Nexormorphosis - Master thesis by Theresa Lohse and Oksana Tyltina

NEXORMORPHOSIS A COMPUTATIONAL EXPLORATION OF A MODULAR AND DIGITALLY FABRICATED SPACE STRUCTURE EMPLOYING RECIPROCITY PRINCIPLES

MASTER THESIS RESEARCH PROJECT

NEXORMORPHOSIS A COMPUTATIONAL EXPLORATION OF A MODULAR AND DIGITALLY FABRICATED SPACE STRUCTURE EMPLOYING RECIPROCITY PRINCIPLES Theresa Lohse | 376324 Oksana Tyltina | 392605

Collaborative Design Laboratory Institute of Architecture Technichal University Berlin Prof. Dr. Ignacio Borrego Digital and Experimental Design Institute of Architecture and Urban Development,UDK Berlin Guest Prof. Sven Pfeiffer Faculty of Wood Engineering innovationsWerkstatt Holz Eberswalde University for Sustainable Development

ABSTRACT

The focus of this design and research thesis is the computational planning and physical prototyping for a human assembly of a reciprocal timber structure and its potential for morphological alterations.

There are three wider sections to the thesis. The first section forms a literature review within a concise historic and academic research project trajectory of timber reciprocal structures. This is followed by an extensive chapter covering the design and physical prototyping of a pattern, beam, joint, and punctual support for the envisioned structure. Lastly, an exemplary design proposal is applied in a suitable environment.

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TABLE OF CONTENTS

MOTIVATION & AIM

CONTEXT & REFERENCES 8 - 13

METHODS 14 - 25

Abstract

5

System References

Motivation and Aim

10-11

Contextual Background 21-23

System Requirements

12-13

The choice of timber

17-20

25

26 - 31

Methods and workflow

28-31

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DESIGN DEVELOPMENT

PROTOTYPING & FABRICATION 32 - 67

CONCLUSION & OUTLOOK

PROPOSAL 68 - 85

Design process overview

34-35

Robotical Control and 70-73 Operation

Pattern Design

36-41

1:2 Notch Prototyping

74-77

Beam Design

42-49

1:1 Notch Prototyping

78-81

Joint Design

50-51

1:1 Cell Demonstrator/ 82-85 Final Fabrication

Disk Design

52-53

Column Design

54-55

Border Design

56-59

Functionality: Sun Shade

60-67

86 - 103

Component Catalogue

88-89

Span Simulation and 90-93 Analysis in Karamba Design Proposal Drawings

94-97

Design Proposal Visualisations

99-103

104 - 125

Conclusion

107

Outlook

108-109

Acknowledgements

111

Literature References

112-115

List of Figures

116-121

Image Appendix

122-125

MOTIVATION AND AIM

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MOTIVATION

Designer of Instructions Having enjoyed a higher education in architecture which is project-based in Germany, we are using this master thesis project as an opportunity to vigorously depart from the conventional analysis, concept, design and final representation of the proposal through drawings and scaled physical models. We actively aim towards a self-designed process for a conscious exploration of the design development through merging the project phases in a holistic computational approach.

This entails a shift from the classical project set-up towards a deep discovery and understanding of the fundamentals and absolute conditions of formal and technical design drivers that are digitally informed by the entire process in real-time.

This parametric approach allows us to design the guiding rules ourselves, including complex geometry, aesthetics, material and production methods.The constant testing and feedback by the design gives further information about the process and enables full control throughout all

phases of a dynamic system design instead of a static building design.

Therefore, we strive to test validation of the proposed system design through physical prototyping as a broad project phase and test its formal, material and production boundaries.

Design through exploration Not only do we intend to pursue the reconsideration of the project phase emphasis in a digital workflow, but the design itself will be subject to exploration from digital design to digital fabrication.

Current size-related fabrication limits in digital fabrication induced us to research ‘alternative’ structural systems of reciprocal frames.

Our fascination for these interlocked systems consisting of multiple beams shorter than the overall span led to our declared intention to draw on them. Reciprocal frames were subject to various research

schemes, yet they are not being assertively deployed as structural systems except for research pavilions. To meet the sophistication and structural logic of the pattern, computational tools for simulation are essential. Traditionally, reciprocal frames are timber constructions.

To be able to dive into the fabrication process, we want to acquire the system’s principle in order to manipulate and recreate its form and production methods.

“

The challenge is not to construct a research question that can be ‘answered’ [ ... ] but rather to construct a line of thinking that can be investigated intelligently and discussed through experimentation.

[It] is more about the exploration of design intent and how this is inscribed in the design tools [...] rather than specific technology for the integrated delivery of building projects. It is about designing a system, rather than working on a more detailed 3D model.

(Peters and Peters, 2013)

„

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Process Communication and Instructions Outcome

Materialisation Since the production stage usually fails to materialise in academice projects, we wish to implement prototyping and fabrication parameters into the early design process.

The real-time 3D simulation enables us as designers and the framework instructions to be in a constant dialogue with the informed design.

Design Aesthetics The mostly expressed critics of digital generative design have been that the resulting buildings can be classified as avant-garde and tectonics are blurred and hard to read. Moreover, through similar parametric settings in the design stage, similar patterns and therefore similar visual effects are created. As mentioned above, we believe in the attainment of a different visual appearance through inclusion of material fabrication parameters. The use of timber as part of a structural system usually implies a forseen visual appearance

and, therefore, we are refining the hexagonal reciprocal frame pattern to a fluent and woven-like pattern.

Ambition for Spatial Quality We want to consciously reduce the design and structure complexity towards a comprehensible form. To us, this stems from a small amount of parameters that are fully controlled and exploited.

These few parameters can therefore lead to a higher formal and spatial impact from a distinct combination of both.

Despite the focus on research and technical exploration, the project ought to create a space with architectural quality.

Architectural semantics are a classical plan, section and elevation drawings or a scaled physical model of the envisioned project can only be decoded by professionals. The balance of how certain elements are represented, in which fashion (symbolism or tectonics) and emphasis, is a design and a set of compositions on its own. Through computation in architecture, a new language to read ‘the planned’ arose. The fact that the project design, which is a system or process design is not particularly linked to the visual appearance and appointed presentation of such. The semantics can be understood by a wider audience.

With ‘nexormorphosis’ we want to gain literacy of patterns and tools that can be accessed (read) and generated (written) and adapted by others.

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SYSTEM REQUIREMENTS

Is a Bottom-Up System Design the Answer to Overcome Small-Sized Digitally Fabricated Structures?

There are plenty of examples of digitally fabricated structures nowadays, mostly in small-scale pavilions. Using the advantages of the parametrical design, these systems and their elements are optimised in connection to each other for a range of end forms. The final form is evaluated taking into account to the best performance of the elements and the overall shape.

As we can observe, both element and the end form are inseparable in their design. The advantages of such method are both an optimised system and a better structural behaviour, especially while applied in a dome-like final form. However, the system emerges in a thousand different pieces, which must be specifically marked to make an assembly possible by human or by robot. The ease of customising this high amount of different parts in the design process cannot be traversed in the construction. Neither can the parts be reused or reassembled in a different configuration (Figure 1).

To depart from a pavillion-scaled system requires time, finance, human- and computing resources.

To change the form, the element has to be change, too. Only few research institutions like ICD in Stuttgart manage to continue studies on the previously developed principle and improve the structural behaviour of the system for the bigger load or span.

List of our Initial System Requirements to Test Against: • modular / universal element(s) • strength through interlacing – 3D bracing • demountable • self-interlocking – joint through • optimised in size and weight geometry for easy human assembly • parametrically designed and • optimised in material use digitally fabricated • modular element is independent from the structue‘s final form

Our motivation is to create an universal modular element which is independentl form an advantageous dome-like final form.

This way, we can facilitate the growth and scalability of the end product, as the end form and the system are not directly connected.

Thus, the focus consists in the development of the planar system based on the list of requirements extracted from the study of structural system principles, and reference of relevant digitally designed and fabricated spans.

Figure 1: Construction difficulty of a parametrically customised form

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system requirements:

easy assembly /disassembly

modular

digitally optimised and fabricated

strong material and beam section

NO global tension or compression element

self-interlocking self-supporting

STRUCTURAL FORMAL

‚seamlessly‘ interwoven

Figure 2: Design approach through system requirements

NO global tension or compression element

‚digital beam‘

bendy?

NO

CONTEXT AND REFERENCES

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REFERENCES

Binabo Construction Kit This bio-plastic children constructor allows to create stableforms despite the bending properties of its units.

Each element has 2 different joints, (one plug and a hole to insert the plug) placed diagonaly on each element. Through this mirrored joint position the elements can be interconnected in more than one layer and the overall stability of the final form improves.

Appropriation of the principle • Mirrored, asymmetrically positioned joints; • Interconnection in several layers for stability; Figure 3: Binabo constructor made of bio plastic

• From flat, 2D-element to the 3D-structure.

