Tensegral Tipi

Tensegral Tipi uses mathematical symmetry to produce a structure that is in a state of equilibrium. The Tipi merges the concept of a conventional tipi with the structural stability of a tensegrity construction. A tensegrity construction is characterised by a stable three-dimensional structure consisting of members under tension that are contiguous and members under compression that are not. Tensegrity structures provide the ideal solution to the brief, not only are they mathematically symmetrical, they are self supporting and made of consistent sized components. In addition, they only achieve three-dimensionality once all the elements are equally loaded, meaning that, until the last node is connected, the elements remain in a flat-packed condition, a feature excellent for re-deployability. The compression elements will comprise of bamboo, a highly sustainable, easily sourced and cheap material, whilst the tension elements consist of steel cable, a strong and re-useable material capable of taking the tension necessary to achieve structural stability in the system.

 Inspiration

The project began with a study in generating mathematical symmetry using imaginary functions in grasshopper. The use of imaginary numbers created patterns which would be challenging to create manually, all of which were symmetrical either in reflection or rotation. The equation µ(t)= 3√(x+it) created a pattern of straight lines which would combine to create curves in the style of a hyperbolic parabaloid. This outcome would initiate my interest in tensegrity as a way to create beautiful curving geometry through the use of solely straight elements.

Tensegrity Force Testing

Force testing using kangaroo engineering plugin for grasshopper, allowed visualisation of the forces acting on each member of the tensegrity system prior to construction. The first step is to identify the cross sectional area and youngs modulus of the tension and compression elements in the system. This information is applied to a kangaroo physics model, which is already in a state of compression and tension, to reveal the exact force running through each member. The data output is used to analyse if the model can hold its shape and that the materials used can withstand the forces applied to them. In this instance, the hemp rope would have the strength to tension the model, but would not be able to resist the additional force of human touch, resulting in catastrophic failure. A more substantial tensioning material would be required, steel tension cable. In addition, bamboo has a relatively weak shear force, meaning that the twist created from tensioning each end of bamboo would snap the member. To resolve this issue, end caps were developed to spin independently on each bamboo pole, transferring the shear force into the connection.

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Manufacturing & Assembly

There would be two stages to the construction process, the tensegrity module and the connections between modules which form the inhabitable space. The tensgrity module was designed for ease of manufacture, all bamboo components are identical in length at 1220mm (material ships in 2440mm lengths). Pre-manufactured aluminium caps are fitted to the ends of each bamboo piece, then assembled into ‘ladders’ with the use of a jig, steel tension cable and cable crimps. Each tensegrity module consists of three identical ‘ladders’, which are twisted to connect to each other in a spiral arrangment. The module has six connection nodes, five of which can be pre-assembled prior to arrival on site. With the connection of the sixth node the module becomes a three-dimensional, stable shape. This technology results in the assembly of modules in-situe in under five minutes. The second stage of connecting the modules to form the inhabitable space, requires the insertion of pre-cut bamboo poles into the longer aluminium end caps, a process which can be completed in a further five minute period.ma_blog diagrams4ma_blog diagrams5ma_blog diagrams6ma_blog diagrams7

Applicability

This project has many benefits, namely due to its simplicity, it can be built in a garage without the use of specialist tools, requiring only a saw, drill and pliers. Identical length components means manufacturing is intuitive, efficient and cheap, whilst the speed of deployment, and ease of flat pack storage, could have real benefits in the temporary shelter market.tensegral tipi

Parametric Penrose

Inspired by the Islamic pattern, I discovered that some of the Islamic tiling pattern in shrine are similar to the Penrose tiling discovered by Sir Roger Penrose. Looking into the Penrose tiling, it has 3 types and they all follows the rule of golden ratio. These Penrose tiling arrangements each form a reflection and five-fold rotational symmetry.

types of Penrose tiling
Penrose tiling pattern following rule of golden ratio

After doing more in-depth research, I discovered that the rhombic triacontahedron which made up of rhombuses has a similarity to the Penrose tiling type P3, also with rhombuses. These two geometric patterns can be arranged such that by using a single module (golden rhombus), we can form a 3D rhombic triacontahedron with the guide of Penrose tiling as a 2D plane pattern.

five-fold rotation symmetry shown in Penrose tiling arrangement

The rhombus modules are folded in different sets of angles, it can form a volumetric space while still follows the grid of Penrose tiling from the top view. These are done in 4 angles: 36 degree, 72 degree, 108 degree, and 144 degree.

