Perspective Figure 1
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
Table of Contents: 00 Abstract
01 Component Development 02 Global Geometry 03 Fabrication 04 Joint
05 Parametric Legs
06 Parabolic Aggregation 07 1:1 Model
08 Material Budget 09 Conclusion
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
Table of Contents
Abstract: The aim of this exploration is to create a component that provides a rigid base while displacing the load through an arched structure. By testing material properties and connections, I hope to achieve a component that aggregates and supports a rigid form. The initial design was developed through paper model testing that was transferred into digital form. The digital model was then fabricated in different materials and scales to test its strengths and weaknesses in the overall design. The laser-cut components were aggregated together to test the viability of different forms and begin to define the parameters of the final form. The goal of the final form will strive to be parabolic in nature and keep joints attachments to a minimum.
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
00 Abstract
Component:
The initial development of the component was to combine an arched structure with a triangulated form. Both systems maximize load displacements and served as rigid base. The resulting tripod form married both ideas into a rigid form as well as an elegant component.
Arch Supporting Load Diagram 1
Triangular Form for Rigid Base Diagram 2
Final Shape Diagram 3
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
01 Component Development
Technique: A study of axis displacement showed how important the legs of the form will influence the overall design. The stick model shows how the forces of the model converge on a single point which determines the angles of legs. The a further paper study in physical models explored the differences between a four-leg system and a three-leg system. The four-leg model was excessive in materials to form a forth leg that didn’t serve any added purpose. The three-leg model still served as a rigid support while keeping an elegant form.
Axis Diagram 4
Stick Model Figure 3
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
4-Leg Paper Model Figure 2
3-Leg Paper Model Figure 4
01 Component Development
Digital Construction: The digital construction of my model began with equally spaced lines that converged at the center and then offsetting the legs to form the base of the component. The center lines were then extended vertically and the rigid connections formed the exterior framing of the component. Based off of the ridge point, the arch forms the bottom of the component and completes the overall form.
EQ. EQ.
Equal 3-Leg Spacing Diagram 5
Offset of Base Diagram 6
Vertical Lines Diagram 7
Ridge Connections Diagram 8
Arch Construction Diagram 9
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
EQ.
Final Form Diagram 10
01 Component Development
Structural Analysis: The structural analysis was accomplished by using a Rhino Plug-in “Scan and Solve� that tests the forces applied to a given object. The force applied to the component was a single point load directed downward to disperse the force through the other two legs. The structural stresses show how the dispersion of force does dissipate to the base two legs and forms a rigid base.
Force
High Stress
Force Dispurtion Diagram 4
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
Force
Low Stress
Structural Stresses Diagram 10.1
01 Component Development
Platonic Exploration: The next step was to aggregated the component into a system that created a larger form. The first platonic solid tested was the dodecahedron that is a 12 faced archemedian solid. It has 12 - 5 sided pentagons that complete the form. Dismantling the form into individual 3-legged pieces began to formulate how it could be constructed 3-dimensionally. One important observation was that the entire dodecahedron can never be built with only using the 3-leg component. An additional component is needed to complete the entire form. This additional leg could consist of 1 or 2 legs to complete the dodecahedron.
3-LEG
3-LEG
Dodecahedron Form Diagram 11
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
1 or 2-LEG Leg Options from Pentagons Diagram 12
02 Global Geometry
Shape Exploration: This shape exploration is an attempt to break free of the rigid platonic solid and test other forms that could emerge from aggregating the component. What emerged was the combination of various geometries that are applied flat on a plane or vertically assembled. The most influential form was the Table Form (diagram 15) that brought up the idea of mixing a pentagon with a hexagon. This would be achieved by adding an additional third component to form a hexagon.