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REFERENCES

ICD Sewn Timber Shell The system of the Sewn Timber Shell is based on the study of industrial sewing techniques applied to elastic wood sheets that are extremely thin.

The structural capacity is introduced through a multi-layered system and the relation between pliability and stiffness [1].

Appropriation of the principle • A system of multiple, interconnected layers allows the use of extremely thin bending material.

Figure 4: ICD Stuttgart Sewn Timber Shell 2017

REFERENCES

The Italian World Expo 2010 Pavilion The project was a proposal for a pavilion for the world Expo in 2010.

The system is based on the principle of reciprocity, however made out of fiber-reinforced concrete that is a rather atypical material for this type of structure which is usually lighter. (Here, each elements weighs around 25 kg).

The element is optimised in its form to reduce the overlap between the beams without weakening the resistant section. Different patterns were tested for the optimal assembly [2].

Appropriation of the principle • Figure 5: Project of the Italian Pavilion for the 2010 Shanghai World Expo

The geometrical form of the beam is optimised in order interlock the elements within the system.

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REFERENCES

The Dermoid III The Dermoid III is a research project created in cooperation between SIAL (Spatial Information Laboratory) at the Royal Melbourne Institute of Tchnology (RMIT), CITA, Copenhagen, RMIT Fashion and Textiles and the Structural Research Group (KET) at the University of the Arts Berlin.

The aim or the project is to create a wide span out of short memebrs through use of elemetns with a thin section [3].

Appropriation of the principle The elements is conected in one layer on its one end and in two layer on the other. The non-ymetry of the element help it to serve both layer to create a stiff dome-like pavillon.

Figure 6: The Dermoid III

RESEARCH CONTEXT

The Principle of Reciprocity A reciprocal frame can be defined as a three-dimensional grillage structure mainly used as a roof structure, consisting of mutually supporting beams. These structures have been used throughout history and we can find them in Neolithic dwellings, in structures like the Eskimo tent, Indian tepee or even the Hogan dwellings can be named as first reciprocal frame structure, as we can find structural similarities between them (Popovich Larsen, 2008).

Figure 7: Seiwa Bunraku-Kan, Puppet theatre complex designed by Kazuhiro Ishii. Photo: Kentaro Tsukuba

Figure 8: Serlios slab solution. Sketch by A. E. Piroozfar

During the Middle Ages, the principle of reciprocity was rediscovered.

The same principle was applied to the flat slabs solutions by Sebastiano Serlio among others (Figure 8) and in the in grid assemblies as in the sketches of Leonardo da Vinci.

Reciprocal structures were responding to the problem of shorter than the span wooden beams element – at least until the beginning of the 20th century. (Pugnale & Sassone, 2014).

The research and practical use of

reciprocal structures is still present until now. However, the principle is not being used a lot except by small-scale research units or by certain architects. One of the designers, who rediscovered and applied the principle of reciprocity in his work is Graham Brown (Figure 11), who constructed a series of housing units with a reciprocal roof.

A wider range of Asian architects mostly from Japan (as for example Yoichi Kan, Kazuhiro Ishii, Yasufumi Kijima) have been constructing reciprocal structures in their work (Figure 7 & 10). In the eastern Asian cultural context, the principle of mutually supporting beams and interwoven structures transmits a spiritual idea, as this type of structure was used in public and sacred temple spaces. One of the most renowned modern Japanese architects Shegiru Ban, together with the structural engineer structural engineer Cecil Balmond, have done several prototypes and small-scalepavilions using the principle of reciprocity, one of them shown in

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RESEARCH CONTEXT

Figure 10: Reciprocal Frame builduing by Yoichi Kan under construction. Photo Yoichi Ka

Figure 11: Notched connection - Graham Brown Builduing

Figure 9: Seiwa Bunraku-Kan, Puppet theatre complex designed by Kazuhiro Ishii. Photo: Kentaro Tsukuba

Figure 9 (Popovich Larsen, 2008).

The researchers see the most potential in the development of multiple reciprocal frames (Popovich Larsen, 2008), which results in unpredictable, complex geometry.

The system develops naturally outof-plane due to the eccentricity and distance between the axes of connected and mutually supported beams. For the position of the next joint, the neighboring beam has to be placed, but, the geometry is getting unpredictable quite fast, which impedes the planning process of a reciprocal system.

There are two ways to avoid this problem. A) By introducing notching to the beams or B) by aligning elements axes to each other, as for example in the flat slabs that were previously planned by medieval architects (Parigi & Pugnale, 2012).

According to the described complexity, there are few examples of the built structures which are mostly developed in the course of a research project. Current research on

reciprocal structures can be classified roughly into the following main topics: morphology and geometry of the structures, form finding process with computational tool in combination with prototyping, studies on joinery of the reciprocal beams, structural behavior and kinematic potential and presenting a development of practical applies, projects, constructions and prototypes. (Pugnale, Dario, Sassone, Sassone, & Kirkegaard, 2011). the practical design of reciprocal systems is mostly focused on three aspects: 1) the definition of elements, 2) the definition of the composition and 3) the joinery (Pugnale & Sassone, 2014).

The main strategies to gain more stiffness in a reciprocal structure is to design a structure-adding curvature of the end form or modifying the structure into a double-layered space structure (Douthe & Baverel, 2014).

RESEARCH CONTEXT

Specification Reciprocal System Nexor - A beam in a reciprocal structure.

Fan - The smallest modular unit of a reciprocal structure composed out of at least three nexors.

(Asefi & Bahremandi-Tolou, 2019)

Reciprocal System Parameters Length of a nexor - A lenght of a beam element; Engagement length of a nexor - The distance on the beam between the nodes, where load and support are connected;

“

Eccentricity between two nexors - The distance between the axes of mutually connected elements at their connection point;

The complexity of the geometry in my view is the main reason why the RF (Reciprocal Frames) has not been used a lot. However, with modern computers this stops being a problem. [...] Circular and square buildings with RFs work well. Other forms have not been explored enough.

Dr John Chilton (Popovich Larsen, 2008)

„

End dispositions of a nexor - The location of the fan above or beyond the neighbour; Style of a fan - Clockwise or anticlockwise rotation of the fan; Base angle of a nexor - Side angle between nexors.

(Baverel, 2012)

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CONTEXT: WHY TIMBER?

Birch Multiplex Timber (veneer plywood) The potential of digital fabrication helps designers in the expansion of the timber construction domain.

Timber multiplex board has been used for temporary structures in architecture in great numbers due to its availability, good strength to weight ratio and relatively low cost.

Since it is flat sheeted, light and does not have a grain direction, the material is effective for manufacture and assembly.

Birch timber is usually rather soft and not weather-resistant and therefore suitable for futher manufacture. The veneer layers are from a renewable carbon capturing material, and birch wood is one of the most common and available multiplex sheets especially in northern Europe.

In veneer plywood, great stability in all directions is reached through the internal structure which consists of an uneven number of glued veneer layers placed on one another at a 90° angle (Figure 12) . For outdoor

all-weather application, the high pressure gluing procedure is usually done with phenol-formaldehyde adhesive.

Once the layers add up to a panel thickness of 12mm, the plywood board is termed ‚multiplex‘. (Glasner, Ott, 2012, p. 264) Aligning the grain orthogonally to each other increases the dimensional stability of the boards, as wood expands or contracts across the grain due to moisture increase or decrease in the environment. Therefore, expansions or contractions are prevented by the closely pressed adjacent layers. Along the grain, the layers are extremely resistant to tension. In terms of deformation, the cross-layering only allows for little change caused by external tension or compression forces.

As the strong microstructure of multiplex influences the possibilities in the macrostructual set-up, in the case of Nexormorphosis, we want to profit from the following specifications: • light-weight for an easy human assembly, • light-weight for a structure sparsely affected by its dead load > lightweight structure, • cross-lamination for bearing all-directional forces in the hexagonal and triangular configuration, • different grain directions for customised milling of clear joinery without material break out, • ‚global‘ availability for frequent reproduction of Nexormorphosis

Figure 12: Cross-laminated interior structure of Multiplex

Further, the 18mm birch multi plex has the following technical specification relevant for force and weight estimations and calculations. weight: 12,2 kg/m2 bending strength: 40,2 N/mm2 Young‘s modulus / tensile modulus: 10.048 N/mm2 [4]

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METHODS

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METHODS

Seamless Digital Workflow?

Since we defined distinct system requirements and wanted to consciously depart from a reciprocal frame design that derives from a curved mesh, it was evident that applying a bottom-up approach was the best approach. The constant experiments across all scales and design aspects resulted in a working method that had to adapt constantly. The general experimentation and working method bounced between the physical and digital design and construction at a high interval.

Digital planning or parametric build ups do not work without certain known and previously planned input information.

Parametric design records the dependencies of different design steps, components and assigns those with an unknown parameter to control the numerical input afterwards.

We initially explored these dependencies by testing many variations of beam geometries and pattern configuration in cardboard models.

