Rigid/Flexible: An Origami Building Fabric by Mihir Benodekar

Rigid/Flexible: An Origami Building Fabric

Rigid/Flexible: An Origami Building Fabric Mihir R Benodekar

Bartlett School of Architecture

Rigid/Flexible: An Origami Building Fabric Mihir R Benodekar 23 April 2013 Unit 19 BENVGA05 Thesis Bartlett School of Architecture, UCL

Mihir R Benodekar

Rigid/Flexible: An Origami Building Fabric

- | Contents -- Glossary

0 | Abstract

1 | Introduction

13 13 13 15 15 15 17 17 18 18 21

3 | Methodology 3.1 | Introduction 3.2 | Approach

23 23 23

4 | 4.1 4.2 4.3

25 25 29 35

Digital Investigations | Geometric Modelling | Force Simulation | Refined Force Simulation

39 39 43 45 47 49 51 55

6 | Further Work

7 | Conclusions

i | Bibliography ii | Appendix iii | Images

65 67 71

Acknowledgements

Rigid/Flexible: An Origami Building Fabric

-- | Glossary Aggregate

Crease Pattern Angle

Elasticity

Loose particulate material e.g. sand, coffee, sawdust.

Angle at which diagonal creases intersect lateral creases.

Physical property that allows a body to return to its original shape after it has been stretched or compressed.

Axis shift The shifting of the axis of rotation to the valley side of a thick origami crease pattern.

CREASE ANGLE

Face

CREASE ANGLE

Area bounded by lines of the crease pattern.

Grasshopper

Independent components of motion: rotation, translation, oscillation.

Visual programming language that provides algorithmic modelling tools for Rhino 3D. The following plug-ins for Grasshopper are referred to: KANGAROO - live physics simulator. LUNCHBOX - collection of geometric tools for generating panelling systems and mathematical forms. KARAMBA - structural analysis plug-in for shell and beam structures.

Dihedral Fold Angle

Hinge

Angle between two planes.

Crease where folding occurs.

Conduit Reinforced pipe for distributing the vacuum throughout the airtight membrane.

Crease Pattern An origami diagram that consists of all or most of the creases of an origami model.

Degrees of Freedom

Kinematics DIHEDRAL FOLD ANGLE

DIHEDRAL FOLD ANGLE

Branch of mechanics concerned with the motion of objects.

Rigid/Flexible: An Origami Building Fabric

0 | Abstract Mountain A fold that occurs when adjacent faces are folded away from the observer. Represented by a solid line in crease patterns.

Points at which origami behaviour cannot be defined by mathematics or where the model fails. Used to describe fully expanded and fully compressed states of origami.

Strain Mechanical deformation of the face or hinge that leads to changes in its dimensions.

Vacuumatics Technique of applying a vacuum within a membrane in order to generate compressive forces.

Panel A face with thickness.

Valley

POISSON’S ratio

A fold that occurs when adjacent faces are folded towards the observer. Represented by a dashed line in crease patterns.

The ratio between the contraction in the direction of the applied load and the resulting expansion in the direction perpendicular to the applied load.

Rigid foldability The continuous route from flat to fully folded state without deformation of the faces.1

Singularity 1 Mark Schenk, ‘Folded Shell Structures’ (unpublished PhD Thesis, University of Cambridge, 2011).

Vertex Point where creases meet.

Young’s Modulus Measure of elasticity. Ratio of stress to strain.

The aim of this thesis is to explore the use of the Yoshimura origami crease pattern as the basis for a deployable building fabric for use in temporary architecture. The desire is for the building fabric to have flat-foldability for ease of transportation and the potential for irregular deployment to create a variety of forms. Deploying the Yoshimura pattern regularly generates a distinctive single-curving approximated arched form. My interest is in examining the potential for irregular deployment and how this could be achieved within the constraints of this particular pattern. Irregular deployment has the potential to create a wider range of forms, that could be adapted for use in a variety of architectural applications from dividing walls to undulating roofscapes and circulation to pieces of furniture. My research and experimentation shows that as a rigid global system, the structure has limited degrees of freedom when being deployed, as hinges acting around each vertex fold simultaneously. This generates a constrained system to which flexibility needs to be introduced in order to achieve irregular folding. Previous studies have largely addressed kinematic problems associated with introducing thickness into

four-fold systems such as the Miura Ori pattern. The Yoshimura is a six-fold system and so problems caused by axis shift and hinge strains resulting in the potential locking up of the system will be amplified. This thesis proposes solutions in how to overcome such problems with the introduction of flexibility. The introduction of flexibility created further problems; flexibility has the contrary effect of reducing stiffness and therefore the structural performance. Additionally too much flexibility can also create a multi-stable system with multiple singularities and thus results in a situation where the structure will not be flat-foldable. Stiffness has to be reintroduced in a controlled way to overcome these problems. I considered the use of vacuumatics as a method for locking hinges into position after deployment as well as using it as a means of controlling deployment and folding. This thesis takes a scientific approach to document my development of this building fabric through noting observations in response to a series of investigations. Initially these investigations centre around computational testing using definitions in the Grasshopper plug-in for Rhino and then proceed to

introduce thickness through physical experimentation. My findings are backed up by research conducted into the field by the likes of Tomohiro Tachi, Mark Schenk and MIT.

Rigid/Flexible: An Origami Building Fabric

1 | Introduction Origami has the potential to generate structurally efficient collapsible forms that are both flexible and rigid. Crease patterns such as the Yoshimura, the Miura Ori, the Water Bomb and the Fishbone have the potential to generate incredible levels of strength and stiffness within sheet materials as well as having the ability to fold completely flat. Extensive research into origami folding has been conducted for the purpose of designing deployable structures particularly in aerospace applications with examples including telescopic lenses and solar arrays. Precedents for folded plate structures within the field of architecture are generally seen in roofing applications for their aesthetics and their ability to efficiently span large distances such as in the case of the Yokohama Cruise Terminal. Origami-inspired architecture however seldom makes use of origami’s main feature – which is its ability to fold flat.

origami (ˌɒrɪˈɡɑːmɪ) —n the art or process, originally Japanese, of paper folding [from Japanese, from ori a folding + kami paper] Origami. Dictionary.com. Collins English Dictionary - Complete & Unabridged 10th Edition. HarperCollins Publishers. http://dictionary. reference.com/browse/origami (accessed: March 25, 2013).

Looking specifically at the Yoshimura crease pattern, my investigations explore its potential for use in creating a building fabric for a temporary architecture. The Yoshimura pattern offers excellent structural properties as it provides huge increases in bending stiffness for minimal increases in weight. Regular deployment of the pattern generates an approximated arch form. Modifying the crease F1.1 Paper Yoshimura arch

F1.2 Use of origami form as circulation

pattern angle has the effect of altering this bending stiffness as well as affecting the kinematic behaviour of the form’s geometry. The unusual property of this crease pattern is that it generates a form with an effective Poisson’s Ratio that is negative, meaning that compressing the form reduces its dimensions in all directions, providing favourable characteristcs for transportation. My interest lies in the irregular deployment of this structure to generate a greater variety of forms so as to increase the versatility of the building fabric. More organic forms would allow the building fabric to be used in a wider range of architectural applications from roofscapes and walls through to elements of furniture. There are two methods used to explore and test the Yoshimura pattern. Firstly, using computer modelling and analysis to search for efficient crease patterns, forms and compressions looking particularly at the limitations and legitimacies of information generated from 3D geometric and force simulation modelling. Secondly, focussing on problems associated with transforming the design into scaled physical models of the structure, exploring the effects of gravity, material thickness, nature of the hinges as well as

the global behaviour of the structure in terms of kinematics and structural stability. I use these findings to examine how the Yoshimura structure could be deployed into irregular forms and what additional changes are required to accommodate this, such as the introduction of flexibility.

Rigid/Flexible: An Origami Building Fabric

2 | Background 2.1 Origami The art of origami can be dated back to as early as the 17th century however its importance within the fields of science and architecture have been gradually growing especially over the latter half of the 20th century. The advantages offered by origami can be tested simply through the folding of paper. Applying crease patterns to a sheet of paper induces stiffness along the creases without any increase in mass whilst also creating flexibility in the perpendicular direction. Certain crease patterns also allow the sheet to be folded fully flat.

2.2 folded plate structures

generate stiffness within the plate and they need to run in the approximate direction of the span in order to provide structural rigidity. Exploiting the simple principles demonstrated by folding sheets of paper, origami can be transformed from what was initially an art form into a tool that can be used for broad engineering and design applications. These applications can be categorized into three main areas: 1. Deployable structures. 2. Increasing stiffness with minimal expense of weight. 3. Shock absorption devices.

Martin Betchold writes: â&#x20AC;&#x153;Folded plates are thin structural surfaces that can achieve remarkable spans without the complexity of constructing a single- or double-curved surfaceâ&#x20AC;?1 There are many architectural examples that have exploited the origami for the creation of large spans, some of which are pictured overleaf. The fold lines

1 Martin Bechthold, Innovative Surface Structures: Technologies and Applications, 1st edn (Taylor & Francis, 2008), p. 103.

F2.1 Origami crane

F2.2 Stent, Zhong You F2.3 Tokyo Subway Map, Koryo Miura

Rigid/Flexible: An Origami Building Fabric

PREFABRICATION

UNFOLDED SINGULAR STATE

2.3 DEPLOYABLE STRUCTURES Deployable structures take advantage of the fact that certain origami can fold flat. It has been used in the medical industry for the design of stents, in vehicle safety for controlling the deployment of air bags, and often in the design of space exploration equipment for devices such as solar arrays, telescopic lenses and inflatable booms. Deployable structures allow elements to be folded into a compressed state for ease of transportation before being expanded or deployed once they reach their desired location. At an architectural scale, deployable structures have been considered by the likes of Hirschen van der Ryn (F2.4, 2.5), who developed a shelter for Californian migrant farm workers based around a bellows-type vault2 as well as Chuck Hoberman, who has used origami principles in the design of stadia roofs and folding stage sets (F2.9).

