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Robotic zip-bending of wood structures with programmable curvature


Standard wood bending approachesrely either on heavy industrial processes optimized for repeatability or on crafting techniques that are mostly intended for the production of small-scale products. Contemporary research focuses on digital fabrication methods to overcome geometrical limitations and automate freeform wood construction without the need for highly specialized craftsmanship. The presented research focuses on robotic zip-bending to achieve custom curved wood elements with structural properties. The technique uses kerfing patterns applied to two layers of planar wood elements to achieve a zipped composite with precomputed bending and twisting behaviour. The article describes the entire workflow from initial material studies to the realization of a robotically-made 1:1 structural installation. The involved methods, such as mechanical testing, geometrical form-finding, structural FEA simulation, CNC robot programming, and 3D scanning, are described with extensive qualitative analysis and quantitative data. The work demonstrates robotic zip-bending’s structural and geometrical capabilities for prospective applications in the construction industry, including suggestions for future research developments.



Wood bending techniques for architectural structures are based on unflexible industrial processes and large-scale hardware that require resetting for accomplishing specific geometry [1]. The industrial production of curved wood construction elements, in particular, is optimized for mass production of identical components and necessitate heavy-force clamping devices to realize glue-laminated parts with simple curvature. Alternative non-industrial techniques that ensure a higher level of customization are based on traditional woodworking approaches, which utilize steam, water, chemicals, or kerfing to form planar elements into curved geometries [2,3,4,5]. Typically, these techniques are directed to the production of relatively small-scale products, such as furniture, and demand the involvement of highly specialized labour.

The increasing need for flexible, automated, and economically sustainable approaches to shaping curved wood elements has motivated recent investigations into CNC kerfing as a moldless bending technique [6, 7]. The literature indicates the potential to further develop this technique by combining two merged kerfed layers performing as interlocking bent elements, called zippered wood [8,9,10]. This research expands on the topic, focusing on the robotic implementation of zip-bending (Fig. 1), which produces computationally-controlled curved wood components for architectural applications. Robotic machining is here used as a large-scale CNC system that offers high flexibility in degrees of freedom and extended workspace, suitable for large-scale applications.

Fig. 1
figure 1

Roboti c saw-cutting of zipped wood battens

Definition and state of the art

Zip-Bending is the assembly of two kerf-bent elements through an interlocking pattern of zip-like teeth to achieve wood elements with a programmed curvature. Analogously to kerfing, zip interlocks are cut or milled from a solid and planar piece of wood. Only a thin and continuous layer of material is left to achieve flexibility. The glued combination of two layers stabilizes and locks the wood into its final configuration. In comparison with simply kerfed elements which require the use of substructures, zip-bending offers a certain degree of structural integrity. The use of zip-interlocking teeth patterns onto wood elements has been previously investigated for furniture-oriented applications to bend MDF and solid wood boards [11, 12]; or for structural wooden frames obtained from the zip-bending of wood battens salvaged from building demolitions [8,9,10]. Similar interlocking patterns have also been used to induce controlled bending of straight elements sliding onto each other in reversible configurations [13, 14].

The existing literature showcases potential load-bearing zip-bending applications, but no analytical data about the structural performance and the comparison with solid wood elements are found. This research assesses zip-bending as a viable method to produce curved wood components for architectural applications. More specifically, this paper aims to: (i) explore the geometrical features, and material limitations of wood zip-bending, (ii) identify the structural behaviour and properties of this technique, (iii) measure them through mechanical tests and FEM simulations to extrapolate reference parameters and (iv) apply them to a large -scale structural installation, (v) providing an assembly method for zip-bent components.

Research methodology

This work is based on an integrative workflow where the digital and physical domains inform design solutions and construction process. Firstly, empirical explorations and mechanical testing are performed to understand the material properties and behaviour. Secondly, this information is the main source to define constraining parameters for programming the algorithms that describe zip-bent elements. In particular, various geometric parameters of the zipping pattern are studied in relation to the bending behaviour and bending radius of a specific material. These are used to inform the computational form-finding process and related zipping construction of a wide range of bent and twisted wood beams. Results and data from the mechanical testing are used to feed the structural FEM analysis and simulation. In this way, the established simulation parameters are verified and tuned to best represent the real-life behaviour of the zip-bent wood structures. Finally, a demonstrative prototype is designed by implementing the described computational process.

