Introduction

There is currently growing attention toward using wood in the building industry. This derives to a large extent from wood’s ability for carbon sequestration. The development of engineered wood products (EWP) suggests alternatives to the more established construction methods, even for high-rise buildings [1, 2]. When harvesting the wood and using buildings as a carbon sink, the forest areas can be regenerated and continue to absorb CO2 from the atmosphere [3]. Furthermore, the wood used for construction replaces more CO2-emitting production methods, such as the ones related to concrete and steel. The timber industry that delivers wood construction products is characterised by high-level technology and extreme efficiency. As a result of this optimisation and the demands for certification of building components, the variety of available products is limited. To support prefab and montage construction principles, delivering standard-size building components, such as CLT and LVL panels, is necessary. These products are based on equal-sized straight boards or veneer sheets produced from trees that are as straight and homogeneous as possible.

Beyond the problem of increasing CO2 levels, the global society is facing a biodiversity crisis. Human behaviour changes ecosystems and the plantation forests used to produce wood products are characterised by monoculture and low biodiversity [4]. The current methods for timber production are even degrading the forests [5]. Upscaling the use of wood in buildings to reduce CO2 emissions could reduce biodiversity, especially if wild forests are replaced with production forests. This paper presents a more extensive array of wood species and tree parts to make a forest characterised by diversity relevant for production and use in architecture. In other words, we suggest that biodiversity and production forest do not necessarily need to be two opposing solutions. Instead, a more complex combination of tree species could be planted, providing an ecosystem for a much larger variety of other plants and animals than in the typical production forest. We present here a workflow that integrates the inherent properties of naturally shaped irregular oak wood with an expressive architectural design to bring attention to the diversity of natural wood.

We use computational methods to establish an integrated workflow where the intermediate step of standardisation can be bypassed to broaden the range of available wood materials and make a closer connection between material and design. At the same time, the method suggests that novel design-to-production approaches can support higher diversity in forestry.

The overall concept and the initial stages of parts of the method have been discussed in previous publications [6, 7]. In this article, the theoretical and historical context for the proposed workflows is further explained, and the method is laid out as a whole. The article shows the results of a series of destructive testing of joint specimens and discusses the structural implications of the proposed construction principle. Furthermore, it shows a larger prototype, where the system is tested by fabricating and assembling 15 components. The prototype demonstrates the method’s viability and indicates how the principle could be implemented at the building scale.

Research and technological developments in wood manufacturing

This research project is inspired by visits to the Finnish timber industry, where we have established that sawmills and manufacturing companies use advanced digital technologies. Both exterior and interior laser scanning at the sawmills are integrated while harvesting the logs, sorting them when they enter the sawmill, positioning them for cutting and quality control. EWP manufacturers use scanning technology and automated workflows for fabricating LVL and CLT products, and building parts manufacturers are highly based on CNC technology. The research presented here uses technologies present in the wood industry. Following the growing interest in using wood in architecture, many research and experimental projects have emerged in recent years. The development of scanning technology and robot technology has led to new wood-based methods. For example, Helen & Hard Architects have used CNC fabrication and 3D scanning for realising the Ratatosk Pavillon [8]. The approach to using natural tree forms suggested here is in line with projects by Design & Make at Architectural Association’s Hooke Park. For instance, the Wood Chip Barn, where Y-shaped tree trunks are used directly in construction. However, we have set out to develop a method that is more generalised regarding what tree parts can be used and, at the same time, more specific when designing, manufacturing and assembling the components. The construction principle used for demonstrating the workflow is a so-called Zollinger (or lamella) roof, where a large span can be achieved with more minor elements. The principle is well-known and used in various projects related to mass customisation and automated fabrication workflows, such as the Generated Lamella [9]. These projects use standard timber profiles rather than naturally curved wood, as proposed here.

