles is always symmetrical about two axes and asymmetrical about one axis owing to the holes in the organisation of the tiles. The voxel can be used in a condition where a seventh tile is introduced in the voxel space. The seventh tile is partly outside the voxel space. The edge of the seventh tile of the voxel creates an interlocking joint with the void in the next voxel.

Voxelization becomes a tool for application of combinatorial, structural and computational logic to the system since it imposes a spatial grid on the object which instantaneously produces more order and organisation in the system. It also establishes adjacencies and relationships far more easily that irregular or angular forms as every edge of the voxel is always related to the next one in the exact same way even though the content from voxel to voxel may differ. In a printing system, the organisation of the tiles in a voxel space, becomes a tool for collision detection and hence replication of a particular toolpath by expending the voxel space.

System Hierarchy Line to voxatile aggregations

The project developes a hierarchical system starting with the line which is the simplest printable unit. A combination of many such lines based on the body-plan of the tiles in the voxel space forms a fragment of the toolpath. The combinatorics of toolpath fragments within the voxel space creates a varied sequence of printable voxatiles. The development of the voxatile establishes a tool for controlling the system and avoiding collisions in the fabrication process. The voxatile aids in discretizing the continuous process of printing in the digital environment in order to produce larger aggregations with the same set of rules and producing customised variations and heterogenous interesting forms in the process. At a larger scale, the form is produced by the printing of large scale voxatile aggregtions based on analysis and local adaptation of the toolpath. These large scale aggregations are produced and assembled robotically to discretize the process

line

smallest printable unit _line

_ smallest printable unit

combination of line

_combination offragment lines tool path _tool path fragment

tile _tile _combinatorial unit combinationatorial unit

voxel

discretisizing the toolpath _voxel prevents collisions _discretisizing the toolpath control of aggregations

_prevents collisions, _control of aggregations

_voxel aggregation voxel aggregation discrete assembly _discrete assembly

Possible Tile Positions and Orientations in Voxel Space Single tile in voxel space

position 1

orientation 1

orientation 2

orientation 3

orientation 4

Six possible positions of the tile in the voxel space with four rotations for every position of the tile

position 2

position 3

position 4

position 5

position 6

Multiple tile combinations in voxel space

1 Tile

2 Tiles

3 Tiles

4 Tiles

5 Tiles

6 Tiles

Different combinations of one to six tile in the voxel space to produce several types of voxatiles

Voxatile Combinatorics Controlled aggregation of voxatiles

Complete voxel 6 tiles 6 directions of growth

2 tiles 2 directions

Opposite top left to below bottom right : aggregation of the six different types of voxatiles to control the directionality using the square edges of the voxatile which are always aligned to the surfaces of the voxel.

3 tiles 3 directions 2 tiles 2 directions 3 tiles 3 directions

3 tiles 3 directions

closed loop of aggregated voxatiles

Patterning of Voxatile Aggregations Layering and variation in form

The tile within the voxel space is retained as the combinatorial unit and the container of information. The edges of the tiles start to assume the role of lines which maybe of a single type or many types depending on their function or location within the voxel space. The dissolving of the tile faces and formation of lines by the edges of the tiles start to give rise to different patterns with the same aggregation of voxatiles. The transparency this created also adds depth and layering to the form and patterns, creating more interesting forms. The assigning of different colours to different tile edges also talks about the speculation of multimaterial extrusion where material starts responding to conditions of stress, function or aesthetics.

Above and opposite: solid and wireframe tests on voxel aggregations informing decisions on materiality, fabrication and aesthetic appeal of aggregations.

Voxatile Development Testing voxatile patterns in the panton chair

Voxelisation of a panton chair using single scale cube voxels.

6 tiles rotation 0

6 tiles rotation 90

6 tiles rotation 180

6 tiles rotation 270

Patterning of voxatile wireframe consisting of six tiles to produce differenciation and patterning of results by the use of different rotations.

