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Contents

Forward Richard Arthur Ben Lillywhite

Forming from a 2D Form Ben Lillywhite

2Dimensional to 3Dimensional Material Folding with Tension Richard Arthur

Appendices Richard Arthur Ben Lillywhite

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Forward

This book is the exploration and design process undertaken for the Praxis Module of Abstract Machines at Leeds School of Architecture. The work is a response to the Fabrication Brief (shown below) by Masters of Architecture students Richard Arthur and Ben Lillywhite.

“Develop an architectural fabrication system, to be deployed as an installation, as an installation as part of the School Summer Show. The ‘works’ primary objective is to didactically communicate the nature of its being.”

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Contents

Introduction An introduction into the project, a description of the brief, the aims and hopes for the final outcome

Precedence Experimenting with the theme of Origami; learning from past case studies and developing a series of origami models experimenting with a variety of folding techniques

Concept Evolving from origami, the design begins to develop into creating a 3D form, from a 2D sheet material

Design Development Learning from the lessons gathered throughout to advance the design towards a final scheme

Conclusion Analysing the process that has been undertaken and evaluating the work

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Introduction

For the second semester of the 2013/2014 year at Leeds Metropolitan University, the Abstract Machines design studio was tasked with developing an architectural fabrication system; creating an installation that will be displayed as part of the School Summer Show. The aim of this chapter is to describe the process that was undertaken to inform my decision making and reasoning. I endeavour to analyse and test a series of concepts in order to create a fabrication system. By then collaborating my research with Richard, we will then design an installation that can be displayed at the School Summer Show. The brief of the project was to design, analyse, develop, prototype, detail and construct a fabrication system that is to be on display at the show, but likewise could be used in a variety of situations. Furthermore, any proposal was intended to be demountable at the end of the show. We were tasked with finding the resources ourselves and developing a system that could be installed by the studio members. Considering the build ability and costing aspects of the brief, I decided upon developing a system whereby any flat material could be used and constructed into a 3D form. By researching the art of Origami, I aimed to create a system that could fold into place, thereby being easy to construct and disassemble, with a variety of material options as it could be constructed from any sheet material. I hope to show that I have given consideration to a number of concepts, materials and techniques, always with regard to the brief. Through continual development, I will show the reasoning to produce my fabrication system and the key features of the structure that will be taken forward into the group collaboration and eventual installation. Richard and I’s proposed system is to be situated in the 5th floor studio alongside Abstract Machines’ RoboFold product and our first year MArch students’ design models. I hope the diversity of the studio’s designs inspire our audiences and increase their knowledge of parametric design, with the proposed designs being a key attraction of the show.

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Precedence

The form of origami has always inspired me because of the pure forms that are generated and was the initial direction I thought of taking when considering my proposed structure. Precedence is a key starting point of any design and through this chapter I research a student project case study, hoping to learn from their findings and solutions, before developing a series of origami models, aspiring to acquire a variety of folding and cutting techniques, to take forward in my design development.

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Sub Title

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Glass Origami Prototype, Los Angeles

The case study I have researched is that of 2b, the second year undergraduate studio at University of Southern California. The studio agenda focuses on materials, their properties, limitations and effects, similar principles to that of Abstract Machines. The studio started with precedence studies of the primary building materials before embarking on a precedence study of the glass pavilion in Toledo by SAANA. Being unable to bend glass similar to the glass in Toledo, they started to become interested in origami techniques and folding glass. Knowing this, I believe a panel and hinge system could be utilised in a similar fashion to origami folds. Discovering the amazing structural abilities and seductive reflections of folded plates, they became more ambitious. They explored various geometries in paper models and developed a number of detailed solutions. Through smaller prototypes and developments as well as many tight parameters, the glass changed to polycarbonate. A further lesson to learn is that of materiality. Polycarbonate was a preferred option due to a lighter mass, without a decrease in strength, It will therefore be imperative to carefully consider my chosen material.

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Origami Precedence

Using origami as a precedent, I began by creating a series of origami models to help create ideas of form and the type of systems that could be perceived. I initially started with a simpler cutting technique to produce the models, as I could generate a larger quantity of forms quicker, to analyse and evaluate.

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Origami Precedence

I learnt a lot from these models. For example, in the bottom row of images, a facade like structure begins to take shape, however both would require a frame from which to be supported. A favourite aspect of these models are the voids that are created when taking a flat sheet of paper, carefully cutting before folding to create the negative space. Traditionally origami is formed purely by folding, techniques I use in the following pages to develop my skill set.

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Origami

To develop the origami theme and improve proficiency, I take a flat surface and create multiple forms through an intricate pattern of folding from a single sheet. I like the rippling effect of the paper as the shadows create an added depth, whilst it is also possible to bend the “direction,� creating a defined route. It is immediately apparent that when comparing the cutting and folding techniques, the folding method is more complex. However, I believe the forms developed are purer and a truer reflection of what origami is perceived to be.

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Origami

I have simplified the glass origami structure of the 2b students analysed in my case study, into this tunnel. Initially I believed that the structure would be able to fold within itself, creating a “U� - like shape. However, when I attempted this, the generated fold was that of the top left hand corner in a shell like shape. This is useful research towards developing a fabrication system as I can start to witness folding patterns that would be able to fold within itself to be more transportable.

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Origami

Developing the origami models, I have begun to increase the difficulty of the patterns. The adaptability of the systems are amazing, with the model above providing some interesting patterns and contours.

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Origami

A variation from the previous model, this system originates from the image in the top left, before being stretched out to produce the images to the right. This model could be the basis for a facade system, or produce an intricate tunnel as shown in the centre images. As opposed to the folded origami models tested so far, this is the first prototype which can be folded to a manageable size and transported, an objective set out within the brief.