The origin and properties of wood

The properties of a piece of wood result from several factors that impact how the material can be processed, treated and used in construction. Every wood cell reflects the DNA and the life of the tree from where the wood originates, and the state of the material is furthermore affected to a high degree by the way it has been stored and dried after it has been harvested [10]. The long history of using wood has led to general ways of dedicating certain wood species and tree parts for different purposes. Typically, the bottom of the tree trunk is used for planks, cut in sizes that correspond with building standards. For wood floors, an example of a more exclusive product, often the midsection of the tree is used. The branches and the tree crown consist of more irregular pieces and are typically used as firewood. Some conifer species, such as spruce and pine, are characterised by fast growth and long straight tree trunks, making them optimal for construction. Other species, typically deciduous, like oak or ash, grow naturally in a more irregular shape and produce curved tree parts to a larger extent. The inner structure of trees generally reflects the seasons, and it is possible to detect an outer layer of sapwood and an inner core of heartwood. Depending on species, age of the tree and climatic conditions, the fibres of the growing layer of the tree will have a particular direction, spiralling upwards. The microscopic cell structure of different species and tree parts leads to significant variation in properties, such as strength, elasticity, resistance against fungi growth and water. One of the research ambitions is to reinstate a closer connection between the properties of the naturally grown wood, its manufacturing and its use.

Traditional woodcraft

In traditional woodcraft, there was a deeper understanding of wood properties and how to make the best use of different wood types compared to the modern building industry. Therefore, the research is inspired by traditional wood joinery [11] and shipbuilding [12], as well as historical vernacular construction types. Oakwood is strong and resistant and the Vikings’ preferred material for shipbuilding. The Vikings understood wood capacities deeply and chose to cleave the wood to produce boards with little broken fibres even though the saw was invented. [13]. This was done with a mirror cleaving technique – the method results in boards with high strength and less tendency to break [13]. The shipbuilding crafts were also present in the building types used by the Vikings. As with the ships, they selected specific curved wood parts to fit in certain places of the construction [13]. The approach developed into a general method for sourcing materials for the shipbuilding [14, 15]. In historical building culture, we see curved wood parts appear in many different types. Sometimes because they provide a certain strength or spatial advantage, this is, for example, the case in the cruck frame barns in England, where a curved trunk is divided into two halves and forms a mirrored section that curves out on both sides of the room, making it more spacious than if made with straight timber [16]. In other building types, the curved wood appears more like a less perfect material that is embedded in the construction in a way where its irregularity is embraced and placed where it can function as well as a straight part. In extreme versions, this can be found in Danish tobacco barns, for instance at Fredericia Museum, as shown in Fig. 1. A more typical example is many traditional timber frame buildings, where often curved timber is embedded in the construction, as shown in Fig. 2.

Fig. 1
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The tobacco barn at Fredericia Museum. The presumably cheaper curved tree trunks are incorporated as replacements for straight timber [Photo: Niels Nygaard.]

Fig. 2
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In traditional timber frame buildings, curved timber was incorporated in the construction in many cases. The photo shows a historical Danish farm building at Hjerl Hede Museum. [Photo: Niels Nygaard.]

An inspiring aspect of the timber frame typology is modularity. Half-timbered houses have been built in Denmark since the sixteenth century as a modular system where it was easy to expand the building without changing the house’s general appearance. The modular system was connected using timber joints, which enabled the residents to move partitions and insert or remove doors and windows, thereby modifying their environment. There are even several cases where whole houses have been disassembled and moved to another location as part of the agricultural reforms in the eighteenth century. [17]

Digital technologies for analysis of wood properties

To understand the state-of-the-art in the wood industry, Anders Kruse Aagaard and Niels Martin Larsen went on a research trip to Finland in 2018. The complete wood supply chain was studied, from harvesting through sorting and cutting at the sawmill, fabrication of LVL and CLT and production of various building components, such as CNC-controlled processing of wall panels and construction of room-size modules for high-rise housing. The many companies were generally extraordinarily open and willing to share their knowledge and interest on all levels, from economy to technical details. It was apparent that the key to the industry’s success was the close collaboration between the different actors. The supply chain handles a large volume with relatively low profit, paying close attention to optimisation. Every slight improvement can have a significant impact on the companies’ revenues. On the other hand, this also means that there is a growing interest in finding product niches and manufacturing wood products that are more refined than is the case with most of the wood that is exported from Finland.

