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Knowledge-based architectural decision making of kinetic structures Wierzbicki, Madalina Nicoleta 2007

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KNOWLEDGE-BASED ARCHITECTURALDECISION MAKINGOF KINETIC STRUCTURESbyMadalina Nicoleta WierzbickiM. Arch. Faculty of Architecture and Urban Planning, Bucharest, RomaniaB. Arch. Faculty of Architecture and Urban Planning, Bucharest, RomamaA THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THEREQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEInTHE FACULTY OF GRADUATE STUDIESMechanical EngineeringThe University of British Columbia2007© Madalina Wierzbicki 2007AbstractThis thesis concerns kinetic engineering structures, which can be quickly resized andadjusted to conform to frequently changing needs, folded for transportation or storageand be easily deployed by means of unfolding. Unprecedented technological, economicand demographic growth is subjecting the traditional building codes and constructionstandards to test. The questions underlying this thesis are whether kinetic buildingstructures could better address the demanding requirements of the modern world;importantly, could they provide better protection when exposed to extreme circumstanceslike natural or man-induced disasters; could they provide means of rapidly deployable,robust and adaptable sheltering for the population that has been affected by catastrophicevents; and in the end, could they effectively contribute in saving more human lives?Advances in design tools and materials engineering open up possibilities forkinetic structures, which may offer unprecedented functional performance andadaptability to changing conditions. Such structures may respond better to the demandsof increasingly dense urban development, better space management and reducedenvironmental impact. Foremost, they may be very well suited for rapid, on-demanddeployment in emergency situations. The essential feature of such structures is a kineticcomponent that allows the spatial geometry to be adapted according to changing needs.Kinematic chain geometries borrowed from traditional mechanics and robotics can bedeveloped into a variety of topologies suitable for architectural structures. Modulardeformable grids can provide the functionality of expanding and collapsing as well as theability to be infinitely arrayed. The thesis investigates these aspects. The demands of thedesign process that is needed to develop kinetic structures will expand the traditional11architectural workflow to include the parametric modeling tools, motion analysis toolsand fuzzy logic-based optimization algorithms that are common in mechanicalengineering. The thesis explores these issues as well.In particular, the thesis focuses on conceptualizing kinetic structures that employrigidly foldable shells and frames derived from kinematic chains. It studies theapplication of human knowledge through fuzzy logic for the process of designing andautomatically manipulating the kinematic properties of a kinematic structure. Itimplements the fuzzy logic formalism to develop a design optimization tool that can formthe foundation for design workflows that target kinetic structures. Folding structures thatprovide adjustable, on-demand coiifigurations can be effectively conceptualized ifappropriate interdisciplinary expertise including engineering, architecture, andknowledge-based decision making is brought together, as highlighted in the thesis.111Table of ContentsAbstract iiContents ivList of Tables viiList of Figures viiiNomenclature xiiAbbreviations xiiiAcknowledgments xivDedication xvChapter 1 — Introduction 11.1 Objectives 11.2 Scope and Motivation 21.3 Related Work 31.3.1 Historical Context 31.3.2 Modern Examples 51.4 Future Trends and Applications 111.5 Contributions and Thesis Organization 13Chapter 2— Concept Development 162.1 The Geometrical Concept 162.1.1 Historical Overview 17iv2.1.2 Kinematic Chains 202.1.3 Rectilinear Grid Development 202.1.4 Converging Grid Development 212.2 Development of Kinetic Structures 232.2.1 Foldable Frames 232.2.2 Arrays 232.3 Development of Shells 242.3.1 The Controlling Grid 242.3.2 Rigid Folding 252.3.3 Conceptualizing of Rigid Foldable Shells 262.3.4 Development of Freeform Shells 302.4 Functional Structure Development 332.4.1 Modular Segment 332.4.2 Arrayed Assembly 342.5 Operation and Applications 342.5.1 Deployment 342.5.2 Typical Scenarios 372.5.3 Typical Lifecycle and Sustainability 382.5.4 Overview of Advantages 38Chapter 3— The Design Process 403.1 Design Objectives 403.2 Design Workflow 413.2.1 Available Design Tools 413.2.2 Interdisciplinary Approach 433.2.3 Integrated Design Environment 463.3 Management of Kinematic and Functional Dependencies 493.3.1 Operational Parameters 49V3.4 Conceptualization of Shells .503.4.1 Kinematics of Rigid Folding 503.4.2 Foldable Shells 503.5 Simulation and Testing of Shell Folding 52Chapter 4— Knowledge-Based Design Optimization 534.1 Optimization Challenges 534.2 Decision Making Using Fuzzy Logic 584.3 Optimization through Fuzzy Logic 604.3.1 Fuzzy Logic-based Process Overview 604.3.2 Test Conditions and Membership Functions 634.3.3 Inference Clauses 674.3.4 Knowledge Base 68Chapter 5— Design Study and Results 695.1 Design Case Study 675.2 Testing of the Optimization Algorithm 705.2.1 Modeling of 3d Mesh Behavior 715.2.2 Development of the Test Set-up 735.3 Testing Results and Evaluation 75Chapter 6— Conclusions 836.1 Conclusions 836.2 Future Research Directions 84Bibliography 86viList of Tables4.1 Input/output parameters and their fuzzy representations, M. Wierzbicki 65viiList of Figures1.1 Iris Dome by Chuck Hoberman 51.2 IBM Pavilion by Renzo Piano 61.3 Macro Mod Tent by Michael Fox 61.4 Pantographic mast, University of Cambridge 71.5 Spherical roof concept, University of Cambridge 81.6 Coilable mast, NASA 91.7 Foldable solar panel, NASA 101.8 Deployable mesh reflector, Astro-Aerospace 101.9 Deployable ring structure, University of Cambridge 112.1 Geometrical concept, M. Wierzbicki 172.2 Schemer’s geometrical construct 182.3 da Vinci’s mechanism 192.4 Franz Reuleaux, Models of Mechanisms 202.5 Four bar linkages 202.6 Arraying of rectilinear kinematic chains, M. Wierzbicki 212.7 Arraying of converging kinematic chains, M. Wierzbicki 222.8 Converging iso-angular module, M. Wierzbicki 222.9 Swept trajectories of a folding structure, M. Wierzbicki 242.10 Folding of flat sheets and foldable shells, M. Wierzbicki 262.11 Controlled folding of a flat sheet, M. Wierzbicki 272.12 Adjustment of folding parameters, M. Wierzbicki 27viii2.13 Constructing a 3d mesh, M. Wierzbicki .282.14 Range of transformation, M. Wierzbicki 292.15 Development of a foldable module, M. Wierzbicki 292.16 Details of a foldable module, M. Wierzbicki 302.17 Ridge and crescent primitive coded as a height map, M. Wierzbicki 322.18 Concept structure utilizing a crumpled shell, M. Wierzbicki 332.19 Foldable frame, M. Wierzbicki 332.20 Complete modular segment, M. Wierzbicki 342.21 Arrayed modules, M. Wierzbicki 342.22 Adjustable shading system, M. Wierzbicki 352.23 Applications: Shelters and exhibition, M. Wierzbicki 362.24 Mobile system, M. Wierzbicki 362.25 Exhibition space, glulam structure, M. Wierzbicki 372.26 Details of glulam frame, M. Wierzbicki 373.1 Sketch of a facet, M. Wierzbicki 413.2 Assembly constraining, M. Wierzbicki 423.3 Interdisciplinary requirements for kinetic structures, M. Wierzbicki 443.4 Fuzzy logic and interdisciplinary context, M. Wierzbicki 453.5 Matrix of disciplines and tools, M. Wierzbicki 473.6 Design workflow, M. Wierzbicki 483.7 Kinematic diagram of a serial robot (left)and a parallel robot (right), M. Wierzbicki 51ix3.8 Kinematic diagram of a foldable shell (left).Parallel topology of the ridges (right), M. Wierzbicki 514.1 Gough platform topology, Proc. IMechE, 1965 554.2 Block diagram of the design process, M. Wierzbicki 604.3 Block diagram of the FIS, M. Wierzbicki 614.4 Flow diagram of the optimization algorithm, M. Wierzbicki 624.5 Input membership functions, M. Wierzbicki 664.6 Output membership functions, M. Wierzbicki 664.7 Node movement versus the degree of folding and magnitude ofadjustments, M. Wierzbicki 674.8 Knowledge base statements, M. Wierzbicki 695.1 Mapping of the geometry between topological spaces, M. Wierzbicki 725.2 Folding of 2d lattice: initial (left), optimized (right), M. Wierzbicki 735.3 Modules of the optimization program, M. Wierzbicki 745.4 The interface of the testing application, M. Wierzbicki 755.5 Sample optimizations: Mamdani method (left);Sugeno method (right), M. Wierzbicki 765.6 Input/output surface plots: Mamdani (left);Sugeno (right), M. Wierzbicki 765.7 Typical behaviors: ceiling (left), oscillating (center),diminishing progression (right), M. Wierzbicki 785.8 Progress of optimization of a complex 2d lattice, M. Wierzbicki 785.9 A case of over-adjustments of geometry, M. Wierzbicki 80x5.10 A case of under-adjustments of geometry, M. Wierzbicki 815.11 Sample optimization of a complex 2d lattice, M. Wierzbicki 82xiNomenclatureA Angle of the segmenta1 Angle of the controlling grida2 Angle of the controlling griddO Sketch parameterdl Sketch parameterd2 Sketch parameterdA AdjustmentDAPivot distance of the outer linkageDB Pivot distance of the inner linkagedN Relative node movementF Degree of foldingfx Sketch parameter expressed as a formulag Vector of inequality constraintsh Vector of equality constraintsh1 Offset heightOffset heightOffset heightJ Objective of optimizationL Total length of the segmentsL1 Span of the controlling gridL2 Span of the controlling gridxiiLA Length of the outer linkageLB Length of the inner linkageN Neutral point; node; end node; vertexN1 Relative node movementN2 Relative node movement0 Pivot pointP1 PointF2 PointQSingularityr Radius of the inner segmentR Radius of the outer segmentx Vector of the design variablesXlb Lower bounds of the design variablesXub Upper bounds of the design variablesxli’Abbreviations2d Two-dimensional3d Three-dimensionalCAD Computer-Aided DesignFEA Finite Element AnalysisFIS Fuzzy Inference SystemGlularn Laminated woodI/O Input/OutputMDO Multidisciplinary Design OptimizationSOM Smallest of MaximumxivAcknowledgmentsI would like to express my sincere gratitude and appreciation to my supervisor, Prof.Clarence W. de Silva for agreeing to supervise me and for his proactive attitude towardinnovative ideas. His support and guidance, his fine teaching and invaluable advice wereof utmost importance in bringing this thesis to completion. I thank him for taking anactive interest in my research, for his patience in reading and editing my latestpublications, for his consistent encouragement regarding my professional and academicgoals and for providing part of the financial support (through his NSERC grant) for myresearch and for conference attendance.I would also like to thank Prof. Elizabeth Croft, and Prof Don Krug forencouraging this research from the beginning up to the present and for the valuablecomments and suggestions, Prof N. Rajapakse for accepting me in the M.A.Sc. program,Prof Farrokh Sasani and Prof Mu Chiao for their advice, and Prof Lalith Gamage forhis comments during my presentations.Thanks go to all my colleagues in the Industrial Automation Laboratory of UBC, underthe directorship of Prof Clarence de Silva for making the lab a great and friendly place.On a personal note I would like to thank my husband for his patience and support, my sonfor coming up with concepts that defy the restrictions of convention, and fate for myfather being a mechanical engineer.xvDedicationIn a memory of my parentsxviChapter 1 — IntroductionThis introductory chapter sets the stage for the research that is presented in the thesis.Objectives of the research are given and the rationale for these objectives is outlined.Pertinent literature is surveyed starting with a historical overview of kinetic elements andexperiments in architecture. As well, a brief analysis of the potential benefits ofadjustable structures is presented.11 ObjectivesThis thesis concerns kinetic engineering structures, which can be quickly resized andadjusted to conform to frequently changing needs, folded for transportation or storageand be easily deployed by means of unfolding. In particular, the dissertation introducesnovel concepts and methodologies aimed at developing feasible implementations oflarge-scale kinetic structures. Designed as modular and on-demand reconfigurablesystems, such structures are intended to become the key element of a class of buildings,enclosures and shelters. This type of structures has not been developed yet; however,recent advances in design tools, materials and manufacturing methods, and technologicalknow-how, particularly in the field of robotics, provide fertile ground for initiatinginterdisciplinary projects targeting novel concepts of folding structures as well as viablemethodologies for developing a knowledge-base and assisting design-related decisionmaking.First, the thesis provides an overview of the concepts and significance of kineticstructures and theoretical concepts and classifications necessary for developing kinetic1architectural elements. Within this context, the thesis proposes and investigates noveltopologies for folding structures. The applicability and limitations of available designtools is examined to present a practical workflow scenario. The difficulties encounteredin designing foldable geometry are analyzed. This thesis proposes a knowledge-baseddecision making solution which