Free-form Transformation Of Spatial Bar Structures

Developing a design framework for kinetic surfaces geometries by utilisingparametric tools

Hussein Hussein1, Asterios Agkathidis2, Robert Kronenburg31,2,3Liverpool School of Architecture, University of Liverpool, UK1,2,3{H.E.mohammed|asterios.agkathidis|r.h.kronenburg}@liverpool.ac.uk

This paper presents a design framework for free-form transformation of kinetic,spatial bar structures using computational design techniques. Spatial barstructures considered as deployable, transformable kinetic structures composedof straight, linear members, assembled in a three-dimensional configuration.They are often utilised in portable, mobile or transformable buildings.Transformable systems of spatial bar structures are mostly based on modificationof primitive shapes (e.g. box, sphere, and cylinder). Each system is subdividedinto multiple members having the same shape, the so-called kinetic blocks. Somediverse precedents made to develop other forms of transformation of thesestructures with some issues. This research project will investigate how afree-form transformation of spatial bar systems can be achieved, by redesigningthe kinetic block in relation to architectural, technical parameters. In order todevelop a physical prototype of the kinetic block, and assess its potential inenabling free-form transformation of a spatial bar system, a design frameworkincorporating parametric, algorithmic and kinetic design strategies is required.The proposed design workflow consists of three main phases: form-finding,stability validation and actuation.

Keywords: Parametric design, Kinetic, transformable, deployable, Free-form,design strategy

KINETIC TRANSFORMABLE STRUCTURESThe term ‘Kinetic Architecture’ has not a clear def-inition, but it could be described as the design ofbuildings in which transformable, mechanised struc-tures, are able to change their shape in relation toclimate, function or purpose. Kinetic structures con-sist of transformable objects that dynamically occupypredefinedphysical spaceormovingphysical objects

that can share a common physical space to createadaptable spatial configurations (Kronenburg, 2007).

According to Michael Fox (2009), kinetic systemsin architectural applications can be categorised intothree categories: ‘Embedded’, ‘Deployable’ and ‘Dy-namic’. ‘Embedded’ systems are the ones that existwithin a larger structural whole in a fixed locationto control the larger architectural system or a build-

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ing in response to change. ‘Deployable’ systems aredescribed as the ones that typically exist in tempo-rary locations and are easily transportable. Finally,‘Dynamic’ systems exist within a larger architecturalwhole but act independently with respect to con-trol of the larger context. Dynamic systems can besub-categorised into three subcategories: ‘Mobile’,‘Transformable’ and ‘Incremental’. The ‘Mobile’ cate-gory includes all types that can be physically movedwithin an architectural space to a different location.The ‘Transformable’ category includes systems thatcan change to takeondifferent spatial configurationsand that can be used for space saving and utilitarianneeds. The ‘Incremental’ category includes systemsthat can be added or subtracted from (e.g. Lego),to create a larger whole out of discrete parts (e.g.metabolism projects) (Fox & Kemp, 2009).

There are some concerns regarding Fox’s classi-fication, especially in comparison to the ones madeby Gantes (2001), Areil Hanoar (2009), Mazier Asefi(2010), and Esther Adrover (2015). Despite Fox state-ment that “each of these categories is not mutuallyexclusive” (Fox&Kemp, 2009), hemadea segregationbetween ‘transformable’ and ‘deployable’ structures,which havemany commongrounds, such as the ‘spa-tial bar structures’.

SPATIAL BAR STRUCTURES‘Spatial bar’ structures are considered as deploy-able, transformable kinetic structures, composedof straight, linear members assembled in a three-dimensional configuration; They share similaritieswith traditional space frames or space trusses withflexible vertices or intermediate points of their mem-bers (Asefi, 2010).

These structures can be sub categorised into twotypes, ‘pantographic’scissor-pair structures and ‘re-ciprocal’ structures (figure 1) (Asefi, 2010). Panto-graphic structures employ Linear or angulated bars inscissor forms. Reciprocal structures employevenbarsor plates mutually supported and placed in a closedcircuit (Larsen, 2008). These structures are usuallycoveredbyflexiblematerials (e.g. fabrics, PTFE, ETFE),

or rigid materials (e.g. Polycarbonate, Aluminium)with foldable plate mechanism. They are often usedin portable, mobile or transformable buildings, be-ing utilised in surface geometries for transformationof interior elements, exterior envelopes or roof struc-tures of buildings (Gantes, 2001), and sometimesused in kinetic sculptures, artworks and space struc-tures (Pellegrino, 2001).