The analysis of relevant research

papers about general modular systems and their build ups drove us to the conclusion that the beam profile is highly influenced by the system‘s form. The cardboard model beams were diversified with alterations on their ‚arms‘ such as direction, height, being mirroring in all 3 planes (Figue 14-18).

A striking realisation we took from the physical models was that the logic of spatial frames also applies to our multi-layered system and the further interlaced the beams, the more stable the system. However, typical space frame joints cannot be achieved in our beam geometry.

To accomplish braced interlacing, hexagons and triangles in different layers were chosen for further experiments.

The overriding dependencies for our system clearly emerged during this phase.

We defined the dependencies as loops, since a change of one design component bounces back to it via the change of another.

Loop 1: Beam, Pattern, Beam This loop started with physical models and was varified through a parametric build up of the beam in Grasshopper for Rhino3D. Loop 2: Joint, Beam, Pattern, Beam, Joint Once the technical and numerical script was written, structural and topological optimisation was performed, the joint was planned and tested on physical large scale models.

“

Loop 3 Panel angle, Beam After all components were envisioned in and set to certain dimensions, the beam parameters were further exploited to depart from a technical planning into a architectural and spatial value.

Generally, the design itself gave us as deisgners constant feedback through the prototypes. Additionally, we asked for expertise feedback from a computational designer at IFA TU Berlin and former DIA Dessau, a structural engineer from UDK Berlin and two wood engineers from HNE Eberswalde at different stages during the design and fabrication process.

„

After all, nothing is more fundamental in design than formation and discovery of relationships among parts of a composition.

William J Mitchell and Malcolm McCullough, Digital Design Media, Van Nostrand Reinhold (New York, NY), 1991.

METHODS

PHYSICAL

DIGITAL

LOOP 2 LOOP 3

LOOP 1

Karamba

Fusion360 topos Kuka prc

pattern

beam

pattern

Figure 13: Non-linear design process

beam

beam

joint

beam

joint

Kuka prc

beam

pattern

beam & joint

beam & joint

cell design

beam

beam

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30

Paper Model Trials (Beam & Pattern)

Figure 14: Beam iterations for pattern variations

Figure 15: Paper model A: perspective and plan

Figure 16: Paper model B: perspective and plan

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Figure 17: Paper model C: perspective and plan

Figure 18: Paper model D: perspective and plan

Figure 19: Paper model E: perspective and plan

DESIGN DEVELOPMENT

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Non-linear Design Process As previously explained in the methods, we did not face a linear design process in this thesis. The exact dependencies of the main design aspects and their external influences are depicted in figure 20.

Mostly, the external dependencies stem from the system requirements that bring along material specifications or machine parameters to name a few. In each depicted loop, our main decisions are laid out with arrows pointing towards the following one they are influencing.

In this chapter, we extensively touch upon each loop as in its main design aspect, its dependency and resulting influence.

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standardised timber panel 2,40 x 2,07 m

max. beam length 2m

thin profile size

modular system

braced pattern for structural system

hexagonal, triangular pattern

2 layers

self-interlocking

19mm

layout optimisation

z axis securement interlocking component

beam design column connection

Y shape

smooth machine path

pattern

beam >3 axis CNC 7 axes robot with varying milling heads

digital fabrication Figure 20: Design decision map

simple assembly

joint

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PATTERN

Reciprocal Pattern Development The reciprocal pattern was initially tested on paper models from simple geometries as well as different coloured line drawings to understand the consideration of two layers.

We learned from the paper models that a hexagonal grid on its own shows multi-directional instability. It was evident that the second layer needed to be organised counter-directionally, which is an obvious bracing method, especially in space frames (Figure 21e). It also became clear that the hexagonally arranged beam needed to be connected at the center point where shear forces are at a maximum (Figure 21d).

The location and rotation for this second stiffening layer was then tested in Grasshopper making it possible to quickly change the parameters and see the effects.

Through extending the lines of the second layer lines into the adjacent cell (Figure 21f.), another braced triangle emerges under a fan of the hexagon above. This provides extra bracing across the entire pattern.

a. Hexagonal grid edges for a fan

b. clockwise shift of nexors (translation method)

c. asymmetrical shift of fans in the pattern

d. nexor centre point location for second layer connection

Figure 21: Pattern Evolution

PATTERN

e. installation of the second layer in a reciprocal principle

f. rotation and extension of the second layer beam

g. three-dimensional connection of both layers

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Figure 22: Cardboard model of the pattern evolution

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Figure 23: Cardboard model of an alternative pattern option

Figure 24: Cardboard model of the chosen pattern

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PATTERN PARAMETER

a. EL2 - 0.2 m Extension 2L - 0.15 m

Offset 2L - 0.45 m Rotation 2L - 100°

b. EL2 - 0.4 m Extension 2L - 0.2 m

Offset 2L - 0.4 m Rotation 2L - 110°

c. EL2 - 0.4 m Extension 2L - 0.1 m

Offset 2L - 0.1 m Rotation 2L - 90 °

d. EL2 - 0.3 m Extension 2L - 0.35 m

Offset 2L - 0.15 m Rotation 2L - 100°

e. EL2 - 0.2 m Extension 2L - 0.7 m

Offset 2L - 0.45 m Rotation 2L - 120°

f. EL2 - 0.4 m Extension 2L - 0.6 m

Offset 2L - 0.6 m Rotation 2L - 100°

Figure 25: Pattern iterations through the change of parameters in Grasshopper

PATTERN PARAMETER

g. EL2 - 0.25 m Extension 2L - 0.5 m

Offset 2L - 0.4 m Rotation 2L - 110°

h. EL2 - 0.4 m Extension 2L - 0.25 m

Offset 2L - 0.2 m Rotation 2L - 90 °

i. EL2 - 0.3 m Extension 2L - 0.4 m

Offset 2L - 0.2 m Rotation 2L - 120°

j. EL2 - 0.2 m Extension 2L - 0.7 m

Offset 2L - 0.6 m Rotation 2L - 60°

k. EL2 - 0.4 m Extension 2L - 0.5 m

Offset 2L - 0.5 m Rotation 2L - 60°

l. EL2 - 0.4 m Extension 2L - 0.7 m

Offset 2L - 0.4 m Rotation 2L - 60°

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BEAM

Beam Design One of the biggest design challenges designing a multiply reciprocal frame is to define a main component. From a very early stage, we used a high and thin section in our practical model exploration, yet without a clear scale, as the pattern studies were focused on the relation between parts and not on the parts itself.

Manageable and producible dimensions of the beam play a crucial role in the whole design process as well as in the fabrication and future assembly.

The double layered system consists of two main beams; first layer-beam and the second layer-beam. Our focus was located on the design of the first layer-beam, as we also term it Y-beam, which overreaches both layers and presents a geometrical challenge in its formal design.

The complexity of the geometry was one of the drivers for choosing the material. Planar timber boards were

chosen in an early design stage.

The length of the first layer-beam is based on the sum of the hexagonal cell radius, engagement length (EL2) and extension length of the end of the beam (EL1).

The length of the second layer-beam is linked to the size of hexagons in the grid by the distance between the two second layer-beams in the neighbour cell, since they are interconnected. The length of the second layer beam was set to the maximum of 2 meters and the length of the first layer beam calculated accordingly in its relation.

The division of the Y-beam into three components was tested to elongate the span and for better use of the plane material (Figure 26). However, the division of the components into 3 parts and their reciprocal connection create a weak point in the centre of the beam.

Figure 26: Division of the beam into components

Figure 27: First layer-beam

Figure 28: Second layer-beam

BEAM

Parametrical Build-Up The parametrical definition of the system is based on the hexagonal grid. Firstly, the essential fan out of the first layer-beams is defined.

A triangular pattern of the second layer is created by an offset of every first layer fan (Figure 29).

Every intersection point within the pattern results in a notch point of the beam; the pattern lines are divided into segments by every intersection to generate a polyline, which define beam profile line later on.

Fan configurated out of three 1st layer beams

Intersection of the line in the pattern informs the notch points on the beam

Each direction of the fan is a data tree branch

Extension of the beam profile by EL1 and EL2

Figure 29: First layer pattern build up and its connection to the first layer beam

The main advantage of this operation is to specify all notch points of each beam in a separate data list in a certain order. This simplifies the further operation for the computational beam definition.

The final definition of the second layer beam uses only translation (offset) operations in the code (Figure 30). For the second layer beams, an offset instead of a rotation operation was used in order to keep the same notch angles for all joints.

Offset to create the 2nd layer

Location of the intersection points for members in two different cells

Figure 30: Offset of the second layer and the problem of interconnection

Mapping the points in the beam lists

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BEAM EVOLUTION

Technical Beam Build-Up The advantage and the challenge of our system are its parametrical connection between the designed parts. The first loop represents the mutual influence between the forms of the notch, beam and pattern.

This means, the desired design changes in one element can be only achieved by equally considering the other elements.