incorporates the knowledge the designers gain whileobserving the kinematic properties of folding structures. The use and application of fuzzylogic to harness such a knowledge base and make decisions using that knowledge base isdemonstrated.1.2 Scope and MotivationFoldable structures can offer features that are beneficial in responding to the extended setof contemporary requirements of rapid-deployment buildings. These requirements call forbetter safety when faced with natural and man-induced disasters. They encouragemeaningful environmental responsibility and material use. Cost and speed of building andoperation, and the functional flexibility are important as well. Foremost, they define therelevant functional and comfort expectations of societies that are becoming moredynamic, complex, and cost conscious. Kinetic structures prefabricated as modularcomponents can be assembled on site at lower cost and with less environmental impactthan buildings constructed by traditional methods. Furthermore, the inherent ease ofdisassembly and reuse of modular kinetic components facilitates lifecycles based onadjustment and relocation rather than demolition and new construction, which can haveadverse environmental implications in addition to other obvious disadvantages.Functionally, kinetic systems have the capability to play an important role in formingreactive environments, spaces that can intelligently, cost-effectively and rapidly respond2to changing conditions such as occupancy dynamics, environmental conditions andemergencies. Undoubtedly, an added element of kinematics will introduce newchallenges for designers. This thesis pursues critical thinking in this direction andproposes a novel folding topology for structures and discusses the design process. Inparticular, it focuses on difficulties encountered while testing the folding performance ofthe geometry, and develops an approach of knowledge-based decision making, throughfuzzy logic, to overcome the difficulties.1.3 Related Work1.3.1 Historical ContextThe idea of configurable, kinetic elements in architecture is as old as architecture itself.Doors, windows, blinds, gates, trap-floors, draw bridges and other simple-in-conceptdevices have been known for ages. They have been traditionally used to control ingressand manage light penetration and air flow. Simple sliding or pivot mechanism conceptsgave way over the years to countless examples of ingenious engineering solutions andcraftsmanship, as exemplified by elaborate stage and background mechanisms in operahouses that could transform the interior to dazzle audiences.During the last forty years, architects and engineers have shown increasing interest in theapplication of kinetic elements in buildings as means to more effectively address thecomplex requirements of the rapidly developing world. Utilizing computer software,engineering science and technology, and materials advances, designers have shown thatmotion need not be antithetical to our understanding of architecture and that it mayactually make architecture more functional and exciting for its users, while adding3benefits of flexibility, speed of deployment, and cost effectiveness. Professor Zukpioneered the modem philosophy of kinetic design in the late 1960’s with the publicationof a visionary and detailed overview of kinetic concepts (Zuk & Clark, 1970). He madean interesting remark: According to Zuk,“Architecture has often been calledfrozen music. Others have referred toit as a permanent expression ofan age-thefreezing ofan era; thepetrfication ofan idea; the recording in stone ofan isolatedfragment ofhistoiy. The purpose ofthis book is to describe and discuss an emergingapproach to architecture which signficantly rejects these typicaldescriptions ofarchitecture. What is presented is not architecture offantasy, but a predictionfor thefuture based upon a natural evolution, areasoned and reasonable extension ofaccelerated trends, and need tosatisJj’ a dynamically changing society. What will be discussed is anarchitecture that is not static, as has traditionally been the case, but onethat has the capability ofadapting to change through kinetics.”(Zuk & Clark, 1970).Thirty five years later, Prof. Ataman provides an interesting update:Even though, most technological innovations hold the promise totransform the building industiy and the architecture within, andalthough, there have been some limited attempts in this arearecently; to date architecture has failed to utilize the vast amountof accumulated technological knowledge and innovations tosignfIcantly transform the industry. (Ataman, 2005).41.32 Modern ExamplesRecent decades have seen the advent of large, retractable roofs over stadiums and stages,elaborate partition systems in conference centers, configurable floor installations inconcert halls, revolving floor stages, anti-sway devices in high-rise towers andautomatically adjustable columns that compensate for ground settling. Elevators andescalators allow cross-connection to areas that would otherwise be, in geometricaltopology terms, isolated. However, these kinetic elements have mostly a limited,localized function of controlling egress, subdividing space and adjusting some aspects ofthe exterior shell. The most innovative are experiments with kinematic arrangements andnovel forms and applications. Chuck Hoberman’s Iris Dome is a retractable roof thatopens or closes like an iris, composed of sliding and overlapping heavy-gauge metalplates supported by a circular linkage array, as shown in Figure 1.1.Renzo Piano’s IBM Pavilion is an array of pivoting frames that allows partial or completeenclosure of the space, as shown in Figure 1.2. The Macro Mod tent designed by MichaelFox is based on a module composed of a scissor-like, folding frame and a bi-folding roofFigure 1.1. Iris Dome by Chuck Hoberman.5element. An array of these modules forms a non-continuous, vented enclosure, as shownin Figure 1.3.— —The concept of a deployable mast targeted at telecommunication and space applications isshown in Figure 1.4.Figure 1.2. IBMPavilion by Renzo Piano.Figure 1.3. Macro Mod Tent by Michael Fox.6The spherical, diaphragm-like roof shown in Figure 1.5 is one of the very few conceptualstructures that can be continuously adjusted (Jensen and Pellegrino, 2002). However,besides partially open and fully closed positions, it does not offer much of a functionaladvantage.Figure 1.4. Pantographic mast, University ofCambridge.7The conceptual nature of these ideas with little operating experience indicates thatthe concept of a ‘foldable’ building or reconfigurable-on-demand functional layout is notquite here yet. Researchers and designers continue experimenting with kinetic designsand foldable set-ups. In these prototypes, the difficulty of integrating a kinematicstructure with a foldable, adjustable shell becomes apparent. Frequently, the improvised,tent-like patches of external shell do not match the grace and ingenuity of the underlyingstructural skeleton.Space exploration is the locus of many ingenious inventions. However, it is important tokeep in mind the very different environment and applications such devices are designedfor. Orbiting structures operate in a microgravity environment which is ideal for folding,kinetic, and actuated mechanisms, as there are no gravity-induced loads or gravity-induced frictional forces. Ultra-light and ultra-compact structures are the dominant designcriteria. Adverse atmospheric conditions such as wind loads, rain, ice, snow, dust andmoisture are typically absent in these environments. The coiled mast shown in Figure 1.6springs out of a compact spool into an extended and self-supporting position, but it canFigure 1.5. Spherical roofconcept, University ofCambridge.8do so only in a gravity-free environment. A foldable, capton-flim mounted solar arrayreveals its fragile, optimized-for-weight nature even under gravity-free conditions inFigure 1.7.ColIabl long.rors4sFigure 1.6. Coilable mast, NASA.Figure 1.7. Foldable solar panel, NASA.9Figure 1.8 shows an impressive example of how much of a controlled structure can beejected from a compact box. This ultra-light structure deploys a precise parabolic skin asan antenna; however, it is only able to do so in a weightless environment.Figure 1.9 shows a deployable ring constructed from hexagonal and triangular linkagechains that are controlled by two adjustable-length cables.Figure 1.8. Deployable mesh reflector, Astro-Aerospace.10These examples focus on lightweight, pre-stressed structures that offer selfdeployable, kinematically determinate characteristics that are valuable for space-orientedapplications. Such structures are two-state devices: they are either folded into a compact,space-saving shape for transportation or fully deployed into their functionalconfigurations. They are not designed to be adjusted or re-shaped adaptively during use.More important, the pre-stressed and overconstrained concepts shown here, which canself-deploy in a kinematically determinate fashion, have a very limited load capacity andcan operate only under the gravity-free conditions of space. Structures of this kind arebeing developed for the purpose of installing large, controlled surfaces in space where thekey requirement is a single deployment path that takes the structure predictably fromfolded to the fully deployed state (Pellegrino and Gan, 2006). The use of such structuresin architectural, ground-based solutions is not realistic.Figure 1.9. Deployable ring structure, University ofCambridge.111.4 Future Trends and ApplicationsTraditional architectural methodologies hold that building forms are static, non-adaptablecivil engineering infrastructures developed to support social processes. Decisionsregarding function, aesthetics and lifecycles of buildings and the resulting urban grid areconsidered to be part of the initial planning and design process. Once buildings areerected, they form a permanent and unchangeable manifestation of these decisions. Fromthat moment on, inhabitants and authorities have to conform their needs to such fixedcivil infrastructure. The inertia with which these systems can respond to changing socialdemands or functional conflicts and exclusions, is obvious. Short of demolishing andrebuilding the infrastructure to fit the optimal compromise, the logistical conflicts canonly be mitigated by regulatory means such us usage and access restrictions. There aremany examples of urban fabric stratification into functionally unsustainable, fragmentednodes as a result of the limited effectiveness of managing an infrastructure whose originalfunctional specifications have become obsolete yet demolition and rebuilding of thestructure is infeasible. In this context, the potential benefits of structures that offer aspectsof kinematics and adaptability are apparent.Kinetic structures prefabricated as modular components can be rapidly assembledon site with reduced cost and less environmental impact than buildings constructed withtraditional methods. Furthermore, the inherent ease of disassembly and re-use of modularkinetic components facilitates structural lifecycles based on adjustment and relocationrather than on demolition and all-out new construction, the latter having obviousdisadvantages with regard to environmental impact, efficiency, and convenience ofutilization.12Professor Kibert, the pioneer of ecologically viable construction methods, pointsout the importance of managing the ecological footprint ofthe construction industry:• . . the construction sector consumes 40% of all extractedmaterials, produces one-third of the total landfill waste stream,and accountsfor 30% ofnational energy consumption... (Kibert,Sendzimir & Bradley, 2002,p.1).Kilbert also provides a systemic classification of the technical lifecycle aspects of variousconstruction elements:Buildings are assembledfrom a wide array of components that can be generallydivided intofive general categories:1 manufactured, site-installed commodity products, systems, andcomponents with little or no site processing (boilers, valves,electrical transformers, doors, windows, lighting, bricks);2 engineered, off-site fabricated, site assembled components(structural steel, precast concrete elements, glulam beams,engineered woodproducts, wood or metal trusses);3 off-site processed, site-finished products (cast-in-place concrete,asphalt, aggregates, soil);4 manufactured, site-processed products (dimensional lumber,drywall, plywood, electrical wiring, insulation, metal and plasticpiping, ductwork);5 manufactured, site-installed, low mass products (paints, sealers,varnishes, glues, mastics).Category I components, because they are manufactured ascomplete systems, can be more easily designed forremanufacturing, reuse, and disassembly, and thus have anexcellent potential for being placed into a closed materials loop.Category 2 products also have this potential . . . (Kibert et al.,2002,p. 9-10).This classification indicates the potential advantages of modular kinetic components.Such components fulfill the structural tasks of those listed in Category 2 while theirecological lifecycles match the efficiency of the components listed in Category 1. Theunique features of foldable structures may change traditional building deployment,maintenance and lifecycle models and offer reconfiguration as an alternative to13demolition and rebuilding, particularly in urban environments with high populationdensities. Configurable structures, being better suited for re-use, modification and relocation, can be expected to have less