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Origami

By varying the angle of the folds, from an initial square piece of paper, it is possible to generate the circle depicted above, evolving to the fan like shape. A beautiful space is defined in the bottom left image, with the structure lending itself to describing a roof or canopy. This process has been useful as I can now start to develop ideas of how I can generate curves from a rectilinear shape.

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Origami

So far I have experimented with origami folding techniques from square pieces of paper. On this page, by tessellating the hexagon pattern, star like shapes are created that can be folded from an initial triangle shape, into the dome like structure. By testing a variety of styles and techniques, I am developing my skill set and working towards the brief designing a system that offers flexibility.

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Origami

An elevated flat platform is created from this flat sheet, which, when released, forms a domed structure with some fascinating forms. This is an interesting discovery as it perfectly captures the ethos of my study, creating a 3D form, from 2D. Using this folding technique, a thickness has been added to paper which can provide inherent strength and, as stated before, an elevated platform.

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Origami

This is one of my favourite models as the variety of forms that can be produced are beautiful. The adaptability from a relatively simple folding technique can generate a large number of iterations. Again, the system can be folded into a manageable shape, as shown by me holding it, a key concept to the brief. Despite all the variations I have created through these origami models, I realise that they are only possible due to the material properties of paper. I will therefore begin to research panelling models.

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Panelling Systems

In conjunction with the origami studies, I have experimented with panel models. Origami models are fascinating, however they are only possible due to the properties of paper, the thinness and flexibility, to create the folds. In these panel models, the key principle of folding flat remains, whilst a thickness has been added to the materiality to allow me to experiment with the forms that can be created and the limitations of the origami models. Using this panelling method, a hinge component has to be added, which will require further research later in my project.

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Panelling Systems

A variation of the panelling models, whereby a number of iterations can be created from a single pattern. I find the shadows generated from this pattern to be stunning.

Throughout this chapter I believe I have learnt a lot. I have developed my origami folding and cutting skill set, learning that whilst the methods and folding patterns can be utilised, they will have to be adapted in the future to give the material a thickness, meaning a hinge may need to be used. I set out to learn the origami methods. I now aim to take these forward to use in my concept and design development.

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Concept

Having experimented with the art of origami, I have been inspired to develop a system that can fold into position and engage with the audience. In this chapter I aim to develop my concept idea using the results of my precedence studies. Using cardboard as a thicker material, I intend to test possible designs to start to develop a concept form, before developing this in the future.

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Concept

I believe I have learnt a lot from the origami studies. I now understand that a panelling system is the way forward as a thicker material could not be folded in the same manner as paper is. Here, I take a flat panel (square) and fold panels from the centre to create the hour glass form. I believe this could form the basis of my design as it is a simple pattern which can manipulated in a variety of ways. I chose to develop and begin with this design as a square is a shape that people can relate to, like a piece of paper in terms of origami, before folding into an intricate shape. This design philosophy is something I am trying to replicate within my proposal.

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Concept

A key aspect of the brief is to test a multitude of ideas. I have therefore experimented with a variety of initial polygons to examine the results. An interesting outcome of increasing or decreasing the number of sides, is the resultant elevation height, with a higher number of sides causing a taller model. In the following pages I experiment with physical models to test jointing methods of how these proposals could be manufactured.

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Initial Physical Modelling

In this iteration, I have tested the system with a joint that folds and is held in a horizontal position. The joints could be locked in place with a custom locking pin. The system appears to be relatively strong and could support a surface when placed on top. However, if incorrectly balanced, the top half becomes slightly unstable. This problem could be resolved by increasing the number of sides, having multiple modules connected, or a vertical support member. All variations I will test in subsequent pages.

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Initial Physical Modelling

I began by increasing the number of sides to experiment with the models inherent strength. With an increased number of sides, the top half of the system appeared to become less stable and therefore had to be held in position. This was due to the increased number of hinges and components. I now aim to devise alternative solutions. This process has proved useful though as it is allowing me to gain first hand knowledge of systems that work, as well as don’t work, helping to relate the process back to the brief.

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Physical Modelling

Above is a model demonstrating how the system could work, whereby the supporting columns are pivoted in a vertical position, with no additional components required, such as the locking pin as referenced to before. The construction of this method is quite difficult as it was hard to add the pivot components, on a larger scale this problem may be resolved.

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Physical Modelling

By increasing the number of sides I could test the build ability and strength when using the pivoting supports. This system appears to be a lot more reliable and stable than the previous iteration, with the option to stand the system in an upright position. However, I noticed that the supports had to be aligned vertically, otherwise they would buckle, a consequence that didn’t occur in my models due to the stiffness of the joint.

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Tunnel

By mirroring the initial square shape along its edges, a tunnel like form as shown in the images above is created. However, as you can see from the close up image above in the highlighted triangles, the panels would start to cross over and interfere, producing problematic structural clashes and a failure of the system.

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Tunnel

By offsetting the shape, it allows the panels to slide behind one another and slot into place, allowing the system to work. The appearance of the panels in this iteration are starting to define a path, a possible use of the fabrication system. I believe the panels will help to self support each other by being joined together and so increasing the strength of the whole system, a structural problem I encountered when I physically modelled the form with horizontal structural members.

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Tessellation

Similar to when I was creating the tunnel, by keeping the base plan as a regular shape a generic cross is created. When the panels are angled and folded into position, they begin to clash, as can be seen by the image above within the circles. Carrying out a variety of these iterations are extremely useful as it allows me to detect problems such as those encountered on the previous pages and develop solutions Furthermore, it allows me to experiment with a variety of forms, all of which are helping to inspire my design development.

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Tessellation

After offsetting the pattern in plan, the panels are able to slide behind each other, up to a certain point, before they begin to overlap again and hit. This helps to solve the problem and starts to lead me forward in my design as I now know the limits of the system and I am learning about solutions and how they can inform a future design.