Voxatile Design Test Stress analysis

Density and Orientation

As a method of inducing variation and structural logic in the arrangement of voxatiles, a stress vector field is generated for every voxel of the panton chair. The isolated compression and tension vectors are used to determine the rotation of the voxatiles within the chair. The orientation of the voxatiles in the aggregation depends upon the direction of the dominant stress vector for the voxatile. The magnitude of the stress vector determines the density of tiles within each voxatile.

Compression vector field 44

6 tiles stress values 0.30 to 1.00 maximum density

5 tiles stress values 0.15 to 0.30 medium density

4 tiles stress values 0.00 to 0.15 minimum density

Tension vector field 45

Voxatile Design Test Panton chair based on stress analysis

The structural analysis and voxelization of the panton chair gives the local load and stress conditions. These conditions can be used to get information and feed the combinatorial system of the voxatile. The stress values, divided in three groups, informs the tile density inside the voxatile - the greater the stress, the more the tiles. In this case there are three, four and five tiles respectively for each stress value group. The stress vectors inform the orientation and rotation of each voxatile. First, the compression vectors orient the base plane of each voxatile and the tension vectors give the rotation direction, perpendicular to the previously oriented plane.

voxelized panton chair

stress analysis

grouping by stress values

discrete stress vectors

tension vectors

compression vectors

orientation to vector direction

minimum density

medium density

maximum density

Toolpath Development in Voxel Space Variation of toolpath based on tile location and orientation

The toolpath developments starts with the smallest printable unit of a line. The lines follow the bodyplan and combinatorial logics of the tile within the voxel space t form toolpath fragments which are aggregated as voxatiles to form large printed aggregations. The tile can occupy the voxel space in multiple positions and numbers and therefore creates the possibilty of production of a large number of toolpath types. These toolpaths are derived from lines that are printed in a particular sequence within the voxel space to avoid collision. Considering tiles of different body-plan formations in the voxel space we see the formation of several types of toolpaths that adapt to conditions of density, connectivity and orientation in a printable aggregation.

Tile

Voxatile

Tile

Voxatile

Computating Structural Response Voxatile density and orientation automation

The computational logic is based on the idea of structural analysis results affecting the voxatile density and orientation. The stress values inform the number of tiles forming a voxatile. In this case, the values are divided in three groups, giving voxatiles with two, three and four tiles respectively with the stress values. In the next phase, a vector field - deriving from structural analysis or generated by design intension or other rules - this informs the rotation of each voxatile. Specifically, each vector for each voxel of the divided geometry is projected into two planes - the xy plane and yz plane. The angle between these projections and the y and z axis is calculated. The angle values, which are float numbers, are approximated to the nearest perpendicular angle (i.e. 0, 90, 180, 270 or 360 degrees) and this gives the rotation values, which are two, one along the y and one along the z axis.

2 tiles

3 tiles

4 tiles

stress values voxatile density

4 tiles

projection

rotation

vector field voxatile orientation

Voxatile Design Test Toolpath design test using the panton chair

Above left to right: panton chair, voxelization of panton chair with multiple scales based on structural analysis, multimaterial toolpath fragment in voxel space

Toolpath test 1: Replacement of voxels in panton chair with toolpath fragment

Toolpath test 2: Replacement of voxels in panton chair with toolpath fragment

Voxatile Design Test Multi-material toolpath design test using the panton chair

Above left to right: panton chair, voxelization of panton chair with multiple scales based on structural analysis, multimaterial toolpath fragment in voxel space

Toolpath test 3: substitution of multimaterial toolpath fragments in the voxel space based on densities and rotations derived from the structural analysis.

Toolpath test 4: substitution of multimaterial toolpath fragments in the voxel space based on densities and rotations derived from the structural analysis.