Figure 1Types of spatial barstructures

According to Escrig (2010), these structures occur insix different forms (figure 2), ‘Umbrellas’, ‘Bundles’,‘Rings’, ‘Polyhedral’, ‘Planes’ and ‘Double arched’. ‘Um-brellas’ have umbrella folding mechanisms and arecovered by flexible materials (e.g. Madina Mosque,KSA umbrellas designed by Frei Otto and BodoRasch). ‘Bundles’ contain modules of scissor mech-anisms in planar or spherical shapes (e.g. deploy-able structures designs of Buckminster Fuller, EmilioPérez Piñero and Felix Escrig). ‘Rings’ contain multi-angulated bars withmultiple intermediate joints, de-ploy towards their central point from the perimeterof the outer circle that they cover (e.g. Hoberman IrisDome). ‘Polyhedral’ bar structures can transform in aspongy way, as it shrinks and expands with respectto its centre(e.g. Hoberman Sphere). ‘Planes’ havemany pinned bars aligned together forming planarforms (e.g. Santiago Calatrava Milwaukee Art Mu-seum). Finally, ‘double arched’ structures, developedby Felix Escrig, can utilise foldable double-archedsteel frames as space enclosures.

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Figure 2forms of spatial barstructures

Figure 3The kinetic buildingblock and itstransformation.(Hoberman, 1991)

Throughout the analysis of spatial bar structuretypes, it has been noted that these structures arebased on modification of primitive shapes (e.g. box,sphere, and cylinder). Each system is subdivided intomultiple members of the same shape, the so-calledkinetic blocks (Hoberman, 2006) (figure 3). Modifica-tion of each kinetic block leads to transformation ofthe entire spatial configuration, and its design couldbe considered as one of the factors affecting the finalform of transformation.

EMERGENCE OF FREE-FORM TRANS-FORMABLE STRUCTURES.Zuck and Clark (1970) stated that kinetic systems canbe categorised into ‘closed’ and ‘open’ ones. ‘Closedsystems’ can change their shape according to a pre-dictable number of needs, in contrast to ‘open sys-tems’, which cannot be completely predicted or pre-determined during design conception, they acceptmodification and addition/subtraction throughout

their lifecycle (ZUK & H.Clark, 1970). The lifecycle ofa structure depends on its ability to satisfy designneeds; the current solutions of spatial structures of-fer predefined ranges of options with a range of pre-dictable possible states. The process of developinga kinetic motion should consider Ways and Meansfor operability (Fox & Kemp, 2009). Ways are the ki-neticmethods bywhich they perform including fold-ing, sliding, expanding, shrinking and transformingin size or shape. Means, are the impetus for actuationand may include pneumatics, chemicals, magnetismor electrical systems.

There are some newly created precedents ofWays of transformations not listed on the classifica-tion by Zyck and Clark. A deployable ‘hyperboloidPantographic structure’ (figure 4) was developed byAE-Lab, Vrije University, Brussel, as a tower or trusslike mast for temporary tensile surfaces, to ease itstransportation (Temmerman, et al., June 2009). ADe-ployable ‘Hyperbolic Paraboloid’ (figure 5) (i.e. saddlegeometry) structure, proposed by Fufu Yang , JimminLi and Yan Chen, from Tianjin University, China , andZhong You from University of Oxford, UK, using Ben-nett linkages with 1 DOF (degree of freedom), just towiden the deployable structure’s geometrical possi-bilities (Yang, et al., 2015). These solutions are basedon folding-expandingmechanisms regardless the ac-tuation means required for transformation.

Figure 4DeployableHyperboloidpantographicStructures(Temmerman, et al.,June 2009)

Figure 5deployableHyperbolicparaboloidstructures (Yang, etal., 2015).

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Other solutions proposed free-transformation basedon redesigning the linear elements (i.e. 2D framing)and the scissor-pair mechanism itself. Yenal Akgün,in his PhD research at the University of Stuttgart, pro-posed a redesign of the scissor-hinge by utilising twojoints at a specific point in the scissor mechanismand combining it with actuators to obtain unique ex-tensions and rotation capabilities to each scissor (i.e.module) with basic 1 DOF joints (Akgün, 2010). Thiswas to provide adaptive structural surfaces withoutchanging the dimensions of the trusses or the span.He did some digital prototypes of linear elements inone-way (figure 6) and two-ways (figure 7) configura-tions.

Figure 6One-way Linearscissor-pairmechanism(AKGÜN, et al.,2007).

