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Exploring Undulations

Digital Design Techniques for Full Scale Fabrication Rachel Hall, Fall 2013


Exploring Undulations

Table of Contents

Aim

1

Original Component Studies. Documentation of Failures and Explorations

2-4

Exploring the Triangle Ratios Final Component. Component Template Attempt One

7

Diamond Manipulations

8

Aggregation Equations

9

Analysis of Component

10

11

Global Aggregation

12

Material Options with Final Estimated Budgets

13

Global Aggregation Options

14

Case Studies. Nubik

Rachel Hall

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Component Template Attempt Two

Final Aggregations. Final Model

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Chromatex.me

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Resonant Chamber

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Exploring Undulations

Aim

The inspiration for this design comes from the brain coral. Brain coral has an intriguing, natural ability to present an illusion of movement with a rigid structure. The design goal is to create a structurally sound system that mimics that limited flexibility, yet still speaks towards fluctuation or undulation.

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Exploring Undulations

Original Component Studies

Documentation of Failures and Explorations

Component.

First Folding lines.

This first component was developed in a literal sense to mirror the form of brain coral through a series of organic slits in printer paper. The sections created were then raised and folded in order to produce shifts in the component.

Similar to the first component, this one is created with a series of diagonal slits and then folded to generate a change in elevation and a sequence of voids.

This component explores folds. By first creasing the material in a diagonal cross and then tucking in the sides, the component begins to push upwards in a tent-like fashion. Thus, generating a more solid component compared to the previous models.

Cut template.

Failures.

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This component has no structural characteristics. The material is weak, but the form also does not withstand any compression forces. The form is arbitrarily produced, thus making it harder to specify parameters for the future.

Although this component has a fixed cut template, it still remains structurally unsound. A change in material may produce a stronger component, but this component is too linear to have a high potential for an interesting regional system in the future.

This component has the potential to produce a local aggregation that explores volume, however, it has a certain complexity to its form that will be difficult to evaluate mathematically.

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Exploring Undulations

Original Component Studies Documentation of Failures and Explorations

Component.

Fold lines.

After the last component the question of structural strength was risen, but the other element within the aim was lost. The final component must house a sense of movement and undulation. These next few studies are focused on this particular element.

This particular component calls for point connections. However, when the triangles are connected at their tips, there is a major opportunity for failure when there is any sort of load applied in that area. Therefore, the next step was to round off the top tip of the triangle, which increases the surface area of the point and decreases the chance of failure at the connection.

Cut lines.

Failure at Tip.

This component is a modification of the previous one. However, instead of working with only folding lines, this model incorporates cuts and folds. The original shape is a square, which is then divided into four equilateral triangles.

Failures.

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This particular model was created using bristol paper. When a central point load is introduced, the component collapses in on itself. Perhaps with a stronger material the form may become more rigid. However, the aim was to create a component that was structurally sound, so more exploration in this realm is needed.

A triangle was chosen as a basic module because its shape is geometrically simple, yet with slight modifications can be easily altered to ultimately create drastically different aggregations. A simple component can also be controlled with math, making this exploration a logical and organized one.

Rounded Tip to Strengthen Connection at Point.

Creating the Component.

Fold line.

After rounding off the top points of the triangle, mirror the triangle so that it ultimately forms a diamond. The fold line is directly in the center of the diamond - running vertically down the shape.

Next fold the diamond in towards itself.

Then begin to slightly curl the tips back out so that it creates a “wing-like� form.

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Exploring Undulations

Original Component Studies

Documentation of Failures and Explorations

To enhance the illusion of undulation, an element of asymmetry is incorporated in this component. As shown in elevation one “wing” is lower than the other.

This component is connected at the rounded tips in a radial pattern.

High. Low.

When the components are locally aggregated the lower and higher sides of the “wings” are exclusively connected to their respected heights in order to produce consistent changes in elevation throughout the regional system. In elevation an illusion of a wave is created.

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Exploring Undulations

Original Component Studies Exploring the Triangle Ratios.

Component.

Right Triangle.

1:2 Isosceles Triangle.

Equilateral Triangle.

Doubled Scale.

Failures.

Plan View.

Component Perspective.

The right triangle produces no waste in regards to material, which is a positive attribute, however, when it is radially aligned and connected at its points the individual components begin to overlap themselves. This is because the ratio is too square.

The main failure of these components are that there is no way to control the measurement of the curves and thusly, they is at the mercy of the constructor and material as opposed to the math.

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Plan View. Perspective.

The isosceles triangle, with the ratio of 1:2, relating to its side lengths, creates steeper curves in the aggregation. Unfortunately with steeper curves there is less structural stability when a vertical load is applied.

Plan View.

Perspective.

The equilateral triangle is a much better candidate for this component. It does not overlap when aggregated and its curves are not as intense as the isosceles triangle, which allows for slightly more structural stability. However, the scale is too small to successfully repeat this component.

