Unfolding Architecture – Study, Development and Application...

246 ACADIA05: Smart Architecture

M. Wierzbicki-Neagu / Unfolding Architecture

Unfolding Architecture – Study, Development andApplication of New Kinetic Structure Topologies

Madalina Wierzbicki-Neagu1

1 University of British Columbia

Abstract

Advances in design tools and material engineering open new possibilities for architectural structures that mayrespond better to the demands of the increasing density of development, better space management and lesserenvironmental impact. Folding structures that provide adjustable on demand configurations can be effectivelyconceptualized if appropriate interdisciplinary expertise is brought together. Kinematic chain geometriesborrowed from traditional mechanics can be developed into a variety of topologies suitable for architecturalstructures. Rectilinear deformable grids can provide the functionality of expanding and collapsing as well asthe ability to be infinitely arrayed. Converging grids allow for circular arrays and fan like folding. The challengeis to translate a two-dimensional chain concept into a three-dimensional array of interleaved frames that forma stable structure and can bear the necessary loads. In order to complement the folding structure with thecorresponding foldable shell, the algebra of rigid folds can be adapted to develop viable geometrical concepts.The demands of the design process needed to develop kinetic structures will expand the traditional architecturalworkflow to include parametric modeling tools that are common in mechanical engineering. Foldingarchitectural structures require, besides traditional architectural layout development, parametric assemblycapabilities and motion analysis typical for mechanical design. Potential application development, marketing,building code changes and effective multidisciplinary collaboration must take place for kinetic structures toenter the architectural mainstream.

ACADIA05: Smart Architecture 247


Kinetics and Architecture

The idea of configurable kinetic elements inarchitecture is as old as architecture itself. Doors,windows, blinds, gates, draw bridges and other,similar, simple in concept devices were known forages. Recent decades brought large retractableroofs over stadiums and stages, elaborate partitionsystems in conference centers, configurable floorinstallations in concert halls, anti sway devices inhigh rise towers and automatically adjustablecolumns that compensate for the ground settling.However, these kinetic elements have mostly alimited, localized function of controlling egressand adjusting various aspects of the exterior shell.The concept of a ‘foldable’ building or areconfigurable on demand layout is not here quiteyet. The progress in design tools and materialtechnologies offer a potential that has not beenfully exploited yet. This paper focuses onexploring the possibilities of new design methods,tools and recently available materials that can beapplicable for the architectural workflow oftomorrow.

Kinetic Structures

Traditional kinematic chains used in mechanicsmay provide suitable concepts for architecturalstructures. The prerequisite is the ability to beassembled into large and repeatable grids.Rectilinear deformable grids can provide thefunctionality of expanding and collapsing as wellas ability to be infinitely arrayed. Converging gridsallow for circular arrays and fan like folding, butthey require the added challenge of developing akinematic chain that is scalable within iso-angularmodule. A simple kinematic chain, the pantograph,can be developed into both rectilinear andconverging versions. A variety of arraying optionsfurther increases the range of possible solutionsas illustrated in Figures 1 and 2.

In mechanics, kinematic chains are, most of thetime, a part of much larger assembly that providesanchors, supports and constraints therefore theycan be easily modeled as two-dimensional devices.Since architectural structures bear a combinationof static loads of construction materials and

Figure 1. Arraying of rectilinear kinematic chains

Figure 2. Arraying of converging kinematic chains



dynamic loads induced by use and elements, thetwo-dimensional concept chains need to betransformed into a three-dimensional system ofinterleaved frames and off-set joints to assure loadbearing capacity and static integrity. This processis more difficult for converging grids as thearchitectural structures do not scale as easily assimplified mechanical chains. The challenge ofdeveloping two-dimensional concepts into viablefolding structures is a part of developing themethodology of kinetic architecture.

Foldable Shells

Kinematic chains provide good concepts for thedesign of articulated skeletal structures. However,a different method is needed to develop foldableshelling elements that can complement kineticstructures and form a finished, functionalarchitectural solution. Size and shape change canbe achieved by either sliding over or folding theselected facets of the exterior. Folding is a moredesirable method since it results in more rigid andeasier to seal assemblies.