Tent Form Geometry Diagram 13
Planar Form Geometry Diagram 14
Table Form Geometry w/ 3-Leg Diagram 15
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
02 Global Geometry
Truncated Icosahedron: This iteration tested how the component would function when applied to a truncated icosahedron. This platonic solid is a thirty-two faced archimedean solid that has the facial arrangement of 20 - 6 sided faces with 12 - 5 sided faces. The combination of pentagons and hexagons together make for a
3-LEG
3-LEG
3-LEG
Truncated Icosahedron Form Diagram 16
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
Leg Options for Pentagons & Hexagons Diagram 17
02 Global Geometry
Component Adjustment: The truncated icosahedron required the initial component to be restructured to fit its new parameters. The new parameters were that the three legs fit to a pentagon face and two hexagon faces. The angle of the intersection of the legs would also have to adjust to the platonic solids set angles. Pentagon
Hexagon
Extraction of Angles Diagram 18
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
Hexagon
Intersection of Hexagons & Pentagon Diagram 19
02 Global Geometry
Aggregation Template: This shows the truncated icosahedron disassembled into a flat template. The different configurations of hexagon to pentagons clearly displays how each geometry works together. The leg calls out the scale at which it functions within the entire system.
Truncated Icosahedron Template Diagram 20
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
02 Global Geometry
Construction Revision: The digital construction of the component needs to be revised to meet the global angles set by the truncated icosahedron. Starting with the angles and workings backwards you can extend the vertical lines down. Then developing the base lines and offsetting the base to form the width. The arch construction is similar to before with it being set off of the ridge point that defines the curve. The final form resembles the initial component but is altered to fit the truncated icosahedron’s geometry.
Ridge Angles Diagram 21
Vertical Extension Down Diagram 22
Base Lines Diagram 23
Base Line Offset Diagram 24
Arch Construction Diagram 25
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
Final Form Diagram 26
02 Global Geometry
Aggregation onto Platonic: The component is now aggregated on the truncated icosahedron and displays how well the new component forms a structure. Several gaps in the structure appear to form where the geometry of the legs can’t fill the areas without adding an additional single leg piece.
Component Insert onto Platonic Solid Diagram 27
Component on Platonic Solid Diagram 28
Component Aggregation Diagram 29
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
02 Global Geometry
Aggregate Perspective Diagram 29.1
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
02 Global Geometry
Material Fabrication: To further understand the properties of the component I tested four different kinds of materials; chip board, museum board, #100 card stock paper, and 3-dimensional printing. The digital component is reconstructed into a template that was laser-cut out. The interior lines of the template were scored to give the component a cleaner bend in the material. The 1/16” chip board didn’t work very well and tore in multiple different areas. The museum board worked good as well but also had slight tearing. The #100 card stock worked out the best and was very rigid and clean. The 3D printed worked good but wouldn’t print again due to the shops inability to operate the machine.
Form Template Diagram 30
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
1/16” Chip Board Figure 5
#100 Card Stock Paper Figure 7
1/32” Museum Board Figure 6
3D Print Low-Res Figure 8
03 Fabrication
Enlarged Scale: The #100 card stock worked out the best and needed to be tested at a larger scale. The component was enlarged to double the size to test its rigidity and overall ability to hold form. The larger size worked out better than anticipated and had no bending in the form.
Original Scale Figure 9
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
2x Scale Figure 10
03 Fabrication
Leg Connections: The components legs are the ideal location to connect the components together and form a rigid form. The intersection of legs based off of the end point made the first typed of connection by trim off the legs and letting the angle connect the component.
Component Leg Diagram 31
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
Component Intersections Diagram 32
Component Leg Cut Diagram 33
04 Joint
Leg Connections Variation: Three different connection types developed out of different digital modeling. The first was the intersection of the components ends to join together. The second is having a middle “pyramid� shape to connect to that holds the desired angle. The last connection was to have a component that has one leg with a built in connection. The other two legs would slide onto the leg and form the connection.
Point Connection Diagram 34
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
Pyramid Connection Diagram 35
Locking Piece Connection Diagram 36
04 Joint
1/16� Joints Connections Model Figure 11
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
04 Joint
Parametric Modeling: Testing the limits of the aggregated structure began with taking the original geometry and manipulating two main characteristics of the form: the arch of the leg and length of the leg. Through defining the component in Grasshopper, the form manipulation developed varying structural possibilities. Figure 12-12.3 shows how manipulating the arch can create different aperature openings that would alter the sense of enclosure.