Frei Otto column design test 1 Single material toolpath

Frei Otto column column design designtest test11 Multi-material toolpath

Frei Otto column design test 2 Single material toolpath

Frei Otto column design test 2 Multi-material toolpath

Material Realization 67

Material Tests Material and technique exploration

blocks Initial material and fabricaton technique tests were focused on two main aspects; one was that of a material and production method that enhanced the aethetic results of the geometry when aggregated to form aggregations and the secog being that of economies of cost, time and scale of production. The tile was tested as a replicated solid block made by either 3D printing of the geometry or casting in plaster. While the 3D printed tiles were precise in geomtery, the time taken to produce each block made the process unfit for use at larger scales. Geometry of tiles produced by casting of plaster was observed to be unprecise. The solid tiles were observed to add unnecessary weight to the structure while also reducing the dimensionality that was observed in the case of wireframe tiles. MDF, birch ply and cardboard were materials that were tested by laser cutting of the faces and assembling of tiles. The manual assembly of the tiles was observed to be a tedious time-consuming process that was unfit for digital producion. Though these materials exhibited desired qualities of low weight and low cost, the poor strength os the assembly of the form from these materials make the materials unfit for architectural production in

3d printed block

weight

cost

fabrication time

strength

plaster casted block

surfaces

MDF surface

cardboard wireframe + surface

wireframe

MDF wireframe

plywood wireframe

Material Realization Comparison of plastics for extrusion

pellets

The material research quickly progressed from the use of solids and surfaces to a language of lines. These lines were to be varied and bound together by logics of combinations and hence plastic extrusion was chosen as the fabrication method.

ABS pellets

PLA pellets

LDPE pellets

The available compatible plastics were compared using parameters of melting temperature, quality and consistency, cost and strength. For large scale production, the use of the pellet extruder proved to be far more beneficial than the filament extruder which has a low tool cost but high raw material cost. Plastic pellets being recyclable, are much cheaper and could be used with a pellet extruder. The use of pellets also allowed for mixing of platic types and colours and therefore a multi-material output. PLA pellets were chosen over ABS and LDPE pellets primarily because of the emmision of toxic fumes in case of ABS pellets and higher pellet cost. LDPE was discarded as it shows low material strength and low melting temperature which makes it hard to control.

material cost pellet extruder

extruder cost

1200 pounds

strength

melting temperture

less toxic; recycleable

LDPE -- Low-density polyethylene 70

3d-printing filament

PLA

ABS

Carbon Fiber Reinforced PLA

Steel PLA

Nylon (Polyamide)

filament extruder 550 pounds

ABS -- Acrylonitrile Butadiene Styrene

PLA -- Polylactic Acid

Multi-Material Extrusion Mixing of plastics and dyes

Speculation of voxatile with two material identities

Speculation of voxatile with two material identities using a combination of pellets, steel powder and coloured dye

Single material and multi-material extrusion tests using plastic polymers

End Effector 75

Tool Comparison Filament extruder vs pellet extruder

Printing Tests Line, surface and spatial printing using filament extruder

Opposite: printing of lines in space to form patterns and surfaces Above: printing evolution of voxatile toolpaths.

Pellet Extruder Development Design process iterations

Carbon fiber roll for combined extrusion. External multi-material feeding tubes. Lateral supply funnel.

Robot bracket support. 6mm air system. “V” type air system support.

Lateral motor frame. Integrated air support system funnel. Increased capacity disc funnel. 60mm Aluminum thermal mass cylinder. 30° Cone nozzle.

“E” Type supporting frame. Local storage cylinder feeders. Open supply funnel.

Vertical axis centralized barrel structure. Local supply funnel.

Top open box motor support. 20° Cone nozzle

Individual solenoid actuator for controlling multi-material feeding. Triangular air system support.

Local supply cone/cylinder funnel with integrated support for air system.

Local supply multi-material elongated feeders with increased supply capacity. Linear solenoids actuators for material supply control. Cylinder/ sphere funnel.