Robotic path planning and simulation for the prototype fabrication are integrated within the same design environment. Here the existing robotic set-up is virtualized, the robot movements are programmed and simulated, and the robot codes are exported. The robotic fabrication of individual zipped components is then executed through saw-cutting and milling operations. The assembly operations are performed manually by first moisturizing the zipped components, then glueing them together and clamping them perpendicularly to the zipping pattern. Finally, the overall accuracy is assessed by 3D scanning and comparing the actual structure with its digital blueprint. The digital domain of the whole above-described process is primarily based on the use of Grasshopper [15] plug-in for Rhinoceros [16] with the integration of custom C# scripts for the form-finding stage, Abaqus [17] for the structural analysis, and GOM [18] for 3D scanning and point cloud generation (Fig. 2).

Fig. 2
figure 2

Computational design-to-fabrication-to-assembly pipeline diagram showing the physical and digital phases of the zip-bending process and the used software for each phase

Material investigation

Constructive technology

The construction principle of zip-bent structures relies on a set of geometrical parameters and their mutual relations, as outlined in Fig. 3.

Fig. 3
figure 3

Geometrical description of the zip-bent section

The construction of zip-bent elements starts from a developable reference surface, i.e., a surface with Gaussian curvature equal to 0 capable of being unrolled on a flat plane without distortions [19]. This is generated through a series of parallel or non-parallel rulings. Each ruling represents a shared edge between two faces. Two main angles are identified as parameters for generating the reference surface. The bending angle (α) is the supplementary angle between two consecutive faces. When the bending angle of consecutive rulings is constant, the resulting developable surface can be described with the geodesics of a cylinder, which is the geometrical space explored in this paper. If the bending angle varies, the resulting developable surfaces are poly-cylindrical. The ruling angle (β) represents the angle between the specific ruling and its adjacent edge of a face, which defines the second direction of the plane that they both lie on. Variations of the ruling angles result in the twisting of the global form. If β is constant, then all the rulings are parallel and the resulting surfaces are cylindrical, while when β varies, the resulting surfaces are conical or poly-conical. The bending radius (r) of a zip-bent element is measured to quantify the bending capacity between a developable surface’s initial and final plane. It is used to measure the overall bending curvature of the zip-bent element.

Individual zip teeth are constructed geometrically, starting from each ruling. Each tooth is characterized by a zip tooth height (ht) and a zip tooth angle (γ). The negative space created between the two zip teeth is called a zip pocket. As a final zip-bent element comprises the two joint elements, the sum of the wood thickness (tw) and one veneer thickness provides the total thickness (tt).

Zip-bending as a material system

Zip-bending is a material system composed of two elastic layers such as wood and an intermediate adhesive layer, which binds the various parts into a unique element transferring forces and loads.

Material setup

In this study, zip-bending experiments are conducted on battens obtained from engineered wood products with good dimensional stability, ensuring higher assembly precision than solid wood. The employed elements are T grade LVL (Laminated Veneer Lumber) spruce battens 39 × 95 × 3000 mm, with a total of 13 layers of 3 mm thick veneer glued together with parallel fibres to the main axis. The adhesive used to bond the zip-bent components is a polyurethane-based (PUR) wood glue with a curing time of about four hours.

Bending capacity

The bending capacity of wood is determined by the material thickness, moisture content, and temperature [20, 21]. Wood flexibility can be estimated with the modulus of elasticity which, given the organic nature of the matabout four hours of curing time the moisture content and temperature [22,23,24]. Specifically, the increase of moisture and temperature in wood determines a decrease of the elastic modulus making the material more flexible, as seen in both industrial and crafting steam-bending techniques.