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Tessellation Development

I wanted to experiment with a larger form in order to test the pattern on a bigger scale and see if difficulties occurred. I increased the number of tessellations and although some waste would be created from a sheet material, a fascinating space would be created within the voids of the pattern when erected. If this was produced on a human scale, a “forest� like grid system is created allowing audience members to wonder through the maze.

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Tessellation Development

By testing the design theory against an alternative base polygon, I found a hexagonal form lends itself to being tessellated, with a tighter end result when folded into position. Waste is also reduced as a result of the closer packing provided by the hexagon shape. Again, I have had to offset the hexagons to one side in order for them to be able to fold into position. I now aim to test the findings of this digital research by physically modelling patterns and examining the results of adding a material weight.

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Physical Tessellation Modelling

By physically modelling the designs, I am able to test the construction aspect of the proposals, starting to devise methods in which any system could be constructed on a larger scale. The model above is depicting the offset tunnel effect, experimenting with how the panels fit together. The horizontal members have been used in this iteration and as a result the system appears to self support itself with an added number of panels, helping to clarify one of my previous enquiries. Using card for the models however is providing issues. When using tape as the hinging components, the material isn’t rigid enough to give a 100% true reflection. The hinge component therefore needs to be reviewed in the design development.

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Physical Tessellation Modelling

When increasing the number of modules within the tessellated system, the panels all slide together, creating an almost forest like structure. Although shown here, the system runs horizontally, if hung vertically, my proposal could start to form a facade system. With a facade system in mind and when considering the brief, a vertically hung system would require less material, and take up less floor space compared to a horizontal model such as shown above. This is a useful conclusion as it will reduce the cost of materials. Also, being at eye level, it may have a greater dramatic effect when compared to being positioned on the floor.

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Tower

So far I have experimented with the panel creating a tunnel form, before moving onto the “forest” of panels that are created by the pattern shown previously. Experimenting by mirroring the panels on top of each other, these “towers” begin to take form, which are supported by the modules underneath.

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Tower

Throughout the project, I have tested each new iteration against a differing base polygon to assist me in future design development and give me an insight into the types of form created. Again, I find that as the number of sides increases, the height that can be reached by the tower increases too with the same number of modules.

During this concept chapter, I have started to devise a possible basic form and have tested it in a number of iterations, using folding methods I learnt during my precedence. Throughout this stage, I have encountered structural problems, developing solutions which will help to inspire future design development. I have started to devise possible joints, with further testing and analysis required, which could also help inform my final design. I now aim to test this concept on larger scales, continuing to use digital and physical models to test my principles.

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Design Development

The form and design are beginning to evolve with a variety of options available. I hope to progress the system analysing individual components. During this period, I aim to develop the square form from the concept stage and experiment further with the tessellation patterns, exploring the vertically “hung� facade system. Through design consideration, I aim to improve the joint mechanism and research a variety of materials that can be used as well as refine the hinging mechanism. Finally, I hope to test and find further possible opportunities for the system, if for example, created on a larger scale. I will also begin to collaborate my research with that of my studio partner. As described in the introduction, individuals developed their theme and research, before being brought together to combine their findings. My partner has been researching a similar theme to me, creating a 3Dimensional form from 2D, using wire as a tension structure. I plan to incorporate this method into my own design, before we amalgamate our research to produce a final design for the School Summer Show.

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System Development

In tandem with developing the system, I am interested in evolving the form. This can be done in conjunction whilst developing the structure, by altering the length of the vertical support members. The images shown on this page have support members all of differing lengths as can be seen in the plan. This will allow each side to have an overall different height. This means that the panel can no longer sit on a flat surface whilst the support members are vertical. This is caused by the differing angles of the panels generated by the variety of support lengths. The system therefore, could now be suspended from a frame in order to produce a facade system.

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System Development

Following on from the images shown on the page opposite, I have altered the lengths of the support members uniformly on individual modules, allowing the system to lie on a flat plane and so the requirement for a frame is negligible. A sample of the type of pivot joint I imagine using is shown above. I previously experimented with the pivot joint, however believe there is a more suitable solution in terms of construction, that can be developed with another material. Whilst this concept allows for easier tessellation due to the symmetrical nature of the panels; by allowing the support members to be able to be individualised, the system takes on a unique form with complex geometry and a variety of views to be created.

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Tessellating the System

Tessellating a module with a variety of lengths for the support members creates a fascinating form. In this instance I have used the same length for the support members on opposite panels within the individual modules to create a flat plane between adjoining squares. As you can see in the elevation, the heights reached by the panels varies across the system, although the difference doesn’t appear to be as severe when compared to the variety of length of the support members. By off setting the panels in plan, the clashes are avoided as learnt earlier in my development. Tessellating along a horizontal plane shown here is keeping true to my design principles of being able to take a flat material, and construct the 3D form.

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Tessellating the System

On the opposite page, I investigated having support members at a variety of lengths, even on the same panels. Here, each individual module has had its support members set at a strict length to investigate the difference in appearance. Again, it is possible to see that despite a severe differentiation in the length of the support members, the final appearance of the system doesn’t alter too much. With the results in appearance negligible and the fact that the system no longer lies on a flat plane, if I was to progress in this current direction the system would need to be suspended from a frame, adding additional structure and components. This could then result in higher costs and therefore would need to be carefully considered as the studio seeks the funding required.

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Tessellation Development

I am beginning to investigate the effects of tessellating out the pattern even further and how this can be achieved. Here I have rotated the system around corner node points and the system expands quickly, whist appearing sparsely populated. In this iteration, I believe the system would be relatively flexible and possibly unstable in the centre as there is not enough structural support. However, there are four clear points to which the system can attach to a frame which would provide added stability.

