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ROBOTIC FABRICATION OF MODULAR FORMWORK

An innovative approach to formwork fabrication for non-standardconcrete structures

Martin KAFTAN and Milena STAVRICGraz University of Technology, Graz, [email protected], [email protected]

Abstract. In this work we address the fast and economical realization ofcomplex formwork for concrete with the advantage of robotic fabrication.Under economical realization we mean reduction of production time andmaterial efficiency. The complex form of individual formwork parts can bein our case double curved surface or complex mesh geometry. We proposethe fabrication of the formwork by straight or shaped hot wire. We illustratedifferent approaches to mould production, where the proposed processdemonstrates itself effective. In our approach we deal with the special kindsof modularity and specific symmetry of the formwork.

Keywords. Robotic fabrication; formwork; non-standard structures.

1. Introduction

The recent advance of CAD/CAM technologies has considerably blended the tran-sition between the digital and its physical counterpart. Efficiency of the processbecomes less crucial, as the data can nowadays be almost effortlessly processed,giving predominance to customization of the produced parts. However, the indus-try still cannot manufacture the building as a single part, which results into anunavoidable issue of fragmentation. Thus, even though the designing of free-formarchitecture has been for architects easier to access, the building must be dividedinto set of parts which are subdivided into another set of parts, and so on. Forexample, one global fragment is the facade of these buildings, further locally sub-divided into many different parts. The most common technique is to discretize thecurved shape into planar elements, which requires techniques that have beenresearched in the last decade (Eigensatz et al., 2010; Pottmann et al., 2008a;Shelden, 2002). Without discretization needs to be for every part produced costly

R. Stouffs, P. Janssen, S. Roudavski, B. Tunçer (eds.), Open Systems: Proceedings of the 18th InternationalConference on Computer-Aided Architectural Design Research in Asia (CAADRIA 2013), 75–84. © 2013,The Association for Computer-Aided Architectural Design Research in Asia (CAADRIA), Hong Kong, andCenter for Advanced Studies in Architecture (CASA), Department of Architecture-NUS, Singapore.

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formwork, whether it’s for glass, concrete or other material. The problem of thesetechniques is that for every part of the facade must be created a unique mould. Themost common type of formwork is the polystyrene (EPS or XPS) mould which is3D formed using a CNC milling machine. This technique is very accurate, but itrequires time and produces a lot of waste material. On the other hand, the poly-styrene is commonly cut fast and with minimum waste by heated wire, especiallywhen both sides of the cut foam can be used. Therefore, the aim of this project isto explore the mould forming of complex geometries by using a hot wire cuttingtechnique that can potentially diversify and spatially enrich the repetitive aspectsof modular systems still pertinent in the production of architecture today. Can wemake a use of hot wire cutting technique operated by industrial robotic arm to cre-ate a complex mould while minimizing the production time and the wastematerial?

2. Designing the Negative

2.1. CONCRETE AND FORMWORK

Being an amalgam, concrete does not have any implicit shape; it can be mouldedinto any form imaginable. Also the steel reinforcement does not have significantembedded constrains. This suggests the possibility of a biomorphic utility of rein-force concrete, similar to working with clay. However, the limitation lies in theformwork, characteristic by its rigidity.

Ideally the form finding of a load bearing structures origins in complexity ofstructural logic, but the most often reality is that the resulted shape is blend ofstructure and the most economical formwork achievable. As an attempt to lowerthe cost to minimum, over the past, the construction has developed into modularand reusable formwork layout (Figure 1a,b), which unfortunately fails when eachformwork differs in shape (Figure 1c).

2.2. HOT WIRE

The hot wire cutting technique uses typically straight heated wire. This constrainsthe design process into ruled surface geometry, as the ruled surface is formed bycontinuous sequence of straight line segments. Ruled surfaces already have beenused in creating complex architectural forms. One example is the pioneering workof Antoni Gaudi and his Sagrada Familia Cathedral (“Ruled Surfaces”, n.d.). Thehyperbolic paraboloid geometries of the cathedral’s ceiling vault system are ruledsurfaces that can be created by using hot wire. However, the wire can be also shapedto research beyond the ruled surfaces and to explore more geometrical possibilities.