environmental impact than traditional technologies.In this context, the field of kinetic structures introduces a “mechanical engineeringflavor” to an area that is traditionally dominated by architects and civil engineers.1.5 Contributions and Thesis OrganizationThis thesis presents original contributions in the conceptualization of new topologies forkinetic structures, analysis of design workflows, research of potential problems andapplication of fuzzy logic for developing automated, empirical knowledge based designtools capable of modeling the kinematic behavior of foldable geometries. An novelconcept of folding structures is introduced based on integration of two innovative ideas: arigidly folding shell modeled as a general case of an under-constrained 3d mesh, and afolding structural frame based on a pantographic kinematic linkage. The proposedsolution uses the folding frame to support the shell, engage its available degrees offreedom, and control its motion.The design challenges are identified related to achieving a desired, error-freedegree of folding and linked them to the topological characteristics of foldable shells. Anoriginal analysis of the design workflow aimed at kinetic structures based on a matrix ofapplicable computer-assisted design (CAD) tools and a typical design processes isintroduced. The analysis identifies the areas that require development of additional,customized tools.14The thesis also introduces a novel method of emulating the forward kinematicsbehavior of complex parallel geometries using a two-dimensional construct for thepurpose of developing efficient test simulations. Finally, a novel application of fuzzylogic is developed for the purpose of constructing automated design algorithms, whichmake design decisions that employ the accrued knowledge-based design information.Chapter 1 outlines and justifies, by presenting the potential benefits of adjustablestructures, the objectives and contributions of the thesis against a historical overview ofkinetic elements and experiments in architecture.Chapter 2 provides an overview of the historical developments in geometry andkinematics relevant to designing kinetic structures, and explains the conceptualizationprocess. The initial layout of controlling geometry, modularization scheme anddevelopment of a linked foldable shell are detailed. The original research on foldingshapes is presented as a comprehensive classification of transformable geometries thatare applicable to kinetic structures. The design stages of a novel concept of a foldingstructure are detailed and the kinematics illustrated. Possible applications, lifecyclespecifics and potential benefits are analyzed.Chapter 3 discusses the overall design methodology with special attention paid toefficient and productive workflows. The interdisciplinary context as the key element inprojects that pursue novel solutions is detailed. The available design tools, theirsuitability for integrated design workflows and the areas requiring new design algorithmsare reviewed. The kinematics of the developed folding structure are explained and theperformance validation process is outlined.15Chapter 4 investigates the design challenges stemming from the topologicalcharacteristics of foldable shells. The history and current status of algorithmic andcomputational methods developed for analogous geometries in robotics are presented.The limitations of these methods for designing folding shells and achieving the desiredkinematic performance are discussed; in particular, error-free folding. A novel approachtoward optimizing the geometry in order to achieve the desired folding range isintroduced. The optimization technique proposed here utilizes the knowledge-basedmethods originating from human designers. Fuzzy logic is used to develop algorithmsthat are capable of implementing a knowledge-based approach to decision makingassociated with design and deployment of a kinetic structure. The structure of thedeveloped fuzzy logic system together with its knowledge base and the decision makingmodule are detailed, as well as the programmatic structure of the developed algorithm.Chapter 5 details the testing and evaluation process of the developed optimizationalgorithm. The strategies involved in modeling the behavior of a foldable shell and indeveloping the testing simulation environment are explained, and the structure and theinterface of the testing program are described. Test results are presented and discussedand the behavior and performance of the algorithm are evaluated. Main contributions ofthe thesis and the planned future research directions are outlined in Chapter 6.16Chapter 2— Concept DevelopmentThis chapter provides a review of the geometric concept and past developments ingeometry and kinematics relevant to designing kinetic structures. It presents theassociated conceptualization process. The initial layout of controlling geometry,modularization scheme and development of a linked foldable shell are detailed. Theoriginal research on folding shapes is presented as a comprehensive classification oftransformable geometries that are applicable to kinetic structures. The design stages of anovel concept of a folding structure are detailed and the kinematics illustrated. Possibleapplications, lifecycle specifics and potential benefits are analyzed.2,1 The Geometrical ConceptA pantograph like geometrical construct forms the basic concept for a folding structuralframe. Inscribed into a rectangle or a symmetrical trapezium to enable modular arraying,it can fold into a narrow, elongated shape or expand to increase the coverage, as shown inFigure 2.1.Figure 2.1. Geometrical concept.17It can therefore be adapted for kinetic structures that need to be folded for storage ortransportation or need to be adjusted during use. Next section discusses the historicalroots of this construct.2.1.1 Historical OverviewGerman mathematician Christoph Schemer devised the geometrical construct ofpantograph in 1630 (see Figure 2.2). It is, in simple mechanical terms, a linkage ofpivoting arms. It is a variation of the four bar linkage that employs the geometry of aparallelogram. Its original purpose was to help with making scaled copies of 2-dimensional shapes, patterns and drawings. Certainly, it deserves to be termed as anarchetype of a reprographic device.Such translatable, or in other words: deformable geometrical constructs, if executed asmechanical devices, form kinematic chains. The most common, practical purpose ofkinematic chains is to convert one kind of motion into another. For instance, circular, orrotational motion into linear motion.Figure 2.2. Schemer ‘s geometrical construct.18Interestingly, Schemer’s geometrical model was preceded, some 40 years earlier,by the concept of a kinematic chain that introduced elements of similar, pantograph likegeometry. The mechanism, devised by da Vinci, is depicted in his Codex Madrid, asindicated in Figure 2.3. This document dates back to the 1490s. Da Vinci complementedhis concept with a screw type actuator. Even by today’s standards, da Vinci’s CodexMadrid is a treasure chest of various, sometimes very elaborate, actuation mechanisms.More than three centuries later, in the late19thcentury, a German engineer namedFranz Reuleaux formed a systemic mathematical methodology for designing kinematicdevices. He used physical, functional models of mechanisms to illustrate the theoreticalconcepts and demonstrate the motion effects. It is fair to acknowledge this as the first useof conceptual motion simulation. His research resulted in a vast collection, some 800, offunctional models of mechamsms that illustrated his ideas, as exemplified in Figure 2.4.‘=1Figure 2.3. da Vinci’s mechanism.192.1.2 Kinematic ChainsFour bar linkages are examples of the simplest closed ioop kinematic chains. Despitetheir simplicity, they can execute complex motion patterns of great variety. Some popularfour bar linkage configurations are, as shown in Figure 2.5: drag-link, crank-rocker,double-rocker and crank slider.IMany kinematic chain geometries borrowed from traditional mechanics may provideinspiration for developing concepts for kinetic architectural structures. One of theprerequisites is the ability to be assembled into larger, repeatable grids.Figure 2.4. Franz Reuleaux, Models of Mechanisms.Figure 2.5. Four bar linkages202.1.3 Rectilinear Grid DevelopmentRectilinear deformable grids can provide the ftinctionality of expanding and collapsing.A simple geometrical construct based on the original Schemer’s concept can bedeveloped into a rectilinear kinematic chain and arrayed to create a variety ofconfigurations, as shown in Figure 2.6.4Figure 2.6. Arraying ofrectilinear kinematic chains.2.1.4 Converging Grid DevelopmentConverging grids allow for circular arrays and fan like folding, as illustrated in Figure2.7. However they add the challenge of retaining a coordinated angular envelope, asshown in Figure 2.8.21RFigure 2.7. Arraying ofconverging kinematic chains.rAFigure 2.8. Converging iso-angular module.222.2 Development of Kinetic Structures2.2.1 Foldable FramesThe challenge of developing two-dimensional geometrical concepts into viable foldingframes is the cornerstone of designing kinetic structures. In mechanics, kinematic chainsare, most of the time, a part of much larger assembly context that provides anchors,support and constraints therefore they can be easily modeled as two-dimensional devices.Since architectural structures bear a combination of static loads of construction materialsand dynamic loads induced by use, operation and elements, they need to be self-supporting and statically stable. Therefore the two-dimensional concept chains need to betransformed into a three-dimensional system of interleaved frames and off-set joints toassure load bearing capacity and static integrity. This process is more difficult forconverging grids as the architectural structures do not scale as easily as simplifiedmechanical chains.2.2.2 ArraysTo realize the full potential of modular flexibility, the folding frames must incorporatefeatures that facilitate arraying into large assemblies. This requirement places additionaldemands on detailing of the interlocking elements and analyzing the geometry of motionwithin the context of a complete assembly, as shown in Figure 2.9.2323 Development of ShellsKinematic chains provide a good conceptual basis for the design of articulated skeletalstructures. However, a different method is needed to develop foldable shell assembliesthat can complement kinetic structures and form a finished, functional architecturalsolution. Size and shape change can be achieved by either sliding over or folding theselected facets of the exterior. Folding is the desirable method since it results in morerigid and easier to seal assemblies.Figure 2.9. Swept trajectories ofafolding structure.242.3.1 The Controlling GridIn order to be able to complement a folding frame with a folding shell, a geometricalinterface between these entities needs to be established. The points of mechanical andgeometrical interface form the controlling grid. Such a grid is the consequence ofselection and configuration of a particular folding frame geometry. It forms the definingand parameterizing geometry for the purpose of designing a matching folding shell.2.3.2 Rigid FoldingCommonly, transformations of folding are associated with flat sheets and play a key rolein sheet metal fabrication, packaging industry and art of origami. A more generalizedapproach is to consider folding as the manipulation of the degrees of freedom available inan under-constrained mesh. This mesh may be, in a special case, a tessellated flat sheet.Generally, however, any 3d mesh can be subjected to folding. A flat pattern and a flatfold define the extreme states of a foldable mesh. Only a flat sheet can form the flatpattern while the state of a flat fold can be applied as well to some non-flat meshes.Foldable structures do not reach the extremes of a flat pattern or a flat fold.Physical dimensions of components as well as assembly offsets limit the range oftransformation. The purpose of the folded state for a foldable structure is to achieve acertain practical level of compactness. The deployed state forms the functionalconfiguration that satisfies the design requirements. Geometrical constraints required tosatisfy the full range of folding from the flat pattern to the flat fold are most restrictive.Since they do not apply to practical folding structures, significant freedom of possibleconfigurations is available to the designer. The only requirement that a foldable mesh25must satisfy is the condition of rigid folding, which means that mesh facets cannot bebent or twisted. Figure 2.10 illustrates various types of folding and their correspondingstates.Figure 2.10. Folding offlat sheets andfoidable shells.233 Conceptualization of Rigid Foldable Shells3d meshes provide seemingly unlimited desigu possibilities which may increase thedifficulty of initial conceptualizing. This thesis proposes a simple method for developingthe primary concepts of folding geometries. A basic geometrical configuration of theeight crease sheet fold provides a good introduction to the kinematics of folding.RIGIDFOLDFREEFORMFOLD-rTRAVSFORMATJONDEPLOYEDSTATEFOLDEDSTATEADJUSTEDSTATE26Figure 2.11 illustrates the process of controlled folding of a flat sheet. Acontrolling grid comprised of two pairs of pivoting points is imposed over a pattern ofcreases. If the sheet is folded by bringing in the corners to coincide with the points of thecontrolling grid, the result is a three-dimensional, fully constrained and rigid shell. Theshape of the shell can be varied by adjusting the parameters of the controlling grid, asshown in Figure 2.12. In a practical applications, usually only the angle ‘a’ of thepivoting grid provides means of adjustment.