After doubling the size of the equilateral triangle the regional system was much more successful. There is a clear sense of undulation and the structure can withstand small amounts of loads at the point connections. The act of point loads actually plays on the illusion of movement and turns it into a reality--making the component spread away from its original state when compressive forces act upon it (as seen in the diagram below)

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Exploring Undulations

Final Component Template Attempt One

The component begins as a simple triangle with an angle of 120 degrees at the top.

Next vertically score the triangle in half and fold down.

This creates a ridge in the center of the triangle, seen in elevation view here.

Fold lines.

Cut lines.

Edge Connections.

Next the component is mirrored at a central point to create a local system with edge connections.

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Due to the triangle component and edge connections, the regional system becomes plenary dominate. The final aggregation will need to have more volume and change in elevation to reach the concept of undulation, so a change must happen in the original component.

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Exploring Undulations

Component Study

Attempt Two

The simple triangle changes into a subtle diamond.

The added geometry slightly manipulates the local system and eventually the regional system.

Keep the same elevation as previous component.

Plan View of Interior.

Again, mirror the component at a central point and connect at the edges to create this local system.

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Even with a small change in shape the regional system is now less planar. The aggregation begins to slightly fold in upon itself. The next step is it to see which manipulations of the diamond, within certain parameters, will produce the most intriguing aggregations.

Perspective View of Exterior.

Plan View.

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Exploring Undulations

Component Study

Diamond Manipulations

Component.

One.

Two.

Three.

Local.

Regional. plan view

Gaps in Regional Aggregation.

Regional. perspective

Failures.

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After only three local systems were produced the regional system had reached its limit.

The diamond created such an extreme edge connection that only two local systems could be generated.

The thinnest and least symmetrical diamond created the most successful aggregation in the regional aspect. However, due to a lack of geometric calculations on the other angles of the component, there are gaps in the regional system. 8


Exploring Undulations

Component Equations

Solving Aggregation Problems with Math

The main problem with the global aggregation is an inaccuracy with the outside angles of the component. To create a module that is completed when globally aggregated, the local component has to be solved considering the projected and actual angles.

First, the local component is solved. The eventual goal is to create a regional component that connects five separate local components at the edges with one predominate point connection. To achieve this the outside angles of the original component equal 31.72 degrees.

Next, the point near the 120 degree angle is determined as the stagnant base point. The elevation of the point opposite the base point is manipulated manually within Grasshopper. As this point increases in elevation the local component becomes steeper and the global aggregation closes in on itself quicker.

Eventually a system that successfully aggregates with edge connections of the regional components is achieved. The regional component consists of five local components coming to a center point. However, when three regional components are connected a secondary regional component is formed with six local components connecting at

Base Point

Six local components

120 31.72

Five local components

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Exploring Undulations

Component Analysis

Understanding Loads

This component was chosen due to regional performance and its opportunity for a larger, more interesting global assembly.

This component can withstand small vertical compression forces, all the while, encompassing the sense of undulation by pushing its exterior points away from the loaded area.

The component will have edge connectionsincreasing its rigidity.

Loads will most likely be applied at the tips at which five local systems connect.

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Exploring Undulations

Final Model

Fabric is sandwiched between these three triangles to create a continuous connection. Eventually this will be how these 12 wings will be connected as show in the below image.

Local component.

Top view of the regional component. The bass wood triangles are bond together by folding and gluing plastic strips across the edge connections.

Top view of connection between two regional components.

Plastic strip connection detail.

Global aggregation with an edge connection.

Failed connection attempt. Using fabric as the central connection device did not hold the needed rigidity of the component. Arch 491

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Exploring Undulations

Global Aggregation

Global aggregation is completed with four to five regional components and then mirrored and connected with a simple edge connection. A pavilion like structure is found within this certain global construction.

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Exploring Undulations

Material Options

Full Scale Measurements with Estimated Budgets

Sizing and Amount.

Each triangle will have the dimensions of: 1.66’, 2.66’ and 2.75’ There will be a total of 240 triangles and 240 “L” Brackets

Material

Polycarbonate plastic is a light weight material that holds its structural integrity, but also has an element of translucency to bring in the element of light. This comes in sheets of 1/2” x 48” x 72” at $313.62 per sheet.

3/16” thick Aluminum Metal sheets are light enough to develop the undulating form and rigid enough to hold the structural integrity. This comes in sheets of 3’ x 3’ at $21.98 each.

1/8” thick Plywood is still light enough to hold the global aggregation and strong enough to remain structurally sound on its own. This comes in dimensions of 4’ x 8’ at $6.91 each.

Fabrication and Connection Methods.

Each wing will be glued together by colored or clear sheer fabric, depending on the desired aesthetic. Thin galvanized metal “L” brackets will be shaped to the correct angle and screwed into each edge connection (replacing the plastic strips that were shown in the final model).

Thin galvanized metal “L” brackets will be shaped to the correct angle and screwed into each edge connection (replacing the plastic strips that were shown in the final model).