The notch form, for example, which by intersection of the different beam profiles can result in a too deep notch (Figure 31, case 1); unclean, overcomplicated for the fabrication form (Figure 31, case 2); clean simple form, created by placing a specific segment (notch base line) on the beam profile (Figure 31, case 3 and 4).

The advantage of changing the beam profile insists in the possibility of creating a strong section with no additional height added by the notch, and minimising the notch depth. Despite that, shifted notch on points all beams in each layer are intersected in one common XY-plane.

Case 1: a straight beam profile results in a deep notch thus weaker section Figure 31: Beam evolution

Case 2: the shifted notch points result in a curved beam profile; the notch depth descreases, but the notch form is unclean

BEAM EVOLUTION

Case 3: notch form and depth are optimised by adding a notch base line segment to the beam profile line

Case 4: the beam outline is optimised and smoothened for better structural performance and fabrication results

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BEAM PARAMETERS

The Parameters Multiplex boards were chosen due to strong cross-laminated interior texture and according together with this material choice, all beam parameters (Figure 32) can be varied through the following inputs: EL – engagement length, distance between two neighboured notches; BA and NA – beam and notch angle, according to the definition of the system at the same angle of 120°; ND – depth of the notch, influence the beam profile; NB – notch base line, a straight line put on the curvy beam outline to avoid unclean notch shapes; SH – section height; MW – width of the multiplex board; ZD – distance between the profile of the first layer beam and its arm or between the both layers.

Figure 32: Beam input parameters in meters

BEAM PARAMETERS

MW

EL1

EL2

SH

NA

EL2 EL1 NB

ZD ND

BA

E/2 EL2 EL1

EL1 EL4

MW

SH

EL3 EL1

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FUSION 360 TOPOLOGICAL ANALYSIS

Analysing the Beam Geometry After the rough beam geometry was set and shaped by the pattern and connection parameters, Fusion360 was used for a rough topological and structural check-up of the Y-beam.

For this, a single beam was simulated with its point loads of the beams it is supporting as well as with the support points where it is placed on top of another one (Figure 33).

Each load was calculated at the half of single beam‘s weight using 18mm birch multiplex board (Figure 33).

In a topological analysis report, a value towards 1 stands for areas in the model which are necessary to withstand the applied load (Figure 34).

A value towards 0 stands for geometry areas that are not absolutely necessary for the load bearing capacity.

The initial value of this variable for all model elements is 1. Therefore, areas that must be maintained at the constant value of 1 [5].

Figure 33: Load and support cases in the Fusion360 Y-beam model

Figure 34: Fusion360 topolocigal analysis of the Y-beam

applied loads and suppurts

mass ratio/ criticality

FUSION 360 STRUCTURAL ANALYSIS

Stresses and Deformation Simulation As a visual output from the brief structural analysis, it was important to see the shear forces as well as the deformation through the applied loads.

The stresses in the beam are indicated in Megapascal, equal to 100N/ cm². The maximal stress at the notch base counts approximately 0,38 MPa or 3800 N/cm² (Figure 35). stress in MPa

deformation in mm

Figure 35: Y-beam stresses simulation in Fusion360

Figure 36: Y-beam deformation simulation by Fusion360

As for the deformation, it becomes clear the that position of the arm that carries a load is deformed the most. Yet, the deformation is kept rather small, at about 0,004mm from the original shape (Figure 36).

49

50

JOINT - LAP JOINT

Advantages of lap joints in reciprocal frame structures

Interlocking Joint Testing

• • • • • •

In an early stage of the notch design, the possibilities of fabrication with a 3 axis milling machine were tested.

The strategy to reduce the complexity in the fabrication process while producing the notch in a 120° angle to the beam, was to inclinate the surfaces of the notch only in one direction. This would help to avoid rotating the element on the work bench in the fabrication process.

Angle control resulting in the possibility of free patterns and forms Easier subsequent erection on site Pre-cut in a controlled environment No forces on material edges No other joining element needed if structural balance is given A member depth smaller than the eccentricity results in required notching (Godthelp, 2019 p.63) • Reduced machine time and cost through simple geometry • Simple manufacturability in terms of the geometric cut • Transfer of shear and axial forces is enabled (Godthelp, 2019 p.80)

Disadvantages of lap joints in reciprocal frame structures • Decrease of structural height resulting in a weaker section • High precision needed with angles • By notching the beam at the point of the highest shear stress, the beam is weakened at its least desirable place. Each beam contributes with its own weight in a point load applied to the supporting beam. (Popovic, Larsen, 2012)

Our response/ solution • Decrease notch depth and reshape beam to connect all beams in one XY-plane • 7 axis milling machine for the notch fabrication

The complete documentation of the joint design through prototyping is detailed in the Fabrication and Prototyping chapter.

To close the resulting openings and lock the elements in all directions, additional wedge-shaped elements were designed. There are several variants of these are shown in figure 37, with either one or two additional elements.

Despite the advantage of a wider prototyping and fabrication possibilitiy by using more available and common 3 axis machine, the wedges are quite complex and small in their geometry. This can result in too little tolerances in the entire system, causes assembly problems and breaking of the wedge geometry.

JOINT

Figure 37: Examination of interlocking wedge elements

51

52

DISK

Additional Locking in the Vertical Axis The importance of this additional element surfaced when building the 1:2 prototype of one cell (Figure 38 left).

While assembling one nexor at first (Figure 38 right), the beams tended to tilt sidewards despite the angled notch. Seemingly, the notch does not provide enough angled surfaces to keep the entire beam into place and to take on the high force of the entire beam. Moreover, if the press fit of the material is slightly too big, the connection becomes lose and critical (Figure 39 left).

For a facilitated assembly, a locking element in the Z-direction would be needed.

In a dome-like overall form this would most-likely not be a difficulty, but since this structure is all planar, the elements are at no point secured vertically.

Having tried to tackle this problem in the notch design with wegdes, we were advised against a Z-axis lock in the connection point by the wood engineers. Quick solutions were tried in the workshop that vi-

Figure 38: 1:2 prototype of one cell

Figure 39: Ad hoc soltion for a Z-axis locking due to fabrication tolerance

DISK

sibly did not prove to work either (Figure 39 right).

Consequently, this was solved through an additional element we termed as ‚disk‘.

This triangular, horizontal element is slided into the first layer beam at its thickest part under one of the reciprocal fans (Figure 40).

Through a 70° rotaton, the disk locks itself into the horizontal beam notch (Figure 41).

Generally, this is a strong solution, yet if the structure is scaled down in size, this could also become too thin and unfirm during assembly.

~70°

Figure 40: Disk placement before the locking rotation

Figure 41: Disk rotation to vertically lock it in the Y-beam

53

54

COLUMN

Proposed Column Design The sophisticated and dynamic design of the roof structure is complemented by a clean and conventional column solution.

The point of departure in the design was that we saw the opportunity in the disk element enabling a horizontal piece in the structure to connect to. As a consequence, there are two options in terms of placement of the column beneath the structure as shown in figure 42. One option is at the centre of one cell and the other is at the intersection point of three adjacent cells.

The assembly principle follows traditional wood joinery with two Multiplex

planks bracing another one at each side with additional bolts. The cantilever beams reaching out to the disk are double width as they take on the highest forces. Each cantilever beam is braced twice by a couple of column legs each. The principle is shown in Figure 43.

The bench elements are not only an added social quality, but they function structurally essential as plate slabs to keep the columns in position.

Figure 42: Optional column position in the structure

Figure 43: Column build-up principle

Figure 44: Axonometric view of the column below one cell

55

0,50m

3,60m

COLUMN

1,60m

Figure 45: Exploded axonometric view of the column and its assembly components

Figure 46: Column elevation

56

STRUCTURE’S BORDER

How to End an Endless Pattern?

Traditional reciprocal roofs are erected on top of a set of walls and latest reciprocal frames have been built as self supporting curved surfaces or domes. As set in the system requiremets, Nexormorphosis is neither covering a set geometrical space, nor is it equipped with a global tension element around the border.

Moreover, we are facing the challenge to ‚cut‘ an endless pattern that relies on its closed cells and interlaced double-layered set up.

Reciprocity functions on the principle of the balance between supporting and being supported. Consequently, this logic is crucial to keep when cutting into the pattern.

Four sides of the cell were chosen to become subject to cutting. The ideal position for a cut is determined with respect to the least cut beam cantilever and most reasonable proximity to reconnect cut beams (Figure 48).

Closing or reconnecting one cut cell is accomplished through additional

border elements. Each of the four sides requires at least one extra beam that is carefully positioned to ensure reciprocity (Figure 4952). This means a border beam is connected through a lap joint to a cut beam at least three points.

These four cutting sides of one cell can be adopted to any form of non-rectangular curve that ought to be used as a structure outline (Figure 47). If a free form curve is determining the final form, the cutting curve position needs to be adjusted to the set position of the planned border pieces.

Figure 47: Possible final forms through border beams

STRUCTURE’S BORDER

The following diagram shows the optimal cut for each side of the cell.