76 M. KAFTAN AND M. STAVRIC

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2.3. ROBOTIC FABRICATION

The big challenge was the optimization of the robot data flow from parametricdesign to a physical model. A Grasshopper component was generated within theproject that included inverse kinematics and all the necessary calculation for directrobot programming with an automatic code generation. The basic robot code wassupplemented with special strategies depending on individual specific designmeant to facilitate the transformation of the desired design to the basic robot code.This approach provided great flexibility in design and real time feedback to thedesigner due to the robot constrains. The used industrial robotic arm – Robot ABBIR140 constrained the cutting size into 250x250x160mm EPS blocks (Figure2)that could be to cut into stackable ornamental components, which then composedthe negative form-work for the concrete wall design.

These constraints necessitated the adaptation of the individual design, startingwith changes of the initial design, selected tool or EPS tool cutting strategy. Sinceone of the projects aims regarded cost-effective use of materials, the first part of

ROBOTIC FABRICATION OF MODULAR FORMWORK 77

Figure 1. From left – a: Miguel Fisac with his pre-cast pre-stressed concrete elements,b: reusable forkwork, c: “Urban nebula” – concrete bench by Zaha Hadid.

Figure 2. Robot ABB I140.

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the research was started with modular ornamental parametric elements. By vary-ing their parameters and positions it was possible to obtain a huge number ofvariations of the final design.

3. Patterning

Patterns can be found in different parts of a building. In “The Self-MadeTapestry”, Philip Ball describes patterns as “arrays of units that are similar but notnecessarily identical, and which repeat but not necessarily regularly or with awell–defined symmetry” (Ball, 1999, p. 9).

3.1. P4 SYMMETRY

3.1.1. Periodic tilling

The tiling is based on a symmetry group p4 (Figure 3). This symmetry group hastwo-fold rotation (in points A and C) and two four-fold rotations (in points B andD) – Figure 3a.

Geometrically the p4 border pattern consists of two curves a and b. These twocurves are rotated around points B and D for 90° in order to generate border curves.The 3d shape is generated by extrusion of pattern in the direction normal to the plane


Figure 3. Variation examples and assembly of p4 parts.

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ABCD. The used 3D form is optimised and enables cost–efficient use of materialand time efficient cutting technique. The three–dimensional form was achieved withthe cutting of boundary box with one symmetry plane that divided block into twoparts. The second cut was the shape cut of 2D pattern that makes final shape.Generally for this symmetry group the both base curves can have different shape(Figure 3c), which opens other possibilities and freedom in the design process.

With only two cuts, it is possible to get four elements, two positives and twonegative parts of the desired pattern. Negatives are used as formwork for concrete,while the positives can be used as an insulating facade element (Figure 4). Thisshape also enabled over lock between the individual moulds in the four–fold rota-tional point that has a positive static influence onto whole assembling structure.

3.1.2. Aperiodic tiling

Aperiodic tiling has been discovered on quasicrystals and can be generated by pro-jection of higher dimensional grids into two or three dimensions. Theoreticallythere can be infinite different patterns in one plane without any holes that are ableto be continued indefinitely. They are comprised of structures made of few differ-ent tiles which are combined in a non-repetitive manner. Rotational symmetrymakes their non-repetitive combination possible as opposed to periodic structureswhich only have translational symmetry (can be copy and paste next to each


Figure 4. Assembled foam blocks – positive cut.

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other). An example of aperiodic tiles is the Penrose tiles, discovered by the Britishmathematician Roger Penrose in the 1970’s prior to the discovery of quasicrys-talline structures in 1984. The Penrose tiling can be derived from the projection offive dimensional grids onto a two dimensional plane (De Bruin, 1981). Thegrowth of the tiling is regulated by a finite number of (local) matching rulesbetween tiles (Figure 5). In the pattern a1 = b1 and a1 = c1 = d2 = b2 = d1 = c2.The B1 and A2 corners can be moved into the z-direction by equal value. Anotherz-value has to be used equally for the other corners. All of the edges which arecoming from the vertex shifted in z-direction have to be identical. Each of theother corners has to be mirrored around their centre.

This formwork for this tiling can be created by assembly of two different shapesin the form of rhombuses, one with the corner angles of 72° and 108° and the otherwith corner angles of 36° and 144°. The height of the corners of those two rhombuseshas to be the same in order to form continuous surface, but the shape of the edges canbe arbitrary. Figure 6 shows the generation of such pattern. The main pattern consistsof only two different curves a and b that are rotated around points A and D for 72°and points C and F for 144°. Actually, one can choose any two different border shapesin order to generate pattern with the penrose symmetry. In 2D generated form is themain penrose cell (Figure 6a, b, c) which borders are straight lines.