Each wing will be glued together by fabric, as seen in the final model. Thin galvanized metal “L” brackets will be shaped to the correct angle and screwed into each edge connection (replacing the plastic strips that were shown in the final model).

30 sheets of plastic = $9,408.50

120 sheets of metal = $2,637.60

30 pieces of wood = $201.30

60 packages of “L ”Brackets (4 brackets and screws in each) = $280.80

60 packages of “L ”Brackets (4 brackets and screws in each) = $280.80

60 packages of “L ”Brackets (4 brackets and screws in each) = $280.80

Estimated total Budget.

16 total yards of fabric (depending on color it is $3.50$4.25 per yard) = $68 TOTAL

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=

$9,756.50

16 total yards of fabric (depending on color it is $3.50$4.25 per yard) = $68 TOTAL

=

$2,918.40

TOTAL

=

$550.10

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Exploring Undulations

Global Aggregation

In order to allow this system to reach a more human scale and be used as a pavilion, the material must remain light and be able to hold a strict structural characteristic. This could be potentially done by creating a plastic mold of two original components and connecting those tent-like shapes with metal hinges to eventually recreate the regional component.

In order to create a pavilion the components must be a certain scale at around 2’ long. With that scale the material becomes an expensive component. However, this project instead can be an installation. One would need to scale the component to an 1/8 of this proposed size. This will be much more feasible than a pavilion for a realistic class fabrication.

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Case Studies

Nubik by Ammar Eloueini

Programmatic Purpose.

Installation for the Grand Arts Gallery in Kansas City. The piece is meant to tie in all the different musical genres of the MASH-UP performances within the space.

Became a suspended canopy of small pods of various sizes to house the dynamism of the space.

Easy and quick to install.

A stage that is constantly “changing” with the various performers by applying dynamic design.

Material.

Poly carbonate a translucent glossy material that is very light weight yet holds structual integrity. Connections zip Ties slotted through precut holes. Cables to suspend the system above the ground

Recyclable. Leaves a small footprint.

Methods.

Used 3-D software to generate form and pattern by unfolding volumes. Components meet and “pool” at one point and get thinner in shape as they reach the edges of the global system.

Optimization.

Use CNC router to cut partially hollow poly carbonate panels. By “revealing” the structural integrity of the panels, each one functions as a perforation, allowing the panels to hinge together. This generates a variety of tesselations and a sense of undulation.

Fabrication Process.

Each surface can be unrolled. They are assembled by looping zip ties between each edge along the seams and tightening to appropriate and control the tension of the system and ultimately the aesthetics of the project as well.

Physical constraints of the material make a rigid folding angle. The width of the bit cut in the CNC router also determines the angle--the wider the cute the tighter the angle. Arch 491

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Case Studies

CHROMAtex.me by Softlab

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Programmatic Purpose.

Site specific installation for the bridge gallery in New York City. It was designed to produce a complex environment with a spatial experiment of a combination of six colors. Explores the concept of inverted design by showing the connections on the exterior and “hiding” the colors within the system. The exciting parts of the system are discovered by looking through the various tunnels within the room.

Material.

High gloss photo paper over 4000 uniquely laser cut panels Connections binder clips (produce a universal joint that holds any angle as long as a rigid material is in place every few feet. Acrylic rings reinforce the tunnel shape Cables to suspend the system above the ground

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Highlights of the printer paper give the illusion of rigidity of the system. The connections, on the other hand, address a more billowing form. One tunnel opening faces out the window towards the pedestrian dominated street to draw in observers.

Fabrication Process.

Used only shelf products and donated material to produce the system. To easily assemble, the form was broken into over 4,000 unique panels and then connected with the use of binder clips. From there, the form was found in 200 different “chunks” that were placed around the rigid acrylic rings

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Case Studies

Resonant Chamber by rvtr

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Programmatic Purpose.

An interior envelope system designed to transform an acoustical environment with the use of rigid and parametrically designed geometry. The system is created with dynamic, spatial, and electroacoustical technologies. The aim is to create a sound sphere that is able to adjust its properties in response to the changing sonic conditions of the space.

Material.

Electro-acoustic panels absorb and reflect sound. Clustered around electronic panels that contain circut controls for linear activation. Speakers are also embedded within the system. Connections flexible hinges. Cables to suspend the system above the ground

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Fabrication Process.

Modeled in Rhino with the plug-ins Grasshopper and Kangaroo in order to script the relationship between the vertices and applied forces. Therefore, it makes the optimal global system predictable with chosen parameters. Such variations include reverberation time, absorption coefficient, directional amplification, and acoustic responses.

The rigid geometry is the operating factor and is the main parameter for determining the global system. The rigidity of the material and the amount of sound the system needs to absorb will also determine the fold angle of the components. This approach allows one to modify the aesthetic form while simultaneously manipulating the acoustics of a space.

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