Geometria Kine by Lauren Leigh Brown

KADIM ALASADY LAUREN BROWN PROFESSOR PAOLA SANGUINETTI UNIVERSITY OF KANSAS SCHOOL OF ARCHITECTURE, DESIGN, AND PLANNING ARCH 359 INDEPENDENT STUDY ARCH 692 DOCUMENTATION SPRING/SUMMER 2012 LAWRENCE, KS

PRECEDENT STUDIES

this is where you will find the studies informing design objectives.

RESEARCH OBJECTIVES this is where you will find the objectives driving the design.

00 01 02

this is where you will find the framework driving the design process.

PARAMETRIC STRUCTURE

PARAMETRIC CATALOG

this is where you will find the parametric capabilities of the component array.

CONTINUED DEVELOPMENT

this is where you will find the postcompetition developments and evaluations.

03 04 05

06 07 this is where you will find the process of fabricating portions of the design.

FABRICATION

this is where you will find the final submitted design.

COMPETITION ENTRY this is where you will find the basis for the component design.

GEOMETRIC EXPLORATIONS

359/692 INDEPENDENT STUDY & DOCUMENTATION TOPIC OF INTEREST: The use of computational fabrication in architectural design and the building industry is in its infancy and is gaining special interest in the academic field where it is being heavily experimented with. Computational fabrication is interdependently based on parametric modeling and digital fabrication, and its possibilities of generating new or improved geometries, structures, and material applications is many and varied. While the architectural profession eagerly seeks the application of such new and efficient designs, it lacks the involved time and resources for experimentation. Similarly, the fabrication industry seeks the methods of production and manipulation of flexible and efficient systems, but requires the demand for such systems to produce and experiment with them. In academia, the freedom to experiment with parametric modeling and analyze it critically is widely abundant, but opportunity for the

true application of such computergenerated experiments is not often available and is therefore sometimes unrealistic and unrealizable. INTENT: Through computational fabrication, we seek to recognize common problems in the built environment that can be addressed with simple yet effective solutions. In the context of the competition we also pose a provocative solution that may or may not be directly understood as architectural. The significance of such a study addresses the current and pressing issues of health and wellness, sustainability in the production and life cycle of buildings and structures, and formal play. These issues are indicative of a larger societal issue that concerns the shift into the modern era and mankindâ&#x20AC;&#x2122;s dependence on technology. The logical application of mathematics and patterns through the efficiency of computer genera-

tion and analysis demonstrates a critical use of technology that aims to improve a material use in the built environment as well as a greater interrelationship between academic research and experimentation, professional application, and fabrication.

The bulk of the study is fostered by the objectives laid forth by the APPLIED Research Through Fabrication competition hosted by Tex-Fab and sponsored by Buro Happold. However, the scope of the design project encompasses more than the creation of an object; it is heavily involved in deconstructing the genealogy of parametric logic and framework as it relates to systems in architecture.

then reverse-engineered in order to understand part-to-whole and parametric relationships in space frame design. Beyond this further geometric explorations are done to develop an expandable component system in which energy-collecting modules can be deployed and used in a multiplicity of environments. Rhino Grasshopper is used to explicitly define a system of rules and logic based on algorithms and parametric patterns, giving the system hierarchies and parameters with numeric values. The Grasshopper definition is then adjusted to produce multiple iterations, critically tested and analyzed to determine a prime sample of the design and its production method, and a parametric catalog describes the variations of the system based on site.

Therefore, the design process begins with an understanding of a parametric framework as patterns, described in Elements of Parametric Design by Robert Woodbury. Expandable structures by Charles Hoberman are

Once the component and system are firmly established, the further development of optimal energy production is tested through the use of Grasshopper, and fabrication methods are tested through half-scale mock-ups.

METHODS:

A consistent and critical dialogue between professor and students throughout the project shapes and revises the methods of creation and production and allows for critical reflection of the tools and processes of the project as it develops.

TEX-FAB APPLIED: RESEARCH THROUGH FABRICATION BRIEF: Within the field of architecture, exploration involving parametric modeling and digital fabrication â&#x20AC;&#x201C; what we will call computational fabrication â&#x20AC;&#x201C; is both wide and varied. There is no standard of how the technology is developed or no singular focus on how it will impact the design process or the construction of buildings. And yet there is growing evidence the application is quickly evolving in a variety of unique directions. From novel geometries and innovative structures to improved material and environmental performance it is clear there is a focused agenda towards a more rigorous implementation of the digital toolset. The impetus for this development is coming simultaneously from three positions that collectively provide a critical nexus in the field of computational fabrication: First, the professional demands for buildings to have greater performance capacity, stylistic coherence, and economic ef-