Figure 3. Folding of flat sheets and foldable shells

Commonly, transformations of folding areassociated with flat sheets and play the key role insheet metal fabrication, packaging industry andart of origami. A more generalized approach is toconsider folding as degrees of freedom availablein an under constrained mesh. This mesh may be,in a special case, a tessellated flat sheet but, ingeneral, any 3d mesh can be subjected to folding.A flat pattern and a flat fold define the extremestates of a foldable mesh. Only a flat sheet canform the flat pattern while the state of the flat foldcan be applied also to some non-flat meshes.

Foldable structures do not reach the conceptualextremes of the flat pattern or the flat fold. Thephysical dimensions of components as well asassembly offsets limit the range of transformation.The purpose of the folded state for a foldablestructure is to achieve a certain practical level ofcompactness. The deployed state forms thefunctional configuration that satisfies the designrequirements. Geometrical constraints required tosatisfy the full range of folding from the flat patternto the flat fold are most restrictive. Since they donot apply to practical folding structures, significantfreedom of possible configurations is available todesigners. The only requirement that a foldablemesh must satisfy is the condition of rigid foldingwhat means that mesh facets can not be bent ortwisted. Figure 3 illustrates the basic stages offolding of flat sheets and 3d shells.

Figure 4. Controlled folding of a flat sheet

3d meshes provide seemingly unlimited designpossibilities what may increase the difficulty ofinitial conceptualizing. Therefore, basicgeometrical configuration like the eight creasesheet fold provides a good starting point for thedesign development. Figure 4 illustrates theprocess of controlled folding of a flat sheet. Acontrolling grid comprised of two pairs of pivotingpoints is imposed over a pattern of creases. If thesheet is folded by bringing in the corners tocoincide with the points of the controlling grid,the result is a three dimensional, fully constrainedand rigid shell. The shape of the shell can be variedby adjusting the parameters of the controlling gridas shown in Figure 5. In a practical applicationonly angle ‘a’ of the pivoting grid provides feasiblemeans of adjustment.

Non-flat folding meshes can be easily developedby constructing individual facets directly over thecontrolling geometry as illustrated in Figure 6. Thecontrolling grid is transformed into a network of



3d controlling edges by means of offsetting aneutral point N off the grid’s plane to define aconstruction vertex. Four sectors are formed in thiscase. They can be independently populated withfacets that follow locally relevant geometricalconfines. The stretched sector requires that the sumof the vertex angles of the facets is larger than theangle between the controlling edges in order toavoid the singularity of a fully stretched state.

The requirement for all the facets to form a flatpattern is irrelevant since the assumed controllinggeometry as well as the practical motion rangewere not intended to reach either fully stretchedor fully folded state. In this example, the total ofthe vertex angles is more than 360 degrees andthe facets form a saddle type compound surface.The pivoting angle ‘a’ is the parameter thatcontrols the folding of the finished shell. Figure 7indicates the available range of transformation.

To gain more freedom in forming a foldable mesh,selected corner points of the controlling grid canbe offset off the construction plane. Figure 8illustrates the development of offset points over aconverging controlling grid. The asymmetricallylifted edges allow for shell overlapping in arrayedconfigurations. The constructed shell is coupledto a folding frame that employs the sameconverging controlling geometry. As a result, amodular segment of a foldable structure is formed.

The design decisions made while constructing thefolding mesh define its functional folding range.Figure 9 illustrates the deployed and folded statesof the example module. The compactness of thefolded form can be further optimized if needed byadjusting the controlling grid and refining the meshfacets. More compact shape may be beneficial forthe ease of transportation if a mobile solution isrequired.

Figure 5. Adjustment of fold parameters

Figure 6. Constructing a 3d mesh

Figure 7. Range of transformation



Design workflow

The scope of the traditional architectural workflowis already undergoing expansion as motion andactuation elements migrate gradually into buildingstructure designs. The design of kineticarchitectural structures will expose architects tothe unique demands of modeling of the translationgeometry and simulation of the motion range. Thedesign tools that perform similar tasks are widelyavailable in mechanical engineering. In particular,parametric assembly environments offer the easeand flexibility of both forward and inversekinematics to model complex kinetic designs. Theincreasing importance of detailing of lightweightand reliably performing fittings will benefit fromstress analysis tools that are readily available inthese software packages.