The light grey side remains in the structure and dark grey side will be trimmed. The colours refer to each side and are used in the three-dimensional cutting procedure representation on the following spread.

East West South North

Figure 48: Border cutting line for each side of the structure

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58

a. East side cutting surface Figure 49: Structure‘s East side border solution

b. East side cut and dispatched beams

c. East side border beams

a. West side cutting surface Figure 50: Structure‘s West side border solution

b. West side cut and dispatched beams

c. West side border beams

59

a. South side cutting surface Figure 51: Structure‘s South side border solution

b. South side cut and dispatched beams

c. South side border beams

a. North side cutting surface Figure 52: Structure‘s North side border solution

b. North side cut and dispatched

c. North side border beams

60

FUNCTIONALITY: SUNSHADE

Parametric Variation Among others, one of the system requirements was to have modular but identical components to reach a flat span roof. As shown in figure 53, this logically results in a very homogenuos visual appearance even though it is parametrically designed with the option to create a heterogenous image.

By adding light panels to the wide cell openings at the top layer and triangles at the bottom layer at different locations within the system, a more losened and varying look can be achieved.

Functionally, covering these gaps can serve as sun protection through light textile applications.

The exact position and angle and its resulting shadow opportunities are tested in the following study (Figure 54 and 55). It becomes apparent that angled panels can be enabled through an adjusted beam geometry.

Figure 53: Sun shade panel variation and their location in the system

61

Elevation of alternating panel angles

Angled Panel Opportunities

Plan view angled panels and resulting shadows

Plan view shading panels in the structure

Elevation angled panels in structure Figure 54: Sun shade angle variations

Figure 55: Exemplary beam variations through angled panels

62

Reaching Alternating Angles and the Resulting Beam Geometries Within one cell, there are many options to tilt the panel by extending the first layer beam‘s ‚arm‘ that changes the second layer position which that the panel is attached to. Either two sides and therefore two beam arms are stretched downwards or one is stretched downwards and the other two stay in place (Figure 56). This operation allows for angles to six clear directions. These angles can even be defined further by adapting the height of one of the equal two beams to be at a height between the other.

Angle: 9,2°

a.

Z-distance: 45cm

The Z-distance between the centre line of the first layer top and bottom arm line is 23cm at a flat panel state. Figure 56d. shows the largest angle that is defined as possible for the structure as the 1st layer beam‘s structural soundness decreases as the form modifies too much.

In the Grasshopper script, the angle serves as an input to alter the overall structure.

Angle: 7,3°

b.

Z-distance: 39cm

Figure 56: Angle options of hexagonal panel and the altered beam forms

Angle: 8,4°

c.

Z-distance: 42cm

Angle: 14,0°

d.

Z-distance: 55cm

63

Sunshade and Eccentricity Due to the rotation of the sunshade panels, the eccentricities between the different cell members increase (Figure 57).

As a number range is used to create a rotation of the panels, meaning that every angle diferenciates from the other, the eccentricity has to be recalculated for each pair of beams.

To overcome the problems in data tree structure, a simple ‘geometrical’ way of relocating points is being used (Figure 59).

Figure 57: Eccentricities created by the rotation of the sunshade panels

Beams are remapped in the lists due to their orientation Figure 59: Grasshopper code extract

Figure 58: Remapped points and new beam profiles

The neighbour points are detected and divided into new groups

Every relocated point is inserted in the list of verticies of every beam

The new beam profile is set

64

FUNCTIONALITY: SUNSHADE

N

0° 15°

345°

30°

330°

Zones of Use and Activities as Shading Angle Input

45°

315°

To determine the panel angles in a more reasonable manner, the roof‘s activity zones during the day can be assigned to areas in the structure (Figure 60). To provide ideal shadows for each time of the day, the sunshades in these areas are then angled accordingly.

60°

300°

75°

285°

19h

Moning 11:00h Museum staff having a coffee and a cigarette to start the day.

Lunchtime 13:00h Museum visitors enjoy their lunch outdoors as a break from the exhibition.

Afternoon 16:00h An elementary school class revisits their experiences from the exihition in a circle outside.

Evening 17:30h Museum guests after their tour as well as passerbys sit down for an espresso or aperitivo in the evening sun in the backyard.

7h

18h

W

270°

90°

8h

17h

9h

16h

10h

255° 15h

105°

11h 14h

12h

13h

240°

120°

135°

225°

210°

150°

195° 180°

S

Figure 60: Exemplary activity zoning for a free form structure

165°

E

65

FUNCTIONALITY: SUNSHADE

Adaption of Shade Panels to Zones To reach ideal (large) shadows under the roof, the panels need to be at a steep angle at a high solar altitude and rather flat at a low solar altitude.

Once the zones are determined, the angle input for each of the zones is set within a small range. This range ought to vary the panels‘ rotation for a more diverse and dynamic architectural landscape of textiles in the roof (Figure 61).

To keep the structure structurally sound and not too visually different, the cells at the border and around the columns are eliminated from any zoning determination.

12h

11h

13h 14h

10h

9h

15h

8h 16h 120°

7h

150°

135°

165°

S

180°

105°

195°

E 90°

17h 210°

75° 225° 18h

60°

240° 45° 255°

19h 30° 270° 15° 285

N

300° 145° 330°

Figure 61: Envisioned sun shade rotation according to activity zoning

315°

W

66

Grasshopper Logic for the Panel Angles The rotation of the sun shade panels is controlled two inputs: Activity zoning and the optimal range of angles for the sun position. To create an envisioned ‘light landscape’ and control the interconnected system parameters, a clear data input which follows the logic of the data tree structure of the system must be generated. The zones are defined in Grasshopper by the input curves. The panels are divided into data lists according to their position (inside or outside a specified zone). Each zone receives its own numerical input according to the optimal rotation angle and the desired aesthetic.

The final rotation result can be different by the same numeric (list of angles) but different graphic (zone curve) input due to the logic of data organisation in Grasshopper (Figure 63).

Figure 62 shows two different tested strategies to create a desired lists of input for the specified activity zone.

Figure 62: Script for the generation of the input angles

67

14°

12.5°

11°

9.5°

8°

2°

3.5°

5°

6.5°

8°

9.5°

9.5°

8°

8°

6.5°

6.5°

Figure 63: Angle variations to create a diverse landscape in the structure

5°

5°

6.5°

9.5°

3.5°

3.5°

5°

11°

2°

3.5°

3.5°

12.5°

0°

5°

2°

14°

0°

6.5°

0°

8°

PROTOTYPING AND FABRICATION

70

MACHINE AND FABRICATION PARAMETERS

Subtractive Digital Fabrication in Timber with a 6(+) Axis Robot The integration of digital fabrication into architectural design and production spawns a variety of geometric and functional opportunities. CAD (computer-aided design) methods are now conntected to CAM (computer-aided manufacturing) methods and with the help of design and machine operation visual interfaces such as Grasshopper for Rhinoceros 3D, these methods can be applied across all professions without extraordinary expertise knowledge.

Large fabrication robots we have been able to use are originally employed in car procution processes, but have now entered the architectural academic and small-scale construction realm.

In our case, the robot is used for subtractive manufacture as traditional timber manufacturing is usually performed. The multipex sheets are layed out flat and the robot with a milling head acts as a saw.

Conventional CNC milling machines

can perform this exact procedure and are widely emloyed in carpentry, yet they are limited to 3 axes.

For the structural pattern of Nexormorphosis, the lap joints require a cut notch into more than 3 directions, whereas the beam outline could be conventionally cut with a CNC machine. The six axes shown in the image on the opposite page (Figure 64) allow all-directional workpiece manipulation. To shorten the work and production flow and to avoid inaccuracy in the press fit, it was the ambition to manufacture all pieces with the same machine in one operation. This means no moving or turning of the workpiece to reach certain angles for milling.

For this, we requested cooperations with either local carpentries or academic institutions in possession of a large manufacturing robot.

The availability of these machines is however still limited due to spatial, safety and supervision requirements and their high costs.

Additionally, the idea of a universal recipe as manufacturing instructions that can be posted and produced anywhere is limited by the machine‘s installation.

Fortunally, our successful cooperation with the Faculty of Wood Engineering‘s timber workshop at Eberswalde University for Sustainable Development is equipped with a KUKA KR90 KR170 hanging down from a linear axis allowing a 7-axis movement in a rarely large build space of about 6 by 10 meters.

This movement range allows to scale the structure or to use larger sheets to reduce waste material.

The multiplex boards for the 1:1 cell demonstrator measure 1,5 x 3m, but with a differently installed milling robot, this size would most probably have to be decreased.

The general difficulties of working with these high force machines are singularities and in our case the position of the linear axis. Singularites are positions of the robot to reach

a certain point that lead to the collinearity of two of its axes. The operation code is unable to distinguish which of the two axes the movement is allocated to [6].

In the prototyping iterations we experienced a more inaccurate milling resolution if the linear axis movenent was included in the movement for the notch milling. Accuracy increased after ‚locking‘ the linear axis to one position while milling the notches.