ficiency; second the academic realm where experimentation, research, and theory, continue to push technological exploration forward; and third, industry where innovative development is both an economic imperative and a generative vehicle for technical application and testing. From each of these positions, applied research is gaining traction as a critical and vital part of connecting the design process into a deeper knowledge base of information that is raising the intelligence and thus efficacy of architectural design. Whether following traditional models of research or pioneering new forms of hybridized working models between these three categories, those working within this field are now able to activate a broader and more fully coordinated spectrum of information about the design decision-making process. We seek research proposals that actively connect academia, the profession and the fabrication industry. As a center of gravity the proposals must illustrate work of designers who

are forming an integrated relationship between disciplines in the area they practice and build. As this is a “design to fabricate” competition, TEX--FAB will match our network of fabricators and consultants with the projects that best manifest research through computational fabrication and apply it toward more intelligent integers of materiality and construction. Through a panel of experts we propose to identify projects that warrant a higher degree of realization and exhibit them to foster a discussion that engages an audience in our region and beyond. From this selection a final project will be selected and optimized with a team of experts for the purpose of full-scale production. CRITERIA: You are encouraged to submit in either of two categories: Continuing Research or Speculative Proposals. Continuing Research is a category that seeks to enable a more specific and regimented design research project already underway. Encompassing all works that are at a significant stage within their development that warrant a substantial shift in the

scale and or material usage to further the research. This includes any and all previously funded work at any stage of development. Speculative Proposals is a broad based category with the intent to kick-start a design research project. It is an open category and freely interpretable. New ideas, or concepts are welcome and present the entrant an opportunity to further develop their ‘flash of genius’. No previously funded research work may be submitted. CONTEXT: APPLIED is a two-stage international design competition established to foster the deeper developments within the field of computational fabrication. We are soliciting design proposals that further existing research, by enabling prototyping at a larger scale or full-scale, and proposals to jump-start new research and design concepts. WINNER: APPLIED is a two-stage competition. In the first stage a total of 4 selections that will be awarded a 1000

USD stipend to further develop their project in a scale model (2 selections From the Continuing Research category and 2 from Speculative Proposals category). For the second stage, the models with revised boards will be exhibited October 18-21 at San Francisco at ACADIA 2012, (a shipping fee stipend of 250 USD will be provided), during which the second round jury will announce a winner made public during the conference. The final winning entry will be built, exhibited in Dallas, Texas for the 4th annual TEX-FAB event. No additional design fee will be paid, however a 1,500 USD stipend will be awarded for travel to partake in the installation of their work and to present the design on the day of the exhibition opening. MATERIALS AND FABRICATION: There is no specific material or fabrication requirements for the submissions, as we are encouraging you to develop this competition to further your research or propose a speculative project. You are encouraged to develop and propose a specific fabrication method based on your research, thus you must specify

techniques and materials used in the proposal for the competition entry. SUBMISSION REQUIREMENTS: This is a digital competition; hard copy proposals will not be accepted. All entries are to be submitted via e-mail on/or before midnight June 2, 2012 Central Standard Time (23:59 CST). Board size is set at 24” x 36”. Only one board per proposal/ entry, no more than one board will be accepted per project. Board resolution must be 150 dpi, RGB color mode in JPEG format. Entry identification code (which was generated during registration) must be positioned in the upper right corner with required dimensions of 1” tall x 4” wide. No other form of identification permitted. Disqualification of entries may occur if the guidelines are not met. The language of the competition is English. Entries are encouraged to include all necessary information to clearly explain the proposal. The choice of the graphic representation is completely open to the entry team. ELIGIBILITY: APPLIED is open to all architects, artists, designers whether student or

professional without limit to country or nationality. Team collaboration is permitted and encouraged. If you so choose, participants may enter more than once as either individuals or in a team (Bell, McClellan, and Vrana â&#x20AC;&#x153;APPLIED: Research Through Fabricationâ&#x20AC;?).

ELEMENTS OF PARAMETRIC DESIGN FABRICATION

MAPPING

STRUCTURE

PLACE HOLDER

JIG

CONTROLLERS

The hardest new skill for designers is abstraction. Why? It involves thinking more like a computer scientist than a designer. But does it? Designers use abstraction all the time, in organizing projects and drawing sets. To remove unneeded detail empowers concentration on the issue to hand. Abstract representation enables progress on concrete issues such as circulation, light and structure. Just as a designer would never specify a building (beyond a doghouse, of course) completely in a single drawing, a parametric modeler should never work in a single model. A complex model is made of (mostly reusable) parts. Reusable, abstract parts are a keystone of professional practice. Over the last several years, my research group at Simon Fraser University has used patterns as a basis for understanding, explaining and expressing the practice and craft of parametric modeling in design... A pattern is a generic solution to a well-described problem. Its description includes both problem and

solution, as well as other contextual information. Patterns have become a common device in explaining systems and design situations, and their structure varies across the domains in which they have been used. Here we use a simple pattern form comprising Title, What, Use When, Why, How and Examples. The Title should be a brief and memorable name by which the pattern will be known. What uses an imperative voice to describe how to put the pattern into action. Use When provides context needed to recognize when the pattern might be applicable. Why gives motivation for using the pattern and outlines the benefits that accrue to its use. How gives the mechanics of the pattern. For us, a distinguishing feature of a pattern is that it has an explanation of mechanism, that is, all instances of the pattern have similar symbolic structure. Examples, which we call Samples, provide concrete instances of the necessarily abstract pattern descriptions (Woodbury 185274).