---Figure 2.11. Controlledfolding ofaflat sheet.Figure 2.12. Adjustment offoldingparameters.a127Non-flat folding meshes can be easily developed by constructing individual facetsdirectly over the controlling geometry, as shown in Figure 2.13. The controlling grid istransformed into a network of 3d controlling edges by means of offsetting a neutral pointN off the plane of the grid to define a construction vertex. In this case, four sectors areformed. They can be independently populated with facets that follow local geometricalconfines. The stretched sector requires that the sum of the vertex angles of the facets islarger than the angle between the controlling edges, in order to avoid a singularity of afully stretched state.The requirement for all the facets to form a flat pattern is irrelevant since theassumed controlling geometry as well as the practical motion range were not intended toreach either fully stretched or fully folded state. In this example, the total of the vertexangles is greater than 360 degrees and the facets form a saddle type compound surface.The pivoting angle ‘a’ is the parameter that controls the folding of the finished shell.Figure 2.14 shows the range of transformation.Figure 2.13. Constructing a 3d mesh.28Figure 2.14. Range oftransformation.To gain more freedom in forming a foldable mesh, selected corner points of thecontrolling grid can be offset off the construction plane. Figure 2.15 shows the placementof offset points over a converging controlling grid. The asymmetrically lifted edges allowfor shell overlapping in arrayed configurations.Figure 2.15. Development ofafoldable module.The design decisions made while constructing the folding mesh define itsfunctional folding range. Figure 2.16 shows the deployed and folded states of the finishedmodule. The compactness of the folded form can be further optimized if needed byadjusting the controlling grid and refining the mesh facets. A more compact shape maybe beneficial for the ease of transportation if a mobile solution is required.29>0<___4Figure 2.16. Details ofafoldable module.2.3.4 Development of Freeform ShellsThis section explores the question whether more flexible design concepts that employnon-stretchable and rigid, non-fabric media can be developed for folding structures. Thecumulative effect of constraints and kinematic dependencies described in the previoussection restricts design flexibility. Final adjustments of the shell geometry can be tediousand usually involve many trial-and-error iterations. Most importantly, the topology of thefinal shape is predefined by the controlling grid, thus limiting the variety of expressiveforms that can be generated.This thesis suggests that the physics of crumpling can be considered as a logicalextension of research on rigid folding and that it may be beneficial in developingfreeform foldable structures. Crumpling is the logical direction for exploringdeformations of sheets and meshes once all the possibilities of rigid folding areexhausted. In fact, rigid folding is a large scale and orderly application of the kinematicsof crumpling. What sets crumpling apart is the build-up of stresses in a crumpled object.Freeform folding of a flat sheet along pre-defined curved paths does induce stresses aswell and can be considered as a transitional process between orderly, stress-free rigidfolding and stochastic, stress accumulating crumpling.30The pattern of ridges and crescents in a crumpled sheet is random andunpredictable. However, a crumpled sheet of paper (or a sheet of metal) can be stillstraightened out into the original rectangle. Therefore the effects of crumpling do notnecessarily involve non-reversible stretching or other non-elastic effects.Crumpling has gained a surge of attention recently in circles of physicists. Thequestion of interest is why a physically insubstantial leaf of tissue or sheer foil, ifcrumpled, gains a more enduring shape that can gradually build up a sizable resistanceagainst the deforming force. Crumpling is a result of elastic folding and buckling. Thebuild-up of elastic deformations in a sheet is analogous to cocking a spring. It results in apre-stressed, pre-loaded state that stores static (potential) energy. This energy resistsfurther deformation and lends to a much more robust form of a crumpled sheet.The ridges of a crumpled sheet act as springs whereas the ridges of rigidly foldedobjects perform the role of pivoting hinges. Crumpling may be considered as ageneralized case of mesh folding where the conditions for explicitly defined, sharp bendlines are relaxed to allow for gradual bend radii and the line intersection point nodes arereplaced with stretched crescents. In other words, the loosely abbreviated fold patterns ofcrumpled meshes can be expressed as geometries of higher entropy to reflect the aspectof perceivable unpredictability and disorder of patterns.This thesis highlights the following characteristics of crumpled bodies as having apotential significance for architectural structures. The underlying fractal character ofcrumple patterns is advantageous for developing freeform shaped shells and pursuingexpressive and dramatic architectural forms. Crumpling assures the highest rigidity for agiven thickness of the material. Therefore application of crumpled geometries may result31in more efficient and economic structures that also offer ecological benefits in terms ofreduced embedded energy and reduced material waste. Most importantly, crumpledgeometries exhibit properties that are crucial for safety. Crumpled bodies gain resistanceas the deforming forces increase, which is beneficial for developing structural systemsthat collapse gracefully under catastrophic conditions.This thesis lays out a practical design methodology for developing concepts basedon crumpled geometries. The features that contribute toward the resilience of crumpledsheets are also quite difficult to incorporate into standardized manufacturing processes. Itis virtually impossible to algorithmically model the networks of randomly distributedcrescents and ridges. However, if an elementary geometrical primitive of the crumpledtopology is abstracted, then such a construct can be replicated in controlled andpredictable patterns as shown in Figure 2.17.Figure 2.17. Ridge and crescentprimitive coded as a height map.Such a ridge-crescent can be tiled over larger areas and interleaved with other, largescale, folding patterns to model desired shapes. A concept application of this method isshown in Figure 2.18.322.4 Functional Structure DevelopmentThe following sections will focus explicitly on rigidly foldable shells. The purpose of thediscussion of crumpling in the previous section is to provide a better understanding ofconstraints that rigid folding imposes and explore venues for developing solutionsbeyond these constrains.2.4.1 Modular SegmentThe controlling grid and the derived folding frame, Figure 2.19 outline a modularsegment of the foldable structure, as shown in Figure 2.20.Figure 2.19. Foldableframe.-4.Zt .1Figure 2.18. Concept structure utilizing a crumpled shell.3324.2 Arrayed AssemblyArrayed assemblies of typical modules (Figure 2.21) can form a variety of on-demandadjustable configurations. The next section discusses possible applications of suchassemblies.2.5 Operation and Applications2.5.1 DeploymentAn adjustable and portable shelters, as shown in Figure 2.22, offer beneficial features foroutdoor exhibitions as the space can be easily adapted to accommodate differentFigure 2.20. Complete modular segment.Figure 2.21. Arrayed modules.34scenarios and weather conditions. It also allows for dramatic changes in the appearanceof the space.Figure 2.22. Adjustable shading system.Figure 2.23 left, illustrates mobile shelter systems deployed in a desert This particularsolution proposes integration of solar panels into the structure.Folded shells can be used for creating adjustable and visually expressive solutions forexhibitions, as depicted on figure 2.23 right. The development of quickly deployable,mobile shelters may be useful for emergency situations and harsh climatic conditions.Figure 2.24 illustrates a foldable system that can be deployed off a dedicated, motorizedplatform.Aj A35Figure 2.23. Applications: Shelters and exhibition.Figure 2.24. Mobile system.36Figure 2.25 shows an application of laminated wood frames for a folding structure.Figure 2.26 illustrates details of such a frame. All these are potential applications ofkinetic structures.Figure 2.26. Details ofglulamframe.2.52 Typical ScenariosFree standing kinetic structures can fulfill a variety of functions ranging from emergencyshelters and remote exploration stations to temporary exhibitions, seasonal installationsand adjustable protection systems. If integrated with existing buildings, they can increasethe flexibility of space sharing between different programs, for example between37Figure 2.25. Exhibition space, glulam structure.commercial and residential. Kinetic structures are well suited to create adjustable andreconfigurable buffer zones to shield against elements and extreme weather conditions.2.5.3 Typical Lifecycle and SustainabilityFoldable structures can be temporary or permanently installed according to the intendeduse and function. Unlike traditional buildings that are static and lasting, they are portable,adaptable and evolving. They are sustainable, and typical construction, renovation anddemolition work can be complemented with assembly, adjustment, reassembly, relocationand reuse. This inherent versatility facilitates reduced ecological footprint and economicburden.25.4 Overview of AdvantagesThis thesis postulates that further research of kinetic structures can benefit socialfunctioning within a confined urban space. For example, connecting spaces of an atriumcan be time shared between commercial and residential functions to provide a convenientway of managing complex and dynamic access patterns. Close integration of commercialand residential spaces in urban centers facilitates revival of street based retail andreduction of commute. Adjustable structures protect, on demand, Street sectors to providea regulated, comfortable climate for the inhabitants. Kinetic structures can be used in anurban context during sunny and hot weather conditions to shield people from excessivesolar radiation while allowing for air circulation. Most importantly, such structures canoffer better protection during emergencies. They facilitate faster evacuation and canprovide on demand protection from hazards and controlled fire containment.38The many unique features of foldable structures will change the traditionalbuilding maintenance and lifecycle models and offer reconfiguration and portability asoptions to demolition. In general, configurable structures will provide less environmentalimpact than traditional technologies as they are better suited for re-using, modificationsand re-location. Being inherently modular, they facilitate assembling of infinite variationsfrom a limited set of prefabncated components.39Chapter 3— The Design ProcessThis chapter discusses the overall design methodology for kinetic structures with specialattention paid to efficient and productive workflows. The interdisciplinary context isdetailed, which is the key element in kinetic structure projects that pursue novelsolutions. The available design tools, their suitability for integrated design workflows andthe areas requiring new design algorithms are reviewed. The kinematics of the developedfolding structure are explained and the performance validation process is outlined.3.1 Design ObjectivesDesign inputs for traditional building structures outline an initial set of functionalrequirements projected onto a conceptual, sketchy spatial layout. Subsequent detaileddesign develops construction specifications for the building to be erected. Kineticstructures add the need to consider temporal functional variations as well as resolve thekinematics of the moving elements. In particular, resolving of the motion for morecomplex, architecturally expressive shapes introduces considerable challenges to thedesign process.Design objectives for any building encompass the development of detailedspecifications for its structure. In addition, kinetic elements require specifications for aviable foldable geometry. These new design objectives focusing on the foldable geometryand how to address them are an important consideration of this thesis and will bediscussed in detail.403.2 Design Workflow3.2.1 Available Design ToolsMainstream CAD tools are, by now, mature and feature rich 3d design environments.Most of the packages targeted for mechanical design offer parametric control of thegeometry, assembly modeling and motion analysis. Typically, a 2d sketch is the startingpoint for modeling a 3d geometry. Individual facets of the foldable shell are initiallyoutlined as 2d sketches, for example as shown in Figure 3.1.If needed, the parametrically driven dimensions can be used to embed formulas thatexpress desired dimensional dependencies. In-progress adjustments can be easily appliedas all dimensions remain editable. For further assembly into a foldable shell, theindividual facets can be extruded or lofted into 3d shapes or retained as 2d