This is only one example, and similar to all prototyping experiments, every case of application demands tweaks and adaptions according to the available machine and its practised behaviour.

-

A1

71

+

r ea

in + l

is ax

“

Prototype production means more than just the fabrication following completion of the design phase. Rather, it means taking into account material [and machine] performance at the very beginning of the design process throughout the entire fabrication process.

+ A2 -

+

A3 -

Philip F. Yuan, 2017

-

+ A5 Figure 64: 7axis distribution at HNEE Technikum Kuka Robot

A6 +

-

+ A4

„

72

MACHINE AND FABRICATION PARAMETERS

Code and Toolpath Logic The Assoctiation for Robots in Architecture developed a Grasshopper for Rhino 3D plug-in called ‚Kuka I prc‘ that allows robot control through the parametric input interface in Grasshopper. This was used to load the prototyping geometries from Rhino and allocate toolpaths to cut the beam‘s outline and notches from the timber boards.

Three different rides and therefore toolpathes were written and sent to the robot sequentially.

The first path is the beam outline without the notches at a 1mm depth to mark the outline on the timber board. This is to indicate the beam‘s position on the board in order to screw each beam into the workbench (Figure 68 left). The robot‘s high force would otherwise move the workpiece off the workbench. We further created an operation code to mark the positions for the screws with a 1mm deep point on the workpiece. This operation can be run on a righer speed than the others since there

is no horizontal pressure on the milling head. The second iteration is an outline formatting at half of the material width to increase pressure on the milling head (Figure 65; top orange curve in figure 66; figure 68 centre). Milling the outline is called formatting. Following is a second formatting at the material‘s full width (Figure 65; bottom orange curve in Figure 66; figure 68 right).

The final path is cutting the notches at an angle including several downwards movements in a loop manner (turquoise curve in Figure 66). Each path has an additional component to manouver the ride to and from the toolpath start and end points in their curves.

Figure 65: Extract from a complete toolpath for a beam and its notches

Figure 66: Extract from the formatting and notch toolpath

MACHINE AND FABRICATION PARAMETERS

Code Parameters/ Inputs • Robot Type • Timber board size and its 0,0,0 coordinate in the set coordinate system of the robot.

• Geometries of workpieces to manufacture • Geometries‘ outline curve • Customised tool path for extra milling (notches) • Milling head radius (tool dimensions) • Milling head tip point

Figure 67: Grasshopper script for the tool specification input

Figure 68: First layer beam formatting in 3 milling depths

73

74

PROTOTYPING THE NOTCH - 1:2 SCALE The 1:2 prototypes were performed on a 9mm MDF sheet.

Figure 69: Fabrication nesting for the 1:2 prototype

lap joint notch

milling head diameter

notch angle

Iteration 1

8mm

120°/30°

9mm

Iteration 2

8mm

120°/30°

8mm

Iteration 3a

8mm

120°/30°

8mm

Iteration 3b

8mm

118°/32°

8mm

notch width

PROTOTYPING THE NOTCH - 1:2 SCALE

2D tool path and cut notch

3D tool path

3D cut notch in the beam

comments/ findings notch assembly is too loose, unwanted movement

notch assembly is still too loose and rotating sideways due to the ‚mickey mouse ears‘

satisfying result of the press fit, yet no bottom surface contact due to the tool diameter - notch width ratio

Figure 70: Toolpath for the 1:2 prototype

75

76

PROTOTYPING ONE CELL - 1:2 SCALE

Figure 71: Full assembly of the 1:2 cell prototype from above

Figure 72: Full assembly of the 1:2 cell prototype from below

PROTOTYPING ONE CELL - 1:2 SCALE

Figure 73: Notch prototype 1:2 iteration photos

Iteration 1

Iteration 2

Iteration 3a Iteration 3b

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78

PROTOTYPING THE NOTCH - 1:1 SCALE The 1:1 prototypes were performed on a 19mm MDF sheet.

lap joint notch

milling head diameter

notch angle

Iteration 1

10mm

120°/30°

17mm

Iteration 2a

10mm

120°/30°

18mm

Iteration 2b

10mm

120°/30°

18,8mm

Iteration 3a

8mm

120°/30°

18,6mm

notch width

Iteration 3b The settings and tool path stayed exactly like in iteration 3 Figure 74: Fabrication nesting for the 1:1 notch prototypes

yet the linear axis was set to the same proportional position for every beam.

PROTOTYPING THE NOTCH - 1:1 SCALE

2D tool path and cut notch

3D tool path

3D cut notch in the beam

comments/ findings too tight to assemble

outer edges rather sharp and hindering assebmly

conic form benefitial for assembly >loose top and tight bottom

Figure 75: Toolpath for the 1:1 notch prototypes

inaccuracy at the curved tops due to the loose linear axis

79

80

Figure 76: Robotically milling the angled notches

Figure 77: Series of 1:1 notch prototype

81

Figure 78: Notch prototype 1:1 iteration photos

Iteration 1

Iteration 2

Iteration 3a

82

1:1 FABRICATION OF ONE CELL

Figure 79: Fabrication nesting first layer beams for the 1:1 cell

Figure 80: Snapshot of the first layer beams 1:1 production

1:1 FABRICATION OF ONE CELL

Figure 82: Milling head used for the 1:1 production

Figure 81: Fabrication nesting second layer beams for the 1:1 cell

Figure 83: Snapshot of the second layer beam 1:1 production

83

84

1:1 FABRICATION OF ONE CELL

The full production process of the 1:1 cell was recorded and compiled to a short video available to watch here:

https://youtu.be/A6sShceIJXs

The assembly video of the 1:1 cell is available to watch here:

https://youtu.be/2rlDr66-wa0

Figure 84: Required elements for the assembly of the 1:1 cell

1:1 FABRICATION OF ONE CELL

Figure 85: Assembly process of the one cell

85

DESIGN PROPOSAL

88

COMPONENT CATALOGUE

a

roc

ip rec

n

m olu

c

o ipr

l ca

rec

Figure 86: Component Catalogue of each required elements for the structure, its border and columm

ll

ce

r

rde

o lb

COMPONENT CATALOGUE WEIGHT CALCULATIONS

reciprocal border

column

reciprocal cell

weight in 19mm weight in 41mm multiplyer

total weight in one cell

Kit components

area

1st layer beam 2nd layer beam connection disk

0,29m² 0,23m² 0,03m²

3,71kg 2,94kg 0,38kg

9 3 3

33,39kg 8,82kg 1,14kg

2x3=6 2x3=6 3 2x3=6 3 3 3 3 3

25,32kg 29,16kg 24,18kg 2,28kg 1,14kg 20,34kg 20,34kg 9,18kg 9,18kg

column beam inside column beam outside cantiliver beam two sided disk connector connection disk bench bottom layer bench top layer bench support outside bench support inside

0,33m² 0,38m² 0,29m² 0,03m² 0,03m² 0,53m² 0,53m² 0,11m² 0,11m²

4,22kg 4,86kg

border beam A border beam B.1 border beam B.2 border beam C border beam D.1 border beam D.2

0,25m² 0,29m² 0,33m² 0,23m² 0,28m² 0,29m²

3,20kg 3,71kg 4,22kg 2,94kg 2,58kg 3,71kg

birch multiplex (27,8kg/m²)

for one cell and column

birch multiplex (12,7kg/m²)

8,06kg 0,38kg 0,38kg 6,78kg 6,78kg 3,06kg 3,06kg

43,35kg

141,12kg

89

90

STRUCTURAL ANALYSIS

Structural Behaviour of the System To analyse the structural behaviour of the system Karamba software for Rhino and Grasshopper was used.

The span of 9 to 16 m was analysed (aproximately 4 to 8 cells).

Different behaviour was detected according to the relation of the distance from the supports to the end pieces of the structure.

For this, the cross section of the elements was set to 0,018m in with and 0,12m in height.

Case 1

Case 1 The first analysis case is a rectangular shaped system supported by 4 columns (Figure 87). The dimensions of the form are 9,8 x 8,3 m (5 by 4 grid cells) which cover an area of about 81 m². The span which has been tested reaches 5 cells or approximately 9,8 m. The maximal displacement in this case amounts to 2,25cm.

Figure 87: Case 1: displacement and axial stress

PROOF OF SPAN

Case 2

Case 2 A second case is a bigger system supported by 8 equally distributed columns (Figure 88). The dimensions of the form are 9,8 x 12 m (5 by 6 grid cells) and a covered area of about 117 m². The maximal span which has been tested in this case reaches 6 cells, approximately 11 m. The maximal displacement in a beam is 1,23cm.

Figure 88: Case 2: displacement and axial stress

91

92

STRUCTURAL ANALYSIS

Case 3

Case 3 The next two cases are based on a free form system covering an area of approximately 182 m² (Figure 89). Eight columns support each system, the maximal span reaches about 15 m.