PATTERNS Place Holders have two parts. The first is the proxy object itself: a simple object that carries the inputs for the module. For example, a rectangular module may require four input points, one for each corner. A four-sided polygon can act as a proxy for these points: each of the vertices of the polygon provides one of the points. The proxy simplifies the arguments needed for the module: instead of four points, use only one polygon. The second part relates the proxy object to the model. For example, a polygon proxy can be placed using a rectangular array of points by relating the ij polygonâ&#x20AC;&#x2122;s vertices to the points Pij, Pi+1j, Pi+1j+1 and Pij+1.. The code placing a generic object such as a polygon is more simple and reusable than the code for a specific module (Woodbury 218-222).

A Jig should appear and behave like a simplified version of your end goal. An physical example is the strongback and stations used in building a small boat. The stations locate and support the hull when it is being constructed. Fairing, the process of making the hull smooth and continuous, can be done much more simply with stations than with a complete hull. Jigs are like construction lines in that they help locate elements. They are unlike such lines in that they are linked to the controls that enliven the parametric model. Jigs typically connect to the model they control more richly than controllers, but still with a limited number of links. Most of these links should come from \afit{sink} nodes. This is not necessity---it is good programming style (Woodbury 201-206).

The key concept in a Controller is separation. You build a separate model whose outputs link to the inputs of your main model. The separate model is the Controller. It should express, simply and clearly, the way you intend to change the model. Controllers can abstract or transform and they can do both at the same time. An abstracting Controller is a simple version of the main model that suppresses unneeded detail. Parameters on lines and curves are very simple case of a Controller: they abstract a location on a curve into a single number. The layout of controls on a properly designed stovetop directly abstracts the layout of the burners. In contrast, the vast majority of stovetop controls fail to do this well. A transforming Controller changes the way you interact with a model. For example, polar coordinates transform Cartesian coordinates into a different set of inputs. A rotating knob on a stovetop transforms the amount of energy delivered into an angle (Woodbury 191-200).

In the early phases of design collapsible structures were an avenue by which to think about parametric structures (relating to parametric modeling) and novel mechanics (related to digital fabrication). Charles Hobermanâ&#x20AC;&#x2122;s multiple inventions provided a platform on which a critical analysis of parametric design and its physical manifestations could be made. Three of his designs were specifically chosen for their variability in mechanics as well as their moderate scale and spatial complexity. Using the original patents, the designs were reverseengineered in AutoCAD. This revealed a complexity in the designs that had never been anticipated; the elements were found to be exceptionally simple while their relationships to one another were found to be exceptionally complex. Rigorous proportion among geometric shapes and relationships were usually demonstrated in a small component of the designs which was then multiplied to create the larger operating whole. These discoveries made a profound impact on the next phase of design in which there was no longer a blind search for something entirely original and ground-breaking, but led to a search for elegance in rigor and simplicity. As a result of the Hoberman studies, the design became primarily concerned with structure and its ability to collapse, which requires many intricate parametric relationships. The design was equally concerned with the spatiality of geometry and the ways in which parameters could affect the movement of the body through space.

Charles Hoberman U.S. Patent Number

6,082,056 REVERSIBLY EXPANDABLE STRUCTURES HAVING POLYGONAL LINKS

Charles Hoberman U.S. Patent Number

7,100,333 LOOP ASSEMBLIES HAVING A CENTRAL LINK

Charles Hoberman U.S. Patent Number

6,739,098 RETRACTABLE STRUCTURES COMPRISED OF INTERLINKED PANELS

Charles Hoberman U.S. Patent Number 6,082,056

Reversibly expandable structures are formed from loop assemblies comprising interconnected pairs of polygonal shaped links. Each loop assembly has polygon links with at least three pivot joints and at least some of the polygon links have more than three pivot joints. Additionally, these links lie essentially on the surface of the structure or parallel to the plane of the surface of the structure. Each polygon link has a center pivot joint for connecting to another link to form a link pair. Each link also has at least one internal pivot joint and one perimeter pivot joint. The internal pivot joints are used for connecting link pairs to adjacent link pairs to form a loop assembly. Loop assemblies can be joined together and/or to other link pairs through the perimeter pivot joints to form structures. In one preferred embodiment of the present invention link pairs may be connected to adjacent link pairs in a loop assembly through hub elements that are connected at the respective internal pivot joints of the two link pairs. Similarly hubs elements can be used to connect loop assemblies together or loop assemblies to other link pairs through the perimeter pivot joints. In yet another embodiment of the