outlines.An initial geometrical concept for the folding geometry can be, with reasonableease, modeled as an articulated assembly of facets and subjected to simulated motion.Starting with the controlling grid layout, individual facets of the shell are added to theassembly and bonded together using typical assembly constraining tools that allow the41Figure 3.1. Sketch ofafacet.modeling of desired joint behaviors. This is achieved by locking together the edges ofneighboring facets while retaining the rotational, hinge like degrees of freedom, as shownin Figure 3.2.Common within engineering CAD packages, motion analysis tools allow theanimation of selected driving parameters as well as collision detection thus allowing adetailed inspection of the kinematic performance of the constructed shell. However,achieving an error free, adequate range of folding becomes challenging as the complexityof the model increases. As explained in detail later, the mostly parallel character offolding shell topologies is difficult to express algebraically. Therefore, the parametriccapabilities of CAD cannot be readily utilized for the development of algorithmic toolsthat facilitate performance-targeted, intentional shell adjustments.Figure 3.2. Assembly constraining.423.2=2 Interdisciplinary ApproachVarious specialized disciplines of science, engineering, architecture and manufacturing,though they often share common roots in the underlying theoretical formalism, havedeveloped their own methodologies, problem solving methods and software tools that aretailored to their specific needs. Such specialized, disciplinary methodologies are efficientand reliable when applied to problems that are defined within the boundaries of a givendiscipline or domain. For example, architectural CAD tools emulate the operations ofconventional design and construction documentation development. They efficientlyhandle designing and detailing of static structures in compliance with the applicabledrafting and building standards.Introduction of new technologies and solutions, however, may often exceed thecapabilities of the established workflows and tools that are available within them. In caseof folding (kinetic) structures, though the final design deliverables are to be co-developedand integrated with conventional building structures, the kinematic requirements cannotbe readily resolved with traditional building design tools. Interdisciplinary exchange isinstrumental for developing novel concepts that exceed the boundaries of traditionaldisciplines. The incorporation of kinetic structures in buildings introduces into thearchitectural domain expertise from mechanics and mechanical engineering, therebysignificantly expanding the traditional involvement of science and engineering inarchitectural projects, as expressed in Figure 3.3.43Technological advances in the area of information exchange, processing andmanagement afford faster research and development cycles through efficient access tovast knowledge resources and ease of global communication. However, the very sametechnological tools do not necessarily assure simultaneous effective interdisciplinaryexchange because of the particular focusing and at the same time often isolating thecharacters that the well-established disciplinary processes tend to exhibit. Therefore it isprudent to augment novel and exploratory research scopes with a clear matrix ofanticipated interdisciplinary dependencies. Such a matrix will evolve together with theknowledge gained through the project development process as necessities emerge inregards to new design tools, computational methods and standards.Initial design development of a foldable shell has highlighted the quite apparentapplicability of mechanics and especially kinematics in the mechanical engineeringdomain for providing geometrical concepts and modeling methods. Detailed motionsimulations that followed have revealed a necessity for a tedious geometry adjustment44KINETICBUILDINGSSTRUCTURESFigure 3.3. interdisciplinary requirementsfor kinetic structures.process to achieve a desired, error free degree of motion. The search for an effectiveadjustment method has proven to be a challenging one as the topology of folding shellscould not be easily expressed in terms of forward kinematics equations as explained inSection 4.1. Involving yet another expertise, the methodology of fuzzy logic has allowedto build an algorithm based on intuitive, manually performed adjustments as described inSection 4.3. Interestingly, fuzzy logic as well as many other domains of science andengineering have started out as interdisciplinary initiatives, as indicated in Figure 3.4.Overall, the present study illustrates a number of benefits of interdisciplinaryexpertise sharing. Methods and concepts from mechanical engineering includingmechanics have been introduced into an architectural project for the purpose ofdeveloping novel structures. Furthermore, fuzzy logic has been incorporated to developFUZZY LOGIC BASEDDEGREE OF FOLDINGOPTIMIZATION ALGORIThMFigure 3.4. Fuzzy logic and the interdisciplinaiy context.45effective design utilities for such structures, through the use of human-originatedknowledge and knowledge-based decision making.3.2.3 Integrated Design EnvironmentThe scope of the traditional architectural workflow is already undergoing expansion asmotion and actuation elements migrate gradually into the building structure designs. Thedesign of kinetic architectural structures will expose architects to the unique demands ofmodeling of the translation geometry and simulation of the motion range. The designtools that perform similar tasks are widely available in mechanical engineering. Inparticular, parametric assembly environments offer the ease and flexibility of bothforward and inverse kinematics to build initial models of complex kinetic designs. Theincreasing importance of the detailing of material efficient assemblies that can reliablyhandle the structural and usage/operational loads will benefit from stress analysis toolsthat are often integrated with CAD packages. Furthermore, specific design challengeslike kinematic performance can be addressed with engineering computing tools. Figure3.5 illustrates a matrix of disciplines that have been involved in the process ofdevelopment of the concept of the kinetic structure presented in this thesis and typicalsoftware tools available within these disciplines.46MATHEMATICS ENGINEERING ARCHITECTURE PHYSICS—(COMPUTING/ MECHAMCAL\ (RCHITECTURALfFEAICFD\SOFWVARESTRUCTURALCADSOFTWARE-CAD - ‘________ -ENGINEERINGCOMPUT1NG..SOFTWARE,CATIA =ARCHICADTHINK3MAPLE MATLABARCHITECTURALANSYSMATHEMATICAINVENTORDESKTOPFLUENTREVITREVITSTRUCTUREARCHITECTUREBLUERWGEDESIGN TOOLS FORGEOMETRY MOTION FUNCTIONAL STRUCTURALKINETIC STRUCTURESCONCEPT OPTIMIZATION DESIGN LOADSFigure 3.5. Matrix ofdisciplines and tools.Figure 3.6 illustrates the logical phases of the kinetic structure design development andthe benefits of the integrated parametric CAD environments that are readily availabletoday. The key CAD feature that helps with handling the complexities of foldablestructures is the flexibility of switching between bottom-up and top-down methods whiledeveloping the design. The assumed initial concept of the controlling grid and the foldingframe can easily be put together while starting with components, progressing to theassembly level and employing then algorithmic capacity of forward kinematics modeling.This is a straightforward bottom-up design strategy. The development of a foldable meshrequires a different approach. The kinetic complexity of three-dimensional meshes makes47algorithmic descriptions tedious to define. However, a loosely improvised set of facetsthat follows locally applicable geometric restrictions can be easily appended into analready defined controlling grid and quickly verified by means of inverse kinematics.COMMERCIAL CADPARAMETRIC CADPARTASSEMBLYFINITE ELEMENTDESIGN DATA IDESIGN: CONTROLLiNG FRAMEDESIGN ASSUMPTIONSAND REQUIREMENTSDESIGN INPUTDESIGN: FOLDABLE SHELLANALYSIS: LOADS, STRESSES, VIBRATIONSITO OTHER DESIGN OUTPUT___J ‘— ___J ‘.—____DESIGN PROCESS CUSTOM TOOLSFigure 3.6. Design workflow.48The initial draft can be further refined through a sequence of design iterations.The efficiency of this process relies on the seamless integration of a solid parametricmodeler with a parametric assembly modeler. Once the components can be modifieddirectly within the environment of kinematic simulation, the development processfocuses on optimization of the form without the overhead of switching between differentdesign environments. Overall, the concept undergoes a series of design iterations as itprogresses through development stages. An effectively integrated design environmentstreamlines the process of adjustments by retaining the overall initial geometry andproviding the means to modify it as needed.As most of parametric modelers have the finite element analysis capacity fully integratedwith them, the verification of the tweaked in configuration in terms of safety and loadperformance can be performed within the same design environment. The design data canbe shared with various development workflows, architectural development for instance,in a variety of commonly supported 2-d and 3-d formats.3.3 Management of Kinematic and Functional Dependencies3.3.1 Operational ParametersThe most obvious characteristics of a folding structure are the difference between thefully unfolded and fully collapsed states. The range of folding as an operationalparameter reflects important functional requirements as it determines how much thestructure can be compacted for transportation or storage, how much it can be adjusted inresponse to ambient weather conditions and the level of usage or what maximumcoverage it can provide. In the next section, kinematic aspects which affect the folding49range are discussed. Challenges related to achieving the sufficient folding range as wellas proposed automated tools to automate this important design step are addressed inChapter 4.3.4 Conceptualization of Shells3.4.1 Kinematics of Rigid FoldingIn a foldable shell, the topology of an isolated node and the surrounding facets is that ofan array of closed spherical kinematic chains. At the same time, any node issimultaneously supported by three or more parent nodes acting through the connectingridges. This results in complex, compound kinematics that merges characteristics of aclosed spherical linkage chain with characteristics of an actuated parallel geometry whichis explained in more detail in the next section.If the parent nodes become the driving, controlling points of the shell, then themotion of the driven node is a complex output that represents the intersection of allpartial input geometries. The motion of the end node is the result of simultaneousactuation by multiple connecting ridges.3.4.2 Foldable ShellsComputational challenges encountered in designing industrial robots provide goodcontext for understanding the folding of shells. Two basic geometrical topologies ofrobots, serial and parallel, are illustrated in Figure 3.7. In the serial configuration,linkages form an open chain where only a single linkage attaches to the end node (N). Inthe parallel configuration, multiple linkages attach simultaneously to the end node (N).50NFigure 3.7. Kinematic representation ofa serial robot (left) and a parallel robot (right).The topology of a foldable shell is analogous to that of a parallel robot, as shownin Figure 3.8, since multiple supporting ridges attach simultaneously to the supportedvertex (N). Such parallel geometries are difficult to calculate in terms of forwardkinematics. If all the positions of the controlled ends of the ridges are given, expressingthe position of the supported vertex (N) as a set of formulas can be challenging even forrelatively simple geometries.Figure 3.8. Kinematic representation ofafoldable shell (left). Parallel topology oftheridges (right).51A number of characteristics of parallel topologies are advantageous for kineticstructural building elements. Since any end node is simultaneously supported by multipleconnecting ridges, the carried loads are effectively distributed across the structure, whichresults in high payload-to-weight ratio. When compared to serial linkage arrangements,parallel topologies exhibit much greater inherent rigidity. Also, motion accuracy is bettersince joint errors are shared rather than accumulated.3.5 Simulation and Testing of Shell FoldingWhat separates folding structures from traditional building elements is an added elementof motion. The conceived geometry of the folding frame and linked folding shell needs tobe verified in terms of kinematic performance. The goal is to achieve a range of foldingthat is free of interference and singularities and satisfies assumed functional requirementslike, for instance, the maximum size after folding. Since the folding frame is astraightforward pivoting mechanism, the importance of simulations relates to thekinematics of the foldable shell.Kinematics of the concept can be fairly easily simulated in any 3d modelingenvironment that provides tools of assembly constraining and motion parameterization.By using a collision detection function, an error free range of available motion can betested. Usually, the initially conceived geometry will have a rather limited range of errorfree folding. In order to increase the range of motion, adjustments to the facets of theshell are needed. The next chapter focuses on encountered challenges and the methodsconceived