Material thickness

In the case of zip-bent components, the bending capacity of an element depends on the thickness of the top/bottom veneer layers. Previous studies used a layer thickness of 2–3 mm layer thickness to balance material flexibility and final strength [8,9,10,11,12]. This work employs a 6 mm thick veneer layer to enhance the post-assembly structural performance. This leads to stiffer elements that require thermal and moisture alteration during the production process to achieve considerable bending.

Moisturizing method

Different moisturizing methods have been compared to tune the flexibility of the zipped layers and prevent cracking during the assembly. An empirical test was performed, where a 6 mm thick 500 mm long LVL element was moisturized with three methods: soaking in water (10 min), steaming (10 min), and soaking and steaming (5 + 5). The elements were tested in a three-point bending with a constant load, where the midspan deflection was measured to compare the flexibility achieved with the three methods. The results highlighted that a combination of soaking and steaming increased the material flexibility more consistently than the other methods.

Curvature radius

The achievable curvature radius of LVL zipped battens have been analyzed after the moisturizing process. Two different veneer thicknesses have been tested, 3 mm and 6 mm, on zipped battens that measured 39 × 95 × 1000 mm. The experiment compared the achievable curvature of zipped specimens with different veneer thicknesses and a constant moisture content MC = 18%. The specimens were elastically bent and the minimum curvature radius was measured from the geometrical construction of the circle tangent to the elastic curve formed by each specimen. The results have been expressed in curvature radius r and bending capacity r/tw, where tw is the total wood thickness (39 mm). The 3 mm veneer achieves a curvature radius of r = 260 mm when bending with zip teeth outwards and r = 280 mm in the opposite direction; the bending to thickness ratio is r/tw = 6.66 in the first case and r/tw = 7.14 in the second one. In the case of the 6 mm veneer the minimum bending radius is r = 435 mm with r/tw = 11.35 with outwards zip teeth and r = 570 mm, with r/tw = 14.61 in the opposite direction of bending (Fig. 4).

Fig. 4
figure 4

Elastic bending test for minimum bending radius on zip-bent battens 39 x 95 x 1000 mm with veneers layers of 3 and 6 mm thick; tw is the wood thickness

Applying the last result, insofar as the most conservative one, to a zip-bent batten made up of two layers - one top and one bottom - the total thickness of the component is tt = 39 + 6 = 45 mm and, therefore, the bending capacity obtained, measured on the minimum curvature radius r = 570 mm, is r/tt = 12.66. In the literature, the value achieved is r/tt = 10 for solid oak wood panels with r = 250 mm, tt = 20 mm and a veneer thickness of 2 mm [7].

Mechanical testing

Determining the basic mechanical properties of the zipped LVL material is fundamental for a comprehensive study on the structural applications of zip-bending. In this work, a simplified test series was conducted, including:

  • Compression test parallel to the fibre direction;

  • A tensile test parallel to the fibre direction;

  • Three-point bending test perpendicular to the fibre direction.

Each test involved at least three specimens of both solid and zipped wood with a cross-section of 39 × 95 mm and 45 × 95 mm respectively. The acquired data is further used to verify and calibrate the Finite Element Method (FEM) simulation in Abaqus.

Compression testing

Four zipped wood specimens and three solid wood specimens with a length of 150 mm were tested. A compression test machine ToniPACT II with a 3000 kN load cell was used. All the experimental specimens were preloaded with 5 MPa pressure. The resultant curves demonstrate that the zipped specimens reached the strength of about 20 MPa, which is roughly half the strength of the solid specimens. In the case of the solid wood test, it is observed that all three specimens have almost the same elastic modulus with a perfectly corresponding linear segment in the stress-strain curve. However, a considerable gap is observed among the specimens in the necking phase, due to the non-uniform distribution of the wood defects within the individual LVL layers (Fig. 5).

Fig. 5
figure 5

Compressive stress-strain curve parallel to the grain

In all the zipped tested specimens, a similar failure mechanism was observed - firstly, the outer layer is damaged, and afterwards, the failure develops towards the inner layers, resulting in their separation and individual bending or breaking (Fig. 6).