6,082,056 REVERSIBLY EXPANDABLE STRUCTURES HAVING POLYGONAL LINKS

present invention the pivot joints can be designed as living hinges. Structures built in accordance with the subject invention have specific favorable properties, including: a) The ability to use highly rigid materials rather than bending or distortion of the mechanical links, allowing for a smooth and fluid unfolding process; b) The use of compact, structurally favorable and inexpensive joints in the form of simple pivots; c) Retaining the strength and stability of the structure during folding and unfolding since all movement in the structure is due to the actual deployment process, without floppiness in the structure (Hoberman 2000).

Charles Hoberman U.S. Patent Number 7,100,333

Improved reversibly expandable structures are formed from novel loop assemblies comprising a plurality of links, each of said links having at least one center pivot joint and a plurality of end pivot joints, each of at least two of said plurality of end pivot joints proximate to the outer edge of said loop assembly and connected to another link; each of said plurality of links being connected to another one of said plurality of links by at least two end pivot joints thereby forming a link pair, said loop assembly comprising at least three link pairs, each of said at least three link pairs connected to at least two other link pairs through at least one of said end pivot joints; each of said at least three link pairs connected to a central piece that is central to the loop assembly, said central piece being rotatable around a central axis, wherein the rotation of the central piece reversibly expands said loop assembly. Structures built in accordance with the subject invention have specific favorable properties, including: a) The ability to use highly rigid materials rather than bending or distortion of the mechanical links, allowing for a smooth and fluid unfolding process; b) The use of compact, structurally favorable and inexpensive joints

7,100,333 LOOP ASSEMBLIES HAVING A CENTRAL LINK

in the form of simple pivots; c) Retaining the strength and stability of the structure during folding and unfolding since all movement in the structure is due to the actual deployment process, without floppiness in the structure; d) A wide range of geometries; e) Inexpensive manufacture of structures with flexible hinges that are formed continuously with the links themselves; f) Convenient assembly of structures of many different shapes through kits of the necessary parts; g) The ability to create a space-filling structure by arranging linkages in a three-dimensional matrix; h) Structures have additional stability and structural stability because of the central piece, while still retaining its ability to expand and contract; and i) Structures have a central location to provide a means to mechanically drive the entire assembly.

Loop assemblies can be joined together and/or to other link pairs through the perimeter pivot joints to form structures. In one preferred embodiment of the present invention link pairs may be connected to adjacent link pairs to form a loop assembly through hub elements that are connected at the respective internal pivot joints of the two link pairs. Similarly hubs elements can be used to connect loop assemblies together or loop assemblies to other link pairs through the perimeter pivot joints to form structures. In yet another embodiment of the present invention the pivot joints can be designed as living hinges as described more fully below (Hoberman 2006)..

Charles Hoberman U.S. Patent Number 6,739,098

This invention discloses tongs-linkage, which, in its extended position, provides an essentially triangularshaped surface, whereby the links of the tongs-linkage are themselves the panels that form the surface. Such assemblies may be planar, or, by use of intermediate hub elements, may form a surface with curvature. As such an assembly is compressed, the panel-links slide over one another, compressing down to a compact stack. Such tongslinkages may be joined to similar linkages by pivots lying along their respective edges thereby forming extended structural surfaces. Surfaces that are planar, cone-shaped and doubly-curved surfaces of revolution are disclosed. In each case when the structure is retracted it compresses down to a compact linear element or ring. In accordance with the present invention, a retractable structure is presented that incorporates an additional useful feature. I have discovered a way to construct such retractable structures whereby the links are themselves panel elements. Thus, the structural members themselves form a continuous surface, leading to a more economical, structur-

6,739,098 RETRACTABLE STRUCTURES COMPRISED OF INTERLINKED PANELS

ally sound and cleaner design. Such links can be assembled to form planer and threedimensional structures. In their planar embodiments, retractable structures according to this invention may be comprised exclusively of panels hinged together. In their three-dimensional embodiments, whether conical, hemispherical or other shapes, panels are connected to one another via small hub elements. This discovery represents a significant improvement over the earlier invention, and offers the promise of building of practical architectural structures with retractable features (Hoberman 2004).

ACCORDION

The intersection of two lines (at their ends) at which the lines can rotate laterally about the same axis.

A quadrilateral that has two pairs of opposite sides that are parallel.