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Tessellation Development

Developing the system so that there was a “denser� core which would help to support the structure, I found that support members all had to be of equal length for the structure to fit together and work. I like that the uniform pattern is created and can picture it being pulled in and out, sliding along a frame, adding another dimension to the installation and interacting with the audience. By only using hinging components, I am reducing the number of materials required, therefore reducing costs and simplifying the construction process

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Facade System

From the previous tessellation images, it appears as though the system can be utilised as a facade system. With this in mind, I decided to apply a method so that the light intensity informs the angles and therefore the “openness� of the structure. In this iteration, as light intensity increases, the modules begin to open, almost like a flower, and so allowing an increased level of light through. This technique would be possible using a light induced polymer, however the cost of this material could prove to be too much for what the studio could raise, although the future possible system is already there.

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Facade System

By adding in a series of random holes, fascinating shadows will appear, with the dispersing of light being scintillating. The holes could open and close depending on the light intensity, or be further tested to experiment with the light deflection. If the material allowed, etching patterns could be produced on the surface to manipulate the light in a defined way as an alternative or additional option. On this page I have considered the finishes of the structure and how it could be perceived by the audience. I want to bear this research in mind when I finalise the design.

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Facade Development

Continuing with the theme of creating 3D forms from a 2D sheet, it is possible to create seating out of the panels, which can be folded down. Alternatively they could be designed so as to provide shelving for an Exhibition. Considering future possibilities for the system, a key concept of the brief, this idea shows how the proposal could be taken forward. Although the scale I am using doesn’t lend itself to being used as a seat, the system highlighted on these two pages show future possibilities of my system, if construction and time allowed for my proposal to be built on a human scale.

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Facade Development

I developed two possibilities of creating a shelf component in the panels and modelled them as detailed above. In the top iteration, there is a fixed pivot point at the base, a hinge located along the chair, with a pin attached either side that slides within a defined track. This proved to be relatively strong. However, this would be difficult to construct as the track would need to be milled out to allow the pins to be placed. This would mean the centre hinge of the chair being the difficult part to slide into place. An easier construction method is the lower option. Consisting of two pivot points, the internal panels rotate into their positions as shown above and provide a strong base.

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Material Development

During the entire project, I have been researching a variety of materials which will fulfil my requirements. Di-bond is a material I have been introduced to through this course. It is a composite material made up of 2 layers of 0.3mm aluminium sandwiching a polyethylene core, the thickness of which can be changed. The advantages of this material are that folds can be created, reminiscent of the origami structures I researched earlier in my project. Therefore, di-bond is the only material required as it can be its own hinge, as well as frame and so greatly reduces lead time and construction times. In the model I created I devised a double hinge joint as can be seen in the images, that support the upper portions. This joint had to be aligned perfectly vertical, otherwise the strength was lost.

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Material Development

Unfortunately I discovered that the joints had been milled too deeply and so failed after relatively few number of folds. This is because as the joints get folded, the material has a workload limit and therefore snaps. The image in the bottom right shows that all of the joints have the ability to fail, and it is not restricted to a single component. The solution for this is to reduce the depth of the milling for di-bond. Whilst this will make the joint stiffer, it should reduce the failing. This proved to be an important model though as it has helped me to find the limitations of the material and therefore can take the findings into consideration in future development.

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Joint Analysis

Within this chapter, I set out to not only develop the system, but also the fabrication aspects. Here, I aim to analyse the joints that I have used throughout the project. I will also incorporate the wire tension technique researched by my partner in order to enhance my scheme. Originally I had the support beams running horizontally, picturing a locking mechanism that supported them. This meant that the top half of the system was unstable, however, when this pattern tessellated out, the structure self supported itself, resolving the issue. The vertical support system was the second iteration, helping to solve the unstable top half of the structure. Whilst this structure works well, it relies on friction with the ground it sits on. Combining my research so far, now with my partner, I have begun to experiment with a wire tension supporting method. Shown here are the first iterations, exploring my understanding of the system and learning that it is crucial to get the distances between the panels correct.

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Joint Analysis

Horizontal Supports Top half of structure becomes unstable

Vertical Supports System relies on friction

Tensioned String Using the string to act in tension

By using the string in the final diagram, the whole system is held in tension and therefore may become distorted if a force is applied on one of the panels. Difficulty may arise when tessellating out this system. A decision would need to be made as to whether this would become one tile of a pattern, with each module individually strung, or the more complex alternative would be to string the whole system together. This method of one continuous string holding the complete tessellated pattern may be infeasible as difficulty arises when the string attaches to the next “tile,� before the need for it to return to its original point. I plan to use the di-bond as described on the previous page as it neglects the need for a traditional hinge and reduces the number of materials required.

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Design Development

Digitally modelling an individual piece of the system, allows me to analyse the lengths of the required string between the panels. By tessellating the pattern out, it is possible to see that the strings don’t intersect and that the system works. I am pleased with the way this digital model works. I have also witnessed through the development of my partners work that the system works well in a physical model. Using the tension in wire, a number of hinges can be removed, therefore, simplifying the whole structure and reducing the number of components that can fail.

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Design Development

Relating this system back to one of my earlier iterations, if the modules were to be stacked vertically, there is a higher possibility that a single piece of string could be used to hold the system in tension, as a more visible method of doing so arises. In the iteration shown to the right, a lot more material is required to create an installation, when compared to a system which lies in a vertical plane. The floor space required is also increased when the modules tessellate horizontally. With an increase in materiality, costs also increase, a major disadvantage to the system as it will detract from the resources available for others.

In this chapter, I am pleased with the variety of designs created, digitally modelling a multitude of iterations and tessellation patterns, before physically modelling to examine the construction aspects. I researched an assortment of materials, concluding di-bond was the best option as it reduced the number of components and materials required, therefore reducing costs. Combining my efforts with that of my partner, I am excited about the direction we can take and look forward to working together on our proposal for the School Summer Show. Digital Fabrication 2D to 3D

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Final Design

Having analysed possible avenues, I now aim to conclude my design options into a succinct proposal. Using the folding philosophy of origami, in conjunction with the design research I have conducted in this book alongside that of my partner, I will collaborate my ideas into a final design. A final design which will fulfil the requirements set out in the brief, be easily constructable, cost-effective and inspire audience members.