Increased rigidity for lower air system support.

Admission sluices with connecting rods for material supply controlled by linear solenoids. Central air cross distribuitor support. Aluminium circular air tubes support with insulation. 110mm Aluminium thermal mass cylinder. 24V heat

Two-part dismountable funnel. Whitworth mechanism sluices. Funnel teflon insulation.

Working Principles Multi-material pellet extruder

~20C° SOLID PELLETS

~100C° PREHEATED PELLETS

~180C° LIQUID PLA

~80C° SOLIDIFYING FILAMENT

~20C° SOLID FILAMENT

Pellet Extruder Design and Advantages

The tool embraces multi-materiality and versatility. It is fabricated with cost effective, low-tech processes. Multiple material feeders are controlled by solenoid hatches and connected to a motorpowered auger that conveys the pellets while heating them gradually inside the chamber until reaching melting point to be printed out of a replaceable custom-made nozzle and cooled down while in motion.

Customized plastic pellet extruder design and building for printing in 4 mm diameter

Final End Effector Design Single material pellet extruder

Final end effector design Multi-material pellet extruder

Extruder Design Composition and assembly of electronic parts

The pellet extruder is controlled by a custom made circuit board, controlling the two basic parts of the tool, the heating system and the stepper motor, which parts are situated at the right and left part respectively. The heating cartridges are controlled by a relay module board, operating as on and off switches and interfacing the 5Volt of the Arduino board, which actually controls the operation of the heating system, with the 24Volts required for the cartridges. Apart from the relay module, the Arduino board receives heat values from the extruder, provided by a 10Kohm thermistor. When the heat is reaching the PLA melting point (180C), the Arduino switches the relays circuit from normally close to normally open and consequently the cartridges are not receiving any electricity from the power supply. When the temperature falls below the 180C, the circuit turns back to normally close, so electricity flows again through the heat cartridges.

The other part of the circuit board controls the stepper motor as already mentioned. Central to this part of the board is the motor driver, which is interfacing with the toolpath program through an Arduino board. The latter is controlling the speed of the motor rotation. In some parts of the toolpath there has to be some delay points for cooling purposes. As the robot needs to stop in certain points, the motor also needs to synchronize to this delays. This coordination is possible by a relay module, which interfaces the robot with the Arduino board. The robot sends a signal when it stops moving, using the relay as a switch. When it stops moving, it stops sending electric signal to the relay. The Arduino is receiving this signal and sends the motor driver the signal to stop rotating, thus the necessary coordination is achieved.

Electronic parts for power and robotic connection of pellet extruder

Printing Tests Testing with different plastics

Single material and multi-material extrusion tests using plastic polymers in a pellet extruder

Customized plastic pellet extruder design and building forprinting in 4 mm diameter

Nozzle design Design iterations

(mm) Total lenght:

100

120

Extension lenght:

30°

20°

Printing diameter:

Minimun voxel range:

Cone angle:

Tool Design Pellet extruder assemble

Robotic printing using PLA pellets and pellet extruder

Pellet extruder Assembly Parts Fabrication and Multi-material pellet testing extruder process

Tool Design Pellet extruder assemble

Robotically printed high resolution panton chair

Toolpath Development 99

Toolpath Design and Printing Direction Discrete toolpath - Continuous printing

While investigating the voxatile containing information, there was an attempt to establish a printable toolpath within it. Through many tests and attempts, we concluded to the idea of having two main tiles forming a perpendicular axis and the rest surrounding tiles would be â&#x20AC;&#x2DC;supportiveâ&#x20AC;&#x2122; ones. The first diagram shows four tiles in total. two in the main - here coinciding with the z - axis and two supportive ones. The generated toolpath enters and leaves the voxel in the same position, making it difficult to form a continuous toolpath. In the second diagram, excluding one of the

helping tiles and keeping only one, gives the chance of forming a toolpath that enters and leaves the voxel in one direction. The supportive tile helps the toolpath to go up from the bottom to the top level and also the opposite so the toolpath can leave the voxel in one direction. The matrix bellow shows all possible rotations of the two main tiles and which tile should be aded so there is a useful toolpath generated. Apart from linear ones, there are some toolpaths that change direction - by 90 degrees - so the toolpath can