PARALLELOGRAM

DIAMOND

A quadrilateral that has four equal sides that are parallel.

The intersection of two lines at which the lines can rotate laterally about the same axis.

SCISSOR

The intersection of two lines at which the lines can rotate laterally about the same axis.

SCISSOR The scissor joint is the most fundamental element of a collapsible structure, as was demonstrated by the Charles Hoberman precedent studies. This joint is useful because it can be multiplied and attached to itself on every side to create an infinite array of scissor joints, creating a grid by which to provide stability and attachment. Parametrically, the scissor is generated from a single point and has motion in only two dimensions. The joint has a scalable member length and intersections based on the radius and diameter of that length. The jointâ&#x20AC;&#x2122;s most fundamental parameter is its range of rotation, and its most unique parameter is its joint offset which can permit a structure to curve.

ACCORDION

The intersection of two lines (at their ends) at which the lines can rotate laterally about the same axis.

An accordion joint is useful in a parametric structure to flexibly connect two members as well as set a range of motion for the relationship of those two members. In this design, the accordion joint serves to control the range of the scissor jointâ&#x20AC;&#x2122;s rotation, and its members simultaneously serve as the structure supporting the attached thermoelectric generators (TEGs). Like the scissor joint, its function is dependent upon a scalable member length and the intersections of the circles that align with the member lengthâ&#x20AC;&#x2122;s radius and diameter. Because the accordion is expected to behave only in a limited range of motion, conditional statements are applied to the intersection of the circles driving its member relationships.

A quadrilateral that has four equal sides that are parallel.

DIAMOND The diamond joint, which shares lineage with each of the other basic geometries in the structure, serves as the binding joint of the component. However, unlike any of the other joints it does not array and attach to itself; it sits in the axis perpendicular to the scissor joint in order to connect it to the four parallelograms. The definition for the diamond joint is the simplest due to its limited number of parameters as a closed condition. The diamond has four similar sides used to uniformly control the opening and closing of the parallelograms. The size of the diamond relative to the scissor joint, controlled by member length, is the primary parameter controlling the scissor rotation.

A quadrilateral that has two pairs of opposite sides that are parallel.

PARALLELOGRAM The purpose of the parallelogram joint in this design is to provide volume, structurally and spatially. Unlike the accordion and scissor joints, it is closed and does not require direct attachment to other members like it to have stability. The parallelogramâ&#x20AC;&#x2122;s members are scalable and their primary relationship lies in the range of the angle at each joint. The joint has an especially complex relationship of circle intersections as they relate to applied conditional statements; this is caused by the joint moving two-dimensionally relative to its own members but three-dimensionally as it relates the full component. By the adjustment of its member length and condition, the joint is geometrically simple yet provides the greatest spatial complexity.

50 These four joints (accordion, scissor, diamond, and parallelogram) come together here to form a single component, Geometria Kine. The specific coordination of these joints allows the component to be collapsible yet highly volumetric in its open position. The component’s primary purpose is to create a module that can be mass-produced from a small amount of material and compactly shipped. When the component is arrayed to create a system it can be collapsed for shipping and then easily installed on site. The ‘front’ of the component (accordion) houses the thermoelectric generators (TEGs) that are meant to be sited near a consistent heat source, and in most cases the sun is the best source, so the ‘front’ would be outward-facing (see pages 52-55). The ‘back’ of the component balances the weight of the front and uses the four parallelograms to create structural stability and visual depth. The scissor joint at the center of the component ultimately controls the full motion of the component as it connects the ‘front’ and ‘back.’ The diamond acts as a mediator between the scissor joint and the parallelograms, transferring the force of motion from the scissor joint to the parallelograms. Parametrically, when any parameter of one joint changes, all other joint parameters change simultaneously due to the number of intimate connection of all the joints. When the component is arrayed into a larger system, the change in one joint parameter has the power to completely transform the overall shape of the system. As in the Charles Hoberman precedent studies, simple geometries and relationships come together to create a complex whole.

TEGs THERMOELECTRIC GENERATORS

The thermoelectric technology for which Geometria Kine was developed is the invention of students and professors at MIT in Cambridge, Massachusetts. “The conversion of sunlight into electricity has been dominated by photovoltaic and solar thermal power generation. Photovoltaic cells are deployed widely, mostly as flat panels, whereas solar thermal electricity generation relying on optical concentrators and mechanical heat engines is only seen in large-scale power plants. Here we demonstrate a promising flat-panel solar thermal to electric power conversion technology based on the Seebeck effect and high thermal concentration, thus enabling wider applications. The developed solar thermoelectric generators (STEGs) achieved a peak efficiency of 4.6% under AM1.5G (1kWm -2‌) conditions. The efficiency is 7–8 times higher than the previously reported best value for a flat-panel STEG, and is enabled by the use of high-performance nanostructured thermoelectric materials and spectrally-selective solar absorbers in an innovative design that exploits high thermal concentration in an evacuated environment. Our work opens up a promising new approach which has the potential to achieve cost-effective conversion of solar energy into electricity.” (Kraemer, Chen, et al. 532)