The maximal displacement locates on one of the edges of a cut cell and counts 7.97 cm.

Figure 89: Case 3: displacement and axial stress

PROOF OF SPAN

Case 4

Case 4 In this case the displacements were influenced and tried to be improved by a different column distribution (Figure 90). Without adding any new supports, the maximal displacement was lowered to 6.50 cm.

Figure 90: Case 4: displacement and axial stress

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94

Build-Up Proposal In order to simulate and test the parametrically defined structure at the proposed shade sun shade in an architectural quality, we chose the backyard of the Maritime Museum in Barcelona as a deployment location. Through the connection to the museum and the public realm via the connecting street, its is naturally a space where people rest and stay during the entire day. This proved very suitable to sample the planned sunshading according to the activity zones as well of an overall wide span strucure (Figure 91).

DESIGN PROPOSAL DRAWINGS

Figure 91: Plan view drawing

95

96

Figure 92: Section drawing

DESIGN PROPOSAL DRAWINGS

97

98

Figure 93: Perspective view from sitting level

DESIGN PROPOSAL VISUALISATION

99

100

Figure 94: Perspective view from child eye level

DESIGN PROPOSAL VISUALISATION

101

102

Figure 95: Bird-eye perspective view

DESIGN PROPOSAL VISUALISATION

103

CONCLUSION AND OUTLOOK

106

REVIEW AND CONCLUSION

In this conclusion, we want to reflect upon three aspects we aimed to appoint with this master thesis.

Firstly, the adherence of the system requirements with regards to the final design result; secondly, the feasibility of a digital workflow; and thirdly the prospect to implement more design processes like ours in university projects.

Due to the fact that a clear bottom-up design approach was chosen for this thesis, the system requirements could be defined in the first stage and initial experimenting went directly to the beam itself.

This crucially helped to become clear about each parameter and its dependency to others influencing the overall form. Knowing these parameters and knowing how to control and adapt them facilitated meeting the set requirements.

Once the designer parametrically masters a design frame, the concept can be strengthened through these carefully chosen parameters for a design within a large spectrum

of possibilities.

Reviewing our system requirements, we can state that we reasonably selected a set of parameters to accomplish them. However, this counts for the numerical and technical design input, but not for the aesthetic and functional one.

In terms of wide span and size of the result, we selected parameters that are in fact still feasible for a human assembly, but through this requirement we limit the function to overcome a temporary use pavilion.

Yet, the roof size stays unlimited as the system can be arbitrarily extended to all sides if columns are continuously placed. This proves the advantage of a flat span and column principle in contrast to pre-defined dome shapes.

Once the chosen parameters for the beam section, therefore the structure’s size and therefore the span extend a certain size, the requirements of human assembly, weight performance and machine space cannot be met anymore. This is the reason why it is substantial to be

aware of all dependencies between the technical design parameters.

As laid out in our methods chapter, the goal was a nearly uninterrupted digital workflow we quickly realised that the employment of such can only be realised from a certain stage onwards. As touched upon above, a certain set of known parameters is essential to set up design script.

For us, knowing the fabrication parameters was most fundamental to further design decisions in the process. If the fabrication method is not considered as a design input, there are two ways the process can develop ahead: A) the morphological space of the machine is exited or miscalculated, or B) the design stays within its ‘comfort zone’ without having considered material and planned a precisely tailored production.

Lastly, we realised that it is challenging to preserve the mindset to stay within a digital workflow without departing from it at any complica-

ted point. Especially because we were educated to design with rather static 2D techniques that do not give much freedom to change the design in the process.

We are aware of the fact the consultation of too many production experts in the design process can lead to a too technically restricted design, but for our case, we made the experience that expert knowledge in the design process was essential for further decisions.

Generally, we believe that the connection to experts in fabrication and also computational design should be implemented into architectural education. For us, architecture as ‘the art of joining’ remains too far in the background to the detriment of student’s mindsets in an architectural education that is rather politically influenced. The aspect of exploration through seeing, touching and understanding ought to be revitalised.

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108

Figure 96: Potential structural behaviour in a building scale

OUTLOOK

Further Potential The presented design research development shows the potential of a structural roof system that, through its geometry, can be quickly erected by a human.

The exemplary application case as a sun shelter in Spain is suitable in terms of scale and optional temporary use.

The following aspects we think have the potential be developed further if further research effort on them is realised.

Linking back to scalability, it can be tested to which extent the structure can be applied in a building scale and also integrated into a building.

The structure‘s overall planar shape suggests a light-weight floor slab construction that can be covered with additional stability and flooring layers. It can be examined whether the double-layered system has potential for a slab use where the intermediate space accommodates insulation or the like. The connection or support on a wall will have

to be tested. The scaled cardboard models showed no disadvantage in placing the strucutre on other shapes than the proposed column.

Nevertheless, the scale of the elements and therefore the structure need to be reconsidered for a building implementation since the current size allows for a maximum of a 4 cell wide span. Scaling up the design brings along the question of human assembly and its weight limits.

The hexagonal and triangular pattern can geometrically comply with the standard building shapes of rectangular forms if the border is particularly adopted and kept under control.

The beams‘ cut ends could be tightly clamped in a customised formwork from concrete for example, but the exact joint of the two materials would have to be elaborated.

Another option for the edges would be a global timber plank placed orthogonally to the beam ends with customised slots and a lap notch

principle for each beam end.

This advanced idea was briefly checked in an examplary digital model of 9 x 12m with the structural analysis tool Karamba for Grasshopper (Figure 96) For this case, the beam section was increased to 2,1 x 15cm since the section definitely has to be scaled up for a building scale application. The deformation would otherwise be even more distinct.

On the contrary, if the system is deployed in buildings, the additional function of the sun shade becomes redundant and therefore the sophistication in the changed beam parameters gets lost.

But this exact parameter that is relevant for the panel angles, can be studied regarding its effect on the overall structural height and restulting stability. Does this concept of an increased overall structural height lead to a lager span?

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We would like to express our sincere gratitude to the Faculty of Wood Engineering at Eberswalde University for Sustainable Development and Prof.

Dr. Klaus Dreiner, for the opportunity to test and robotically fabricate our physical prototypes at their Technikum workshop.

We extraordinarily appreciate Tassilo Goldmann and Tim Peters for their continuous willingness, interest and endurance to support us during the prototyping phase and introduce us to robot control.

We wish to sincerly thank our supervisor Prof. Dr. Ignacio Borrego and our advisor Sven Pfeiffer for their consistent valuable conceptual guidance on this thesis.

Finally, our great appreciation goes to Jakob, Jonas and Tiago for their all-time advice and support.

ACKNOWLEDGEMENTS

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REFERENCES & LITERATURE

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LITERATURE REFERENCES Ahlquist, S., & Menges, A. (2011). Introduction. In S. Ahlquist, & A. Menges. Computational Design Thinking. Chichester: John Wiley & Sons.

Asefi, M., & Bahremandi-Tolou, M. (July 2019). Design challenges of reciprocal frame structures in architecture. Journal of Builduing Engineering 26.

Baverel, O. (2012). A Review of Woven Structures with Focus on Reciprocal Systems - Nexorades. International Journal of Space Structures. Vol. 25, Iss. 4.

Douthe, C., & Baverel, O. (2014). Morphological and Mechanical Investigation. Nexus Network Journal, 16 (1), 191-206..

Glasner, B., & Ott, S. (2013). Wonder Wood: A Favorite Material for Design, Architecture and Art. Basel: Birkhäuser Verlag GmbH. Hemmerling, M., & Nether, U. (2013). Digitale Architektur: Vom Entwurf zur Produktion. In U. Pottgiesser, Produktentwicklung Architektur : Visionen, Methoden, Innovationen (p. 24-33). Basel: Birkhäuser.

Leach, N., Menges, A., & Yuan, P., (2018). Introduction. Digital Fabrication. Shanghai:Tongji University Press.

Parigi, D., & Pugnale, A. (2012). Three-dimensioned reciprocal structures: morphology, concepts, generative rules. IASS-ApCS-2012 symposium: „From spatial structures to space structures“. Seoul.

Pawlyn. (2011). In Biomimicry in architecture. London: Riba publishing.

Peters, B. (2013). Introduction. AD Architectural Design, 222 (March/ April), p.10-15.

Peters, T., & Peters, B. (2013). Introduction. In B. Peters, & T. Peters (Hrsg.), Inside Smartgeometry - Expanding the Architectural Possibilities of Computational Design (p. 8-19). Chichester: John Wiley & Sons Ltd. Popovic Larsen, O. (2008). Reciprocal Frame Architecture (First Edition). Oxford: Architectural Press Elsevier Ldt. Pugnale, A., & Sassone, M. (2014). Structural Reciprocity: Critical Overview and Promising Research/Design Issues. Nexus Network Journal, 16 (1), 9-35.

Pugnale, A., Dario, P., Sassone, M., Sassone, & Kirkegaard, P. H. (2011). The principle of structural reciprocity: history, properties and design issues.