Fig. 6
figure 6

Zipped specimen before (A) and after (B) applying compressive loading

Experimental results show that the mechanical behaviour of the zipped elements depends on the type of glue, the quality of glueing application, and the correct curing process. The measured mean compressive strength was 21.03 MPa for the zipped wood specimens and 39.16 MPa for the solid ones, while the measured mean elastic modulus was 0.8 GPa and 6 GPa respectively.

Tensile testing

Four zipped specimens and three solid wood specimens have been tested and compared. Two M16 steel bolts were used to facilitate the clamping of dog-bone specimens in a Zwick/Roell Z1200 testing machine with a 1200 kN load cell (Fig. 7). The measured resistance of the zipped specimens resulted in about 25% of the solid ones, where the mean tensile strength for the solid wood was calculated to be 42.48 MPa and 9.56 MPa for the zipped wood. An elastomer-like behavior is particularly observed in the specimens TZ-P-02 to TZ-P-04, which shows that the glue enters into action earlier than wood. However, wood showed to be dominant and had a higher elastic modulus for the specimen TZ-P-01, but it eventually failed after a slight deformation (Fig. 8).

Fig. 7
figure 7

Tensile zipped specimen under loading

Fig. 8
figure 8

Tensile force-deformation curve parallel to the grain

3-point bending

Three-point bending tests were performed over three zipped wood specimens and three solid wood specimens of 800 mm length, with a span between the supports set to 576 mm. All flexural specimens were tested by a Zwick/Roell Z050 with a 50 kN load cell (Fig. 9).

Fig. 9
figure 9

Flexural zipped specimen under loading

The resulting flexural strength of the zipped wood specimens greatly varies due to inconsistent tolerances between the glued parts. This led to a high instantaneous release of energy during the applied load, where the glue between the zip teeth is immediately damaged and makes the specimen unstable. However, when the glue and wood were tightly bonded, the flexural strength of the zipped specimens reached 50% of the solid ones. To calculate the flexural strength of the zipped beams, the glue strength is neglected and it is assumed that each part of the zipped elements operates separately. Therefore, the flexural strength is calculated elastically using the following equation.

$${\sigma}_{\mathrm{b}}=\left[\mathrm{F}/2\ \left({\mathrm{L}}_0/2\right){\mathrm{y}}_{\mathrm{i}}\right]/{\mathrm{I}}_{\mathrm{i}}$$



applied load of the hydraulic jack


length of the beam span


the distance of farthest edge from the neutral axis


moment of inertia for each zipper at the middle of the span

A flexural strength of around 50 MPa was found in the solid wood tests. Figure 10 shows that when the bottom veneer layers fail because of material inconsistencies, the specimen loses around 50% of its flexural strength.

Fig. 10
figure 10

Bending force-deflection curve (stress direction is parallel to the grain)

Computational programming of zip-bent structures

Geometric form-finding process

In this work, zip-bent structures are geometrically generated through a multi-parameter form-finding process based on a custom Grasshopper and C# script, developed to generate cylindrical developable surfaces [25]. The process inputs are the bending angle, the twisting angle, the total length of the zip-bent element, and the width of the zip-bent element. In particular, a cylindrical stripe of a defined length is divided into a number of linked planar quads that fold around each ruling, forming an angle equal to the bending angle value. This naturally defines the size of the quads and, therefore the distances between the consecutive rulings. The bending radius design space has been previously defined through preliminary bending tests, and within the existing limits, it can be explored to obtain a large variety of shapes (Fig. 11).

Fig. 11
figure 11

Computationally generated cylindrical stripes with varying bending and ruling angle values

The form-finding process outputs two sets of data:

  • Two lists of points - which correspond to the quad’s vertices, sorted to define the start and end points of the surface rulings. By performing the lofting operation from the obtained rulings, the final developable surface is defined.

  • Two lists of planes - namely the surface planes, where the Y-axis is always oriented in the direction of the surface development, and the ruling planes where the X-axis is always oriented along with the ruling. These are stored and used later for the robotic cutting toolpath generation.