53 VACUUM TUBE

THERMOELECTRIC COMPONENT

THERMOELECTRIC SYSTEM

Software: Rhinoceros 3D (NURBS modeling) Plugin: Grasshopper 3D (generative modeling for Rhino)

ENERGY DEFINITION Using the STEGs developed at MIT, Geometria Kine is a highly productive system for providing energy directly to buildings in many various contexts. Below, is a Rhino Grasshopper definition demonstrating the ability of Geometria Kine to supply the electricity needed for an average home each year (Energy.gov). Essentially, the system designed at a scale large enough to support thirty-two STEGs per component can fully supply one house for a year with only two components; this production requires minimal material and surface area and can be easily installed on-site. A larger system used by an average home would allow surplus energy to be supplied back to the grid.

WORK FLOW Geometria Kine is a site-based design, parametrically adaptable to the various conditions of many urban and some rural sites to take advantage of heat gain for energy production. The design is logically adapted through the use of Rhino Grasshopper, arranged to employ the parametric patterns of Jig, Place Holder, and Controllers. The proper setup of these parametric patterns creates an â&#x20AC;&#x2DC;equationâ&#x20AC;&#x2122; in which a particular set of input values (site-based) determine sets of output values (forms). As a result of the efficiency and systemization of the parametric framework a few permutations can satisfy multiple site conditions and allow the design to be mass-produced and distributed.

DIMENSION grid spacing module scale

HEAT DIRECTION 1-dimensional 2-dimensional 3-dimensional

INSTALLATION freestanding attached

JIG

SITE CONDITIONS residential industrial commercial institutional

CONTROLLERS member radius parallelogram length accordian length scissor length scissor rotation joint offset

PLACE HOLDER

GRASSHOPPER: LOGIC DEFINITION

INPUT

algorithmic sine wave hyperboloid

archetypes arc vault dome

CONDITIONED PERMUTIATIONS

OUTPUT

Software: Rhinoceros 3D (NURBS modeling) Plug-in: Grasshopper 3D (generative modeling for Rhino)

LOGIC DEFINITION This Rhino Grasshopper definition coordinates the full parametric capability of the single component, Geometria Kine. As defined in section 01: Parametric Structure, the definition creates a framework including a Jig (1 - the entire definition), a Place Holder (2), and Controllers (3).

61 3

By using just a few controllers that are associated with the basic joints making up the component, multiple dynamic variations can be created. Adjusting the scissor joint rotation transforms the component in the most basic way: fully collapsed to fully open. The set of images displayed here, in plan and section, are useful in understanding the role of the parallelograms to expand the volume of the component in all directions. The controller producing the greatest number of variations is the scissor joint offset, demonstrated to the right in the second set of images. Here, each row is testing a different joint offset: the first row at the standard half-distance of the member length, the second row at one-third, and the third row at one-fourth. This taxonomy of output values is also testing scissor rotation; as you move from left to right in each row the scissor rotation is increased by an increment of fifteen degrees. This taxonomy can quickly allow one to analyze what variation might be appropriate to a specific site. The third image to the right reveals a change in only one simple parameter: parallelogram length. This variation is best suited to be a canopy or a vertical wall partition. One can imagine the play of volume and space walking under or next to such a form. The remaining three controllers in the set to the immediate right (accordion member length, scissor member length, and member radius) allow the component and the resulting arrayed variations to be scalable, making Geometria Kine optimally adaptable to its environment. These variation samples are only a few of many possible forms. Again, the Hoberman studies served the design well, encouraging simplicity in geometry and mechanics to create a shifting and variable complex object.

The permutations generated by the variable parameters of the component are seemingly infinite. There are demonstrated here five of the most basic and universal permutations; three of them are categorized as archetypes as they are timeless geometries, and two are categorized as algorithms since they are derivatives of pure mathematic functions.