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
Original Geometry Figure 12
Arch Manipulation 1 Figure 12.1
Arch Manipulation 2 Figure 12.2
Arch Manipulation 3 Figure 12.3
Original Geometry Figure 13
Leg Elongation 1 Figure 13.1
Leg Elongation 2 Figure 13.2
Leg Elongation 3 Figure 13.3
Original Geometry Figure 14
Hybrid 1 Figure 14.1
Hybrid 2 Figure 14.2
Hybrid 3 Figure 14.3
05 Parametric Legs
Parabolic Aggregation: The components global aggregation to a parabolic form started with the simple parabolic arch to form the enclosure. Searching for the best way to develop the surface began with breaking it down into individual smaller shapes to understand the forms complex surface. Parabolic Arch Side View Diagram 37
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
Parabolic Arch Top View Diagram 38
06 Parabolic Aggregation
Parabolic Box Morph: Using Grasshopper to apply the component to the surface developed one strategy to aggregating the component to the global surface. Unfortunately, the components three legged form proves to be a difficult shape to box morph onto the surface. The resulting global form doesn’t have any connections and isn’t a viable application for the structure.
Top View of Box Morph Aggregation Figure 15
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
Perspective Box Morph Aggregation Figure 16
06 Parabolic Aggregation
Parabolic Aggregation:
5th Tier
Another approach to aggregating the component onto the surface is to tier the components size to match each progressive component. The next tiered size is determined by the separation of the lower tiers legs which thus lock the components together.
4th Tier 3rd Tier 2nd Tier
Parabolic Arch Diagram 39
Base Component
Components Aggregated Diagram 40
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
06 Parabolic Aggregation
Light Study: The projection of light patterns through the structure displays various shadows in and around the enclosure.
Side Shadows Figure 18
Entrance Shadows Figure 17
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
Top Shadows Figure 19
06 Parabolic Aggregation
1:1 Model: The 1 to 1 scale models string connections gave a nice aesthetic to the component but didn’t provide enough strength to form a rigid connection. Zip-ties were added to the joint connections to lock the components legs together and helped keep the angles of the parabolic form. The sheets of African Mahogany veneer was laser cut into individual leg pieces and assembled together.
Top View of Aggregation Diagram 41
Full Scale Model of 3 Component Connection Diagram 42
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
07 1:1 Model
Material Budget: The materiality of the final structure is being considered through four different mediums. African Mahogany is the most expensive material to produce and would involve extensive wood craftsmanship to manipulate the joinery. Clay would produce a beautiful structure and has great potential with glazing. Aluminum is also expensive but would be very durable and add a thinness to the structure that could be achieved by other materials. The last material is concrete that is very cheap to produce and easy to manipulate but less elegant in its appearance.
African Mahogany
$8 per board foot Nominal Thickness 2” Nominal Width 6” Length 2’ Number of Boards 60
Total Board Feet ((2 x 6 x 2) / 12) x 60 = 120 Total Cost $960
Clay
$90 per 100lbs 40lbs per Component 20 Components Total Pounds 800lbs Total Cost $720
Aluminum $45 per 2’x4’ Sheet 1 Component per Sheet 20 Components Total Sheets 20 Sheets Total Cost $900
Concrete $7 per 80lbs 40lbs per Component 20 Components Total Pounds 600lbs Total Cost $53
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
08 Material Budget
Conclusions: The component has evolved to show good potential in its aggregation. Breaking free of the parabolic shape to form a more elliptical footprint that creates two entrances to the structure as well as forms as tighter sense of enclosure. The final structure still needs a more rigid connection between components but shows great promise in dispersing the load of the arch through the structure. The larger base components provide a strudy foundation to the structure as well as grounding the enclosures visual sense.
Final Structure Perspective Figure 20
Parabolic Enclosure Digital Fabrication
Professor Mary Polites By Ryan Rideout
09 Conclusion