Structural simulation

Wood is a non-homogeneous and complex material highly affected by numerous environmental parameters. In construction, this leads to a significant challenge in geometry, cross-section, and wooden structures’ overall mechanical behavior [26]. These complexities need to be considered carefully in the simulation of zip-bent wooden structures.

In terms of elastic engineering models, wood batten is defined as a linear orthotropic and porous material [26,27,28] and it is here modelled as such. The FEM simulation is here used in three steps: (1) for initial analysis and design of experimental specimens; (2) for numerical simulation of final specimens and verification; (3) for a simplified FE model simulation for large-scale structural members. The experimental specimens from all the mechanical tests (compression, tensile, and bending) and cases (solid and zipped) were simulated in parallel.

Static analysis is adopted to simulate and verify the models. The interaction between the two layers is defined as cohesive behaviour with damage capability. Therefore, the layers can be separated after reaching the maximum strength capacity of the glue mid-layer. The simulation of large structural elements adopts simplifications to conduct a time-effective structural study. Hence, the first-order element type C3D8R is chosen [29]. An elastic orthotropic material model is defined using experimental and nominal material data. For this purpose, a local coordinate system is defined for the fibres and transverse directions assignment. Due to the multi-layered nature of the LVL battens, the solid experimental models are simulated in two cases, multi-layer and single-layer. Afterward, the zip-bent models were investigated and verified as well.

Firstly, an initial single-layer model was simulated. Although the model shows the correct elastic behaviour, the deformation distribution is relatively symmetric, differently from the experimental test, affected by non-uniform material imperfections (Fig. 12B). Therefore, the LVL wood compressive specimen is modelled as a multi-layer material to present local deformations (Fig. 12C), and the stress-strain curves state match appropriately as observed in Fig. 12A.

Fig. 12
figure 12

A Stress-strain curve of multi-layer solid specimens showing compressive behaviour of LVL batten material; B Experimental results; C Numerical simulation of multi-layer solid specimen by considering glue effect between layers

Based on these findings, solid LVL and zipped specimens are modelled and analyzed in compression, tension and three-point bending. The following figures (Figs. 13, 14 and 15) demonstrate comparative results of experimental and FEM simulation cases, including the stress-strain curves and failure mechanisms. Overall, the results show sufficient accuracy of the numerical simulation.

Fig. 13
figure 13

Comparative results for zipped model under compressive loading: A Stress-strain curve; B Experimental results; C Simulation results

Fig. 14
figure 14

Comparative results for the zipped model under tensile loading: A Force-displacement curve; B Experimental results; C Simulation results

Fig. 15
figure 15

Verification of simulated model for zipped specimens under 3-point bending conditions: A Force-deflection curve; B Experimental results; C Simulation results

Design and development of zip-bent wood prototype

A demonstrative Zip-bent prototype was designed and developed following an iterative process of geometric form-finding, informed by structural simulation feedback, and realized through robotic fabrication (Fig. 16). The prototype features six zip-bent curved beams that have been designed as cylindrical geodesic stripes with varying bending radii and fabricated from LVL battens. After the form-finding process, the generated zip-bent beams have undergone geometric constructions of a zipping pattern. The zippered stripes are unrolled into flat elements, ready to be robotically fabricated.

Fig. 16
figure 16

Detail of the zip-bent batten prototype

Design for Fabrication

Geometric construction of zipping pattern

Starting from a generated developable surface in a bent state, zipping patterns are generated. Each ruling is offset on its adjacent planar quads, twice on each side at equal distances. The newly constructed lines are then translated along the normal vectors of the planes on which they lie. A zip tooth is created by lofting these four lines with planar segments. The resulting planar surfaces between the zip teeth form the zip pockets. The translation distances of the rulings are defined by the height of the zip teeth, resulting in ht/2 for each direction.