Two tiles along the z axis and two extra tiles toolpath enters and exits the voxel in the same point

Two tiles along the z axis and only one extra tile toolpath enters and exits the voxel in same direction

100

Continuous toolpath formation within an array of voxels, following a predettermined direction of printing

101

Toolpath Combinatorics Collision Avoidance

While testing the toolpaths generated with the previous voxatile arrangements, there were some collisions detected. The collisions occurred on the voxatiles found on the left side of the toolpath direction. What needed to be checked though was the left neighbouring voxatile for each of the two possible directions of the toolpath. The matrix on the bottom of the page shows the types 1, 4 and 6 which form a linear toolpath tested with each

type 1 combinations

102

type 4 combinations

type 6 combinations

Combinations of toolpath types that are printable without colllsions.

103

Toolpath Combinatorics Printability

rotations

tile addition

104

90 180

270

105

Toolpath Combinatorics Vertical support study

The bottom and top lines of the toolpath perform the function of support structures for the aggregation of the toolpath. The first printed voxatile layer is supported by the ground plane. All the layers above the first layer rely on the previous layer for supporting the aerially printed lines in order to maintain continuity and provide rigidity to the structure. Therefore, the toolpath is formed in a way to reverse the top and bottom lines in opposite directons of printing in order to achieve a stable toolpath.

Case 2 change direction per level

Case 1 same direction

Common - 1 point Common - 2 points

Common - 1 line

Common - 1 point and 1 line

106

107

Topological Deformation D’Arcy Thommpson: Theory of deformatin of species

Using 3D printing as a fabrication method gives the opportunity of fabricating variations of the formed toolpath using the same set of logics to retain its discrete proprties rather than printing of the same toolpath repeatedly. The discrete method of toolpath formation in specific types is informed by a continuous logic of topological deformation. Based on the same body-plan, numerous new types arise by the topological deformation of the specific types, in a similar manner to D’ Arcy Thompson’s theory that argues for a common body plan in species which is deformed to form to give rise to these types. This process is a hybrid state between continuity and discreteness as the discrete typology of toolpaths is becoming continuous by topological transformations. The voxatile is deformed using two points of the voxatile - the central one and one in one of the voxel sides - are being moved towards the direction that the vector indicates. The central point follows the direction of the vector whereas the peripheral point follows the perpendicular axis of the voxel side and moves to the opposite direction of the central point.

Deformation of body plans and the formation of new species by D’arcy Thomspson

108

Pattern lines for deformation

Deformation lines

Global recognition of deformation

Local recognition of deformation

109

Optimization Strategy Deformation and material deposition

The toolpath within each voxel space is adapted to the local forces in the voxel space. This is done by the process of deformation of the central voxel lines and depositon of material in high stress zones. For example, if a three-tile voxatile is considered forming the printable lines or the body plan, the central line of the printed tiles first snap to direction of the discrete vector in the voxel space. These lines are then printed as double, triple or quadruple lines, depending on the magnitude of the active stress vector. The remaining lines in the voxel adhere to their roles of level change, support and connectivity to the adjacent voxel space. The adaptation of the deformation line of the printable toolpath always adheres to the corners and midponts of the edges of the voxel space.

110

111

Toolpath Automation Checker algorithm

The computational rules of the system are set using a checker which checks the neighbouring 28 voxels for every voxel in a three dimensional space. The checker checks the neighbouring voxels for the direction of printing, and preventing of collisions in maintaining the printing direction. The checker also checks the deformation vector for every voxel space in order to adapt the printable line to maintain continuity. Further the condition for continuity is checked for material deposition and optiimization to produce toolpaths of heterogenous nature.