PERMUTATIONS ARC

archetype

Any unbroken part of the circumference of a circle or other curved line. (Dictionary.com)

VAULT

archetype

An arched structure, usually made of stones, concrete, or bricks, forming a ceiling or roof over a hall, room, sewer, or other wholly or partially enclosed construction. (Dictionary.com)

DOME

archetype

A vault, having a circular plan and usually in the form of a portion of a sphere, so constructed as to exert an equal thrust in all directions. (Dictionary.com)

HYPERBOLOID

algorithm

A quadric surface having a finite center and some of its plane sections hyperbolas. Equation: x 2 / a 2 + y 2 / b 2 â&#x2C6;&#x2019; z 2 / c 2 = 1. (Dictionary.com)

SINE WAVE (CANOPY)

algorithm

A perpendicular line drawn from one extremity of an arc of a circle to the diameter that passes through its other extremity. (Dictionary.com)

ARC

VAULT

DOME

HYPERBOLOID

SINE WAVE (CANOPY)

Tex-Fab APPLIED Competition Entry Number 69308335

GEOMETRIA KINE jee-om-i-tree-uh kin-ee KINETIC GEOMETRY It is a human desire to impart control over the environment, to designate the hierarchies of space. Geometry is intrinsic to constructed space. Complex hierarchies of simple geometries create perspective and scale that move the body forward through space. Transformation, variety, and motion create qualitative space. The composition of inherently simple mechanics, are joined here to create a dynamic component. Computationally multiplied, the component becomes a firm system, capable of generating dozens of spatial variations when arrayed along any number of complex lines or grids. The component is a deployable placeholder for the recently developed thermoelectric generators. This technology is used to capture heat and produce energy for the built environment. GEOMETRY Four geometries were studied according to their geometric behavior; accordion, scissor, diamond, and parallelogram. These simple geometries are composed to create a collapsible component that can be multiplied or aggregated into different archetypes: the arch, the vault, the dome, and the inverted dome, or hyperboloidw. PARAMETRIC BEHAVIOR A workflow for the modeling process was established based on a set of input parameters; site condition, installation, heat direction, and dimension. Then three parametric definitions were used in the modeling process: the jig, the placeholder, and controllers, such as member length, member rotation, radius, and offset define controllers that manipulate the behavior of the component as a whole. FABRICATION The component will be made from a 4’ x 8’ x 3/8” water jet cut stainless steel plate. Two full components can fit on a single plate. The following diagrams demonstrate the arrangement of the kit of parts on a plate and their assembly. ENERGY “The thermoelectric generator consists of a flat plate placed inside a glass vacuum tube,covered with a black plate of copper to absorb heat. The temperature difference on the two sides of the plate induces a flow of electricity.”

EXISTING CONDITIONS

SITE

CONCRETE

BRICK

RAINSCREEN 5

CURTAIN WALL

EARTH 6

COMPONENT SYSTEM

ARC

VAULT

DOME

HYPERBOLOID

CANOPY

CONNECTION

Along with the further development of Geometria Kineâ&#x20AC;&#x2122;s energy production and site connection, the fabrication method and mechanical efficiency of the component was tested through half-scaled mock-ups made of basswood. The fabrication testing defines an essential area of development in the project, as the Tex-Fab competition considered plausible fabrication techniques as a requisite for a successful design. While confident that the geometries of the component performed in harmony in digital models, the true mechanical fluidity had yet to be tested with the forces of gravity and the strength of materials acting upon them.

PROCESS FABRICATION ITERATIONS The efficient fabrication, materially and mechanically, of Geometria Kine is paramount to its success as a useful and economical design. Two halfscale mock-ups of the component fabricated out of basswood were made to test its material proportion and mechanical fluidity. As anticipated, the mock-ups revealed several inaccuracies, although mostly minor ones. The three-dimensional joints connecting the parallelograms to the diamond and the parallelograms to their central anchor (joint extension) were especially difficult to resolve. On a limited budget with limited resources, simple hardware comprised all joints. The three-dimensional joints were resolved mostly with ball socket joints and l-brackets and twodimensional joints were resolved with nuts and bolts. As a result of the fabrication some members were found to be either too small or too large. For example, the long central anchoring piece for the parallelograms (joint extension) began as a simple rectangle. The first mock-up revealed that it was too long, causing an obstruction to

the closing of the scissor joint. In the second mock-up, although the piece was shorter in length, it was too short in width causing the parallelograms on either side to collide when opened. In the final drawings, the central anchor is now an optimized member, having mass where it needs be strong and material cut away where other members interact with it. To the right is a series of iterations this single member has gone through, with all of those iterations compounded into a single drawing to the immediate right. Another significant design flaw revealed during fabrication was the connection of each component to the one above or below it. The missing pieces in the component are two members the same size as those of the accordion that connect each open end of the scissor joint to the end of the central anchor. Without these additional pieces, the permutations and arrayed systems would have little vertical stability.

PARALLELOGRAM (PG)

Here, each geometric part of the component is detailed. It is noteworthy that while nearly all members have the same width, they are sound proportionally. At the ends of most members is an opening for the joint connection and the material around the opening is ‘bumped out’ to provide enough surface area for the joint hardware. Many of the joint openings are sized the same in order to maximize the speed of production and installation. The entire method of fabrication and installation is meant to be standardized and straight-forward in order to be useful to any level of technical understanding. At their standard scale, all of the members needed for two components can fit on a single 4’ x 8’ sheet of stainless steel. According to the energy definition in the previous section, this means that a single standard sheet of stainless steel can supply the full structure for the number of components needed to supply a house continuously.