The size of the zip-bent components depends on the fabrication constraints, such as the robot reach and the available cutting area and material size. In this regard, a segmentation strategy has been employed to allow for the construction of structural components which are larger than the original material stock. The top and bottom zipped segments are shifted to provide structural and visual continuity and avoid interrupting the curvature to fit mechanical joints. This means that for each top-side component, there are two bottom-side complementary components. This method allows having an entire zip-bent strip as a single composite piece (Fig. 17).

Fig. 17
figure 17

Segmentation diagram showed on one of the beams from the Zip-bent prototype

Unrolling and nesting

All the designed components are automatically unrolled onto the XY plane and organized into top and the bottom sub-components through a custom algorithm. Since the zip-bent stripes have been developed from cylindrical sections, they can be unrolled into straight wood battens of the corresponding length. Multiple zipped stripes were nested within 3-m long battens to optimize material use and fabrication time.

Robotic simulation and fabrication

Fabrication procedure

The unrolled geometries of the zip-bent elements were robotically fabricated using a KUKA KR240 R3330 industrial robot equipped with a 12 kW rotary spindle, moving along a six meters long linear unit, which allows it to process lengthy wood battens. Two end-effector tools are used, namely, a circular saw blade of 350 mm diameter and 3.5 mm thickness and a 10 mm-diameter flat-end milling bit, to perform linear cutting and milling operations, respectively. A set of welding tables are used as a four-meter long fabrication base to which the wood battens are clamped. The fabrication workflow is summarized in the following steps: (1) fixing a batten to the fabrication plane with the use of standard clamps and screws; (2) outlining the reference paths with the milling tool and indicating slots where to place several custom-made metal clamps that prevent the battens to lift during the machining; (3) cutting the sloped sides of the zipping pattern with the circular saw with (50 mm/s); (4) milling out the pockets of the zipping pattern (100 mm/s) (Fig. 18).

Fig. 18
figure 18

Robotic milling of zip pockets

The two end-effector tools are constantly interchanged during the fabrication process through an automatic tool-change procedure. The cutting feeds and speeds, as well as the tool-change process were iteratively optimized to reduce the total production time. The robotic procedures are run in automatic mode which allows for high-speed motions. An element of 2400 mm is positioned, fixed and processed in a total time of 15 min.

Path planning and simulation

Grasshopper and HAL Robotics Framework plug-in have been used to define the cutting tool path of the robot. Two types of procedures are defined based on the two end-effector tools. Accordingly, two sets of targets are established (Fig. 19).

Fig. 19
figure 19

Robotic simulation and path planning of the zipped battens (cutting + milling)

Saw-cutting targets

The unrolled battens’ geometry is used to define the robot targets for the saw-cutting procedure. The sloped faces of a zipped Brep geometry are extracted and used to generate robot target planes. A new plane is constructed for each surface using the normal vector to the specific surface and the ruling line that corresponds to the surface bottom edge (Fig. 20). These two axes provide enough information to assure that the tool is oriented correctly while cutting. These defined planes are then offset in multiple directions to account for the blade thickness - in the direction perpendicular to the cut, blade radius - along the direction of the cut and travel moves - at the safe Z-axis offset between the cuts. The speed for the travel moves is 400 mm/s.

Fig. 20
figure 20

Multi-TCP scheme showing three different TCPs and the construction of their corresponding targets

Milling targets

Milling targets are defined starting from the zip-pockets planes. The width of each pocket is evaluated and used to parametrically define the number of tool passes, considering one-third of the tool diameter as the target “overstep” dimension. Similar to the saw-cutting procedure, cut and travel moves are distinguished and assigned different speeds.

Multi-TCP planning

The Tool Center Points (TCPs) are defined to make the multi-tool path planning feasible. Two TCPs are set at the perimeter of the circular saw to allow for different tool orientations. In particular, two sets of cuts are defined to approach and cut the material with a clockwise saw rotation. When the angle between the vertical axis and the inclined zip face is acute, the TCP1 is used and the robot approaches the cutting path from its closest point on each cutting curve, outwards (Fig. 20A). On the other hand, when the angle is obtuse, the TCP2 is used and the robot approaches the cutting path from outside in (Fig. 20B). In this way, safe robot joint positions are assured. In the cutting procedure, firstly the cuts with TCP1 are made, followed by a safe reorient move during which the TCP is relocated, and lastly, the other cuts are executed. The third TCP is set at the tip of the flat end-mill (Fig. 20C). After the tool-change is performed, the TCP is reassigned and the corresponding fabrication step is performed. All the procedures are simulated in Grasshopper to ensure the codes are collision-free before they are compiled and transferred to the robot.