in this thesis for performing such adjustments.52Chapter 4— Knowledge-Based DesignOptimizationThis chapter investigates the design challenges stemming from the topological andkinematic characteristics of foldable shells. The history and the current status ofalgorithmic and computational methods developed for analogous geometries in roboticsare presented. The limitations of these methods for designing folding kinetic shells andachieving the desired kinematic performance are discussed, particularly in relation toerror-free folding. A novel approach toward optimizing the geometry in order to achievethe desired folding range is introduced. The optimization technique proposed here utilizesthe knowledge-based methods originating from human designers. Fuzzy logic is used todevelop algorithms that are capable of implementing a knowledge-based approach todecision making associated with design, deployment, and operation of a kinetic structure.The structure of the developed fuzzy logic system together with its knowledge base andthe decision making module (fuzzy inference system or FIS) are detailed, as well as theprogrammatic structure of the developed algorithm.4.1 Optimization ChallengesThe initial step of developing a folding shell is to outline the intended form with meshfacets constrained to the controlling frame. Typically, the intended form defines theunfolded state of the structure which represents the target functional, layout and aestheticrequirements to be fulfilled.The next step determines the adjustability range of the folding shell. Adjustabilityis one of the defining design criteria that set it apart from traditional building structures. It53is also a parameter that needs to be validated early in the development stages as it drivesa number of design detailing dependencies such as element sizing, folded state envelope,actuation and articulation. This validation focuses exclusively on the kinematiccharacteristics of the initial construct.The topology of shell ridges is analogous to that of parallel robots. Most of thetypical disadvantages of parallel arrangements for robotic applications like limitedmotion envelope, low dexterity and more frequent singularities are irrelevant forarchitectural structures. However, algorithmic difficulties related to calculating forwardkinematics solutions pose a considerable challenge. For example, an industriallysuccessful implementation of a parallel robot known as Gough platform, as shown inFigure 4.1, was first documented by V. E. Gough in 1956 (Gough, 1956). However, theresearch on forward kinematics of this six strut parallel device has progressed onlyrecently. The number of possible theoretical forward kinematics solutions was firstidentified in 1991 (Raghavan, 1991) while only in 1998 that all possible poses weredeterrmned (Dietmaier, 1998). Regardless of this progress, an algorithmic model has notbeen developed yet.54In contrast, the inverse kinematics is straightforward for parallel geometries sincethe end node positions explicitly define the sizing and position of the linking ridges. As aresult, 3d meshes are easy to use for approximating a desired spatial form by outlining itsshape with the end node points. 3d meshes, even in simple arrangements, tend to be muchmore complex from a kinematics point of view, than a six linkage topology of Goughplatform. Motion simulation is a practical and reasonably readily available method ofevaluating their kinematic performance in terms of the range of motion and the finaldegree of folding. In most cases, the initial shell will fall short of the desired motionperformance requirements due to interferences between facets or singularities whilefolding. Next two chapters will focus on the design process of folding shells.The initial shell needs to be adjusted in terms of physical dimensions of itselements to improve the folding range. This task can be expressed as an optimizationproblem (Siddall, 1982) where design variables are the ridge lengths of the shell mesh55Figure 4.1. Gough platform topology.expressed as vector x. The upper and lower bounds (xlb, xub) of ridge lengths are dictatedby the overall geometry size and shape, equality constraints are the nodes of thecontrolling frame expressed as vector h, inequality constraints are the limits of thedesired geometry envelope expressed as vector g, objective (J) is the desired degree offolding, and the model is a kinematic geometrical construct. The underlying optimizationproblem is expressed byfind x that minimizes J(x)subject to g(x) 0, h(x) = 0 andXlb x (4.1)In a general case, the objective would be formulated as the target of aMultidisciplinary Design Optimization (MDO) problem (Eschenauer, 1990) andexpressed as a weighted result of optimum folding, optimum structural strength andoptimum actuation. In such case, the goal of the optimization would be finding the bestfeasible solution within the collection of available feasible solutions. Optimum foldingwhich calls for a perfect flat fold conflicts with both optimum structural strength whichcalls for material thicknesses and the resulting assembly offsets as well as with optimumactuation which calls for a zone separating from singularities and the resultingindeterminate directions and infinite forces. However, for the purpose of clarity andfocusing on the issues pertinent to the kinematics within the working range of a parallelgeometry, the objective is expressed only as the degree of folding while the structuralstrength and actuation requirements are culled into a reasonable, discrete and non nullvalue that becomes the target for the degree of folding. Once the best feasible kinematicsolution is determined, this target forms the limits for the development of the dynamicand structural aspects of the design. At that stage, components would be sized towithstand static and dynamic loading and actuation elements would be added and56calculated. Another phase of the design would need to deal with safety. This wouldencompass operational safety parameters like motion envelope that interferes withoccupants, potential pinch points and maximum velocities within occupied zone. Mostimportantly, failure modes like failure of actuation and collapse under excessive loadswould need to be investigated. Such investigation would, for instance, define the desiredweakest structural points to control the mode of potential collapse. Again, the focus ofthis thesis is the development of the initial kinematic model which, as explained earlier inthis chapter, poses considerable challenges because of lack of formulaic methodology.Though the desired degree of folding can be expressed as an optimization target,practical impossibility of conceiving an applicable algorithmic model for the parallelgeometry prevents from utilizing conventional optimization tools. The only immediatelyavailable recourse is the manual approach based on trial and error. Iterations ofadjustments to the lengths of ridges and folding simulations can be performed to seek animprovement of the degree of folding. This manual process is tedious and timeconsuming even for relatively simple geometries.The issue of developing manageable tools for optimization of the kinematicperformance may be the deciding factor in successful commercialization of kineticstructures based on rigidly foldable shells. Mainstream design workflows traditionallydepend on methods that can assure a certain degree of predictability, productivity, andease of application. For solving rigidly foldable shells and, for that matter, any complexparallel geometry, the forward kinematics formalism does not offer, at present, anyusable methods.574.2 Decision Making Using Fuzzy LogicManual adjustment of shell elements is based on readily observable local dependenciesbetween ridge length adjustment and their kinematic behavior changes. In general terms,the manual methods rely on accumulated experience and learned knowledge aboutrelationships between element sizing, proportions and exception occurrences.Intuitive and experience-based adjustments are applied in gradual steps to theinitial geometry until the desired degree of folding is achieved. Obvious disadvantage ofthis method is unpredictability which is the result of underlying trial and error approach,in addition to the design duration which can be prohibitively long and tedious. Alsoapparent is the difficulty to automate this process since missing is a clearly definedalgorithm that links the performance (the degree of folding) with the sizing of the shellgeometry.This scenario is well suited for implementing Fuzzy Logic as an automation andprocess efficiency tool.Fuzzy Logic is useful in representing human knowledge in a specy’Ic domain ofapplication and in reasoning with that knowledge to make useful inferences oractions. (Karray and de Silva, 2004)Fuzzy Logic offers the possibility of using intuitive, often imprecise and conflictinginstructions based on human knowledge and reasoning to build robust and reliablealgorithms. As explained in chapter 4.1, traditional optimization approaches can not beapplied because of impossibility of parametrizing of complex parallel geometries.In the present thesis a set of typical steps one would perform while adjusting areal life prototype of a folding structure is examined as a prelude to the use of fuzzylogic. Such an exercise yields numerous clues and hints about the kinematic behavior of58the geometry and possible ways of improving the degree of folding. Based on readilyobservable parameters like collisions or slopes and intuitive remedial actions likeshortening or lengthening of linkages, they capture ‘cause and effect’ dependencies in theshell geometry and can be further formulated as ‘If-Then’ statements or “rules.” Such acompilation of statements readily interfaces with Fuzzy Logic and forms the KnowledgeBase of the Fuzzy Inference System (FIS). The Knowledge Base is then used to identifrproblem conditions and infer appropriate corrective actions, through a suitable method ofdecision making; particularly the compositional rule of inference (Karray and de Silva,2004).The advantage of the Fuzzy Logic formalism lies in its effectiveness when dealingwith human-originated approach which, while intuitive and easy to understand, usuallybrings along ambiguities, contradictions, uncertainties, redundancies, qualitativeattributes, and in essence a degree of “fuzziness.” Experiential clues are local in nature asthey relate to the immediate circumstances of an observed singularity or interference.Fuzzy Logic allows the inference of geometry adjustments based on these local andloosely defined indications. More importantly, it allows forming algorithms that attemptto reconcile iterations of such adjustments within the context of performance of thecomplete shell thus negotiating contradictions and overlaps between locally madedecisions.594.3 Optimization through Fuzzy Logic4.3.1 Fuzzy Logic-based Process OverviewDesign process delivers a solution to a set of initial requirements or perfonnancespecifications. The solution, typically, is a result of numerous iterations through stages ofdesign modification and testing (Cross, 1994), as indicated in Figure 4.2. The FuzzyInference System is intended to govern the modification ioop in the design workflow thatis aimed at foldable shells.TYPICAL DESIGN PROCESS ITERATIONFUZZY LOGIC BASEDDESIGN OPTIMIZATION I______gji.Figure 4.2. Block diagram ofthe design process.The purpose of implementing Fuzzy Logic for the design of a kinetic structure isto avoid the prohibitively difficult forward kinematics modeling of complex parallelassemblies. Instead, the designer would devise a sketchy geometrical topology and relyon the optimization process which implements a FIS to fine-tune the linkage sizing. Thecornerstone of such FIS is a set of simple, intuitive, empirically-derived adjustmentdependencies compiled into the Knowledge Base, as indicated in Figure 4.3.60Inputs- initial Geometry- Motion RequiremenisFuzzy Inference SystemFuzzification of Inputs- Membership FunctionsKnowledge BaseInference Engine- EmpiricalGeomefry-MotionDependenciesDefuzzificationof Outputs- Membership FinictionsGeometry AdjustmentsFigure 4.3. Block diagram ofthe FIS.FIS block interfaces with the crisp domain of a geometrical model through thesteps of fuzzification (of crisp inputs) and defuzzification (of fuzzy outputs). TheInference Engine interprets the fuzzified input data and infers appropriate adjustmentsbased on the Knowledge Base. A detailed flow of the optimization algorithm is illustratedin Figure 4.4.61The algorithm is inserted into a typical design iteration ioop where an action ofdesign change is performed and then followed by a qualifying test step. Depending uponthe results of the test, two possible outcomes are available. Either further modificationsteps are continued or the ioop terminates with an optimized solution. Hence, clearlydefined are two distinct process flow loops: verification (on the right side) and62Figure 4.4. Flow diagram ofthe optimization algorithm.optimization (on the left side). Fuzzy Inference System plays a key role in theoptimization loop where it generates the necessary adjustment data. For practicalprogrammatic reasons, a timeout test is inserted. It prevents run-away code execution ifthe optimization cannot be reached in a specified number of design iterations.The algorithm allows, through its FIS module, the utilization of the empiricallyobserved, knowledge-based dependencies to infer appropriate geometry adjustments. Itperforms all the necessary