ON SITE DEPLOYMENT

GRADUAL FOLDING

FLAT FOLDED

DEPLOYMENT

RECONFIGURING

STIFFENING

FLAT FOLDED

in weight such as in the case of aircraft fuselage design. Architectural examples include St Paulus Church in Neuss, Germany by Fritz Schaller, the Air Force Academy Chapel Cadet Chapel in Colorado by Skidmore, Owings and Merrill (F2.7) or the roof of the Yokohama Cruise Terminal by Foreign Office Architects (F2.11). In some cases however, architects PREFABRICATION ON SITE DEPLOYMENT have exploited origami folding purely for aesthetic reasons. UNFOLDED SINGULAR STATE GRADUAL FOLDING FLAT FOLDED TRANSPORTATION FLAT FOLDED DEPLOYMENT

RECONFIGURING

STIFFENING

FLAT FOLDED

TRANSPORTATION TO SITE

TO SITE

FLAT FOLDED

2.5 SHOCK ABSORPTION Thirdly, origami has been used in shock absorption applications whereby patterns have been exploited for their ability to resist buckling. Origami has inspired the design of crumple zones in vehicles and packaging design. With most buildings being static, this aspect of origami is seldom used in architectural applications.

2.4 INCREASING STIFFNESS There are many instances where origami inspired folding has been used as a method of increasing the stiffness of a flat plate at the minimal increase

2 Vinzenz Sedlak, ‘Paperboard Structures’ (Surrey University, 1973).

F2.4, 2.5 Shelter for migrant farmworkers, California, Hirschen and Van der Ryn F2.6 Hyperbolic solar sail, NASA

F2.7 US Air Force Academy Chapel, Colorado, SOM F2.8 St Paulus Church in Neuss, Germany by Fritz Schaller

F2.9 Hoberman Arch, Salt Lake City, Chuck Hoberman F2.10 One Way Colour Tunnel, Olafur Elaisson

F2.11 Diagram of fabrication and deployment F2.12 Cruise Terminal, Yokohama, FOA F2.13 Facade, Biomedical Research Centre, Vaillo Irigaray

Rigid/Flexible: An Origami Building Fabric

CREASE ANGLE

2.6 Principles

2.7 YOSHIMURA PATTERN

When mathematically modelling origami, we consider the plate to be rigid and of zero thickness. The process of folding turns what is in effect a rigid surface into a “beam-like surface structure”3. But this zero-thickness truss-like system is an untrue representation of origami in the physical realm, particularly when it is considered as part of a mechanism at architectural scales. We need to begin to consider thickness for elements that will “cope with gravity, bear loads, and insulate heat, radiation, sound, etc”4.

After exploring many different flat-foldable origami crease patterns, I decided to focus on the Yoshimura.

DIHEDRAL FOLD ANGLE

3 Martin Bechthold, Innovative Surface Structures: Technologies and Applications, 1st edn (Taylor & Francis, 2008), p. 101. 4 Tomohiro Tachi, Motoi Maubuchi and Masaaki Iwamoto, ‘Rigid Origami Structures with Vacuumatics: Geometric Considerations’, <http://www.tsg. ne.jp/TT/cg/VacuumaticOrigamiIASS2012.pdf> [accessed 28 February 2013].

F2.14 Origami-inspired beams

F2.15, 2.16 Paper folded Yoshimura arch

F2.17 Defining the Yoshimura pattern

This was a pattern originally discovered during research into the buckling patterns of thin-walled cylinders by the scientist Y. Yoshimura, whom it was consequently named after. Since then, developments of the pattern have inspired the design of deployable booms, shock absorbing structures in vehicles as well as inspiring architectural forms. This particular pattern generates an arched form making it particularly well suited for the creation of sheltering elements. The form is structurally efficient, self supporting and, in my opinion, is aesthetically pleasing. The pattern also offers a degree of simplicity that should make it easier to transform to an architectural scale. The pattern is defined by two main parameters: The crease pattern angle and the dihedral fold angle. These can be varied across the plate that they are applied to, in order to create varying geometries within the folded form.

F2.18 Yoshimura-inspired shelter, Hastings Pier, dRMM F2.19 Foldable Yoshimura plastic tube, Matts Karlsson

Rigid/Flexible: An Origami Building Fabric

2.8 Previous Research

the introduction of thickness to the system.

Much of the existing research into origami structures focuses on patterns such as the Miura Ori or the Water Bomb, due to their versatility in engineering and aerospace applications and so investigating the Yoshimura pattern should offer a new insight into deployable architectural origami.

Mark Schenk has conducted extensive research into the behaviour of textured sheets - in particular their structural behaviour. His study entitled “Origami Folding: A Structural Engineering Approach” looks at the modelling of the kinematics and stiffness of the Miura Ori and the Eggbox6. This provides insight into how origami might be modelled computationally as a pin-jointed bar framework and provides concise documentation into the behaviour of the patterns. The forms once again are treated as having zero thickness and do not highlight the problems introducing thickness could cause.

Osvaldo L. Tonon’s study into the Geometry of Spatial Folded Forms, provides a geometric analysis of the Yoshimura pattern and what parameters affect its behaviour. He uses the silhouette method to show the mathematical relationships between crease angles and the dihedral fold angles.5 He explores both regular and irregular patterns as well as linear and radial deployment. This document provides key information in how to model the rigid Yoshimura pattern in static geometric terms but gives no insight about the kinematic behaviour, including problems that might be generated during the folding and unfolding of this constrained system. The other issue is that this document treats the planar elements as having zero thickness and does not address issues resulting from

5 Osvaldo L Tonon, ‘Geometry of Spatial Folded Forms’, International Journal of Space Structures, 6 (1991), p. 227.

F2.20 Mathematical analysis of the Yoshimura pattern, Osvaldo L Tonon

2.9 The over-constrained problem Geometrically describing the configuration of the Yoshimura pattern, we can say that there are six crease lines and faces that meet at, and hence are constrained around, each vertex. Tomohiro Tachi states that: “This approach produces three degrees of constraint 6 Mark Schenk, ‘Origami Folding: A Structural Engineering Approach’ <http://www2.eng.cam.ac.uk/~ms652/files/schenk2010-5OSME.pdf> [accessed 28 February 2013].

for each interior vertex that fundamentally correspond to the rotations in the x -, y -, and z -directions of facets around the point of intersection of incident fold lines. As a result, a rigid origami produces a kinetic motion where the fold lines fold simultaneously.”7 In a rigid system, creases have to work concurrently to ensure that the global pattern can fold and unfold. This can causes the system to behave in one of two ways: it either becomes over-constrained or it has limited degrees of freedom - both of which can result in the system locking up. Introducing thickness causes further problems. Through placing hinges on the valley side of the crease pattern, we are exposing the system to what Tachi terms as ‘axis shift’, where the axis shifts to the valley side of the pattern. This introduces translations into a constrained system resulting in six constraints for each transformation8. In addition the fold lines no-longer line up, resulting in a system that becomes over-constrained whereby folding becomes impossible. He goes on to say: “Even if we

7 Tomohiro Tachi, ‘Rigid-Foldable Thick Origami’ (Taylor & Francis, 2011), p. 254. 8 Tomohiro Tachi, p. 255

succeeded in designing a consistent pattern for a finite number of states, this would at best produce a multistable structure without rigid foldability.”9 Multistable structures could create forms that cannot be folded flat due to the system having multiple singularities. Thus the resulting system may lock up in various undesirable configurations due to a lack of control over the actions of the hinges. A solution he suggests for eliminating axis shift is the use of tapered panels. This arrangement however is not completely flat-foldable and created panels that could be more complex to manufacture. A paper written by Martin Trautz and Arne Kuenstler explores the potential for using sliding hinges with the Miura Ori pattern. They describe the implications of modelling thickness together with placing the hinge on the valley side, which results in hinge folding that is limited to 0 < a < 180 as opposed to -180 < a < 180 - a condition which would be possible in the zero-thickness case. Sliding is introduced into the hinge mechanism so as to avoid the panels folding into each other as the system is compressed. The sliding hinges introduce additional degrees of freedom as their translations need to be uncoupled to allow the thick system to unfold. This creates multiple 9 Tomohiro Tachi, p. 255

translations as the system is folded, which affects the system globally. In addition, each translation creates “successive enlargements of the hinge translations in adjacent folds” 10. The sliding hinges also impact on the structure’s load-bearing capacity. Shear forces that may be caused by the “different geometries of the adjacent plates or unbalanced live loads” cannot be transmitted11. The paper concludes with the suggestion that elastic plate materials could be considered to allow greater modes of deployment at the expense of load-bearing capacity. Observing the issues generated when trying to create rigid, thick foldable origami, I would question why we need the folding to be rigid. If we can achieve sufficient levels of stiffness in the structure with the use of deformable or elastic hinges or faces, we might be able to create more interesting forms, which would otherwise be difficult to achieve due to the constraints created by rigid origami.

10 Martin Trautz and Arne Kuenstler, ‘Deployable Folded Plate Structures - Folding Patterns Based on 4-Fold Mechanisms Using Stiff Plates’ (International Association for Shell and Spatial Structures, 2009). 11 Martin Trautz and Arne Kuenstler.

F2.21 Tapered hinge solution to axis shift problem, Tomohiro Tachi

Rigid/Flexible: An Origami Building Fabric

DEPLOYED STATE MUSCLES DEFLATED

2.10 FIXING AND DEPLOYMENT STRATEGY The Yoshimura pattern can be stabilised to some degree by pinning the boundary of the form, however the reality is that there could still be some structural flexibility within the system. It is therefore necessary to consider methods to lock each hinge into position. Tomohiro Tachi considered the use of vacuumatics as potential method. He proposes the use of thick rigid panels where the gaps in between them were filled with “aggregate particles packed in a breathable material” with the entire structure then being placed in an “airtight membrane”12. Removal of air from the membrane caused a compressive force to be applied to the aggregate particles – balanced by the tensile force in the enclosing membrane. As long as these forces remained greater than those caused by loading, the structure locked into position. Releasing the vacuum caused the hinge to become flexible once again allowing the panels to be reconfigured. The key disadvantage with this system is that the structure needs to be manually manipulated and the act of applying the vacuum simply locks the structure 12 Tomohiro Tachi, Motoi Maubuchi and Masaaki Iwamoto, ‘Rigid Origami Structures with Vacuumatics: Geometric Considerations’, <http://www.tsg. ne.jp/TT/cg/VacuumaticOrigamiIASS2012.pdf> [accessed 28 February 2013].