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Computational Generation Processing code for panton chair

stress values

Toolpath formation

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Digital panton chair with local adaptation to shifting vector field

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Computational Generation Processing code for large scale column

text >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>

stress values

Toolpath formation

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Digital column with toolpath adapted to stress vectors

locally

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Discretization of Flowfield N45 degrees of freedom

The deformation of the toolpath body-plan is so far informed by a vectorfield generated from curves crossing a voxel space. As seen in the first picture of the diagram bellow, the lines are crossing a two dimensional voxel space produce a vecto field. Each voxel point detects the closest curve point and after that the tangent of that curve point is assigned to every voxel point. In this way, a continuous flow field is produced by curves entering a voxel space. In the third part of the diagram bellow, a discrete adjustment of that same flowfield is depicted. By this translation and effectively by discretiizing the the vector field, a form of continuity is produced.

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Apart from continuity achievement, this principal is necessary for developing the toolpath. Due to the fact that the toolpath body-plan is based on the voxatile and therefore points of a cube, a random vector field with N angle possibilities might be an obstacle in printability, as collisions are observed. It is necessary to adjust the toolpath that is informed by a random vector field towards an approach that is inherent to the system. This principal is named N-45 degrees of freedom as the system has the freedom to adapt to local conditions but under the constrain of deforming to angles that are multples of 45 degrees.

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Discretization of Flowfield Application in three dimensional space

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The same conditions of achieving continuity from a discrete vector field can be produced in a three dimensional space. The discrete vectors can be achieved from the stress analysis of the primary structure which then get grouped together to form continuous lines that help the structure to adapt to the loading conditions.

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Discretization of Structural Data Production of discrete vector field

Stress field produced for a typical simply supported condition with central loading

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Discretization of vector fiels to 45 degrees based on primary stress direction for every voxel space

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Toolpath Automation High resolution panton chair

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Digital panton chair of 40 mm voxel size with optimized material deposition based on adaptation to stress direction and magnitude

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Opposite: Multi-material digital panton chair with optimized material deposition based on adaptation to stress direction and magnitude

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Toolpath Informed by Discretization High resolution panton chair

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Digital panton chair with optimized material deposition based on adaptation to stress direction and magnitude in high resolution with 60 mm voxel size

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Toolpath Generation Toolpath generation based on stress deformations

The first printed protoype of the panton chair was developed in the digital environment using a panton chair that was voxelised with a voxel size of 8 cm. The toolpath was developed step by step by analysis of stress conditions of the panton chair produced by loading of the chair. The primary stress lines were isolated from the stress field produced from the loading of the chair and re-grouped to for continuity that is adapted to give rigidity and strength to the robotically printed chair. The toolpath is first generated using the combinatorial rules based on supports, printing direction and printability and then these toolpaths deform locally to adapt to the direction of the active stress vector in the voxel space.

panton chair

compression lines

The toolpath generated was robotically fabricated by printing the chair in two continuous halves. The toolpath is printed by layer by layer printing of voxels starting from the central voxel layer of the chair.

re-mapping of stress field

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voxelised panton chair

Digital model of first printed prototype toolpath for panton chair

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Robotic Fabrication of Panton Chair First Prototype

Layering of voxels and sequence of layer by layer robotic fabrication

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Robotically printed chair fabricated in two halves

prototype

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Robotic Fabrication of Panton Chair Second Prototype

Digital model of second printed prototype toolpath for panton chair

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Digital model of second printed prototype toolpath for panton chair

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Architectural Development 137

Meta-Voxatile Systemic Hierarchy Tile, voxatile and meta-voxatile relationship

Large Scale Discrete Unit Tile

One of the biggest challenges in 3D printing or aerial printing with regards to architecture is the intrinsic continuous nature of the process. This often iimits the reach of projects involving 3D printing to an object or sculpural scale. The development of a large scale discrete unit was done in order to extend the hierarchy of the system to architectural scale and development of a unit that is a derivation of the basic tile. This large scale unit would be robotically assembled on the site and hence responds to constraints of robotic assembly rather than human labour and can therefore be larger in size and heavier in weight than a clay brick, typically used in construction.