steps automatically in a progressive succession where theworst, from the folding viewpoint, areas of the shell are adjusted first. The strategy is tobe able to achieve the optimization of relatively large geometries by iterating throughlocalized corrective actions on geometry fragments. The scalable nature of this approachfacilitates application for optimization ofvery complex geometries.4.3.2 Test Conditions and Membership FunctionsObserved simulated folding of articulated shells provides designers with apparentinformation about typical behaviors and error conditions. One of geometrical attributes offacets in a 3d mesh-like shell is the angle between each facet and the reference horizontalplane or, in other words, the slope. In an unfolded state, this angle assumes values that arefairly far from the vertical condition of 90 degrees. As the shell is being folded and itsshape becomes more compact, and the slope becomes steeper. In a perfectly folded shell,most of the facets have a slope that is close to vertical. If the slope happens to exceed 90degrees, it means that the particular facet has flipped over and, together with itscompanion facet, is nearing a singular state where both facets coincide. Therefore, slopesof facets have been observed as an effective source of information about the kinematicbehavior of the shell and utilized, in the algorithm, as the primary test condition. During63folding, if any slope becomes too steep, further folding is aborted and corrections to thegeometry are initiated. Effectively, the slope condition is used to intercept pre-singularstages. The algorithm detects conditions that precede a singular event rather than detectthe singular event itself. The corrective action involves adjusting the lengths of linkagesthat formed the undesirable angle. The values of the adjustments are determined based onthe following contextual conditions: the degree of folding and the relative node height.The degree of folding expresses quantitatively the actual kinematic state of theshell as a complete system. In absolute terms, any of the angular geometricaldependencies in the underlying controlling grid can be used to express the degree offolding. In relative terms, it is the ratio between the actual, folded angle and the angle inthe fully unfolded state. The larger the degree of folding, the smaller should be theadjustments, as minimal linkage tweaks cause large slope changes for steep conditions.The relative height of the subject node in relation to neighboring nodes affects theratio of shortening and lengthening of sibling linkages. The reason is to avoid asystematic, excessive vertical drift of the subject node while performing multipleadjustments.In the developed algorithm, angles of slopes have been utilized as test conditionsto detect folding errors. The degree of folding and the relative height of the subject nodeare the inputs of the algorithm while the adjustment values are the outputs.The fuzzy logic formalism is used to infer design decisions from pre-compiled,knowledge-based data. However, the model of the geometry, the driving parameters, thetest conditions as well as adjustments to the geometry are discrete numerical sets.Interfacing between the fuzzy logic system and the discrete inputs and outputs is64accomplished by means of fuzzification and defuzzification where fuzzy parameters areassigned to numerical variables, as indicated in Table 4.1.Table 4.1. Input/output parameters and theirfuzzy representations.variables fuzzy valuesUnfoldedDegree-of-Folding Half-Folded__________________________Fully-FoldedINPUTSLowerRelative-Crown-Node-HeightEqual__________ ___________________________HigherMinimallyLengthen-Subject-Linkage ModeratelySignificantlyOUTPUTSMinimallyShorten-Sibling-Linkage Moderately____________________________SignificantlyMembership functions are used to correlate the numerical input (Figure 4.5) and output(Figure 4.6) subsets with fuzzy parameters (fuzzy states).65Fully-FoldedFor the outputs, the relationship between the actual degree of folding F and themagnitude of necessary length adjustments dA is nonlinear if the resultant relativemovement dN of the node being adjusted is to be maintained within a consistent range, asshown in Figure 4.7.Figure 4.5. Input membershipfunctions.output variable ‘Shorten-Sibling-Linkage”Figure 4.6. Output membershipfunctions.66Fgure 4.7. Node movement versus the degree offolding and magnitude ofadjustments.For example, at a folding rate of 80%, a 5% relative adjustment to the linkage lengthresults in similar lateral adjustment of the subject node (N2) as a 15% adjustment at afolding rate of 40% (N1).4.3.3 Inference ClausesTo develop the algorithm, a set of typical steps one would perform while adjusting a reallife prototype of a folding (kinetic) structure has been considered. Based on readilyobservable effects like collisions or slopes and intuitive remedial actions like shorteningor lengthening of linkages, the knowledge acquisition process can capture ‘cause andeffect’ dependencies in the shell geometry which can be formulated as ‘If-Then’6720%0%statements. For example, a rule may take the form: if a set of neighboring facets wouldfold onto each other while the shell folded very little then increase significantly theappropriate dimensions of the bottom facet and reduce significantly the appropriatedimensions of the top facet. The ‘if’ part expresses a set of input conditions (antecedent)while the ‘then’ part describes the desired actions (consequent). Though simple andlocalized in their scope, such statements are sufficient to build the so-called KnowledgeBase which can interface with fuzzy decision making (or, the inference engine) toidentify problem conditions and infer appropriate corrective actions.4.34 Knowledge BaseThe knowledge base comprises a compilation of if-then statements or rules which expressthe expert knowledge of human designers. The scope of these statements needs to becorrelated with the spectrum of possible scenarios as coded through input membershipfunctions. Otherwise, an incomplete knowledge base would not be able to identify someof the scenarios or infer solutions for some of the problems. Figure 4.8 presents the set ofif-then statements as compiled for the knowledge base in the present thesis. Theutilization of such a knowledge base in the present problem is illustrated in the nextchapter.68I IF (Degree-of-Folding IS Unfolded) AND (Relative-Crown-Node-Height IS Lower)THEN(Lengthen-Subject-Linkage IS Significantly)21 IF (Degree-of-Folding IS Unfolded) AND (Relative-Crown-Node-Height IS Equal)THEN(Lengthen-Subject-Linkage IS Significantly) AND (Shorten-Sibling-Linkage IS Signficantly)3: IF (Degree-of-Folding IS Unfolded) AND (Relative-Crown-Node-Height IS Higher)THEN(Lengthen-Subject-Linkage IS Moderately) AND (Shorten-Sibling-Linkage IS Significantly)4: IF (Degree-of-Folding IS Half-Way) AND (Relative-Crown-Node-Height IS Lower)THEN(Lengthen-Subject-Linkage IS Moderately)5: IF (Degree-of-Folding IS Half-Way) AND (Relath’e-Crown-Node-Height IS Equal)THEN(Lengthen-Subject-Linkage IS Moderately) AND (Shorten-Sibling-Linkage IS Moderately)6: IF (Degree-of-Folding IS Half-Way) AND (Relative-Crown-Node-Height IS Higher)THEN(Lengthen-Subject-Linkage IS Minimally) AND (Shorten-Sibling-Linkage IS Moderately)7: IF (Degree-of-Folding IS Fully-Folded) AND (Relative-Crown-Node-Height IS Lower)THEN(Lengthen-Subject-Linkage IS Minimally)8: IF (Degree-of-Folding IS Fully-Folded) AND (Relative-Crown-Node-Height IS Equal)THEN(Lengthen-Subject-Linkage IS Minimally) AND (Shorten-Sibling-Linkage IS Minimally)9: IF (Degree-of-Folding IS Fully-Folded) AND (Relative-Crown-Node-Height IS Higher)THEN(Shorten-Sibling-Linkage IS Minimally)Figure 4.8. The knowledge base ofstatements.69Chapter 5— Design Study and ResultsThis chapter details a case study to illustrate the implementation, testing and evaluationprocess ofthe developed optimization algorithm. The strategies involved in modeling thebehavior of a foldable shell and in developing the testing simulation enviromrient areexplained. The structure and the interface of the testing program are described. Testresults are presented and discussed and the behavior and performance of the algorithmare evaluated.5.1 Design Case StudyThe subject of the experimental phase of the thesis is the elementary module of thecircular, arrayed folding structure as introduced earlier in the thesis. In order to achievethe desired folding range, manual adjustments were applied to the initial geometry withinthe parametric modeling CAD environment. The process was tedious, unpredictable andtime consuming. The proposition of the thesis is that an effective optimization algorithmthat implements a Fuzzy Inference System and an experiential knowledge base can beused for adjusting such parallel geometries instead of using prohibitively complexforward kinematic computations.5.2 Testing of the Optimization AlgorithmThe important part of the present thesis is the evaluation of the effectiveness of a FuzzyLogic based optimization algorithm. If proven to be feasible, efficient and effective, suchoptimization tools hold a significant potential for the development of design workflows70aimed at foldable structures. Consequently, they can greatly contribute toward theintegration of kinetic structures with mainstream design.The purpose of the optimization algorithm is to use a sketchy, initial geometry,simulate its kinematic behavior and, if necessary, apply adjustments to achieve thedesired kinematic performance. For most practical applications, the kinematicperformance reflects the desired, error free degree of folding.5.21 Modeling of 3d Mesh BehaviorIt is important for the test simulation to be able to accurately model the key kinematiceffects that occur in a 3d shell that is being folded. On the other hand, it is also beneficialfor the efficiency of the simulation to avoid modeling of features and phenomena that arenot relevant for the kinematic aspects of folding. Kinematics deals with non-real-timeaspects of the subject geometry. In this case, the focus is achieving the desired motionrange by adjusting the sizing of the geometry while retaining its original topology. Issuesof load bearing, vibration and actuation are dynamic issues that do not affect the degreeof the folding; therefore, they are not considered during this stage of the design process,and in the present thesis. Also, the general shape of the envelope as set by the initialtopology is not the subject of this optimization.While developing the simulation model, an advantage has been taken of the fact that a 2dprojection of a 3d mesh is, topologically, a continuous function (Artin, 1991). Thisrepresents the morphism between 3d and 2d topological spaces, as indicated in Figure5.1. As such, it maps the parallel character of the geometry, the motion range as well asall the kinematic exceptions like interferences and singularities from one space into theother. For instance, if the distance between P1 and P2 diminishes in the 3d space, it will71also diinimsh in its 2d projection. The detection of interferences and singularities (fullystretched or flat folded states) and performing adjustments that eliminate them is theobjective of the optimization algorithm. Therefore, a simulation model that employs a 2dlattice instead of a 3d mesh is equally effective in validating the performance of such analgorithm. Figure 5.2 illustrates a singularity instanceQoccurring in a 2d lattice.Figure 5.]. Mapping ofthe geometry between topological spaces.The main advantages of using a 2d construct for simulation are simplerprogramming, effective use of computer resources and fast execution of simulation code.Such streamlined approach facilitates thorough testing of the algorithm andimplementation of the necessary parameter adjustments in a resource efficient manner.3d SPACEilLxMORPHISM 2d SPACEIi72Figure 5.2. Folding ofa 2d lattice: initial (left), optimized (right).5.2.2 Development of the Test Set-upA virtual testing experiment has been developed entirely using MATLAB while utilizingits Fuzzy Logic Toolbox for programming the Fuzzy Inference System. The program isdivided into logical modules that are easy to modify or replace (see Figure 5.3). Eachmodule is accessible as an individual MATLAB script file.Expanded StateFolded SlateExpanded Slate-HF&dedFoldableLatticeControllingF,ameControllingFrame73The application models a pre-defined 2d lattice, subjects it to a simulated foldingoperation, and performs adjustments to linkage lengths in order to meet the target degreeof folding.The main components of the interface (see Figure 5.4) are:• The lattice plot window where the progress of folding as well as all consecutiveadjustments are shown in real time (1).• Trigger condition plot window which displays, in real time, all linkage slopevalues imposed over the slope membership function (2).• FIS edit and review pane (3).• Optimization progress plot (4).