Figure 10 illustrates the logical phases of thekinetic structure design development and thebenefits of the integrated parametric CADenvironments that are readily available today. Thekey CAD feature that helps with tackling thecomplexities of foldable structures is the flexibilityof switching between bottom-up and top-downmethods while developing the design. Theassumed initial concept of the controlling grid andthe folding structure can easily be put togetherwhile starting with components, progressing to the

Figure 8. Development of a foldable module

Figure 9. Details of a foldable module

assembly level and employing then algorithmiccapacity of forward kinematics modeling. This isa straightforward bottom-up design strategy. Thedevelopment of a foldable mesh requires adifferent approach. The kinetic complexity ofunder constrained meshes makes algorithmicdescriptions tedious to define. However, a looselyimprovised set of facets that follows locallyapplicable geometric restrictions can be easilyappended to an already defined controlling gridand quickly verified by means of inversekinematics.

The initial draft can be further refined through asequence of design iterations. The efficiency ofthis process relies on the seamless integration ofsolid parametric modeler with parametricassembly modeler. Once the components can bemodified directly within the environment ofkinematic simulation, the development processfocuses on optimization of the form without thecumbersome burden of switching betweendifferent design environments. Overall, theconcept undergoes a series of design iterations asit progresses through development stages. Aneffectively integrated design environment makesthese iterations feel more like intuitive adjustmentsrather than a frustration of starting all over again.



As most of parametric modelers have the finiteelement analysis capacity fully integrated, theverification of the tweaked in configuration interms of safety and load performance can beperformed within the same design environment.The design data can be shared between variousdevelopment workflows, architectural forinstance, in a variety of commonly supported 2dand 3d formats.

Material engineering is another area that willfurther expand its role in the architectural designworkflow. Composite materials of significantly

increased load capacity to weight ratio areparticularly suitable for kinetic structures. Highstrength fibers can be effectively integrated intofinal components where properties like weight,mechanical performance, transparency andaesthetic finish can be easily designed in thanksto advances in manufacturing processes of pull-truding, molding, injection molding andlamination. The success of developing of this newbreed of architectural structures will depend oneffective interdisciplinary collaboration to bringtogether an unprecedented range of expertknowledge.

Figure 10. Design workflow



Applications of Foldable Structures

An adjustable shading system offers beneficialfeatures for outdoor exhibitions as the space canbe easily adapted to accommodate different

scenarios, Figure 11. It also offers dramaticchanges in the appearance of the space.

The development of quickly deployable, mobileshelters may be useful for emergency situations

Figure 11. Adjustable shading system

Figure 12. Mobile system



Figure 13. Applications

and harsh climatic conditions. Figure 12demonstrates a foldable system that can bedeployed off dedicated, motorized platform.

Figure 13 illustrates mobile systems deployed inthe desert and the interior of an exhibition space.

Closing Remarks

The development of feasible applications,assessment of benefits and marketability mustadequately support the design effort. Safety andperformance tests need to be conducted as well asappropriate changes to building codes need to takeplace. The unique features of foldable structuresmay change the traditional building maintenanceand lifecycle models and offer reconfiguration asan option to demolition. In general, configurablestructures will provide lesser environmentalimpact than traditional technologies as they arebetter suited for re-using, modifications and re-location. Inherently modular, they facilitateassembling of infinite variations from a limitedset of prefabricated components. Design ofconfigurable habitable spaces in highly populatedareas is another area that kinetic architecture mayresolve better than traditional solutions.

References

Calvert, J.B. (2003). Mechanism. Retrieved fromwww.du.edu/~jcalvert/ on March 24, 2005.

Hull, T. (1994). On the Mathematics of FlatOrigamis. Congressus Numerantium (100), 215-224.

Zuk, W., Clark R.H. (1970). Kinetic Architecture.New York, NY: Van Nostrand Reinhold.

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