Voxatile

Meta-Voxatile The meta-voxatile is a large scale discrete unit of about 90 cm height. The Meta-voxatile resembles in form to the voxatile with a seventh tile, however it is formed by the agregation of voxatiles. The seventh tile projection of the meta-voxatile helps it to interlock with other such units and creates a larger flat surface for the printing of the unit, avoiding a double sided cantilever. Archtecture was speculated using combinations of metavoxatiles at different scales which were rotated and put together.

Meta-voxatile

Voxelized meta-voxatile

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Meta-Tile Systemic Hierarchy Tile, voxatile and meta-tile relationship

Tile

Meta-Tile The meta-tile resembles the basic tile in form which is elongated to form a more linear unit. The metatile is a printed aggregation of voxatiles and tiles which are maximum at the bottom of the metatile and reduce in number towards the edges and the top. The meta-tile is 180 cm in length and 45 cm is diagonal height (along the triangular edges).

Voxatile

The meta-tile consists of 6 faces of which two are rhombuses, two are triangles and one rectangular edge. The meta-tile is always printed along its flat rectangulr edge. The toolpath generated for the meta-tile follows the discrete logic of combination of tile orientations and densities in the voxel space. This makes the process discrete right from computational logic used for design generation to aggregation at architectural scale.

Meta-tile

Voxelized meta-tile

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Meta-Voxatile Design Test Composition & connection of discrete meta-voxatiles

Scaling of Meta-Voxatiles in Panton Chair The size of the meta-voxatile depends on the application. When tested on the panton chair, the largest meta-voxatile is 25 cm in size. The smallest meta-voxatiles in the chair (3.12 cm) are printed together as meta-voxatile aggregations to achieve economies of scale and time.

25.00 cm

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12.50 cm

6.25 cm

3.12 cm

Parameters for Variation Each meta-voxatile resembles a scaled up version of a voxatile with seven tiles. The seventh tile of the meta-voxatile creates asymmetry in the unit and helps to develop an inter-locking mechanism. Each meta-voxatile is composed of voxatiles of different tile compositions and scales. Edges of the meta-voxatile that connect to other meta-voxatiles are smaller in size and form dense edge conditions. The scaling down of the toolpath generates surfaces that help in connecting one meta-voxatile to the adjacent one. meta-voxatile to meta-voxatile connections The orientation of the voxatile in the object depends upon the direction of the dominant stress vector for the voxatile. The magnitude of the stress vector determines the density of tiles within each voxatile.

meta-voxatile form

meta-voxatile voxelization

vector field generation

deformation and density based on vector field

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Meta-Voxatile Design Test Discrete aggregation of meta-voxatiles

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Opposite: Aggregation of discrete metavoxatiles to form panton chair (top left to bottom right)

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Above: Panton chair aggregated using meta-voxatiles of three different scales

Meta-Voxatile Design Test Single material panton chair

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Panton chair aggregated using metavoxatiles at three scales producing different densities and pattern variation.

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Meta-Voxatile Design Test Multi-material panton chair

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Panton chair aggregated using metavoxatiles in a combination of two materials indicated in white and yellow.