DIAMOND (DM)

JOINT EXTENSION B (JE-B)

JOINT EXTENSION A (JE-A)

SCISSOR (SC)

ACCORDION (AC)

MEMBER SPECS.

The first iteration of the component was created in Revit. At the time little was understood about the realistic functioning of a three-dimensional joint, which would be used in multiple connections within the component. Initially, the design specified ball bearing joints. Once fabrication began, the ball-and-socket joint was discovered and was used to control the motion of the parallelograms. The connections from the diamond to the scissors and the parallelograms was also simplified during fabrication with the use of simple, adjustable hardware.

From initial design, all members with relationships in only two dimensions were expected to be attached with simple joints at the ends (or the center, in the case of the scissor joint) of each member. During the fabrication of the first half-scale mock-up hex nuts and bolts and washers were used and the ends of each of the members had expanded surface area to reinforce the joint. For the final half-scale mock-up the washers and expanded surface area were found to be excessive at most joints and were replaced with only the nut and bolt. The design remained the same at the more robust joints: the scissor and accordion.

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1. COMPONENT MEMBER 2. COMPONENT MEMBER 3. HEX BOLT 4. WASHER 5. FLANGE BALL BEARING

JOINT DETAIL

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1. HEX BOLT 2. COMPONENT MEMBER 3. COUPLING NUT 4. BALL SOCKET JOINT 5. COMPONENT MEMBER 6. L-BRACKET 7. HEX BOLT AND NUT 8. PHILLIP’S HEAD NUT 9. COMPONENT MEMBER 10. HEX BOLT AND NUT

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BIBLIOGRAPHY Annenberg Learner. “Geometry Glossary.” Annenberg Foundation. WGBH Educational Foundation, 2002. Web. 31 July 2012 < http://www.learner.org/ courses/learningmath/geometry/keyterms.html>. AST Bearings and Related Products & Services. “Ball Bearings: Tapered Outer Diameter, Flanged.” AST Bearings LLC, 1963. Web. 2 August 2012 < http://catalog.astbearings.com/db/service?domain=ast&command=locate&cat egory=tapered_od_flange>. Bell, Brad, Kevin Patrick McClellan, and Andrew Vrana. “APPLIED: Research Through Fabrication.” Tex-Fab, Digital Fabrication Alliance. 10 March 2012. Web. December 2011 <http://tex-fab.net/>. CAD Corner. “Fasteners CAD Blocks.” CAD Corner Canada. Web. 2 August 2012 < http://www.cadcorner.ca/fasblocks.php>. Dictionary.com. “Dictionary.” Dictionary.com LLC, 2012. Web. 17 August 2012 < http://dictionary.reference.com/>. Energy.gov. “2009 Energy Consumption per Person.” U.S. Department of Energy. Web. 14 July 2012 < http://energy.gov/maps/2009-energy-consumptionperson>. Hamamatsu, Kiyoharu Kanegawa. “Ball joint socket.” Patent 4,681,475. 21 July 1987. Hoberman, Charles. “Loop assemblies having a central link.” Patent 7,100,333. 05 September 2006. Hoberman, Charles. “Retractable structures comprised of interlinked panels.” Patent 6,739,098. 25 May 2004. Hoberman, Charles. “Reversibly expandable structures having polygonal links.” Patent 6,082,056. 04 July 2000. Kraemer, Daniel, Gang Chen, et al. “High-performance flat-panel solar thermoelectric generators with high thermal concentration.” Nature Materials 10.7 (2011) : 532-38. Online pulbication. Woodbury, Robert. Elements of Parametric Design. New York, NY: Routledge, 2010.

IMAGES 1. LaMonica, Martin. “Thermoelectric Generator Powered by Sun’s Heat.” Solar 23 May 2011. March 2012 < http://energydeals.wordpress.com/2011/05/23/ thermoelectric-generator-powered-by-suns-heat/>. 2. Renata. “Solar-thermal flat-panels that generate electric power.” Solar Daily 2 May 2011. March 2012 < http://www.setyoufreenews.com/2011/05/02/solarthermal-flat-panels-that-generate-electric-power/>. 3. Ando, Tadao. 15 July 2012. Courtesy of www.toya.net. 4. Kahn, Louis. 15 July 2012. Courtesy of constructionphotography.com. 5. Herzog & DeMeuron. 15 July 2012. Courtesy of media-cache0.pinterest.com. 6. Norman Foster & Partners. 15 July 2012. Courtesy of photos.travellerspoint. com. 7. Gehry, Frank. 15 July 2012. Courtesy of www.torange.us.

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