• Optimization progress statistics (5).Figure 5.3. Modules ofthe optimization program.74Program flow parameters and controls (6).5.3 Test Results and EvaluationVarious linkage arrays extrapolated from the geometry of the folding module have beencoded into the optimization program. Initially, a basic construct has been tested toanalyze the behavior of the algorithm. Figure 5.5 presents a set of sample optimizationresults, using Mamdani inference an Sugeno inference (Karray and de Silva, 2004). Boththese optimizations iterated 40 times and reached a folding rate in excess of 80%, whichis a notable improvement when compared with the initial folding rate of 12%. Figure 5.6gives the surface plots for the input/output correlation for these two optirnizations.IFigure 5.4. The interface ofthe testing application.75-These results provide resources to discuss practical aspects of the programmaticimplementation of various FIS options. The Knowledge Base reflects empiricalobservations and contains directives based on partial statements--statements that ignoresome of the input/output parameters. In this case, the knowledge base contains a fewstatements that ignore one of the outputs. The implementation of Mamdani’s methodexpects all of inputs and outputs to be in the fuzzy domain. An ignored I/O becomes adiscrete assignment, a singleton which causes problems with most defuzzificationmethods as they interpret such null assignment as a constant value. One possibleworkaround uses SOM (Smallest Of Maximum) as the defuzzification method. It76;:zzzzzzzzI-Figure 5.5.-I30 - 40 81%—Sample optimizations using: Mamdani method (left); Sugeno method (right).-Figure 5.6. Input/output surface plotsfor: Mamdani method (left); Sugeno methodfright).The observations gathered during the testing of simple 2d lattices help withcharacterizing the dynamic behavior of the algorithm, sensitivity to parameters andmembership functions adjustments as well as the overall effectiveness of increasing thedegree of folding. This analysis is helpful in applying optimization to more complexgeometries (see Figure 5.8).Figure 5.7. Typical behaviors: ceiling (left), oscillating (center), diminishing progression(right).xl6.3%Figure 5.8. Progress ofoptimization ofa complex 2d lattice.78interprets a zero assignment as a zero value thus preserving the programmatic intent. Thedrawback of this approach is a significantly stepped, non-smooth surface of input/outputfunction.The Sugeno implementation is well suited for managing a mix of fuzzy domainsand discrete singletons. More importantly, it is designed to assure smooth input/outputfunctions under these conditions. The difference is noticeable in Figure 5.5 where theoptimization progression plot for the Sugeno method is smoother and exhibits less ripplethan the corresponding plot for the Mamdani method. Interestingly though, despiteobvious differences in the I/O surface plots, both methods have been capable of achievinga similar degree of optimization.Figure 5.7 illustrates typical behaviors of the algorithm when reachingoptimization limits that are attainable within the preset programmatic constraints. Thesecan be described as: ceiling, where the degree of folding fixates at a certain value;oscillating, where the degree of folding toggles within a certain reasonably broad range ofvalues; and diminishing progression where the degree of folding consistently improves asthe optimization continues. Diminishing progression is the desirable behavior as itassures that the last performed iteration results in achieving the highest degree of foldingthus simplifying the programmatic automation. Also, it delivers improved folding withprolonged optimization. The behavior of the algorithm is influenced by many factors. Ingeneral, the Sugeno method helps reduce the tendency toward excessive outputoscillations. However, tweaks to mapping of input functions also play a significant roleas all plots shown in Figure 5.7 are outputs of the Mamdani method.77As the kinematic behavior of a lattice is highly susceptible even to minoradjustments to linkage lengths, careful management of magnitudes of these adjustmentsis important for achieving a feasible and efficient optimization. The adjustments aregoverned through three components of the algorithm. Two of them are part of the coreFIS: Membership Functions provide precise means of coding and decoding of physicaladjustment ranges as fuzzy logic values like ‘Significant’ or ‘Moderate’ while If-Thenstatements contained within the Knowledge Base determine which of the fuzzy valueswill be used within a given set of circumstances. The computational outcome of FuzzyInference as governed by the Membership Functions and the Knowledge Base, may beexpressed as Input/Output plots, as depicted in Figure 5.6.The third method applies, if desired, uniform scaling to the Input’Output plots. Itprovides additional control of the magnitude of the adjustments depending upon thedynamics of the optimization. If frequent over-adjustments of geometry affect theprogress of optimization (see Figure 5.9), flattening of the Input/Output function byapplying a reducing coefficient will bring the adjustment values down and out of theerratic range.7990%.76%-40 Iterns28 MIX: 58.8%___________Pretou: 0.9% rLdst: 48.8%___________Figure 5.9. A case ofover-adjustment ofgeometry.Adjustments that are consistently too small will significantly prolong theoptimization duration, as indicated in Figure 5.10. In such cases, increasing the dynamicsof the Input/Output function will improve the efficiency of the algorithm.80Current FIS type: Mamdanl‘-IThe scaling coefficient can be governed by an additional ‘supervisory’ FuzzyLogic thread that is dedicated to monitoring of the optimization outcome. Such asupervisory function would be able to detect erratic output due to over-adjustments ofgeometry or consistently low rate of optimization progress and, consequently, wouldapply appropriate adjustments to the global magnitude of the geometry corrections. Suchan approach provides programmatic means of performing optimizations that are efficientand can reach the feasible degree of folding within a reasonably short timeframe whileavoiding over-adjustments. Figure 5.11 presents an example of desired dynamics of thealgorithm.Figure 5.10. A case ofunder-adjustment ofgeometry.81r.68 IteraboMr68 MAX: 6.7%;.,ur-_---....Prcvous 64.8%L.ast65.7%Figure 5.11. Sample optimization ofa complex 2d lattice.82_,Tc_—1Current RB type: Mmdani71/I)(fl/\\1/T\J1VVV\4Chapter 6— ConclusionsThis concluding chapter summarizes the main contributions and significance of the workpresented in the thesis. Also it provides some possible directions for further work in thearea.6.1 ConclusionsThe complexities of the forward kinematics parameterization of parallel geometries posesignificant challenges when fine-tuning their motion range. The only recourse availablewithin mainstream parametric CAD packages is a manual process based on trial anderror. Such an approach, although occasionally successful, has proven to be tedious, time-consuming and unpredictable, as discussed in the thesis.This thesis has outlined the potential benefits of folding or “kinetic” architecturalstructures based on parallel geometries. It proposed novel topologies for such structuresand detailed their structural and functional integration. The thesis identified thedifficulties of the forward kinematic modeling of parallel constructs as a serious obstaclethat needs to be addressed before broader commercialization of the various free-formfolding structures can take place.A significant contribution of the thesis is the development and testing of anapplied Fuzzy Logic Inference System for motion range optimization of parallelgeometries. The optimization algorithm implementing fuzzy logic offers the possibility ofusing a human-oriented knowledge-based approach to build on easily observabledependencies, as well as intuitive inferences to reliably and predictably emulate the83kinematic effects of adjustments to parallel geometry elements. Subsequently, analternative to fonnulaic forward kinematics algorithms was provided.The algorithm developed as part of this thesis has been tested on structuralgeometries of various complexity. Despite its conceptual simplicity, based solely onlocalized adjustments, it performed reliably and always improved the folding range by asubstantial margin within a practical number of iterations. These promising resultsencourage continuing the work on this type of algorithm, with significant practicaladvantages in the domain of kinetic structures.6.2 Future Research DirectionsThe overall goal of the work presented in the thesis is to develop a foundation for reliabledesign tools that can be utilized within existing workflows. The areas that need furtherresearch fall into three categories: performance improvement of the Fuzzy LogicInference System, and systematic design of program flow control and programmaticinterface shell. It is important to gage the theoretical limits of optimization basedexclusively on localized adjustments when applied to very complex geometries. Potentialimprovements may involve expanding the Knowledge Base with statements reflecting abroader awareness of the geometrical context.As mentioned in Chapter 5, an additional, program flow supervisory function ofthe Fuzzy Inference System may significantly improve the performance of the algorithm.Further improvements may include the training and learning capabilities of the algorithm.For example, an approach based on neural networks (Karray and de Silva, 2004) may beused to progressively improve an initial, human-oriented knowledge base while it is84applied to various problems of kinetic structure design. Furthennore, genetic algorithms(Karray and de Silva, 2004) may be incorporated to optimize the overall fuzzy inferencesystem. Production tools based on this algorithm will need to interface directly withCAD models and their 3d geometry, which will require research and development oftoolkits for various CAD environments.Further development of folding structures needs to include real-time motion anddynamics issues such as dynamic loading, actuation, sensors, and automatic control, priorto product commercialization. This enhancement may be pursued as an integration ofFuzzy Logic based motion optimization with the FEA and dynamic-system capabilities ofa selected (or developed) CAD package.85Bibliography1. Arkin, E., Fekete, S., and Mitchell, J., “An algorithmic study of manufacturingpaperclips and other folded structures,” Computational Geometry, Vol. 25(1-2),pp. 117-138,2003.2. Artin, M., Algebra, Prentice Hall, Englewood Cliffs, NJ, 1991.3. Ataman, 0., Proceedings ofAssociationfor Computer-A ided Design inArchitecture Conference, ACADIA 2005 Smart Architecture, Savannah, Georgia,pp.4, October, 20054. Craig, J.J., Introduction to Robotics, Addison-Wesley, Reading, MA, 1989.5. Chen, Y., Design ofStructural Mechanisms, PhD Thesis, Department ofEngineering Science, University of Oxford, England,pp. 58-59, 2003.6. Cross, N., “Forty years of design research,” Design Studies, Vol 28,pp.1-4, 2007.7. Cross, N., Developments in Design Methodology, John Wiley & Sons, New York,NY, 1984.8. Cross, N., Engineering Design Methods: Strategiesfor Product Design, JohnWiley & Sons, New York, NY, 1994.869. Dietmaier, P., “The Stewart—Gough platform of general geometry can have 40real postures,” Advances in Robot Kinematics: Analysis and Control, J. Lenarcicand M. L. Hust, eds., Kiuwer, Norwell, MA,pp.7—16, 1998.10. Eschenauer, H., Koski, J., and Osyczka, A. ed, Multicriteria Design Optimization,Springer Verlag, New York, NY, 1990.11. Escrig F, Arquitectura Transformable, Escuela Tëcmca Superior de Arquitecturade Sevilla, 199312. Escrig F and Valcarcel J P, Geometry of Expandable Space Structures,International Journal of Space Structures, Vol. 8, No. 1 & 2,pp7 1-84, 1993.13. Gough, V. E., Automobile stability, control, and tyre performance, AutomobileDiv., Inst. Mech. Eng., UK, 1956.14. Hoberman C, Reversibly expandable doubly-curved truss structure, USA Patentno.4,942,700, 1990.15. 8. Hoberman C, Radial expansion/retraction truss structures, USA Patent no.5,024,031,1991.16. Karray, 0. F. and de Silva, C. W., Soft Computing and Intelligent System Design,Addison Wesley, New York, NY, 2004.17. Kassabian P, You Z, and Pellegrino S, “Retractable roof structures,” ProceedingsInstitution ofCivil Engineers Structures and Buildings, Vol. 134, Feb 1999,pp.45-56.8718. Medina, J., Ojeda-Aciego, M., and Ruiz-Calvini, J. “Multi-lattices as Basis forGeneralized Fuzzy Logic Programming,” Proceedings ofthe 6th InternationalWorkshop, Fuzzy Logic and Applications, Crema, Italy,pp.6 1-70, September2005.19. Pellegrino S. and You Z, “Foldable ring structures,” Space Structures, Vol. 4(edited by G A R Parke and C M Howard), Thomas Telford Publishing, London,England, pp. 783—792, 1993.20. Raghavan, M., “The Stewart platform of general geometry has 40 configurations,”ASME Design andAutomation Conf, Miami, FL, Vol. 32(2),pp.397-402, 1991.21. Rittel, H. and Webber, M., “Dilemmas in a General TMerlet, J.,” Parallel Robots,Kluwer, Norwell, MA, 2000.22. Siddal, J. N., Optimal Engineering Design, CRC Press, Boca Raton, FL, 1982.23. Rittel, H. and Webber, M., “Dilemmas in a General Theory of Planning,” PolicySciences, Vol. 4,pp.155-169, 1973.24. Wohlhart K, “Double-Chain Mechanisms,” Proceedings ofJUTAM-IASSSymposium on Deployable Structures: Theory andApplications, (edited by SPellegrino and S D Guest), Kluwer Academic Publishers, The Netherlands, pp.457-466, 2000.25. You Z, “A new approach to design of retractable roofs,” Proceedings ofJUTAMlASS Symposium on Deployable Structures. Theory andApplications (edited by S88Pellegrino and S D Guest), Kiuwer Academic Publishers, The Netherlands,pp.477483, 2000.26. You Z and Pellegrino S, “Foldable bar structures,” International Journal ofSolidsand Structures, Vol. 34, No. 15,PP.1825—1847, 1997.27. Zeigler T R, Collapsible self-supporting structures and panels and hub therefore,USA, Patent no. 4,290,244, 1981.89


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