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Above: Frei Otto column assembled from discrete meta-voxatile units Opposite: Replacement of meta-voxatiles by robotically printed toolpath in Frei Otto column

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Meta-Tile Size, scale and orientations

The meta-tile remebles the shape of an elongated tile which is 180 cm in length and 45 cm in diagonal height. The meta-tile is voxelised using cube voxels of side 8 cm in order to produce a toolpath using the discrete computational logic. The topmost layer of voxels is used keeping only the bottom layer of tiles to maintain the tapering profile of the meta-tile. In theory therefore, the meta-tile is voxelised using three and a half layers of voxels. The voxels in the meta-tile are further substituted by tiles to achieve the correct profile of the metatile. The toolpath production and orientation of the tiles is dependent on the direction and magnitude of stress in each voxel space in order to produce a toolpath that responds to local conditions.

45 cm 180 cm

voxelisation

12 cm 8 cm 8 cm

substition with tiles in voxel space

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Meta-tile orientations generated from orientation of tiles in voxel space. Each horizontal and vertical conditions has 4 rotations and therefore directions of

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Meta-tile Stress Analysis Loading condition and orientations

Continuous Stress Field for Different Orientations and Loading Cionditions

Horizontal and vertical meta-tiles with continuous stress fields generated by stress analysis based on simply supported and cantilevered condisions

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Discrete Stress Field for Different Orientations and Loading Conditions

Discretizing of continuous stress fields to generate local deformation conditions for every voxel space

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Meta-Tile Stress Analysis Loading condition and orientations

Continuous Stress Field for Different Orientations and Loading Conditions

Horizontal and vertical meta-tiles with stress lines produced by rationizing the discrete stress field to 45 degrees based on simply supported and cantilevered

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Toolpath Generation for Meta-Tile Types Based on Orientations and Loading Conditions

Generation of discrete toolpath for each meta-tile condition which uses the adapted stress field to deform and adapt the toolpath to produce zones of high strength by high material deposition

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Meta-Tile Combinations Stress pattern generation for different loading conditions

Stress lines

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Discretizing the stress field

centered simple support for column type 1

centered simple support for column type 2

centered simple support for column type 1

left cantilevered support for column type 1

right cantilevered support for column type 1

left cantilevered support for column type 1

left cantilevered support for column type 2

double cantilevered support for column type 2

left cantilevered support for column type 2

Continuity through combinatorics

centered simple support for column type 2

centered simple support for column type 1

centered simple support for column type 2

right cantilevered support for column type 1

left cantilevered support for column type 1

right cantilevered support for column type 1

double cantilevered support for column type 2

left cantilevered support for column type 2

double cantilevered support for column type 2

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Architectural speculation View of meta-tile of clumn column assembled using 1 mrtrt long meta-tiles

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Site Strategy On site assembly of robotically printed meta-tiles

Meta-tile assembly on site

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The meta-tiles are the architectural units that are robotically printed in a controlled environment, transported to site and and assembled on site by pick and place method.

Dispatch to site (perfectly packing geometry)

Robotic fabrication (controlled environment)

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Architectural Developement Form generation using meta-tiles based on stress vector directions

Stress analysis of structure

Discretizing the stress lines to stress vectors

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Orientation of metatiles based on stress vector directions

Replacement of meta-tiles with toolpath

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Architectural Speculation Meta-tile house

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Opposite: top view of meta-tile house

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Architectural Speculation Meta-tile house

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Architectural Speculation Meta-tile house

ACKNOWLEDGEMENTS: We would like to express our gratitude to our tutors Gilles Retsin and Manuel Jimenez Garcia (MereoLab, Research Cluster 4 tutors at Bartlett School of Architecture, UCL) for their advice and support in both the research and design projects throughout the year. Particular gratitude is also due to Vicente Solar Senent (WonderLab, Research Cluster 5 tutor at Bartlett School of Architecture, UCL), who helped us a lot on robotic fabrication with technical matters. We are also deeply indebted to all the staff at the B-MADE.

The Bartlett School of Architecture

MArch Architecture Design Wonder Lab Research Cluster 4

Voxatile | Palak Jhunjhunwala Efstratios Georgiou Juan Rico Yiheng Ye Tutors | Gilles Retsin Manuel Jimenez Garcia

ATILE