Figure 7Two-way linearscissor-pairmechanisms(Akgün, 2010).

Daniel Rosenburg, in hismaster of science research atMIT, proposed some prototypes utilising scissor-pairmechanismswith twooff-centre jointswith sliders, tocontrol the degree of freedom utilising basic 1 DOFlinkages, (i.e. to transform from centre to off-cen¬treposition and vice versa)(figure 8) (Rosenburg, 2009).Despite The solutions offered by these researchersdepends on linear elements; they highlighted the ef-fect of changing the basic module (scissor mecha-nism) on the transformation of the entire system.

Figure 8a latticeworkcomposed ofscissor-pairmechanisms withtwo off-centrejoints (Rosenburg,2009).

Some researchers proposed solutions for makingthree-dimensional transformable modules withoutemploying them in structural applications. WilliamBondin, Francois Mangion and Ruairi Glynn, re-searchers at BMADE Robotics Lab, Bartlett School ofArchitecture, UCL, created a project called ‘Morphs’[1] (figure 9). It is a robotic mechanism with octahe-dral structure, which can move around public spacesand respond to its environment; utilising twelve ac-tuated struts that shifts the CG (centre of gravity) ofthe entire structure.Robert L. Read, a computer scien-tist and a contributor in Public Invention repository,commenced a project called ‘The Gluss’ in August,2015 (announced in September 2016) [2]. Inspiredbythe ‘GEOMAG’ toy, he developed ‘Tetrobot’, a roboticmodule prototype (figure 10), based on tetrahedraland octahedral geometries, utilising a set of linearservo motors and 3D printed open source ‘Turret’joints, invented by Song, Kown and Kim (Song, et al.,2003), aiming to createmetamorphic robots. Both re-searchers utilised joints with two DOFs, employing alarge set of actuators that make it expensive; Accord-ing to Read, the cost of ‘Tertrobot’ prototype is esti-mated around £2500 [2].

Figure 9Morphs robot [1].

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Figure 10The Gluss Tetrobot[2]

Whilemany researchers proposed solutionsbasedontransforming the ‘kinetic block’, others proposed so-lutions based on bending the entire surface itself. In2014, Jordi Truco and Sylvia Felipe, known as Hybridarchitecture, built the ‘Hybermembrane’ (TRUCO &FELIPE, 2014) (figure 11), a 10 x 20 m prototype, inthe ‘Barcelona design hub museum’. The structuretransforms by hydraulic masts, located on its perime-ter, able to bend the elastic structure members con-nected with universal joints; and it is cladded withelastic materials.

Figure 11Hybermembraneinstallation [3].

Another research team, Filipa Osório, Alexandra Paioand Sancho Oliveira, from the Vitruvius Fab-Lab inLisbon University, Portugal, proposed a free-formtransformation of surfaces by tessellating them withfolding patterns (figure 12), placing the actuatorshorizontally in the surface base (Osório, et al., 2014).

Figure 12the bendingprocess of kineticfolded surface(Osório, et al., 2014)

Both solutions achieved free-form transformation ofsurfaces, however, compared to the previous solu-tions, the resulting surface (i.e after transformation)can not fit a designated form easily nor precisely.

Consequently, we seek to develop a reliable ki-netic system for double layered spatial bar surfaces,which enables precise and controllable freeformtransformation. This will be attainable by develop-ing a system based one 3D kinetic blocks, flexiblejoints, fixed bars and a set of actuators, assembled to-gether in a reliable configuration generated by com-putational design techniques. in relation to archi-tectural, technical or design process related parame-ters. Considering such parameters in an early designphase could improve the system’s transformation ef-ficiency. In addition, investigating surface tessella-tion techniques in relation to the transformability ofeach kinetic block could contribute in optimising thenumberof utilised joints andactuators required to at-tain the designated transformation. In particular, wewill investigate following research questions:

1. What is the relationship between free-formtransformation of spatial bar systems and thekinetic block?

2. How does the modification of the kineticblock affect the entire system?

3. How can we achieve a controlled free-formtransformation of spatial bar systems, achiev-ing a designated form, by utilising parametrictools?

4. How can we develop an optimised and reli-able spatial bar system, composed of multi-ple kinetic building blocks (i.e. controlling theDOF)?

DEVELOPING THE DESIGN FRAMEWORKIn order to investigate the research questions, wewill develop a physical prototype of a kinetic block,and assess its potential in enabling free-form trans-formation of a spatial bar system. Its developmentis based on introducing a design framework incorpo-rating parametric and kinetic design strategies.