Assembly process

The previously described moisturizing method was used to increase the elasticity of the zipped wood elements before the assembly and gluing. The first phase is soaking, performed by simply bathing the wood elements in a customized tank filled with water for 10 min. The second phase involves the steaming of battens within a custom-built chamber consisting of a sealed 2500 mm long steel pipe with a 220 mm diameter, insulated with a 100 mm thick layer of rock wool, wrapped within a PVC cloth. The steam is introduced into the chamber through a hose connected to a commercially available machine. The inner temperature of the chamber is measured through a thermometer placed at the output end. When the temperature of 100° is reached, the battens are inserted and kept in the steam for 20 min. This process increases the material’s flexibility and allows zipped battens with top and bottom veneer thickness of 6 mm to reach the desired bending position without material spring-back and residual tension in the final system. After the desired moisture content is reached through moisturizing, the components are bent and manually assembled. Firstly, the wood glue is applied to the two complementary zipped sub-components, after which the zip-bending process is initiated by inserting the zip teeth one by one into each other. The zipped element starts to bend and twist towards the intended form by intuitively following the geometry (Fig. 21).

Fig. 21
figure 21

Assembly process of a zip-bent element

Experimental construction outcome

A full-scale demonstrator made of 72 m of zip-bent structural elements was installed in the courtyard of the University of Southern Denmark (SDU) (Fig. 22). A composition of six interconnected zip-bent LVL elements was installed in an open area, exposed to weathering and to human interaction for a period of four months. A total of 42 zipped parts, fabricated from 25 LVL battens, were assembled to form zip-bent geometries of varying lengths from 5 to 7 m, with bending radii varying from 676 mm to 927 mm. Production waste consisting of wood chips and dust was collected for upcycling experiments into a new product.

Fig. 22
figure 22

Zip-bent prototype installed at the University of Southern Denmark

For the design and structural evaluation of this full structure, the layer-by-layer FEM was replaced with a simplified homogenized model that includes the zipped mechanical properties as previously tested and simulated, to increase the computing time efficiency while obtaining a sufficient understanding of the structural performance of a large-scale structure. In fact, the interaction between LVL layers and the zipped geometry would involve a large number of interactions, which is here replaced by a homogenization of the effect of zipping and glueing on the six zip-bent beams. The considered loading condition of the prototype is the self-weight, and it is assumed that all members can move in their normal direction to the cross-section at the end of both sides of the members. The simulation result has been compared to the prototype in which permanent deformation has been observed (Fig. 23). As expected from real-life installation, rather large deformation of the zipped battens in relation to their dimensions is reached due to limited restraining in the degrees of freedom. However, if the existing supports are defined as fixed, the resulting structural deformation is reduced by 80%. Figure 24 shows the orientation of defined orthotropic material for simulation in the deformed case.

Fig. 23
figure 23

Magnitude of total displacement for the structural members

Fig. 24
figure 24

Material orientation of deformed shape (black arrows: normal vector to cross-section, pink arrows: transverse direction 1, green arrows: transverse direction 2

Looking at the built demonstrative prototype, after it has been installed outdoors for four months, the zipped material can constitutively be considered as linear elastic since no damage and breakage was observed. No effect of environmental and weathering conditions was observable on the built prototype.