F2.22, 2.23, 2.24 Pneumatic muscles for soft robots, Saul Griffith

into position. Although Tachi claims that locally applying vacuums could help in the deployment of the structure by controlling the levels of flexibility within each hinge, the global resistance within the structure may be too great for a person to overcome and thus mechanical assistance such as the use of a crane may be required. Additionally, the aggregate could add significant weight to the structure, which would contribute to the overall dead loading and would necessitate the implementation of a higher strength material for the hinges and stronger founding elements. In contrast to Tachi, Saul Griffith as part of his company Other Labs looked into the potential for using pneumatic hinges in the creation of his ‘soft robots’. These inflatable robots used pneumatic muscles to generate movement within their limbs. The muscles attach to the outside of the inflated limb and contract when inflated causing the limb to bend13. Once air within the muscle was released, the pressure within the inflated limb provided sufficient force to return it back to its extended position. In the case of

FOLDED STATE MUSCLES INFLATED

applying similar pneumatic muscles to the Yoshimura building fabric, ‘muscles’ would be positioned to the valley side of the pattern and there would need to be a spring system to counter the action of the muscle to provide both a folding and deploying movement. Using an elastic skin over the rigid panels could provide one solution to this. A positive aspect of using this technology is that the building fabric could be self deploying, and therefore may not require additional mechanical assistance. One problem with this method is that because the muscles need to be inflated to apply a compressive force, the system will not be able to fold flat. In addition I feel that in terms of aesthetics this method of control will visually create too much of an intrusion with regard to the beauty of the Yoshimura pattern.

13 ‘Inflatable Robots by Otherlab: A Walking Robot (named Ant-Roach) and a Complete Arm (Plus Hand) | Hizook’ <http://www.hizook.com/ blog/2011/11/21/inflatable-robots-otherlab-walking-robot-named-ant-roachand-complete-arm-plus-hand> [accessed 19 April 2013].

F2.25 Vacuumatic hinge experiment, Tomohiro Tachi F2.26 Pneumatics adapted for use with rigid origami panels

Rigid/Flexible: An Origami Building Fabric

3 | Methodology 3.1 INTRODUCTION The methodology that informs the investigations is designed to explore whether the Yoshimura pattern can be used to create a flat-foldable, deployable building fabric, that can be expanded to into irregular, organic forms. Initially simple paper models were used to gain a basic insight into the Yoshimura pattern, followed by a series of computer definitions using Rhino 3D with the Grasshopper plug-in. This was done to model and test the kinematic behaviour of the pattern as well as to gain an understanding of the potential forms that could be generated. These digital tests were used to inform the creation of physical prototypes that introduced thickness, flexibility and stiffness to the system. The conclusions from these tests were used to inform the design of a suitable building fabric.

3.2 APPROACH After reviewing previous research into the use origami principles in the design of deployable structures,

F3.1 Paper folded Yoshimura arch

I saw great potential in developing a deployable building fabric that was inspired by the Yoshimura pattern. My approach to developing the building fabric examined the following conditions: • • • • •

kinematic behaviour generation of varied forms introduction of thickness hinges stiffness versus flexibility.

By developing a series of prototypes, I was able to critically analyse the performance of the pattern and how it would need to be developed and modified as it was transformed from a paper origami pattern into a potential design for a building fabric. My method is divided into the three following stages: 1. 2. 3.

Digital investigations Physical investigations Building fabric design

Each stage is key for informing the next in the design process. Problems identified in previous research have been addressed and there are certain variables that will impact on the accuracy of the outcomes from each of the investigations.

Investigations documented within this research fall into two categories: digital and physical. The digital investigations allowed the potential and behaviour of the Yoshimura pattern to be quickly tested without introducing the likes of panel thickness, gravity, physics and misaligned geometry. The physical investigations reintroduced these constraints, along with any associated problems. The investigations address the form locally by considering the performance of an individual hinge in isolation but also globally looking at the kinematics of the system as a whole. I used the findings from this report to inform the design of the deployable building fabric.

Rigid/Flexible: An Origami Building Fabric

4 | Digital Investigations CREASE ANGLE

4.1 Geometric Modelling A symmetrical Yoshimura pattern with regular deployment was defined in Grasshopper. As each face is rigid and identical, it was only necessary to define one triangular face by controlling the length of its hypotenuse and the crease angle (F4.1). The dihedral fold angle was also changed by controlling the rotation of the face relative to a vertical plane (F4.1). The overall form was then defined through a series of reflections, translations and rotations. Changing the crease pattern angle and the dihedral fold angle generated changes to the global form (F4.2).

CREASE ANGLE

The behaviour of the Yoshimura pattern across a range of crease patterns and dihedral fold angles are shown in F4.4. There are three main effects of reducing the crease pattern angle: 1. Reduction in the size of the faces. 2. Arch generated has a larger diameter (F4.5). 3. The structural depth of the form as it is folded is shallower.

DIHEDRAL FOLD ANGLE

F4.1 Crease pattern angle and dihedral fold angle

F4.2 Grasshopper definition: varying crease pattern angle and dihedral fold angle

Rigid/Flexible: An Origami Building Fabric CREASE PATTERN ANGLE [DEGREES] - PANEL LENGTH 3M

CHANGING CROSS SECTIONAL RADIUS WITH REDUCING DIHEDRAL ANGLE

RADIUS 98.53M DIHEDRAL FOLD ANGLE 170

RADIUS 49.36M DIHEDRAL FOLD ANGLE 160

RADIUS 33.10M DIHEDRAL FOLD ANGLE 150

RADIUS 25.04M DIHEDRAL FOLD ANGLE 140

RADIUS 20.26M DIHEDRAL FOLD ANGLE 130

RADIUS 17.11M DIHEDRAL FOLD ANGLE 120

RADIUS 14.91M DIHEDRAL FOLD ANGLE 110

RADIUS 13.29M DIHEDRAL FOLD ANGLE 100

RADIUS 12.08M DIHEDRAL FOLD ANGLE 90

RADIUS 11.14M DIHEDRAL FOLD ANGLE 80

RADIUS 10.41M DIHEDRAL FOLD ANGLE 70

RADIUS 9.84M DIHEDRAL FOLD ANGLE 60

RADIUS 9.40M DIHEDRAL FOLD ANGLE 50

RADIUS 9.06M DIHEDRAL FOLD ANGLE 40

RADIUS 8.81M DIHEDRAL FOLD ANGLE 30

RADIUS 8.64M DIHEDRAL FOLD ANGLE 20

RADIUS 8.54M DIHEDRAL FOLD ANGLE 10

RADIUS 48.79M DIHEDRAL FOLD ANGLE 170

RADIUS 24.47M DIHEDRAL FOLD ANGLE 160

RADIUS 16.40M DIHEDRAL FOLD ANGLE 150

RADIUS 12.39M DIHEDRAL FOLD ANGLE 140

RADIUS 10.01M DIHEDRAL FOLD ANGLE 130

RADIUS 8.44M DIHEDRAL FOLD ANGLE 120

RADIUS 7.34M DIHEDRAL FOLD ANGLE 110

RADIUS 6.53M DIHEDRAL FOLD ANGLE 100

RADIUS 5.92M DIHEDRAL FOLD ANGLE 90

RADIUS 5.45M DIHEDRAL FOLD ANGLE 80

RADIUS 5.08M DIHEDRAL FOLD ANGLE 70

RADIUS 4.80M DIHEDRAL FOLD ANGLE 60

RADIUS 4.57M DIHEDRAL FOLD ANGLE 50

RADIUS 4.40M DIHEDRAL FOLD ANGLE 40

RADIUS 4.28M DIHEDRAL FOLD ANGLE 30

RADIUS 4.19M DIHEDRAL FOLD ANGLE 20

RADIUS 4.14M DIHEDRAL FOLD ANGLE 10

RADIUS 32.10M DIHEDRAL FOLD ANGLE 170

RADIUS 16.08M DIHEDRAL FOLD ANGLE 160

RADIUS 10.76M DIHEDRAL FOLD ANGLE 150

RADIUS 8.12M DIHEDRAL FOLD ANGLE 140

RADIUS 6.54M DIHEDRAL FOLD ANGLE 130

RADIUS 5.50M DIHEDRAL FOLD ANGLE 120

RADIUS 4.76M DIHEDRAL FOLD ANGLE 110

RADIUS 4.23M DIHEDRAL FOLD ANGLE 100

RADIUS 3.82M DIHEDRAL FOLD ANGLE 90

RADIUS 3.50M DIHEDRAL FOLD ANGLE 80

RADIUS 3.25M DIHEDRAL FOLD ANGLE 70

RADIUS 3.06M DIHEDRAL FOLD ANGLE 60

RADIUS 2.91M DIHEDRAL FOLD ANGLE 50

RADIUS 2.79M DIHEDRAL FOLD ANGLE 40

RADIUS 2.70M DIHEDRAL FOLD ANGLE 30

RADIUS 2.64M DIHEDRAL FOLD ANGLE 20

RADIUS 2.61M DIHEDRAL FOLD ANGLE 10

RADIUS 23.62M DIHEDRAL FOLD ANGLE 170

RADIUS 11.82M DIHEDRAL FOLD ANGLE 160

RADIUS 7.89M DIHEDRAL FOLD ANGLE 150

RADIUS 5.93M DIHEDRAL FOLD ANGLE 140

RADIUS 4.76M DIHEDRAL FOLD ANGLE 130

RADIUS 3.98M DIHEDRAL FOLD ANGLE 120

RADIUS 3.44M DIHEDRAL FOLD ANGLE 110

RADIUS 3.03M DIHEDRAL FOLD ANGLE 100

RADIUS 2.72M DIHEDRAL FOLD ANGLE 90

RADIUS 2.48M DIHEDRAL FOLD ANGLE 80

RADIUS 2.29M DIHEDRAL FOLD ANGLE 70

RADIUS 2.14M DIHEDRAL FOLD ANGLE 60

RADIUS 2.03M DIHEDRAL FOLD ANGLE 50

RADIUS 1.94M DIHEDRAL FOLD ANGLE 40

RADIUS 1.87M DIHEDRAL FOLD ANGLE 30

RADIUS 1.82M DIHEDRAL FOLD ANGLE 20

RADIUS 1.80M DIHEDRAL FOLD ANGLE 10

My observations are that having a crease pattern angle that is too small results in an inefficient use of the material. The faces become too small meaning that a greater number will be required to cover a given area. This also makes the structure more complex as the number of hinges required also increases. Although the structural depth becomes smaller, the increased number of hinges has the effect of creating a stiffer structure.