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Parametric design StrategiesGloba (2015) proposed a parametric design strat-egy based on an iterative endless process, aiming toachieve the optimum solution ‘reality check’. Globadescribes a design process starting by setting themodelling parameters, followed by interpretation, adigital model, evaluation, leading to data knowledgeclosing the circle back to reset the modelling param-eters (figure 13). Each iteration increases the ‘experi-ence’ of the evaluation process, which produces datato be used in resetting the modelling parameters.

Hudson (2010) proposed another practice-ledresearch strategy integrating the Knowledge De-velopment Strategy ’kDev’, the Knowledge CaptureStrategy ’kCap’, the Model Construction ’mCon’, andthe Design Investigation’dInv’, finally leading to theconstruction documents ’cDoc’ (figure 14). Accord-ing to Tedeschi (2014), this iterative process can beattainable by utilising a genetic algorithm (e.g. theGalapagos plugin for Grasshopper).

Figure 13Iterative parametricdesign loop (Globa,2015).

Figure 14summary ofparametric designstrategies forpractice-ledresearch. (Hudson,2010).

Kinetic Design StrategiesThere are other processes originated in structural andmechanical engineering. Gantes (2001) proposed akinetic design strategy focusing on a stability check,requiring the following three steps: starting with thegeometric design, followed by structural analysis un-der service loads in deployed state (i.e. after transfor-mation) and finally concluding to structural analysisthroughout the deployment process (figure 15) (i.e.during the transformation).

Figure 15deployablestructures designstrategy (Gantes,2001, p. 296)

Wierzbicki (2007) described the mechanical designprocess of kinetic structures, after reviewing the de-sign requirements and assumptions based on foursteps. It can be utilised by starting with a structuralcomponent assembly fitting and movement check,followed by coveringmaterial components assemblyfittingandmovement check, aperformance check af-

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ter load simulation, finalised by generatingmanufac-turing and informationmanagement data (figure 16).

Figure 16kinetic structuresmechanical designstrategy(Wierzbicki, 2007)

Finally, originated in an architectural point of view,Asefi (2009) proposed a transdisciplinary design pro-cess, focusingmainly in the early design stages. Eachstep should be reviewed and receive feedback fromstructural, construction, mechanical, manufacturingand material specialists. The design process, in thatproposed design management model, has five out-comes after defining the design requirements (fig-ure 17). First, a ‘conceptual design’ phase, proposedby the architect. Second, an ‘Initial schematic de-sign’ phase, after defining the structure concept andreviewing it with specialists. Third, ‘ an advancedschematic design’ phase, after checking the trans-formable structure compatibilitywith the basic struc-ture or substructure, and making simulations andtests. Fourth, a ‘detailed drawings’ phase, after mak-ing prototypes, load simulations, and check the de-sign requirements and specialist contractors. Finally,

a construction process after preparing the construc-tion documents, maintenance program, and assemblytests (i.e. porotypes) by the manufacturer. After-wards, POE (post-occupancy evaluation) and struc-ture monitoring should be imposed regarding main-tenance program to assure the building performancethrough its lifecycle (Hussein, 2012).

Figure 17designmanagementmodel ( Asefi, 2010),as edited before bythe first author(Hussein, 2012).

Briefly reviewing the existing parametric designstrategies, one could argue that they are commonlyfocusing on generic design processes and it is up tothe researchers to tailor a suitable design frameworkaccording to their design needs. Moreover, the avail-able kinetic design strategies are mostly focusing onmanaging problems occurring in non-architecturaldisciplines (i.e. structural, mechanical engineeringetc.). Consequently, we will propose a new designframework in order to build the required prototypeof a transformable free-form spatial bar structure.

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FREE-FORM TRANSFORMATION DESIGNFRAMEWORKThe proposed design framework is composed of alarge set of internal iterative design processes and it-erations (figure 19). Summarily, it consists of threemain phases: form-finding, stability validation andactuation (figure 18).

Figure 18the proposedframeworksummary

The form-finding phase is focusing on the deter-mination of the exact deformation geometry of thespatial bar prototype. It will operate as a parametricgrid system allowing variable types of deformationby defining some manipulators or attractor points. Itcould either be adjusted to the user’s individual pref-erence (i.e. custom edit) or be based on a generativedesign strategy (e.g. genetic algorithms), incorpo-rating environmental or functional requirements, re-garding rules, equations, simulations or sensor data.It will be developed as a parametric model focusingmostly on resolving geometric-kinetic relationships,rather than function related considerations.