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Final Design

The defining principle throughout my project has been the ability for a structure to fold out from a 2D form. I am therefore basing my design upon a panel of Di-bond, a material introduced to me during this process and described previously. The centre image shows the main design. The design focuses around the tessellation iterations previously researched. A pattern of 5 squares are rotated around, highlighted in the image to the left, before being tessellated again into a pattern which best fits within the constraints of a 2440mm x 1220mm di-bond panel. Highlighted in blue is the pattern which will be cut out and milled, so that the system can hang from the panel itself, thereby folding back into the completed flat panel when required. The remainder of the panel creates the required frame, therefore producing a secondary function reducing costs. In the image to the right, highlighted in red are smaller patterns which will be completely cut out and form single elements that can be situated around the display, allowed to be picked up by audience members to inspect the system.

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Final Design

3 full size panels will be cut out and this will form the basis of my design. By having 3 different patterns cut out, a variety of shadows will be cast, with a multitude of smaller models being created. I then plan to stack a handful of these on top of each other, to show a variety of possibilities from the one initial shape and fabrication system. The smaller individual components can then be examined by audience members. This participation helps to engage the visitors, an aspect of my initial brief. The axonometric on the following page helps to detail the folding process of the tessellated pattern. This applies to both the smaller cut out modules and the main design feature.

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Final Design

To assist in describing the intention of my design, I have provided an axonometric detailed above. The diagram helps to explain that as the panels are folded into position, the volume in which they encompass reduces and with the red dotted line, it is possible to see where the folded ridges will occur. Over the page are images of the final model, showing the effect of this folded, tessellated pattern in a physical form.

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Final Design

The three panels will then be hinged together creating a self supporting, facade system and frame. When the installation needs to be moved, the panels can be folded up and transported easily, a key aspect of my brief. The whole installation is to be constructed from 3 panels, with 3 hinges placed equally along the edge of the panels. The di-bond helps to form the frame, therefore, reducing the number of materials required. The idea of a panel folding to create a 3D form stems from my initial origami research and like my previous findings, I believe as the modules are folded into place, they will take on another form, not previously witnessed. It is possible to get di-bond with a number of finishes including mirrored, which would reflect and disperse the views in a fascinating way. If this system was therefore used to define a route, a light source from one end could be reflected across the facade system. Although, due to cost constraints we can’t use the mirrored finish, it helps to show future possibilities. I have begun to physically model the final design in order to test the structure and create final visuals. Shown above are the beginnings of this model. I have kept the colour pattern in this model and aim for the system to hang from the uppermost tile. On the following pages are images depicting my final design produced by my model.

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Final Design

The images above are taken when I was constructing my model. The images to the left illustrate the individual components that are created from the red cut out parts, detailed previously. In the centre are images to show how the system would hang when cut out. After doing this process, it was apparent that more of the frame would need to be cut away, as shown in the image to the right. This additional cut away was necessary because, as I found out earlier in the design, when the system is folded up, the area it encompasses contracts and therefore conflicted with the frame.

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Final Design

Above I have depicted the various stages of the system. I wanted to show the development of the system taking place from start to finish to illustrate the construction stages as previously described in this chapter. The above image perfectly shows the distinct variations from when the system is cut out (centre panel) to the finished position and the reduction in area. The system worked perfectly and hung from the uppermost tile as hoped. I was really pleased with the outcome and find it incredible that the whole system hangs off of this one module. Furthermore, the shadows that are generated by the voids both of the frame and the system itself are, I believe, stunning. Having the smaller individual modules around the base of the installation offers another aspect and help to engage with the audience by including their participation. Being able to pick up these modules and examine them, assists them in understanding the system.

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Final Design

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Final Design

I began this process by investigating origami and I believe with this system that I have captured the essence of origami whilst adding a material thickness. I hope that my proposed system engages with the audience in the same manner of awe as origami has captured me. The next stage is to conclude this design system, before moving on and developing the methods learnt with that of my partners to produce the installation for the School Summer Show.

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Conclusion

For the second semester of the 2013/2014 year at Leeds Metropolitan University, the Abstract Machines design studio was tasked with developing an architectural fabrication system; creating an installation that will be displayed as part of the School Summer Show. From the outset, a clear brief was given: to create an elegant system that showed off the philosophy of Abstract Machines. Instructed of the location, the studio were to design, fund and construct the installations. Throughout this chapter, I believe I have demonstrated thought behind all of my decision making and have produced an intricate, beautiful installation, that embodies the origami models I research initially. Having tested a number of ideas, I worked through any problems producing the solutions which ultimately guided my final design. I have learnt a variety of new skills through this process as well as the necessity to continually assess materials and construction techniques. I hope to have proved the efficiency of my proposed system, taking forward with me the key principles of my structure that will be utilised in our joint design efforts. With my knowledge of origami, the panelling systems discussed within this chapter and my understanding of materials, they will be essential in future projects. I now look forward to the next stage of this process, in developing a fabrication facade system combining my efforts with that of my partner. We believe we can construct a stunning installation as part of the School Summer Show that helps to encapsulate the ethos of Abstract Machines and can inspire future students to join and improve on our work.

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2Dimensional to 3Dimensional Material Folding with Tension

Contents Professor Yoshinobu Miyamoto 2D to 3D - Paper Experiments Tension Torus

2D to 3D - Paper Experiments

2D to 3D - Tension Torus Shape Experiments Paper, Digital Scripting and CGI

Tension Torus - Material Study Paper and Fishing Wire MDF and Fishing Wire DIBOND and Elastic

Tessellation on 3-Dimensional Geometry Icosahedron Dodecahedron

Volumetric Tessellation

Tessellation - Facade Systems Varying Number of Arms Varying Depth of Arms

Conclusion & Bibliography

Introduction This chapter will describe the process taken to create a 3-Dimensional geometry or facade system from a 2-Dimensional surface. The progression will move from experimentation to simulation with physical and digital modelling.