CANNOT FOLD FLAT

RADIUS 9.20M DIHEDRAL FOLD ANGLE 160

RADIUS 6.12M DIHEDRAL FOLD ANGLE 150

RADIUS 4.58M DIHEDRAL FOLD ANGLE 140

RADIUS 3.66M DIHEDRAL FOLD ANGLE 130

RADIUS 3.04M DIHEDRAL FOLD ANGLE 130

RADIUS 2.60M DIHEDRAL FOLD ANGLE 120

RADIUS 2.28M DIHEDRAL FOLD ANGLE 110

RADIUS 2.03M DIHEDRAL FOLD ANGLE 100

RADIUS 1.83M DIHEDRAL FOLD ANGLE 90

CANNOT FOLD FLAT

RADIUS 14.87M DIHEDRAL FOLD ANGLE 170

RADIUS 7.41M DIHEDRAL FOLD ANGLE 160

RADIUS 4.91M DIHEDRAL FOLD ANGLE 150

RADIUS 3.65M DIHEDRAL FOLD ANGLE 140

RADIUS 2.89M DIHEDRAL FOLD ANGLE 130

RADIUS 2.38M DIHEDRAL FOLD ANGLE 130

RADIUS 2.02M DIHEDRAL FOLD ANGLE 120

RADIUS 1.74M DIHEDRAL FOLD ANGLE 110

RADIUS1.53M DIHEDRAL FOLD ANGLE 100

RADIUS 1.68M DIHEDRAL FOLD ANGLE 80

RADIUS 1.55M DIHEDRAL FOLD ANGLE 70

CROSS SECTIONAL RADIUS, M

RADIUS 18.42M DIHEDRAL FOLD ANGLE 170

100

CANNOT FOLD FLAT

RADIUS 12.24M DIHEDRAL FOLD ANGLE 170

RADIUS 6.08M DIHEDRAL FOLD ANGLE 160

RADIUS 4.00M DIHEDRAL FOLD ANGLE 150

RADIUS 2.95M DIHEDRAL FOLD ANGLE 140

RADIUS 2.31M DIHEDRAL FOLD ANGLE 130

RADIUS 1.88M DIHEDRAL FOLD ANGLE 130

RADIUS 1.57M DIHEDRAL FOLD ANGLE 120

CANNOT FOLD FLAT

RADIUS 10.20M DIHEDRAL FOLD ANGLE 170

RADIUS 5.04M DIHEDRAL FOLD ANGLE 160

RADIUS 3.29M DIHEDRAL FOLD ANGLE 150

RADIUS 2.40M DIHEDRAL FOLD ANGLE 140

RADIUS 1.85M DIHEDRAL FOLD ANGLE 130

15 45 CANNOT FOLD FLAT

20 20 RADIUS 8.54M DIHEDRAL FOLD ANGLE 170

RADIUS 4.19M DIHEDRAL FOLD ANGLE 160

RADIUS 2.70M DIHEDRAL FOLD ANGLE 150

CREASE PATTERN ANGLE, 3M PANEL LENGTH, DEGREES

RADIUS 1.94M DIHEDRAL FOLD ANGLE 140

By contrast, selecting a crease pattern angle that is too large creates forms that are more tubular due to the generated arched form having a smaller diameter. In some cases the resulting diameter is so small that the pattern is unable to fold flat due to the form intersecting itself.

RADIUS 4.14M DIHEDRAL FOLD ANGLE 10

RADIUS 1.80M DIHEDRAL FOLD ANGLE 10

What this definition did not do was simulate the kinematics of folding together with the resulting strains that may be propagated through the system, and it was limited to providing a purely geometric understanding of how the form behaved (F4.6).

30 35 40 45 50 50 CANNOT FOLD FLAT

0 10 RADIUS 7.14M DIHEDRAL FOLD ANGLE 170

RADIUS 3.47M DIHEDRAL FOLD ANGLE 160

RADIUS 2.20M DIHEDRAL FOLD ANGLE 150

RADIUS 1.54M DIHEDRAL FOLD ANGLE 140

100

110

120

130

140

150

160

170

DIHEDRAL FOLD ANGLE, DEGREES

F4.3 Behaviour of Yoshimura pattern F4.4 Graph plotting dihedral fold angle against arch radius

F4.5 Behaviour of Yoshimura pattern

F4.6 Geometric understanding of the Kinematics of folding

Rigid/Flexible: An Origami Building Fabric

4.2 Force Simulation RELAXATION NEEDS TO BE APPLIED TO THE SYSTEM DUE TO THE FACT IT IS OVER-CONTRAINED AND WE ARE APPLYING IRREGULAR FOLDING.

KANGAROO COMPUTES AND OUTPUTS THE RESULTS

The crease pattern was redefined using the Lunchbox plug-in for Grasshopper (F4.7). This allowed for a simple definition of a flat mesh where each triangular cell represented a face of the Yoshimura pattern. The Kangaroo physics plug-in for Grasshopper was also implemented into the definition, which facilitated the folding of the mesh to be simulated. By selecting adjacent faces, a hinge could be defined between them (dihedral hinge) where folding would occur. Kangaroo was used to define the parameters of the hinge such as its strength and rest angle as well as the force that was applied to rotate the faces about the hinge. In order to allow variable folding across the Yoshimura crease pattern, control curves were implemented whereby the angle of dihedral folding was a function of the distance between each hinge and the closest point to the curves (F4.9). Additional control was added by defining the maximum and minimum dihedral fold angles that each hinge would operate between.

UPPER AND LOWER BOUNDARIES OF DIHEDRAL FOLD ANGLE THE DIHEDRAL CREASE IS DEFINED USING THE HINGE COMPONENT FROM THE KANGAROO PLUG-IN. THE REST ANGLE IN THIS CASE REFERS TO THE DIHEDRAL FOLD ANGLE AND IS CONTROLLED BY THE BOUDARY ANGLES AND CONTROL CURVES

DIHEDRAL FOLD ANGLE CONTROLLED AS A FUNCTOIN OF THE DISTANCE BETWEEN CONTROL CURVES AND CREASE

relaxation was required in order to allow the system to fold (F4.8). This provided the mesh with a degree of elasticity defined by a force component, meaning that any strains that occurred within the system were resolved through small changes in the dimensions of individual faces. Furthermore, the folding force needed to be applied gradually so that the system had time to resolve the geometry within the constraints applied, in order to prevent the definition failing. CONTROL CURVES

GENERATED FORM

RELAXATION IN THE SYSTEM CREATES DEFORMATION OF THE FACETS THAT REMAINS AFTER FOLDING

As we were dealing with a constrained system to which inconsistent folding was being applied, mesh F4.7 Force simulation definition

F4.8 Effect of mesh deformation

F4.9 Relationship between control curve and form

Rigid/Flexible: An Origami Building Fabric

CONCAVE FORMS

CONVEX FORMS

The definition facilitated the creation of some interesting forms as shown in F4.10. By adjusting the position of the control curves three-dimensionally, it was possible to generate a series of forms that were catalogued according to their characteristics. The forms varied in all three dimensions. Depending on their orientation, they could be adapted for use as undulating roof structures or landscape elements. Scaling also provided interesting opportunities to consider certain forms for use as furniture elements within the architecture. Some of the more interesting forms were selected to generate 3D prints to gain a clearer understanding of them (F4.13).

CURVED FORMS

some of which result in unresolvable geometry. In the physical realm this could be attributed to the system locking up or the failure of a hinge. When the definition succeeded in the generating forms, individual faces did not behave as rigid origami should. On average the process of folding the mesh resulted in a permanent 1% - 2% deformation of the faces. This was the result of the definition not being able to resolve the geometry back to its original dimensions after folding had been applied.

Criticisms of the definition are that it frequently failed with causes being:

MISCELLANEOUS FORMS

1. Mesh relaxation 2. Insufficient controls over the hinge behaviour 3. Applying forces too quickly 4. Inconsistent folding patterns that cannot be solved.

F4.10 Forms resulting from the force simulation definition

Mesh relaxation, although implemented in order to assist the mesh to fold, leads to the creation of a multi-stable system. There are multiple solutions generated as the dimensions of the mesh are altered, F4.11 Typical irregular form generated by definition F4.12 Failure of the definition

CONVEX FORMS

Rigid/Flexible: An Origami Building Fabric

Insufficient control over the behaviour of the hinges was also a contributing factor to the failure of the model. There was no control over which direction the hinges were permitted to fold resulting in the incorrect folding of some faces. Also the two types of hinges - lateral and diagonal, were not identified for the purposes of this definition. Stability could be introduced through establishing a relationship between the two as described in Osvaldo L. Tonon’s paper into the mathematical modelling of the Yoshimura pattern14.

CURVED FORMS

Forces need to be applied to the system gradually. Applying them too quickly creates large mesh deformations as the definition tries to resolve the geometry, leading to failure. Trying to find the right balance between providing flexibility within the system to overcome the global constraints allowing the system to fold, whilst trying to maintain sufficient stiffness and control to ensure the system behaves as rigid origami should, is a difficult problem to solve. Defining the hinges more accurately should go some way in helping stabilise the definition. 1 14 Osvaldo L Tonon, ‘Geometry of Spatial Folded Forms’, International Journal of Space Structures, 6 (1991), p. 227.

F4.13 3D prints of selected generated forms

MISCELLANEOUS FORMS

F4.14 Control curves define form

Rigid/Flexible: An Origami Building Fabric

35 Z Y

THE ADDITION OF THIS PART OF THE CODE USES THE BEND FUNCTION IN KANGAROO TO CONTROL THE STIFFNESS OF THE CREASES, ALLOWING CONTROL OVER HOW MUCH THEY DEFORM DURING FOLDING.