In the second phase, after determining the finalstate of the kinetic block geometry, we will continuewith the block’s stability validation, according to itsactual function (i.e. application) and materiality (e.g.a roof structure, a façade system, a shading device)and the technical data of the structure components(i.e. bars, actuators and joints), (e.g. stiffness, iner-tia). This will be achieved by using structural simula-tion tools (e.g. finite element analysis (FEA)). Genetic

algorithms (GA) may be applied, to achieve the op-timal surface tessellation, which would provide opti-mum stability for the structure, in the final state andduring its transformation. After doing so, a feedbackloopwill enable redesigning the kinetic block assem-bly, surface tessellation or the kinetic block itself, incase of the minor issues, or changing the system’scomponents or re-formation of the initial geometry,in case of major issues, to overcome structural effi-ciency problems before moving to the third phase;the actuation of the physical prototype.

In the final phase, we will proceed to the devel-opment of the physical prototype. Its mechanismwill consist of linear actuators, linear fixed elementsand flexible joints. After the first iteration solution,the fabrication data will be generated based on thetechnical data of the structure components, previ-ously defined by the user and adjusted by the pre-vious process. Among the most important technicaldata, required for theactuationprocess, is the calibra-tion of the linear actuators, in order to determine therelation between the numerical input and the actualmovement. Equally important, the mechanical limi-tations related to the linear movement ranges of theactuators, as well as the angularmovement ranges ofthe joints (e.g. 36 degrees for the turret joint [2]).

The actuation of the physical model will be con-trolled through the previously defined parametricmodel, by which the actuation data will be trans-ferred from the computer to the actuator throughcontrollers (e.g. Arduino). The transferred data willderive from a numerical list extracted from a linearactuationmotion simulationof theparametricmodeland will be used as an input to the controller to pro-duce the required actuation.

After the actuation process, the final configura-tion data will become the initial-form data for an-other transformation process; thatmay occur regard-ing any change of rules or states that impose re-designing of the surface. Afterwards, a database willbe created listing each rule, condition, resultant formand actuation data for each transformation process.This will decrease the processing time required for

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Figure 19detailed designframework

the form finding process, as the design decision canbe stated based on the stored data that match thesame rules, states or conditions previously occurredthroughout the system operation.

In addition to the user-based, top-downworkflow described above, we will investigatea developer-based, bottom-up design approach.While the user based approach is starting by devel-oping the kinetic block based on available compo-nents. the developer-based approach will start bydesigning and calibrating the actuators, followed bydesigning the linkages and joints and determiningtheir limitations, moving backwards up to the defini-tion of the necessary elements that should be usedfor the kinetic block. Then, configuring the basic ki-netic block, and determining its stability/feasibility,validating its potential and possibilities, assessingthe movement gained by transforming it and finallyimplementing the kinetic block into a spatial config-uration (e.g. surface).

This research is still in progress; our expectedfindings from the following stage include a trans-formation mechanism and its design framework,which could be applied to different types of sur-faces or geometries allowing them to perform free-form transformation movements. That can be em-ployed for some applications and purposes, such askinetic roofs, transformable ceilings, re-usable form-works, shading devices and other types of applica-tions utilise spatial bar systems.

ACKNOWLEDGEMENTThe authors would like to acknowledge the Egyp-tian Ministry of Higher Education for the scholarshipgiven to the First author, and the Egyptian Educationand Culture Bureau in London for their effort in man-aging the scholarship. In addition, they acknowledgethe University of Liverpool for their support.

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REFERENCESAdrover, E. R. 2015, Deployable Structures, Form+ Tech-

nique, Laurence King, LondonAkgün, Y. 2010, A NOVEL TRANSFORMATION MODEL FOR

DEPLOYABLESCISSOR-HINGESTRUCTURES, Ph.D. The-sis, Institut für Leichtbau Entwerfen und Konstru-ieren; Universität Stuttgart

Akgün, Y., HAASE,W. and SOBEK,W. 2007 ’NEWSCISSOR-HINGE STRUCTURE TO CREATE TRANSFORMABLEAND ADAPTIVE ROOFS’, International SymposiumShell andSpatial Structures-Architectural Engineering,Venice, Italy

Asefi, M. 2009 ’Design Management Model for Trans-formable Architectural Structures.’, Proceedings ofthe International Association for Shell and SpatialStructures (IASS), Valencia