Proceedings of the „IABSE-IASS Symposium 2011: Taller, Longer, Lighter“. London.

ONLINE REFERENCES [1]

https://www.icd.uni-stuttgart.de/projects/icd-sewn-timber-shell-2017/#:~:text=The%20Sewn%20Timber%20Shell%202017,Performative%20 Design%20Methodologies%20based%20on accessed 05.11.2019

[2]

https://www.researchgate.net/publication/50838927 accessed 10.11.2019

[3]

https://kadk.dk/en/case/dermoid accessed 13.12.2019

[4]

https://www.wisaplywood.com/de/?gclid=Cj0KCQjwvb75BRD1ARIsAP6Lcqsj08eBkjtotFMUwjlVNCyyz4adSx3A3U3qU_h9OYQofzJaJxoubrIaA q9NEALw_wcB accessed 27.03.2020

[5]

https://www.ifte.de/lehre/fem/6_Software__FEM_-_Tutorial_-_Strukturoptimierung.pdf accessed 08.08.2020

[6]

https://www.universal-robots.com/articles/ur/what-is-a-singularity/ accessed 24.07.2020

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LIST OF FIGURES Figure

Title

Figure 1 Figure 2 Figure 3 Figure 4

Construction difficulty of a parametrically customised form Design approach through system requirements Binabo constructor made of bio plastic ICD Stuttgart Sewn Timber Shell 2017

12 13 17 18

Figure 5

Project of the Italian Pavilion for the 2010 Shanghai World Expo

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Figure 6

The Dermoid III

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Figure 7

Seiwa Bunraku-Kan, Puppet theatre complex designed by Kazuhiro Ishii. Photo: Kentaro Tsukuba

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Serlios slab solution. Sketch by A. E. Piroozfar

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Figure 8

Reciprocal Frame builduing by Yoichi Kan under construction.

Photo Yoichi Ka Figure 10 Seiwa Bunraku-Kan, Puppet theatre complex designed by Kazuhiro Ishii. Photo: Kentaro Tsukuba

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Figure 9

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Figure 11 Notched connection - Graham Brown Builduing

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Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17

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Cross-laminated interior structure of Multiplex Non-linear design process Beam iterations for pattern variations Paper model A: perspective and plan Paper model B: perspective and plan Paper model C: perspective and plan

Owner and Source Own representation Own representation Source: https://www.manufactum.de/binabo-a22906/ Photo by Bai Yu; Institute for Computational Desgin and Construction, Source: https://icd.uni-stuttgart. de/?p=21883 Photos by Attilio Pizzigoni, Source: https://www.researchgate.net/publication/50838927 Photos by Tobias Titz, Sources: http://designhub.rmit. edu.au/exhibitions-programs/convergence-transforming-our-future-design-research-institute Source: Structural Reciprocity: Critical Overview and Promising Research/Design Issues; https://link.springer.com/ content/pdf/10.1007%2Fs00004-014-0174-z.pdf Source: Olga Popovich Larsen Reciprocal frame architecture https://casaeco.files.wordpress.com/2012/03/reciprocal-frame-architecture.pdf Source: http://www.ricegallery.org/shigeru-ban Source: Olga Popovich Larsen Reciprocal frame architecture https://casaeco.files.wordpress.com/2012/03/reciprocal-frame-architecture.pdf Source: Olga Popovich Larsen Reciprocal frame architecture https://casaeco.files.wordpress.com/2012/03/reciprocal-frame-architecture.pdf Own representation Own representation Photo by Theresa Lohse Photo by Theresa Lohse Photo by Theresa Lohse Photo by Theresa Lohse Photo by Theresa Lohse

LIST OF FIGURES Figure

Title

Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25

Paper model D: perspective and plan 31 Paper model E: perspective and plan 31 Design decision map 35 Pattern Evolution 36 Cardboard model of the pattern evolution 38 Cardboard model of an alternative pattern option 39 Cardboard model the of chosen pattern 39 Pattern iterations through the change of parameters in Grasshopper 40 Division of the beam into components 42 First layer-beam 42 Second layer-beam 42 First layer pattern build up and its connection to the first layer beam 43 Offset of the second layer and the problem of interconnection 43 Beam evolution 44 Beam input parameters in meters 46 Load and support cases in the Fusion360 Y-beam model 48 Fusion360 topolocigal analysis of the Y-beam 48 Y-beam stresses simulation in Fusion360 49 Y-beam deformation simulation by Fusion360 49 Examination of interlocking wedge elements 51 1:2 prototype of one cell 52 Ad hoc soltion for a Z-axis locking due to fabrication tolerance 52 Disk placement before the locking rotation 53 Disk rotation to vertically lock it in the Y-beam 53 Optional column position in the structure 54 Column build-up principle 54 Axonometric view of the column below one cell 54 Exploded axonometric view of the column and its assembly

Figure 26 Figure 27 Figure 28 Figure 29 Figure 30 Figure 31 Figure 32 Figure 33 Figure 34 Figure 35 Figure 36 Figure 37 Figure 38 Figure 39 Figure 40 Figure 41 Figure 42 Figure 43 Figure 44 Figure 45

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Owner and Source Photo by Theresa Lohse Own representation Own representation Own representation Photo by Theresa Lohse Photo by Theresa Lohse Photo by Theresa Lohse Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Photo by Oksana Tyltina Photo by Oksana Tyltina Own representation Own representation Own representation Own representation Own representation Own representation

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LIST OF FIGURES Figure Figure 46 Figure 47 Figure 48 Figure 49 Figure 50 Figure 51 Figure 52 Figure 53 Figure 54 Figure 55 Figure 56 Figure 57 Figure 58 Figure 59 Figure 60 Figure 61 Figure 62 Figure 63 Figure 64 Figure 65 Figure 66 Figure 67 Figure 68 Figure 69 Figure 70 Figure 71 Figure 72 Figure 73 Figure 74 Figure 75

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components 55 Column elevation 55 Possible final forms through border beams 56 Border cutting line for each side of the structure 57 Structure‘s East side border solution 58 Structure‘s West side border solution 58 Structure‘s South side border solution 59 Structure‘s North side border solution 59 Sun shade panel variation and their location in the system 60 Sun shade angle variations 61 Exemplary beam variations through angled panels 61 Angle options of hexagonal panel and the altered beam forms 62 Eccentricities created by the rotation of the sunshade panels 63 Grasshopper code extract 63 Remapped points and new beam profiles 63 Exemplary activity zoning for a free form structure 64 Envisioned sun shade rotation according to activity zoning 65 Script for the generation of the input angles 66 Angle variations to create a diverse landscape in the structure 67 7axis distribution at HNEE Technikum Kuka Robot 71 Extract from a complete toolpath for a beam and its notches 72 Extract from the formatting and notch toolpath 72 Grasshopper script for the tool specification input 73 First layer beam formatting in 3 milling depths 73 Fabrication nesting for the 1:2 prototype 74 Toolpath for the 1:2 prototype 75 Full assembly of the 1:2 cell prototype from above 76 Full assembly of the 1:2 cell prototype from below 76 Notch prototype 1:2 iteration photos 77 Fabrication nesting for the 1:1 notch prototypes 78 Toolpath for the 1:1 notch prototypes 79

Owner and Source Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Photos by Theresa Lohse and Oksana Tyltina Own representation Own representation Photo by Oksana Tyltina Photo by Oksana Tyltina Photos by Theresa Lohse and Oksana Tyltina Own representation Own representation

LIST OF FIGURES Figure

Title

Figure 76 Figure 77 Figure 78 Figure 79 Figure 80 Figure 81 Figure 82 Figure 83 Figure 84 Figure 85 Figure 86

Robotically milling the angled notches Series of 1:1 notch prototype Notch prototype 1:1 iteration photos Fabrication nesting first layer beams for the 1:1 cell Snapshot of the first layer beams 1:1 production Fabrication nesting second layer beams for the 1:1 cell Snapshot of the second layer beam 1:1 production Milling head used for the 1:1 production Required elements for the assembly of the 1:1 cell Assembly process of the one cell Component Catalogue of each required elements for the structure, its border and columm Case 1: displacement and axial stress Case 2: displacement and axial stress Case 3: displacement and axial stress Case 4: displacement and axial stress Plan view drawing Section drawing Perspective view from sitting level Perspective view from child eye level 100 Bird-eye perspective view 102 Potential structural behaviour in a building scale 108

Figure 87 Figure 88 Figure 89 Figure 90 Figure 91 Figure 92 Figure 93 Figure 94 Figure 95 Figure 96

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Owner and Source Photos by Theresa Lohse Photos by Oksana Tyltina Photos by Theresa Lohse and Oksana Tyltina Own representation Photo by Theresa Lohse Own representation Photo by Theresa Lohse Photo by Theresa Lohse Photo by Theresa Lohse Photo by Theresa Lohse Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation Own representation

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IMAGE APPENDIX

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1:10 MODEL PHOTOS

IMAGE APPENDIX

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