components of Penrose landscape
front perspective
cut section
concept model with MDF to show the idea

By doing the physical model with CNC-ing 6mm thick plywood with the desired angle, it allow the folding modules fitting into the shape I wanted. The custom metal bracket in between planes of plywood rhombus also helps in forming the shape. It will also allow insulation and waterproofing which will be further developed next as it comprised of double layer of plywood.

fabrication steps
big scale model to display the spatial quality

Twisted Pellucidity

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Inspired by Japanese basketry weaving, Twisted Pellucidity takes this technique into an architectural scale. Through creating a set of twisted modules varied with a standard weave in between, the design flows between closed and open creating potential for naturally ventilated housing in hot regions of the world. It has been designed for disassembly to ease transportation and enable adaptations of the size and shape of the design. Thanks to the module’s structural strength, very thin ply strips were used making the structure light and delicate whilst allowing elegant passage of light.

 

Research: Material Properties. Physical and Digital Experiments.

The project started with the exploration of weaving patterns and their strength and bending qualities. Through a series of experiments I have tested a number of single and double curvatures that could be potentially applied on an architectural scale.

Since bending quality of plywood, whether as a woven sheet or as a singular strip, has always been of interest, I have started looking into combining both of those methods. Thanks to bending, large volumes can be created – which seemed ideal for potential enclosure areas. I have therefore decided to research further into the bend-active qualities of plywood. Starting with a single bend, I have developed the geometry into a triple – twist which created a very structurally strong, symmetrical module.  Through Grasshopper scripting of the observed geometry of the physical model I have gained a thorough understanding of the behaviour of twisted strip of plywood which I then further enhanced and through a number of Kangaroo physical simulations I have gained a deep understanding of forces acting on a bent and twisted three times strip of plywood. Those experiments helped explain and understand why and how does a strip of plywood gain an extraordinary structural strength.

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Twisting and bending the strip showed a great impact on the properties of the entire module. Thanks to bend-active and torsional forces acting against each other, the module gains incredible strength in both tension and compression with its strength rising about 10 times in comparison to original elements. This allows for almost never-ending possibilities of use when arrayed in different ways.

As I was particularly interested in how the action I have chosen affected the original material, the natural course of action was to test it in a larger scale as an array and combine it with the original research into weaving patterns and their properties. This has naturally created a Field Condition.

Field Condition is any formal or spatial matrix capable of unifying diverse elements while respecting the identity of each. That leads to the overall shape and extent being highly fluid and less important than the internal relationships of parts which determine the behaviour of the field.

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Modules can be added infinitely with the remaining texture woven in between creating a dynamic field condition and an architectural design by starting from the individual element, letting it grow incrementally and defining how it connects to the next one.

Thanks to the overall qualities of the system, the final design became an unexpected result of adding modules and then connecting each the ends to create an enclosed circular space. This can vary in diameter until it reaches the structural strength capabilities of the chosen thickness of plywood. For 0.8mm strips the largest structurally stable diameter is approximately 1m. This could be larger for thicker and wider strips however this required further research.

 

Construction of the Final Model

Assembly of the final model turned out to be time-consuming but rewarding. Due to great intricacy of the module and a number of connections, it took approximately 80 hours to complete the final model.

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Final Model ended up taking shape of a tower – large enough to fit myself in it. This process proved the Field Condition properties of the system allowing to create a variety of designs – displayed tower being one of them.

Overall, it was a challenging but extremely rewarding journey which I am excited to draw further conclusions from in the second semester.

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Marimba Membrane

Coming from a family of artists and musicians I decided to focus my research on the relationship between music and wood how this could be represented in a larger, playful structure of sounds.

Pythagoras discovered that by hitting an object with a hammer weighing half as much as another (a fundamental note), it produced a vibration frequency or musical note twice as high 2:1 (Octave). By hitting it with a hammer weighing 3:2, it sounded a fifth apart (Perfect Fifth) and a hammer of 4:3 the weight, sounded a fourth apart (Perfect Fourth).

The vibratory curves occur within the struck object and emit varying sounds that we find to be consonant (attractive to hear) and we relate these to musical scales. All other musical notes apart from the fundamental, produce additional frequencies which can be heard simultaneously. They are known as overtones and produce what is known as timbre, allowing a musical note to be heard for more time.

The overtones can be specifically shaped through the tone bars of a Marimba, differentiating itself from the xylophone because of this. The curved, undercut part of a tone bar is responsible for the fundamental note and two additional overtone frequencies, giving this instrument a great timbre.