ANCHOR POINTS ALLOW THE FIXING OF THE COORDINTATES OF SELECTED VERTICES IN EITHER ONE OR ALL OF THE X, Y AND Z COORDINATES DURING FOLDING

THIS PREVIEW COMPONENT PRESCRIBES A COLOUR TO EACH PANEL RELATING TO THE LEVEL OF DEFORMATION IT EXPERIENCES. IT PROVIDES A REAL TIME FEED BACK OF WHICH PARTS ARE EXPERIENCING STRAIN DURING FOLDING.

4.3 Refined Force Simulation The development of a more stable system needed to provide a range of angles that the hinges could operate within, consistent with those of the Yoshimura pattern. In this case, the new definition avoided the use of the Lunchbox plug-in, as this did not generate a clean list of mesh vertices and edges (F4.15). The crease pattern was now defined as a surface divided into the triangulated faces of the Yoshimura pattern, which consequently enabled a more precise definition of the hinges. The hinges were divided into three families: two sets of lateral hinges, and the diagonal hinges (F4.16). The folding of the hinges was controlled by defining maximum and minimum angles so that they folded in the correct direction and within the correct limits. The hinges now also provided a resistive force against applied bending, which acted to stiffen the hinges and hence stabilise the system further.

REST ANGLE IS APPLIED TO THE SELECTED CREASES RESULTING IN A MORE ACCURATE BEHAVIOUR

Mesh relaxation was once again added to the faces but this time a colour preview function highlighted the level of strain experienced by each face and provided an indication of how the folding was resolved within the system (F4.18). Once the colours settled to

CREASE PATTERN IS REDEFINED AND ACCURATE LISTING OF VERTICES ALLOWS THE SELECTION OF INDIVIDUAL CREASES.

F4.15 Refined force simulation definition

that of the base colour, we knew that the faces had returned to their original dimensions and that the form was once again geometrically correct. The system began as a flat surface and a crease angle was applied to the faces along the lateral and diagonal hinges. It should be noted that this system could be folded flat. Irregular forms could be created by the selection and anchoring of particular vertices as the dihedral fold angle was increased (F4.16). The vertices that were anchored could be changed as the folding was applied. The x, y and/or z coordinates of the vertices could be anchored depending on the type of form that was desired. Anchoring x and y coordinates when applying folding caused the form to rise in the z direction. Fixing the z coordinates resulted in the compression and curvature of the form. In the physical realm, this process could be attributed to the selective stiffening of hinges during deployment. The key findings from this investigation were that the families of hinges behave differently and it is necessary to take this into account when designing the global system. There is a dichotomy that needs to be addressed between the stiffness and the flexibility to allow folding and deployment as well as the generation of irregular forms. F4.16 Anchoring vertices F4.17 Hinge families

Rigid/Flexible: An Origami Building Fabric

The images in F4.19 and F4.20 show that deploying the mesh irregularly generates increased strains in certain areas. This strain is propagated throughout the mesh resulting in the change in dimension of all the faces to some extent. Even after the model has been left to stabilise, the strain remains. This leads me to believe that in order to generate irregular forms, flexibility in the panels or hinges is crucial. There were still some instances where the model failed. This was probably due to the levels of strain increasing to such an extent that the definition could not solve the problem successfully. Failure was usually caused by constraining too many vertices whilst applying folding, or attempting to apply folding too quickly.

Minimum Strain

F4.18 Resolving strains during the folding of the mesh

Maximum Strain

F4.19 Irregular folding controlled by anchoring selected vertices and creates high levels of strain in the mesh

F4.20 Continuing to apply folding to a system with anchored vertices can result in failure of the definition

F4.21 This definition demonstrates flat-foldability

Rigid/Flexible: An Origami Building Fabric

5 | Physical Investigations 5.1 PLEATED PANELS Hinges are a crucial consideration when creating origami structures with thickness. Hinges form a connection between two rigid panels allowing them to rotate with respect to one another. There are numerous options we can consider for hinges such as type or how they are mounted. Precise, rigid operation can be offered by the use of mechanical hinges, but fabric hinges offer the potential for flexibility. In the context of a deployable building fabric, hinges are the weakest points in terms of the creation of a sealed building envelope. Fabric hinges could facilitate the creation of a continuous building envelope by bridging the gap between panels. In order to perform well, hinges need to offer complete rotational flexibility between panels whilst remaining completely rigid along the panel edge to allow them to carry the loads of deployment. It is also important to consider options for securing the panels into position once they have been unfolded. Research has been conducted into the use of fabric hinges for the purposes of space structures that would need to retain a “separation between the external and

internal environment”15 – a requirement that is also true for a building fabric. Creating continuity in the building fabric across the hinge could involve the use of very thin, but high performance insulation products such as Aerogel or multifoil insulation. Aerogel offers around three times the performance of standard mineral wool insulation16 and is available in thin, flexible blankets, making it ideal for use across hinges (F5.1). Additionally it is hydrophobic and so could be used on the exterior of the building envelope. Multifoil insulation is similarly flexible and efficient with a 35mm thickness being equivalent to 210mm of mineral wool17 (F5.2). This makes it highly suitable for use across the hinge. The pleated panels show an initial exploration into how the hinges could work. The placement of the hinge with regard to the rigid panel was an important consideration, such as whether the material should run along the mountain side, valley side or weave 15 Petra Gruber and others, ‘Deployable Structures for a Human Lunar Base’, Acta Astronautica, 61 (2007), 484–495 (p. 492). 16 ‘ThermablokSP Aerogel Blanket - Thermablok UK’ <http://www. thermablok.co.uk/products/thermabloksp-aerogel-blanket> [accessed 22 April 2013]. 17 ‘ACTIS Insulation - The Benchmark for Hybrid Reflective Insulation’ <http://www.insulation-actis.com/produits-actis.php?p=3&l=3&rub=52> [accessed 22 April 2013].

F5.1 Vacuumatic hinge test F5.2 Multifoil and Aerogel insulation

Rigid/Flexible: An Origami Building Fabric

between the panels. Material for hinges could include Kevlar and polyurethane, which provide strength and flexibility. For the purposes of this investigation, I decided to explore the use of canvas, neoprene and Concrete Canvas. There were four main observations that arose from these prototypes shown in F5.5. Firstly the panels needed to maintain rigidity around their edges for good structural performance, however their mass needed to be kept as low as possible as it would only add to the dead weight of any structure and therefore place additional stresses on the hinges. Secondly, flexibility within the hinge needed to be limited therefore placing the hinge on the ‘valley’ side of the fold was more desirable than placing it on the ‘mountain’ as the additional material that needs to travel around the panels during the fully folded state acted to increase the gap between panels in the unfolded state thus reducing rigidity. Weaving the fabric between panels was a potential solution, however with the Yoshimura pattern having six faces per vertex (F5.6), weaving fabric between panels is not practicable. The third observation was that the thicker the material taken across the hinge, the larger the gap F5.3 Pleated panels: Concrete Canvas with and without Aerogel - cannot be re-folded once set

F5.4 Pleated panels: canvas with weaving hinge

F5.5 Pleated panels: canvas with Aerogel

that needed to be left between the rigid panels in order to allow the structure to fold flat. Maintaining the building fabric continuity across the hinges also acted to increase the stiffness creating a resistive force when attempting to fold the structure. The hinges should therefore be as thin as possible, however this will have a negative impact on the sealability of the building fabric. Fourthly, the use of setting materials such as Concrete Canvas across the hinge acted to stiffen the overall structure by generating a continuity across panels. This effectively reduced the role of the origami to that of being a formwork that could potentially be removed once the concrete has set, leaving behind a stiff shell. The major disadvantage of this was that the form becomes permanently unfolded and cannot be returned to its folded state. Adapting certain hinge arrangements such as weaving fabric between panels may not be possible for the Yoshimura pattern due to its more complex arrangement of having six panels around each vertex. With these prototypes, there was no simultaneous folding as there would be with the Yoshimura pattern and there could be problems created by not carefully controlling the flexibility within the fabric hinges, which could have the undesirable effect of not allowing flat folding.

1 2

5 4

F5.6 Hinges that allow continuity in building fabric weaving, mountain/valley, mechanical hinge with fabric F5.7 Six panels around each vertex

Rigid/Flexible: An Origami Building Fabric

| Tubular |

| Irregular Tube |

| Enclosure |

| Split |

| Twist |

Regular, symmetric deployment of the Yoshimura places the least strain on the hinges and generates this simple tubular form which is has the greatest structural efficiency.

Local expansions and contractions can generate curves and bulges within the form that could be used to create architectural moments. Local compressions and expansions are limited by the global behaviour of the system as well as the thickness of the panels.

By completely expanding one end of the pattern, it is possible to create an enclosed space. By expanding it slightly, a dip in the structure can be created, bringing it down.

Creating splits in the pattern create additional flexibility within the structure allowing it to settle into new forms. Elements that reach the ground could be articulated as furniture or circulation. Additional strain is placed on the hinges surrounding area where the pattern is split.

Twisting the structure generates this dynamic form which curls to the ground. This could be thought of as an internal landscape that guides you through the architecture. Additional strain is placed on the hinges as the load paths are changed.

5.2 THICK YOSHIMURA ARCH - FLEXIBLE HINGE This was the first mock up of the Yoshimura pattern to include thickness. A 20 degree crease pattern angle was selected for the mock up as earlier geometric testing showed that this seemed to offer the best compromise between the efficient use of material, number of hinges and the ability to fold flat. The panels were laser cut from 3mm MDF and masked together on the valley side of the folds to create a flexible hinge (F5.8). The aim of the mock up was to see what forms were possible through the use of a regular crease pattern and to observe the effects of introducing gravity, the dead-weight of the structure and panel thickness. The form demonstrated the ability to generate a regular Yoshimura form as well as the being able to fold completely flat (F5.10). A selection of irregular forms generated are shown in the photographs to the left in F5.8. The model was placed on a rubber mat, where friction between the model and the mat was sufficient to hold the model in place. This was effectively similar to pinning the model at its boundary, and allowed the generation of a range of rigid forms that were self-supporting.