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Professor Yoshinobu Miyamoto 2D to 3D - Paper Experiments

Professor Yoshinobu Miyamoto is a Japanese Architect and Paper Engineer. He is a professor and lecturer at the Aichi Institute of Technology. As a Paper Engineer he transforms 2D sheets of paper into 3D paper geometries, these geometries have increased strength above that of the original surface. This page shows my first experimentation of Miyamoto’s work, the slide-together geometry consisting of twenty triangles with a 45 degree slot cut into each side in a clockwise direction. One slot then slides into an identical slot on another triangle. Once all triangles have been slotted together a triangular ball exists.

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Professor Yoshinobu Miyamoto Tension Torus

The Tension Torus is a concept for structural and construction systems. In this case half-circles become compression arches and the strings become tension cables. Issues that arose were the thickness of the paper and the cotton used for the tensioning cable. Paper thickness was an issue due to the arches and surrounding edges bending under the varied pressure exerted by the cables. As one cable was tensioned the others became slack. The cable strings start and finish on the same arm after being attached to each individual arm.

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2D to 3D - Paper Experiments

To further understand 3D geometries being formed from a 2D surface I have applied Miyamoto’s process of sliding shapes together. This page is showing rather than a triangle slotted together I experimented with a hexagon. The principals stay the same with respect to the number and position of the slots but these slots are spaced at every other edge of the surface rather than on each edge. I have come to the conclusion that this principal should continue to work as long as the shape to slide together has a number of edges dividable wholly by three.

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On the previous page the geometry was formed using twenty identical surfaces. Again using the same sliding principals the scale was changed. Ten surfaces at the original size and ten 50% smaller. Having this range allowed the geometry to take a new but similar form and through the use of different material colours the form was able to have a different visual effect. Further iterations of this form would be possible but within the parameters of the primary principals.

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Half Circle

2 Sided

3 Sided

4 Sided

5 Sided

Half Star

Random

1 to 5 Sides

Depth Variation


2D to 3D - Tension Torus Shape Experiments Paper, Digital Scripting and CGI

Using a the 2 Dimensional diagrams on the left the forms below were generated with the aid of a paper cutter. These iterations took into consideration the issues that had been experienced at the experimentation stage. A thicker paper was used and the cotton which was used previously was replaced by fishing wire, which was threaded under tension as a single length. This created a better outcome for these experimentations.

2 Sided

3 Sided

4 Sided

5 Sided

1 to 5 Sides

Depth Variation

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Input shape

Curve division

Rotate surface around circle for a chosen quantity

Rotation

Circles on points

Curve offset

Create surface

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Find the center of each circle in surface


Sort and number points for threading

Thread holes. Extrude surface and pipe threaded curves

Mirroring on different axis planes Digital Fabrication 2D to 3D

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Shown above is the computer generated control script used to create and manipulate multiple variations of the shown geometry. The scrip only requires the desired shape to be input but further development of this script could take this element away and leave a control slider/s to determine the starting shape. These pages show the computer generated geometries of the 2D shapes shown previously. The key element with the addition of the computer control is the ability to easily transform the single projected geometry by rotating and mirroring. The outcome from this is a geometry which identically mirrors though 180 degrees along the rotation plane or mirrors along the rotation edge giving two mirrored variations. Left page images - 180 degrees creating whole shapes. Right page images - 80 degree difference standard mirror effect created.

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180 degrees

Half Circle = Full Circle

2 Side = 4 Side

3 Side = 6 Side

4 Side = 8 Side

5 Side = 10 Side

Half Star = Full Star

Random Shape


80 degrees

Half Circle

2 Side

3 Side

4 Side

5 Side This digital process has brought to light the issues that may arise when fixing two torus’s together. What will the connection be and how will it be fixed? The exercise has also explained that as more arms are added to the structure the node size at the centre will need to increase. To further this digital experimentation I will experiment using the mirroring process and differing materials for both the structure and cabels. The material changes will study thickness change and how the structure can be fabricated.

Half Star

Random Shape Digital Fabrication 2D to 3D

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Tension Torus - Material Study Paper and Fishing Wire

Using the half circle and a 180 degree mirror effect. The chosen material is card but due to the original restraints and issues surrounding the use of card a stronger card was used. The material choice for the cables is fishing wire as it has a better structural integrity than cotton. This experimentation was both a failure and a success. It failed in terms of size and though human error, a wire was cut whilst removing the central node. Jointing the singular structure to its mirror was also problematic due to the cable connection being in the glued joint. Although there were failures the successes were the that the form was able to hold its shape without a central node or outer frame. To further this experimentation I will test with a rigid material at a larger thickness. I will continue to use the fishing wire as this gave a good finish and the strength properties should be high enough for a model of a larger scale.

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Tension Torus - Material Study MDF and Fishing Wire

MDF was the chosen material for a larger attempt of the previous model and the experimentation iterations. Each side of the form was generated individually from a single sheet of 3mm MDF. The two sides were then fixed together mirroring about the central vertical plane. As mentioned the cable material of fishing wire has been reused. A major difference between the paper model and this model was the hinge joints. With the paper versions this was formed by either a fold or a glued joint. This study required the use of brass hinges and screws with glue also being used where the timber was too thin. Unlike the paper study the central node and outer frame have been retained for structural support. An outer frame could be used to aid in tesselation but through the use of another material the outer frame may become redundant.

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Tension Torus - Material Study DIBOND and Elastic

DIBOND is an aluminium sandwich composite panel with unique properties that allow routing and folding. Using DIBOND removed the need for a physical hinge and has a considerable weight difference to that of the MDF version. To produce the hinge or fold one layer of the aluminium and the plastic inner are removed by a router. This process creates a clean bend but over time the fold can become work hardened and brittle. With this study a similar mirroring process was used as with the MDF study however the external frame was removed. One constraint of using the CNC router is the cutting bit size which requires to be accounted for as sharp angles and tight corners can’t be cut. With this study the fishing wire was substituted by elastic which allowed a little extra flexibility but when pulled taught held the form in the desired fashion. Using this principal I will look at how this form can be tessellated over a geometry or surface.