The fundamental tone produces its vibratory waves with an antinode (marked in green) in the centre of the tone bar. All three variations of the vibratory waves present a node (marked in red) on the extremes of the bar, an opportunity to create a whole to fix them without affecting the note.

The length, width and depth affect the fundamental tone’s frequency: increasing either one with decrease the musical frequency, producing a deeper musical note. Additionally, the orientation and type of wood used will affect the musical note due to its density and capability to transmit sound. I chose to use Poplar for this project due to it being a low-density hardwood (500 Kg/m3) with not many knots and a good capability to transmit sound (5080 m/sec).

In order to form a large structure, I decided to support the tone bars through a tensegrity membrane similar to the Moom Pavilion. The tone bars are aligned in rows, which are fixed on both ends and individually act in compression. Tension cables join each tone bar to the adjacent ones through the vibratory waves’ node. Each row of tone bars is half offset to the adjacent row. The combination of diagonal tension and linear compression gives the structural integrity and creates a vertical lift.

Through digital explorations, I was able to configure a tunnel-like structure that would support 39 tone bars in 7 rows: 4 rows are composed of 6 tone bars each and sitting intermittingly between them are 3 rows of 5 bars each. Through Grasshopper I was able to automate the process of finding the dimensions for each tone bar according to the desired musical note. Each tone bar was then individually cut and sanded down by hand for the desired overtones before being arranged into a grid and joined with cables, crimps and cable tensioners.

The two adjacent extremes of each row of tone bars were fixed to a base I created to anchor them. The most challenging part of this structure is to accomplish the correct tension for it to form a uniform arch. By expanding the base, additional rows of tone bars can be joined laterally to form a larger range of tone bars with an even larger scale of musical notes.

Interpolator

The aim of this project was to develop a sustainable building system, which uses repetition and symmetry to produce a large scale structure. To begin the development process, inspiration was taken from crystal structures to form a panel system with an infinite array.

A rectangular lattice can be simply formed by slotting together regular panels. By interchanging the direction of alternate panels, a continuous standing structure can be formed.

Furthermore, investigating the different possible scales the panel systems can be used for, and the dimensions which would be needed to achieve different forms, lead to the exploration of using different sized panels in the same system.

To design a system which works in many different scales, it become prudent, the test the system with a variety of plywood.

Plywood tests for every possible combination of plywood thickness between 0.8mm to 18mm were conducted, with the intention to design a proposal where the plywood thickness to increase with size of each panels.

For precision to be achieve, a laser cutter and CNC machine are required. This lead to the discovery of some rules:

  • Laser cutting plywood is restricted for use on 0.8mm, 1.5mm and 4mm thickness.
  • The 3mm drill bit on in CNC cutter, is limited to cut plywood sheets with thickness of 9mm, or smaller.
  • The 6mm drill bit on in CNC cutter, is limited to cut gaps, no smaller than 6.1mm and sheets with thickness no greater than 9mm.

Plywood connection test results20190123_193819

To scale up the system even further, the use of Cross-Laminated Timber (CLT) has been explored.

In construction, CLT is prefabricated to fit together making to very easy to construct, therefore very time efficient. Similarly, the panel system being designed requires these properties.

DIY CLT

In order to increase the stability of the overall system, a panel which fits in the z-axis, has been introduced to the system. This is achieved by extending a further slot in the panel on the x-axis, for the new panel can be slotted in without, changing how the system previously fit together.

Additionally, this third panel will then rest on the panels directly below it, to create a ‘floor’ level.

Addition of z-axis (floor) panel

Following the plywood tolerance tests, a slightly differing system for panels to slot together has been develop, to work for the more delicate, thinner plywood. The result is a lattice structure which, seems to be work effectively as a grille, or light filtering device, and therefore would work well positioned at a high level in the final proposal.

Roof system

The process of construction the large scale model included time using the laser cutter and CNC machine, as well as many manual construction hours. The entire process lasted approximately 10 days, including the preparation of files to upload to the cutting machines.

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The result is a large (2.3m tall, 1.8mm width and depth), made entirely of timber panels which intercept each other to form an arrayed construction using repeated elements, with no additional fixtures required. The structure was built to allow uses to enter into it the look above to the roof system.

full model

Wooden Scales

Touching on topics of personal interest including sustainability, synchronicity with the environment and parametric design, my view to create an eventual large-scale structure represented an exciting opportunity to engage with wood, a material I had not yet handled in great detail. It is renewable, can in some form be  sourced locally throughout the world and is incredibly versatile with infinite characteristics that create both solutions and challenges when implemented to the built space.