F5.8 Forms generated by the thick Yoshimura model with flexible hinges

The flexibility within the tape meant that this structure did not behaving as rigid origami. Strains caused by misalignments, axis shift and dragging the structure into irregular forms could be absorbed by the flexibility within the tape. Flexibility also had a negative effect of weakening the structure through a global reduction of stiffness. Other observations included the formation of gaps at the vertices created by the folding of the thick panels. This would create potential problems in the translation of this structure into a building fabric as material covering this point would experience the significant strain. These vertices were also the strongest points of the structure due to the effective triangulated truss created, which could provide potential mounting points for supporting or suspended elements. What has not been tested here is how different topographies will react with the form as this will have a direct impact on the boundary conditions.

F5.9 Fabricated singular state F5.10 Folded singular state

Rigid/Flexible: An Origami Building Fabric

5.3 THICK YOSHIMURA ARCH - RIGID HINGE Much research has been conducted into the use of rigid hinges in conjunction with thick four-fold origami patterns such as the Miura Ori, but less into sixfold patterns such as the Yoshimura. The intention of modifying the previous flexible hinge model by replacing the taped hinges with rigid mechanical ones was to observe what problems this would cause and whether strains within the origami system would lead to the model failing or locking up. In addition it was to examine whether there was a noticeable increase in the rigidity of the deployed system. What became evident whilst manipulating this model, was that there was a far greater level resistance within the system. With the hinges having to operate simultaneously, any small misalignments were causing strains to develop and creating flexing at those hinges. In some cases the strains were too large to be resolved and the hinges failed (F5.13). As the system had to act globally, any misalignments at the hinges near the centre of the structure were propagated towards the edges. The numbers of forms that could be created with rigid hinges was reduced as the system could not cope with the same degree of localised

folding generated whilst trying to deploy the system as an irregular form. The use of rigid hinges did increase stiffness in the overall structure however. Issues of alignment could be corrected if the faces had been marked with the positions where the hinges ought to have been located. In addition, using a continuous hinge along the length of each panel would reduce flexing and provide a stronger connection between faces. They would also improve the rigidity of the overall structure. This same rigidity could create further problems however. The hinges would be even more rigid and so any small misalignments could result in strains that cannot be resolved through flexing, resulting in the system locking up.

F5.11 Thick Yoshimura model with rigid hinges F5.12 Difficulty reaching folded singular state F5.13 Hinge breakage due to excessive strain F5.14 Gaps forming at hinges create interesting light pattern

Rigid/Flexible: An Origami Building Fabric

external polyurethane hinge

vertex wedge

5.4 LARGE THICK YOSHIMURA ARCH - 1:2

vertex wedge

eventual failure of the hinges.

externalrigid polyurethane hinge plywood panel

Two mock ups were constructed at the scale of 1:2. One was testing rigid continuous hinges that were positioned to the valley side of the panels (F5.19) and the other considered the use of a neoprene fabric hinge (F5.15). The aim of these prototypes was to observe if problems were amplified upon scaling up and whether the hinge arrangements worked at an architectural scale. It was also to test how the kinematic behaviour was affected through scaling, in particular the resistance during folding and unfolding. The mock ups were held at their boundaries to provide support and to examine the rigidity of the rest of the structure (F5.16, 5.20). Both prototypes performed well, but revealed how axis shift impacted on the building fabric. The thickness of the panels and hinges caused gaps to form between rigid panels particularly at the vertices (F5.21). On the rigid, continuous hinge model, hinges needed to be very accurately aligned to allow deployment of this over-constrained system. Increasing the number of panels contained within the mock up would only act to increase the chance of misalignments within the global system, which would lead to strains within, and the F5.15 Fabricated singular state - fabric hinge F5.16, 5.17 Deployed fabric hinge arch

F5.18 Underside of the deployed fabric hinge arch

F5.19 Fabricated singular state - rigid hinge F5.20 Deployed rigid hinge arch F5.21 Gap forms at vertex during deployment

The fabric hinge was laid out to the pattern shown in rigid plywood panel F5.23 so that it creased only at the valley side. The hinge had an inherent flexibility that allowed some misalignments to be propagated through the system. A major issue that could arise might be that the plywood panel foiltec insulation very flexibility that is alleviating the problem ofrigid misalignments, itself could cause the system to fail foiltec insulation folded skin by creating a multistable system that could lock up during folding. Additionally, the flexible hinge mock demonstrated that boundary support on its own was insufficient for stabilising the system once deployed internal foiltec hinge insulation and so additional stiffening at the hinges would bepolyurethane required. internal polyurethane hinge

vertex wedge

folded skin

assembled skin

folded skin

assembled skin

internal polyurethane hinge

F5.22 Flat-folded singular state - fabric hinge prototype

F5.23 Fabric hinge layout F5.24 Flat-folded singular state - rigid hinge

Rigid/Flexible: An Origami Building Fabric

5.5 FLEXIBLE HINGE PROTOTYPE The elastic hinge prototype explored the use of rigid panels suspended between two elastic membranes with the hope being that the elasticity within the hinges would allow the system to deal with misalignments and irregular deployment. This model shined away from what we would traditionally consider to be origami, as we are using elastic as opposed to rigid hinges. The hope was that this elastic fabric could also address issues to do with the continuity of the building envelope for improved sealing as well as the ability to generate a far greater range of forms without compromising the structural integrity of the origami inspired principles. This model uses laser cut MDF elements supported between two layers of elastic tight material (F5.29). The tight material could be scored according to the pattern demonstrated on the 1:2 fabric hinge mock-up for ease of folding, but this was not necessary due to the fabric being able to stretch across the mountain folds (F5.25,5.26). There were two main observations that I noted with the use of elastic fabric hinges. Firstly, the structure F5.25, 5.26 Outside of flexible hinge prototype

F5.27, 5.28 Inside of flexible hinge prototype

lost some of its rigidity and stiffness. This was to be expected as the elements that were supposed to provide the form with stiffness – the hinges, were now flexible. To some extent this could be controlled by varying the elasticity of the material used for the hinges. What should be noted however is that using stiffer elastic fabrics with a higher Young’s Modulus, may result in a more rigid, stronger structure, but the resistance provided by that very fabric will act against the ease of foldability of the structure. Conversely, using fabrics with a lower Young’s Modulus may ease the foldability, but may result in a structure that might not be able to support itself and therefore could require additional supporting members. The second observation was that the form did not appear to be flat foldable anymore. The use of rigid hinges, or non-elastic fabric hinges, as on earlier investigations, created fewer degrees of freedom within the global system and therefore allowed the structure to fold flat. Introducing elasticity into the hinges created the situation where the system had too many degrees of freedom and thus created multiple singularities causing it to lock before it could fold fully flat.

In order to develop this system further, more control needs to be introduced. A mechanism that allows the selective stiffening of the hinges would not only provide structural rigidity, but could also aid the system’s deployment or flat-folding. Another option that could be considered is using a hybridised system, whereby only some of the hinges are elasticised with others remaining rigid, so as to reduce the number of degrees of freedom.

Rigid/Flexible: An Origami Building Fabric

UPPER RIGID PANEL

AIRTIGHT MEMBRANE

LOWER RIGID PANEL UPPER RIGID PANEL

5.6 VACUUMATIC FIXING - RIGID HINGE Inspired by Tomohiro Tachiâ&#x20AC;&#x2122;s experiments into Vacuumatics for his Water Bomb design, I constructed a vacuumatic hinge stiffener that could be used with a 1:2 mock-up of the Yoshimura form. The vacuumatic system was attached to valley side of the hinge and was fixed into a double-layer panel. The vacuumatic system consisted of a breathable muslin bag containing an aggregate (rough sand), which was sealed and placed into an airtight membrane (F5.33). When the airtight membrane was not vacuum-pressured, the hinge was free to rotate, allowing the aggregate particles to reconfigure their arrangement. Connecting a vacuum to one end of the membrane removed the air and compressed the membrane onto the muslin bag containing the aggregate. The compressive force of the membrane on the aggregate, balanced with the tension within the membrane resulted in a stiffening of the hinge. The system worked relatively well for a single-hinge situation as demonstrated by image F5.30. Removing air from the membrane did stiffen the hinge and allowing air back into the membrane returned the flexible operation. One variable that needed to be controlled is the quantity of aggregate within the muslin bag.

Over-filling meant that there was insufficient space for the grains to reconfigure their arrangement when rotating the hinge resulting in a weaker stiffening effect.

ASSEMBELED

BREATHABLE AGGREGATE BAG AIRTIGHT MEMBRANE

UPPER RIGID PANEL TO VACUUM PUMP

One problem was that the system could not be folded flat. Because the vacuumatic system was placed toBREATHABLE the AGGREGATE BAG valley side of the fold, it formed an obstruction as the system approached a flat-folded state. One method of solving this problem could be to use a flexible VACUUMmock PUMP hinge as opposed to a rigid hinge as used in TO this up. Another problem was that the aggregate acted BREATHABLE AGGREGATE BAG to increase the mass of the building fabric. In this case I used sand, which is relatively heavy. The increased mass is undesirable due to additional strain placed on the structure as well as the TOextra energy required VACUUM PUMP to transport this mass. Lighter aggregates I could consider include ground coffee as used in iRobotâ&#x20AC;&#x2122;s (Cornell University) universal gripper, saw dust or expanded polystyrene granules. The use of transparent or translucent materials could also be sought in order to allow light penetration through the hinge.