Asefi, M. 2010, Transformable and Kinetic ArchitecturalStructures :Design ,EvaluationandApplication to Intel-ligent Architecture, VDM verlag Dr. Muller Aktienge-sellschaft & Co. KG, Saarbrucken,Germany

Escrig, F. and Sánchez, J. 2006 ’New designs and geome-tries of deployable scissor structures’, InternationalConferenceOn Adaptable Building Structures Adapta-bles, Eindhoven ,Netherlands

Escrig, F. and Sánchez, J. 2010 ’General survey of deploy-able structureswith articulatedbars’, IASS, Shanghai,China

Fox, M. and Kemp, M. 2009, Interactive Architecture,Princeton Architectural Press, New York

Gantes, C. J. 2001,Deployable Structures: Analysis AndDe-sign, WIT Press, Southampton, UK

Globa, A. 2015, SUPPORTING THE USE OF ALGORITHMICDESIGN IN ARCHITECTURE: AN EMPIRICAL STUDY OFREUSEOFDESIGNKNOWLEDGE, Ph.D. Thesis, VictoriaUniversity of Wellington

Hanaor, A. 2009, ’OME STRUCTURAL-MORPHOLOGICALASPECTS OF DEPLOYABLE STRUCTURES FOR SPACEENCLOSURES’, in Motro, René (eds) 2009, An Anthol-ogy of Structural Morphology, World Scientific Pub-lishing Co. Pte. Ltd, Singapore

Hoberman, C. 1991, Radial Expansion/Retraction TrussStructures., United States Patent No. 5,024,031

Hoberman, C. 2006, ’Transformation in Architecture andDesign’, in Kronenburg, R. (eds) 2006, TransportableEnvironments 3, Taylor & Francis, London

Hudson, R. 2010, Strategies ForParametricDesign InArchi-tecture : AnApplication For Pratice LedReaserch, Ph.D.Thesis, Department Of Architecture And Civil Engi-neering, University Of Bath

Hussein, H. 2012, Dynamic Architecture : Definition AndApplications, Master’s Thesis, Zagazig University

Kronenburg, R. 2007, Flexible : Architecture That Respondto Change, Laurence King Publishing Ltd, London

Larsen, P. O. 2008, Reciprocal Frame Structures, Architec-tural Press, Oxford

Mollaert, M., De Laet, L., Henrotay, C., Paduart, A.,Guldentops, L., Van Mele, T. and Debacker, W.2009 ’A Deployable Mast for Adaptable Architec-ture’, Lifecycle Design of Buildings, Systems andMate-rials, Twente, the Netherlands, pp. 47-52

Osório, F., Paio, A. and Oliveira, S. 2014 ’Interaction witha Kinetic Folded Surface’, eCAADe 2014, Newcastleupon Tyne, England

Pellegrino, S. 2001, CISMcoursesand lecturesNo. 412 : De-ployable Structures, Springer-Verlag, New York

Rodriguez, C., Chilton, J. and Wilson, R. 2009, ’FlatGrids Designs Employing The Swivel Diaphragm’, inMotro, Réne (eds) 2009, An Anthology Of StructuralMorphology, World Scientific Publishing Co. Pte.Ltd., Singapore

Rosenburg, D. 2009, Designing For Uncertainty: NovelShapes and behaviours using scissor-pair trans-formable structures, Ph.D. Thesis, Massachusetts In-stitute of technology

Schumacher, M., Schaeffer, O. and Vogt, M. 2010, Move:architecture in motion-dynamic components and ele-ments, Birkhäuser GmbH, Berlin

Song, K., KWON, D. and Kim, W. 2003, SPHERICAL JOINTFOR COUPLING THREE or more links together at onepoint., United States Patent No. US 6,568,871 B2.

Tedeschi, A. 2014, AAD Algorithms-Aided Design. Para-metric strategies using Grasshopper, Edizioni LePenseur, Brienza, ITALY

Wierzbicki, M. 2007, Knowledge-Based Architectural De-scision Making Of Kinetic Structures, Master’s Thesis,The University of British Columbia

Yang, F., Jianmib, L., Chen, y. and You, Z. 2015 ’A deploy-able bennett Network in saddle Surface’, The 14thIFToMMWorld Congress, Taipei, pp. 428-434

ZUK, W. and Clark, R. 1970, Kinetic Architecture, Van Nos-trand Reinhold Company, New York

[1] http://www.interactivearchitecture.org/lab-projects/morphs

[2] https://www.hackster.io/robertlread/the-gluss-project-019ed1

[3] https://www.hybridarch.net/hypermembrane-demo

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