In this project I begin by reviewing the varying available species of wood types that would carry potential for me to work with towards a final piece, taking account of their sustainable qualities I wanted to delve into wood and explore the material’s extremes. Following this I look into several designs, techniques and different structural systems that mirror it in nature as well as architectural projects that have used wood to react to these systems and create methods to benefit from them.

Expectation of model using both methods to accommodate concave and convex curvature.

In being intrigued particularly by Japanese Joinery I investigate the traditional patterns and methods associated with it and begin to analyse how far it can be incorporates into my project. I took elements forward from here to create my models, especially tessellation and symmetry. I was particularly inspired by the linking of pieces, as shingles, together with the integration of the joinery into the design. Trialling which shapes, patterns and scales work best when joined together then evolves into grappling with how to create angles and curvature through overlapping pieces rather than joining organically through grooves and notches.

Expectation of curved model using method as a cladding.

The most important part of my project was in the detail of creating a shape that was versatile enough to form a curving structure when connected together and multiplied with minimum component parts.
In experimenting with different styles of wood, shapes and angled edges, my scale piece evolved from creating a curve on one axis as an arch to a multi-dimensional surface that has a rhythmic, organic quality.

6mm Thick MDF arch.

Throughout the project I encountered many challenges. Manufacturing each scale through out machinery also proved unreliable, especially in the later stages of the project, however I was fortunate that my concept could come to life regardless of the volume of pieces I could create.

Using wood in this format also had an interesting design effect in that despite organising the scales in a uniform way, imperfections in each connection, when multiplied, created a final model that resembled reptile scales that I had originally been inspired by. My project I feel takes into account the natural, flexible characteristics of wood as a material; embracing imperfections in the system rather than attempting to defeat them.

Double curvature achieved with 6mm plywood scales.

By experimenting with different sequences, patterns, dimensions and shapes, this system has the potential to create structures that can be assembled, disassembled, transported and manipulated easily and creatively.

Shape development.

My journey to create this structure using wooden shingles that curves on two different planes creating an organic and sometimes imperfect surface with the relationship of each wooden piece to another was long and challenging but successful in my opinion. 

Final model at the exhibition.

Triangular Origami

My research starts with the art of origami folding with paper and continues to investigates the techniques of kinetic folding with thickened materials. I find it interesting how easily a paper is folded into an origami shape, which can be folded and unfolded easily. Throughout my design research I would like to find an easy way of folding a wooden structure.

Thickness plays a large role in folding paper. It can be observed with simple folding of a sheet of paper, the more it is folded the more difficult it gets to fold it. The traditional origami is done using paper. It can be observed that after folding paper too many times, it losses its folding ability. Most origami rely on the fibers locate within the paper, and their ability to bend and stretch slightly during the fold. That is why the thicker the paper or the material used the more difficult it is to bend it.

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The folding technique using a thin membrane, like fabric, to imitate the behaviour of the hinge joint is used. The membrane is treated as a zero-thickens element, hence it behaves in a similar manner to paper origami. For a 180 degree fold the gap between panels equals to 2 times the thickness of the panel, however if the desired angle is smaller, that distance can decrease.

That investigation led to creating a triangular grid representing the possibilities of the membrane technique.

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Reduction of the size of the triangle in the grid, creates higher number of bend axis. However by doing so, clash points are created, in places where the new grid wants to bend, and the old one has no chamfer to accommodate it. Because of that the first row of the reduced grid, behaves in a similar way to its bigger neighbour.

The fabrication process involves the use of a CNC machine. The fist step is to prepare a digital file and using a using a CNC machine cut out all the pieces. The edges are then sanded and arranged according to their size. The pieces are places on a calico canvas and attached to it using a PVA glue. The fabric is then cut to size and the edges are rolled to avoid ripping.

making-off

Fabric used for the final model is calico canvas. It is a plain-woven textile made from cotton. It is undyed and unfinished. The fabric worked much better than the synthetic mesh used for the initial prototypes. Also it is more resistant to breaking than the Garden Weed Control Fabric, which with time tends to tear apart.

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The model shows that the smaller the size of the triangles the better more flexible the structure becomes. This technique can be used in creating shelters, as well as, sculptural pieces.