F5.30 Vacuum applied maintains dihedral fold angle F5.31 Fabricated singular state for the vacuumatic hinge F5.32 connecting vacuum pump to the vacuumatic hinge

PIANO HINGE

LOWER RIGID PANEL PIANO HINGE

ASSEMBELED UNIT

AIRTIGHT MEMBRANE

LOWER RIGID PANEL PIANO HINGE

ASSEMBELED UNIT

FOLDED ASSE

FOLDED ASSEMBLED UNIT

F5.33 Vacuumatic hinge assembly

Rigid/Flexible: An Origami Building Fabric

UNEVEN DISTRIBUTION OF VACUUM DUE TO COLLAPSE OF MEMBRANE BETWEEN PARALLEL AGGREGATE BAGS TO VACUUM PUMP

Developing this test further, I examined the potential to connect two vacuumatic hinges in parallel to prove the scalability of this system across the overall building fabric. The key to ensuring this worked, was for the vacuum to be applied equally across the parallel arrangement even if the vacuum pump was connected to one side. By simply placing two aggregate bags in one, large airtight membrane, a vacuum was applied (F5.36). What occurred was that areas away from the pump did not experience a vacuum. The collapse of the airtight membrane close to the pump blocked the movement of air from areas further away (F5.37). A method for solving this issue could be to introduce a flexible, reinforced tube that could provide a conduit for transferring air across the entire membrane through to the vacuum pump.

HINGE FABRIC

UPPER RIGID PANEL

VACUUMATIC POCKET

LOWER RIGID PANEL

HINGE FABRIC

AIRTIGHT MEMBRANE

AGGREGATE BAG

AIRTIGHT MEMBRANE

AGGREGATE BAG

RIGID PANEL

RIGID PANEL TO VACUUM PUMP

TO VACUUM PUMP

F5.34, 5.35 Initial test into series vacuumatic mechanism

COMPRESSVE FORCE

TO VACUUM PUMP

COMPRESSVE FORCE

F5.34, 5.35 Initial test into series vacuumatic mechanism

F5.37 Problems of uneven vacuum distribution F5.38 Building fabric layout

Rigid/Flexible: An Origami Building Fabric

PREFABRICATION

UNFOLDED SINGULAR STATE

ON SITE DEPLOYMENT

GRADUAL FOLDING

FLAT FOLDED

5.7 HYBRID FLEXIBLE VACUUMATIC PROTOTYPE This mock up saw the rigid hinges of the previous prototype replaced with an elasticised fabric hinge, which in this instance was a latex fabric. The latex hinge allowed three things to happen. Firstly, the system once again became flat-foldable as the hinge could stretch to accommodate the vacuumatic mechanism. Secondly the system became more flexible and therefore globally speaking, the structure behaved in a similar PREFABRICATION way to the elastic hinge prototype in chapter 5.4 allowing it to be deployed in a variety of forms. UNFOLDED SINGULAR STATE GRADUAL FOLDING FLAT FOLDED Thirdly, it created a double-layered continuous building fabric, which would be more suitable for the purposes of creating a building envelope. As mentioned with the earlier hinge prototype the use of elasticised hinges created too many degrees of freedom, causing the system to lock up and not fold flat. The use of vacuumatics could not only provide the potential to lock the system into place once deployed, but it could also be used to aid deployment by selectively stiffening sections of the structure thus temporarily reducing the number of degrees of freedom (F5.43). The vacuumatic system was only applied to the lateral hinges (as opposed to the diagonal hinges) due F5.39 Rigid panel layout F5.40 Structure with vacuum applied

F5.41, 5.42 Different configurations possible with use of vacuumatics

TRANSPORTATION TO SITE

FLAT FOLDED

DEPLOYMENT

RECONFIGURING

STIFFENING

FLAT FOLDED

to their simpler arrangement as well as the fact that they were fewer in number compared to the diagonal hinges. Also, the lateral hinges define the dihedral fold angle and therefore the deployment and folding of the structure, so placing the vacuumatic mechanism here should be sufficiently effective. The photographs opposite show the performance of the vacuumatic hinge. Once the dihedral panels were folded to the desired angle, the vacuum pump was switched ON SITE DEPLOYMENT on. As the air was gradually removed, the structure stiffened. The system was now less reliant on fixing at FLAT FOLDED DEPLOYMENT RECONFIGURING TRANSPORTATION the boundary and in fact, this prototype was able to TO SITE stand independently once the vacuum had been applied. The stiffening of the hinges also had the effect of strengthening the over all structure. A 10 kg mass was placed on top of the mock up to test its resilience and the structure held its form (F5.41). Switching the vacuum pump off returned flexibility to the hinges and caused the prototype to fall.

RIGID PANEL

AIRTIGHT MEMBRANE

STIFFENING AGGREGATE BAG

LATEX HINGE

FLAT FOLDED

VACUUM CONDUIT

TO VACUUM PUMP

F5.43 Diagram showing how stiffness could be locally applied during deployment and folding

F5.44 Protoype needs to be positioned prior to applying vacuum F5.45 Diagram showing arrangement of vacuumatic structure

Rigid/Flexible: An Origami Building Fabric

LATEX

AGGREGATE BAG

The strength resulting from the stiffening of the hinges allowed the building fabric to be deployed into a wider arched form (F5.42). Flexibility also allowed flat-foldability. Applying the vacuum once the structure was folded flat acted to hold it in its compacted form (F5.49). Unlike the previous iteration of the vacuumatic system, a conduit was installed that allowed the vacuum to be distributed evenly beneath the airtight membrane, thus resulting in a consistent stiffness across two hinges in series (F5.50, 5.51). This proved that this system could be scaled up across the entire building fabric, with the control of local stiffness carried out through the use of valves. This iteration replaced the sand aggregate with ground coffee, which reduced mass significantly and also contributed to an improved stiffness at the hinge. Using an aggregate with a lower density such as coffee on global scale would reduce the overall mass of the building fabric and therefore would reduce the strain placed on each hinge. A lower force would also be required to stiffen the building fabric.

LATEX

AGGREGATE BAG

AIRTIGHT MEMBRANE VACUUM CONDUIT

RIGID PANEL

stiffness at the hinge. This could be solved on the final production hinge through better sealing and valves that maintain the pressure within the airtight membrane. Having said that, it would be very difficult to achieve a perfect seal and a monitoring system would be required to ensure that the vacuum pressure was maintained to prevent the movement of the hinge. Another problem was that the airtight membrane could become easily damaged, particularly because it was attached to the side of the building fabric that was likely to face the weather. Any perforations to the material would cause air to leak and render the mechanism useless. The airtight membrane would therefore need to be made of a material that is sufficiently resilient yet thin enough to deform easily over the aggregate bag. Polyurethane could be a suitable choice. Another solution could be to cover the mechanism, possibly with insulation, so that it remains protected.

The problems with this prototype were that the vacuum pump needed to be run constantly in order to maintain

AIRTIGHT MEMBRANE RIGID PANEL

CONDUIT F5.46 Folded and deployed VACUUM state of vacuumatic hinge

F5.47 Singular fabricated state of latex mock up F5.48 Application of vacuum compresses aggregate bag

F5.49 Vacuum keeps structure in its folded singular state F5.50 Conduit allows the vacuum to be distributed evenly between vacuumatic hinges in series

F5.51 Fabricated sectional layout of building fabric

F5.52 Latex hinges allow forms not possible with rigid hinges

Rigid/Flexible: An Origami Building Fabric

6 | Further Work This study has examined the behaviour of the Yoshimura pattern both digitally through using a zero-thickness model and physically through the development of a series of building fabric prototypes. Furthering investigations in the physical realm, I would consider the construction of a working 1:2 scale vacuumatic building fabric with several bays as essential. It would enable me to see the global behaviour of latex as the hinge material together with examining how the vacuumatic mechanism could work to locally stiffen the structure, particularly during deployment and folding. This would require the implementation of control valves that could locally control the vacuum being applied to each bay or hinge (F6.2). This mock up would allow me to test what configurations the building fabric could be deployed into using vacuumatics. Several examples of this building fabric could be constructed with varying gauges of latex as this will affect the flexibility of the system. Using thinner latex would provide more flexibility, allowing a greater range of forms, which could be counterbalanced by the stiffness provided by vacuumatics. Aesthetically the gauge of latex used could also impact on the quantity of light passing through the hinges providing interesting options for the illumination of interior spaces. F6.1 Form derived functions

Another area of further study would be to test the impact of applying vacuumatics to the diagonal hinges. This would allow me to discover if there were any additional gains to be had with regards to the potential forms that could be generated or the creation of a significantly stronger structure. It would also be fascinating to see whether thickness could be accurately modelled in the digital realm. Using the Karamba structural analysis plug-in together with Kangaroo the physics plug-in, it might be possible to see the effects of varying the degrees of flexibility and stiffness in real time on the forms that could be successfully generated. This could be tested in conjunction with topographic models to observe how a particular form would sit on various sites.

VACUUMATIC HINGE CONDUIT VALVE VACUUM PUMP

F6.2 Diagram showing arrangement for system with valves

Rigid/Flexible: An Origami Building Fabric

The findings of this report will be used to inform the design of deployable dwellings. The design will incorporate a Yoshimura-inspired building fabric used at a variety of scales and for a variety of applications. There is potential for the flowing forms to be used for internal landscapes, circulation, walls and roofs, but also for furniture elements and space dividers. The Yoshimura building fabric could provide the opportunity to create a series of dynamic spaces which could be reconfigured by the user through temporarily folding away sections and elements of the dwelling. The advantages of this building fabric are that it would be very thin, light and materially efficient, and would therefore potentially have a very low embodied energy. Using elasticised materials such as latex for the hinges allows the building fabric to have continuity, creating excellent sealing properties. Combining this structure with thin, yet high performance insulation such as Aerogel or multifoil would allow the creation of thermally comfortable interior spaces. Flat-foldability and low mass would allow for ease of transportation from factory to site and then on to further sites as required. Additionally, these qualities combined with flexibility could allow the dwelling to be placed onto awkward or otherwise unusable sites with the need for F6.3 Speculative interior of a deployable dwelling

minimal foundations - including locations on top of existing structures. The building fabric would contain vacuumatic lateral hinges that would need to be served by a vacuum pump. A single pump could be supplied with each dwelling, whereby the pressure to each section could be locally controlled by valves. These could be mounted into a beam positioned at the end of the building fabric that could provide support and form to the structure at its boundary. Whilst investigating the Yoshimura pattern, I have questioned the need to maintain the triangular panel shapes. The MOOM pavilion by students at Tokyo University showcases a tensegrity structure that has a clear link to the Yoshimura pattern. It consists of two components - aluminium tubes and an elastic polymer membrane to which they are attached. The entire structure weighs in at just 600kg18. What this shows is that the rigid panels of the structure could be reduced to the aluminium tube. A reduction in the panel in this way could not only act to minimise the mass of the building fabric, but also be used aesthetically to control the degree of light penetration or the views depending on whether the material used is translucent or transparent. 18â&#x20AC;&#x192; â&#x20AC;&#x2DC;MOOM Tensegritic Membrane Structure (Noda) by Kazuhiro Kojima | WeWantToLearn.netâ&#x20AC;&#x2122; <http://wewanttolearn.wordpress.com/2012/11/12/moomtensegritic-membrane-structure-noda-by-kazuhiro-kojima/> [accessed 22 April 2013].