3D scanning and accuracy check

The zip-bent arches have been 3D scanned and compared to their digital counterparts, where a maximum deviation of 397 mm is observed (Fig. 25). By combining quantitative analysis and direct observations are identified the key factors that influence such discrepancy: (1) fabrication tolerances in this work were set to nearly zero, with the zip teeth fitting tightly together in the straight form. However, material imprecisions prevent the elements from fully achieving their target position once the elements are bent and twisted. This is particularly true when the curvature is higher. (2) The connection interface between sub-components causes structural discontinuities, where the elements are prone to high deformation. Since the connection is parallel to the rulings and therefore the zipping pattern, these points behave as kinks, and the zip-bent components form curvature discontinuities. (3) The absence of visual reference for a target shape during the assembly process leaves some space for geometrical imprecisions due to the accumulation of tolerances, human imprecision, and material spring back over lengthy element.

Fig. 25
figure 25

Comparison between the digital models (white) and the 3D scanned arches

Conclusions and future work

The integrative design-to-fabrication framework for programmed zip-bending enables the use of curved LVL timber battens as structural elements with complex geometries. The programmed zip-bending patterns applied to developable surfaces allow for the realization of novel lightweight wood structures, which rely on simplified hardware assembly. Compared to conventional wood-bending methods such as glue lamination, only minor hardware is required after robotic processing in this construction process. Along with an in-depth description of the procedures involved, from design to robotic fabrication, this article documents for the first time: (1) the viability of zip-bending for structural applications if appropriately sized; (2) an initial comparison of the expected mechanical properties in zipped elements compared to solid wood; (3) the identification of the failure modes for tensile, compression and bending load tests in zipped LVL elements through physical testing and FE simulation; (4) the development of two FE simulation strategies for both localized and global-scale studies. The authors believe that confirming the structural viability of the technique is a milestone to further pushing developments in construction. Zip-bending indeed promises new applications for curved LVL battens to realize slender twisting columns, complex gridshells, and curved wood beams, as an alternative to less sustainable and more energy-consuming solutions. Moreover, it opens up new possibilities for the design and construction of free-form wood architecture and a shift from straight timber elements.

Future work shall consolidate the structural understanding of such structures and address the existing geometrical imprecisions. To solve this, the insertion of strategically oriented dowel elements between the two zip-bent layers will be studied in future works, along with Augmented Reality (AR) devices to provide real-time positional feedback during the consolidation of the two layers. Fabrication tolerances will also be studied more closely through simulation to identify the distribution of tolerances depending on the curvature development. A deeper investigation of the joint solutions is required for long elements to obtain a seamless structural and geometrical behaviour. Taking advantage of the large versatility of robotic fabrication, the zip-bending technique will be extended beyond the use of straight wood battens, moving towards curved surface elements obtained from planar boards. This will enable the construction of larger components with varying width and the investigation of poly-cylindrical and poly-conical geometries, which exceed the available design space for straight battens.


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This research has been partly conducted within the “Experimental Architecture X Robotic Timber Fabrication” at SDU Summer School 2021.

Organized by SDU.CREATE Group - Led by Assoc. Prof. Dr. Roberto Naboni.

University of Southern Denmark (SDU), Section for Civil and Architectural Engineering (CAE).

Teaching team: Roberto Naboni, Anja Kunic, Luca Breseghello, Dario Marino, Alessandro Zomparelli, Sandro Sanin, Riccardo La Magna.

Material Partner: Stora Enso.

Students: Aina Radovan, Andreas Nicolai Nielsen, Andrew Smith, Angelina Garipova, Anne Katrine Beyer, Asger Gehrt Pedersen, Aske Skovrup Kiehn, Averina Ayshia Annisa, Cyril Novotný, Guijia Zhao, Ilya Lebedev, Jonathan Vestergaard Nielsen, Juraj Stetiar, Mathilde Lykke Eriksen, Maxime Fouillat, Robin Petersen, Veranika Sidorka, Vojtech Vrtal, Xan Browne.

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Naboni, R., Kunic, A., Marino, D. et al. Robotic zip-bending of wood structures with programmable curvature. Archit. Struct. Constr. 2, 63–82 (2022).

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  • Zip-bending
  • Robotic fabrication
  • Finite element method
  • Wood structures
  • Programmed curvature