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Tessellation on 3-Dimensional Geometry Icosahedron

The form used for this experiment is a three armed tension torus with the outer most point forming a triangle. This triangle then forms an icosahedron. An icosahedron is a polyhedron with twenty triangular faces, thirty edges and twelve vertices. A regular icosahedron with identical equilateral faces. These twelve vertices are where five triangles meet and therefor create a new nodal point for the entire geometry. The process moved from creating a geometry with an inner geometry and an outer shell or facade, to the removal of the inner geometry and mirroring shell as explored earlier in this chapter. To expand on this study I will test the principals to explore another geometry.

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Tessellation on 3-Dimensional Geometry Dodecahedron

This study has used the dodecahedron as the inner form. The reason for this is that the dodecahedron is closely linked to the icosahedron in terms of vertices and faces, having twenty vertices rather than twelve and twelve faces compared to twenty. The connection that is formed is between three pentagons which have been produced by joining the outer most points of a five armed tension torus. As previously multiple options of arm design can be used within the primary principals and the form can act over the dodecahedron form or the form can be removed and the torus mirrored within itself. To experiment further, what happens if the inner form is tesselated and the torus added across?

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Volumetric Tessellation

Using the dodecahedron geometry as a 3D tessellation to create an abstract structure. The vertices nodes along with the tensioned cables could potentially become a load-bearing structure. With further exploration of tessellating 3D geometries there would be multiple available iterations to form new variations of the form. As shown here in a basic form this can be linear both horizontally and vertically. Another variation would be to grow exponentially in all directions. This is where using a computer program to aid this growth and apply principals and rules could transform the geometry into a complex growth with openings and the mapping of different iterations. These conceptual structures could vary in scale from lighting installations to building structures.

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Tessellation - Facade Systems Varying Number of Arms After studying the tessellation of the tension torus over another geometry a facade study was carried out (left). This study was looking at how the torus would tessellate as the number of arms was increased. The study proved that three arms and six (below) arms tessellate individually but when they are joined there is an arm that is not connected. Once the arms were increased beyond six as shown there were arms disconnected even when its neighbor is identical to itself. Looking at the increase in arms and the shading created a connection was made back to the varying of depth of the arm profile rater than increasing or decreasing the number of arms.

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Tessellation - Facade Systems Varying Depth of Arms

As described on the previous pages the next stage of a facade system using the tension torus is to fully tessellate the geometry along with addressing shading using a varying depth arm profile. The images to the left show this being implemented. This system could be arranged in any way from accurately assessed and designed to random. It would be possible to use computer programing to design the optimal system.

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Conclusion & Bibliography

This chapter has studied and explored the creation of a 3-Dimensional geometry from a 2-dimensional plane. Studies have successfully evaluated types of materials and differing iterations, paper to dibond and a single curve to multiple edges. Starting with physical studies of work by Professor Yosinobu Miyamoto and logically working through rapid physical prototypes onto using computer programs to control the outputted forms. Using computer programs to control the form allowed the creation of complex forms and geometries. As described these forms could be constructed on both small and large scales. All information within this chapter could be further studied and expanded upon. This will for the fundamental basis for the facade system described within the introduction.

Flickr. Yahoo! 03 Feb. 2014 <https://www.flickr.com/photos/yoshinobu_miyamoto/>. Gjerde, E. (2008) Origami Tessellations: Awe-Inspiring Geometric Designs, Massachusetts: AK Peters LTD Glynn, R., Shell, B. (2011) Fabricate, Ontario: Riverside Architectural Press Iwamoto, L. (2009) Digital Fabrication: Architectural and Material Techniques, New York: Princeton Architectural Press Jackson, P. (2011) Folding Techniques for Designers From Sheet To Form, London: Laurence King

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RoboFold Digital Fabrication Workshop January 2014

Abstract Machines undertook a week long workshop at RoboFold in London. This workshop was used to develop and further our knowledge of curved folding. Starting with paper experimentation though to using robotic arms to fold sheet metal into a desired geometry at a 1:1 scale. Constraints that were discovered were the angle of curve. This was apparent in both the first stage (paper) and the final stage (metal). As a group we successfully designed and constructed a 1:1 facade covering an irregular surface.

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Faรงades

Baker Street Building

Spikerverket

Kunsthaus Bregenz building

Oxford Street

Lightmos Thonglor

Harper Road Housing

Throughout this book we have described our systems developing towards a facade system. A facade is predominantly the front elevation of a building, often called the frontage. Over the next couple of pages we describe how our proposal could be considered a facade system. Shown on this page are a sample of faรงades. Traditionally, the facade is considered to be a fake front, added to the elevation to alter the appearance of the building, whilst assisting little in the structure.

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Façades

RMIT Design School

Torre de Especialidades

BIQ House

The Gardens By The Bay

Bloom Installation

Al Bahar Towers

With advancements in technology over recent decades, the possibilities of what the facade can achieve are continually progressing. Through careful engineering, the facade can now assist in heating the internal environment, provide custom solar shading when required and help to control ventilation, along with many other factors. Defined by a number of factors, the facade can now begin to not only provide an alternative external appearance, but also to control the internal atmosphere. Shown on this page are some extremely intelligent smart façades. The BIQ House’s southern facing façades are covered in a second outer layer containing water and micro-algae. After these micro-algae grow and photosynthesis occurs, they are taken to a room within the building where they are then converted to biofuel, therefore creating a renewable energy source. Whilst at the Al Bahar Towers, there is an external cladding pattern that opens and closes to provide shading and reduce glare from the desert sun for the internal environment. These systems are incredible and help support their building. With these factors in mind, we propose that our system has the ability to be able to be produced and informed by external aspects, if costs and time allowed for. Both of our proposed systems detailed in our individual chapters allow for components to open and close in a similar vain to that of Al Bahar Towers. Not only providing shading, the resultant installation may have acoustical effects too. In the systems shown above, all the systems have been attached to their respective buildings and we believe our system could be introduced to a building in a similar fashion.