F6.4 Speculative reduced structure inspired by MOOM pavilion

F6.5, 6.6 MOOM pavilion, Tokyo University

Rigid/Flexible: An Origami Building Fabric

7 | Conclusion The form generated by the Yoshimura pattern is effectively controlled by two main parameters: the crease pattern angle and the dihedral fold angle, which affects both the efficiency of the form and the radius of the generated arch. The rigid Yoshimura system has limited degrees of freedom due to all hinges needing to fold simultaneously. Its kinematic behaviour requires all hinges to be perfectly aligned and be rigid. This runs in contrast with my requirement for the Yoshimura-derived building fabric to be deployed in irregular forms. This required the introduction of flexibility to the system, and thus demonstrated the wide range of forms possible within the wider constraints of the pattern. What this also led to however was the model failing due to the introduction of too many degrees of freedom creating multistable systems and multiple singularities. The problem therefore centres around the balancing of the flexibility within the hinges and offsetting this with the stiffness needed to create a system that can be folded flat with sufficient levels of structural rigidity. Introducing thickness through the physical investigations raised questions about the optimisation

of the hinges, the continuity of the building fabric and problems generated through the introduction of physics and gravity. It was discovered that forms similar to those in the digital investigations could be generated through the manipulation of a thick Yoshimura pattern with flexible hinges, but these forms would require support at their boundaries. Axis shift caused by placing the hinges so that they were always located on the valley side of the pattern resulted in additional translations being propagated through the system. This caused gaps to form in the building fabric around the vertices and along the hinges themselves. The use of rigid hinges did not allow the resolution of misalignments within the system caused by incorrectly aligned hinges or irregular deployment. This generated strains that either caused the system to have a high level of resistance, lock up, or the hinges to break. Elastic hinges allowed for a greater number of forms with the loss of structural rigidity. These hinges created additional degrees of freedom, resulting in a system that was impossible to fold flat due to the creation of too many degrees of freedom leading to multiple singularities. Insufficient control of the hinge rotation resulted in a system that would lock up before it could fold flat.

Introducing vacuumatics to lateral hinges created stiffness that could be applied once panels were deployed to the correct dihedral fold angle. Using vacuumatics with elasticised hinges allowed the system to be deployed into different configurations whilst also being able to fold fully flat. Taking the development of this building fabric further, a larger prototype would need to be developed with a greater number of panels. This would examine whether vacuumatics could be used in aiding the deployment or folding if the vacuum was applied systematically over the global structure by the local reduction in the degrees of freedom about the hinges through stiffening. This system would need to use a series of valves that would provide local control to groups of hinges fed from a central vacuum pump.

Rigid/Flexible: An Origami Building Fabric

i | Bibliography 1. ‘ACTIS Insulation - The Benchmark for Hybrid Reflective Insulation’ <http://www.insulation-actis. com/produits-actis.php?p=3&l=3&rub=52> [accessed 22 April 2013]. 2. Bechthold, Martin, Innovative Surface Structures: Technologies and Applications, 1st edn (Taylor & Francis, 2008) 3. Gruber, Petra, Sandra Häuplik, Barbara Imhof, Kürsad Özdemir, Rene Waclavicek, and Maria Antoinetta Perino, ‘Deployable Structures for a Human Lunar Base’, Acta Astronautica, 61 (2007) 4. ‘Inflatable Robots by Otherlab: A Walking Robot (named Ant-Roach) and a Complete Arm (Plus Hand) | Hizook’ <http://www.hizook.com/blog/2011/11/21/ inflatable-robots-otherlab-walking-robot-named-antroach-and-complete-arm-plus-hand> [accessed 19 April 2013] 5. Mark Schenk, ‘Origami Folding: A Structural Engineering Approach’ <http://www2.eng.cam. ac.uk/~ms652/files/schenk2010-5OSME.pdf> [accessed 28 February 2013]

6. Mark Schenk, ‘Folded Shell Structures’ (unpublished PhD, University of Cambridge, 2011)

12. Tomohiro Tachi, ‘Rigid-Foldable Thick Origami’ (Taylor & Francis, 2011)

7. Martin Trautz, and Arne Kuenstler, ‘Deployable Folded Plate Structures - Folding Patterns Based on 4-Fold Mechanisms Using Stiff Plates’ (International Association for Shell and Spatial Structures, 2009)

13. Vinzenz Sedlak, ‘Paperboard Structures’ (Surrey University, 1973)

8. ‘MOOM Tensegritic Membrane Structure (Noda) by Kazuhiro Kojima | WeWantToLearn.net’ <http:// wewanttolearn.wordpress.com/2012/11/12/moomtensegritic-membrane-structure-noda-by-kazuhirokojima/> [accessed 22 April 2013]. 9. Osvaldo L Tonon, ‘Geometry of Spatial Folded F9orms’, International Journal of Space Structures, 6 (1991) 10. Tachi, Tomohiro, Motoi Maubuchi, and Masaaki Iwamoto, ‘Rigid Origami Structures with Vacuumatics: Geometric Considerations’ <http://www.tsg.ne.jp/TT/cg/ VacuumaticOrigamiIASS2012.pdf> [accessed 28 February 2013] 11. ‘ThermablokSP Aerogel Blanket - Thermablok UK’ <http://www.thermablok.co.uk/products/thermablokspaerogel-blanket> [accessed 22 April 2013].

Rigid/Flexible: An Origami Building Fabric

ii | Images FURTHER READING De Focatiis, D. S. A., and S. D. Guest, ‘Deployable Membranes Designed from Folding Tree Leaves’, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 360 Mark Schenk, ‘The Art and Engineering of Origami’ <http://www2.eng.cam.ac.uk/~ms652/files/article_ cambridge_engineer_2012.pdf> [accessed 28 February 2013] §‘Rafael García: Concrete Folded Plates in the Netherlands’ <http://www.arct.cam.ac.uk/Downloads/ ichs/vol-2-1189-1208-garcia.pdf> [accessed 28 February 2013] ‘Robert Lang: The Math and Magic of Origami | Video on TED.com’ <http://www.ted.com/talks/robert_lang_folds_ way_new_origami.html> [accessed 03 April 2013] Schittich, Christian, ‘Special Issue. Experimentelles Bauen [Experimental Construction’, DETAIL, 49 (2009), 1368–1376 Schittich, Christian, ‘Special Issue. Lightweight Construction’, DETAIL, 50 (2010), 64–70

Simon David Guest, ‘Deployable Structures: Concepts and Analysis’ (unpublished PhD Thesis, University of Cambridge, 1994) ‘Video Lectures in 6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2010)’ <http://courses.csail.mit.edu/6.849/fall12/lectures/> [accessed 05 April 2013]

Rigid/Flexible: An Origami Building Fabric

Rigid/Flexible: An Origami Building Fabric

VALLEY MOUNTAIN

Yoshimura Crease Pattern

Rigid/Flexible: An Origami Building Fabric

Name

Miura Ori

Miura Ori Pleat

Bellows

Square Bellows

Yoshimura

Deployment

+++

Transportation

Deployed Structural Rigidity Sealability

+++

Material Efficiency

+++

Simplicity

Form

Potential Use

Notes

+++

Non-structural, infill. Supported floor, supported wall, supported roof.

Supported floor, supported roof.

Enclosed space open at two Wall/roof/floor structure. ends - walls, roof and floor. Could be used for cantilevers. A closed form could be created.

Structurally, the performance of this system is poor however it can provide good coverage from a material that could be folded into a very small area.

If supported from four edges of the pleat, the structure remains stable. This makes it unsuitable for use in cantilevers. Deeper folds improves strength characteristics in Z direction. Can be formed into an arch by modifying the crease pattern.

Expanding form reduces structural performance as depth of structure reduced. Can create curved extrusions.

The square fold at the edge creates a strength that maintains the orthogonal edge. Could be used to create curved extrusions.

Name

Water Bomb

Closed Water Bomb

Hyperbolic Paraboloid

Developed Waterbomb

+++

Hexagonal Hyperbolic Paraboloid +++

Deployment

+++

Transportation

+++

Deployed Structural Rigidity Sealability

+++

---

Material Efficiency

---

Simplicity

---

Form

Potential Use

Curtain/wall mounted to additional structure.

Enclosed space open at two Roof structure. ends - walls, roof and floor.

Roof structure.

Could be used as a wall with additional structural support.

Notes

The behaviour of this system is complex. It does not provide sufficient stability on its own to perform as an independent structure. Could be used to create a textured shell structure.

The behaviour of this system is complex. It collapses in a scalar manner in the X, Y and Z direction. The expanded form can be locked into its expanded state by pushing out concave nodes.

The behaviour of this system is complex. It collapses in a scalar manner in the X, Y and Z direction. The expanded form can be locked into its expanded state by pushing out depressed nodes.

The behaviour of this system is complex. It does not provide sufficient stability on its own to perform as an independent structure. The structure can generate a rotated enclosed form around both the x and y axis, open at either end.

+++

Arch roof structure. Could be used for cantilevers if arch is placed on its side. An enclosed form could be created. The approximated arch form creates a structurally efficient form. Can be locked into position by pinning one pair of parallel segments.

By connecting the top two points with a cable and tethering the parabola to the ground, the structure can be stabilised. The structure is very complex. The form could be used to form a shell structure.

Rigid/Flexible: An Origami Building Fabric

Acknowledgements Thanks to the following for their assistance with this Thesis: Eva McNamara, Philippe Morel, Mollie Claypool, Kasper Ax, Tristan Gobin and Mark Schenk. I also thank my friends and family for their continued support.