The 3D form is generated shaping 3D EPS block using rotation in the points Aand F. This rotation is a space rotation of the straight line along space curve c(Figure 6d). This kind of generation allows cutting the EPS blocks with the hotwire, but a shaped hot wire can be also used in order to design possibility. Figure 7shows formwork for 3D Penrose pattern.


Figure 5. Penrose basic tiles – combining rules and their impact on the relocation of cornersin z-direction and the shape of edges.

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3.2. ANTIPRISM

In this study case, the geometry is topologically based on using antiprism as thebase element which can be modified and organized in order to achieve structuralstability (Figure 8a).


Figure 7. Formwork for Penrose pattern.

Figure 6. Penrose tiles – different tile patterns derived from basic Penrose tiling rule.

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The n-sided antiprism is the result of rotating the base m by an arbitrary anglearound axe a. Such a 3D form can we generated by twisting a cube around oneaxes that is parallel with four cube edges. In our case the geometry is based oneither square antiprism (Figure 8c, 8d), the anticube, or on triangular prismocta-hedron. The bottom base m and top base m1 can be connected by triangular faceswhich edges can be further modified by splines curve to generate different shapes(Figure 8b). Therefore, the element can be formed out of ruled surfaces that canbe fabricated by the straight hot wire. Inside of the antiprism the rotational parab-oloid is parametrically generated and subtracted from it. Because the base and thetop faces can be independently scaled, it is possible to create variety of fluidlyformed columns out of those stacked elements (Figure 9).

Each cut can be done precisely and fast with minimum manipulation of thefoam block between cuts (Figure 10). Figure 11 presents cut order and their paths,Figure 12 formwork assembly with resulted concrete part.


Figure 8. Strategy of creating component based on antiprism.

Figure 9. Morphology of the column.

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Figure 12. Formwork assembly and resulted concrete part.

Figure 11. Cut order and paths for the robotic arm.

Figure 10. Cut diagram and assembly of formwork.

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4. Outlook

We performed static load analysis which demonstrated that the geometry can with-stand substantial stresses. Therefore, the component could be used as load bearingbuilding element (Figure 13).


Figure 13. Stacked elements creating load bearing wall.

We are currently working on fabricating full scale prototypes out of ultra-highperformance concrete to test the precision, and the obtained surface quality. Weare also developing a joint system as we anticipate that the jointing between thecomponents will become a critical part of the assembly process. The digitalmethodology of obtaining the geometry will definitely benefit from the datacollected during the physical assembly of the prototypes.

Acknowledgement

We would like to Students of TU Graz: Georg Schrutka, Stefan Rasch, Florian Maroschek, IrinaScheucher, Alice Demenyi, Henrik Jonestrand.

References

Ball P.: 1999, The self-Made Tapestry: Pattern Formation in Nature, Oxford.De Bruijn, N. G.: 1981, Algebraic theory of Penrose’s nonperiodic tilings of the plane, I, II, Nederl.

Akad. Wetensch. Indag. Math., 43, 39–52, 53–66.Eigensatz, M., Deuss, M., Schiftner A., Kilian, M., Mitra, N. J., Pottmann, H. and Pauly, M.: 2010,

Case studies in cost-optimized paneling of architectural freeform surfaces, in C. Ceccato, L.Hesselgren, M. Pauly, H. Pottmann, and J. Wallner, (eds.), Advances in Architectural Geometry2010, Springer, Vienna, 49–72.

Pottmann, H., Schiftner, A., Bo, P., Schmiedhofer, H., Wang, W., Baldassini, N. and Wallner, J.:2008a, Freeform surfaces from single curved panels, ACM Transactions on Graphics, 27(3).

“Ruled surfaces”: n.d. Available from: <http://www.sagradafamilia.cat/sf-eng/docs_instit/pdf/geom_02.pdf> (accessed 22 March 2013).

Shelden, R. D.: 2002, Digital Surface Representation and the Constructability of Gehry’s Architecture,Ph.D. Dissertation, Massachusetts Institute of Technology, Cambridge, MA.

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