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Digital Modelling

AutoDesk AutoCAD

Rhinoceros

Grasshopper

A program used by architectural firms for many years now, AutoCAD is used to create almost everything, from floor plans to door jamb details.

“Rhino” is a 3D modelling programme that specialises in NURBS based design. NURBS (Non-uniform rational basis spline) is a mathematical model that represents curves and surfaces.

Grasshopper is a visual programming language, a plugin for Rhino which assists in parametric design.

We have used AutoCAD throughout this project to create cutting patterns that were then used on the paper cutter by Richard, before we both used it on a CNC cutter to generate our di-bond models.

We again both used this program to digitally model our designs, using the grasshopper plug-in to assist in our design. Rhino can be used to export files types to 3D printers, as well as the laser cutter.

Components with inputs and outputs, are dragged onto a canvas, before being connected together in a “script” or “definition.” Data can be defined locally by a variety of inputs, or linked from a Rhino model. Despite it being a scripting tool, the components create a 3D geometry within Rhino. Grasshopper is our main digital design tool. We use it because of its inherent parametric properties. We can quickly create a number of iterations based on parameters we have defined, then either manipulating the results within Rhino, or adding additional criteria to refine the outcome.

In Abstract Machines, we are encouraged to digitally and physically model all of our ideas in order to progress ideas and gain a fuller understanding of the concept and forces. Interested in parametric design, the studio predominantly use Rhino and Grasshopper to produce our digital concepts. These pieces of software allow us to test a variety of iterations based on a defined list of criteria. The advantages of using digital modelling are numerous. Initial models and minor alterations can be produced instantly when compared to producing a physical model; analytical software can be utilised to assess criteria such as structural stress, analysing a number of simulations. Whilst a final design is not computationally generated, a “best fit” scenario is. This form can then be manipulated by the designer, in the knowledge that it fulfils all of the requirements and defined parameters.

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Physical Modelling

Scalpel & Ruler

Laser Cutter

3D Printer

Bandsaw

CNC Cutter

Robotic Arms

Physical modelling is important whilst designing and prototyping. Having a tactile model which can be reviewed from a variety of angles, picked up and analysed is essential. They help to test structural questions and examine the effects of adding a material weight. In both of our early designs, we used paper. This was because it allowed us to quickly create a variety of ideas and experiment with our design principles, before adding a material thickness using card. By understanding the properties of a given material, we can then analyse and conclude the best equipment to use. As the materials became denser and thicker, the machinery required to cut them became more industrial. To create Richardâ&#x20AC;&#x2122;s MDF study model, he used a template and cut the model out on the bandsaw. This was due to the thickness of the material and the limitations of a laser cutter. Our proposed system is to be constructed from di-bond. As a result of the material build up, described on an upcoming page, di-bond can be milled into to create a hinge. We therefore plan to use the CNC cutter, and import an AutoCAD layout, as it can both cut and mill di-bond in order to produce our design. This is hugely advantageous as it reduces the amount of labour and greatly increases the speed at which our system can be constructed. Digital Fabrication 2D to 3D

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Materiality Analysis

Paper

String

MDF

Cardboard

Fishing Wire

Foam board

Our initial concept models were developed from paper as it allowed us to create the necessary folds due to the thinness and flexibility. However, we quickly realised that a panelling system was required to overcome the lack of these properties in a thicker material. We therefore tested our designs with a thicker and denser material, cardboard. Richardâ&#x20AC;&#x2122;s design focused around using a wire as a tension component. He experimented with both string and fishing wire. Using the string, Richard found that it gave an added flexibility, however, it was prone to snapping. The stronger alternative was fishing wire, which although wasnâ&#x20AC;&#x2122;t as elastic, created additional strength within the system. We both then experimented with additional, thicker materials. Ben used foam board to allow the possibility of using a pivot; however, this would have meant a very thick material when scaled up to 1:1 and therefore, moved away from a pivot joint to a hinge joint. Whilst Richard experimented with MDF, used both as a frame and to form the structure. We have both been developing our systems with a hinge joint and were directed towards di-bond by a studio tutor, the properties and advantages of which are detailed on the opposite page.

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Materiality Analysis

As mentioned throughout this book, di-bond is our chosen material to advance our systems and construct our final proposal. Di-bond is a composite material, consisting of 2 layers of 0.3mm thick aluminium, sandwiching a polyethylene core that comes in a number of thicknessâ&#x20AC;&#x2122;s. There is also a variety of finishing colours, including a mirror effect. Highly resistant to weathering and corrosion, di-bond adds increased stability when compared to the earlier models we developed that had a similar flexibility, especially the card iterations. With these properties, any future proposal would be equally welcome indoors or out. As described on the modelling page previously, di-bond can be easily cut and milled out. This allows for a hinge to be inherent within the structure, therefore neglecting the need for the additional components. As detailed in Benâ&#x20AC;&#x2122;s chapter, there are limitations to the material, if incorrectly prepared. Using these methods, it would be possible to cut out a pattern, using the same panel as a frame, again reducing the amount of material required. We will now progress our designs, with the properties of the material and the construction methods, deeply integrated into our design, using our research to help inform our proposals.

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Digital Fabrication 2D to 3D  

This book is the exploration and design process undertaken as part of the Praxis Module within the Abstract Machines unit. The work develops...

Digital Fabrication 2D to 3D  

This book is the exploration and design process undertaken as part of the Praxis Module within the Abstract Machines unit. The work develops...

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