Even the controlled plantation forestry produces trees with a high degree of variation in both shape, composition and quality of the individual tree parts. This has led to advanced digital technologies for inspecting and controlling the wood throughout the production chain. In modern forestry, each tree is mapped and measured and then followed with digital technology throughout the production chain at the sawmill. For instance, photogrammetry is used for registering the species, current size and position of every tree in a forest area. This can be used to determine the total value of the available wood material. The harvesting machines automatically register the diameter of the tree trunks and match these with the database of dimensions needed for the production at the sawmill. This makes it possible to automatically adjust the sawlogs’ precise length in real-time at the spot during harvesting. See Fig. 3.

Fig. 3
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Clear-cutting in a Finnish forest with instant storage update

When the sawlogs arrive at a modern sawmill, they are evaluated and graded automatically. This happens with multi-sided X-ray scanning that creates a three-dimensional representation of the log’s exterior shape and interior composition. See Fig. 4. The logs are sorted to fit best with optimised saw patterns, which later happen in batches so that several logs can be cut up in the same pattern. The analysis, which takes place in a second, includes information on the log’s diameter, dimensions, internal cracks, curviness, knots and foreign objects, like screws and stones. The evaluation takes up to 400 parameters into account to define the following use of the log. The logs that have not been discarded for their irregularity and crookedness already in the forest are detected and discarded and sent to be used for paper production or combustion.

Fig. 4
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Each log is X-ray scanned to construct a three-dimensional model of its interior when entering the sawmill. The analyses of the log models decide the sorting of the logs

In the fabrication workflow, other scanning methods are used for quality control and steering the processing of the wood, for instance, to mitigate minor deviations when boards are cut. A certain degree of skewness is accepted for some product categories, and this allows optimised use of the log volume. Another example is seen in the production lines for laminated veneer lumber (LVL), where surface scanning and immediate computational analysis of every veneer layer and subsequent mixing of veneer from multiple trees ensure consistency of the final product. See Fig. 5.

Fig. 5
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In LVL production, the veneers are automatically graded with computational analysis of photo-based registration

The wood industry has reached a high technological level. It is optimised for manufacturing standardised products, which again feeds into the efficiency required by the building industry that is increasingly dominated by modular construction systems. The basis for these systems is entirely homogeneous products, such as equal-sized boards, certified timber and EWPs of specific dimensions. The basis for these products comes from the controlled plantation forest and automated production workflows. While these optimised production lines enable the wood to compete economically against other less climate-friendly construction materials, the resulting plantation forest characterised by monoculture has a negative impact on biodiversity [4] and a degrading effect on the forests [5]. Another criticism could be pointed toward the fact that the series of laminated, composite and half-way artificial EWPs deprives the wood of some of its inherent properties, such as fibrous strength or natural shape, and then reinstate these in a more controlled way through extensive use of adhesives, making the material less sustainable and much more difficult to recycle. It should be acknowledged that these EWPs, such as CLT panels, are helping to promote the use of wood in the building industry and provide a clear alternative to concrete panels [2, 18]; however, this way of employing wood seems to overlook its natural properties. The natural strength of wood is already mentioned, and when the wood fibres are generated, they organise into optimised layers as a result of the growth pattern and the changing climatic conditions. Some of these embedded qualities are lost when reconfiguring the wood into laminated products through cutting, slicing, unrolling and glueing.

As mentioned above, the wood industry uses a large spectrum of advanced computational technologies to maintain highly optimised workflows. Similar technologies have been adopted and explored in various experimental architectural projects and architectural research laboratories, but with other aims than mere optimisation. Here, the focus is more on exploring new adaptable design-to-fabrication workflows that allow for a significant degree of variation in the architectural expression and are open to developing new construction types. [19,20,21]. We seek to demonstrate with the following workflow that there might be possibilities for making better use of the capacities found in natural wood by employing technologies that are already present in today’s modern sawmills and manufacturing companies.

Experimental workflow development

The research trip to Finland that gave insight into some of the various technologies used for scanning and analysing wood motivated a series of lab-based experiments with irregular wood logs. The idea is to use technologies parallel to those found in the timber industry but to develop methods that focus much more on the inherent properties of the specific wood piece and establish a design-to-production workflow where physical material and digital modelling are interlinked.

The immediate problem that arises from working with irregular materials is how to match the complex shape of the raw material with the instructions for fabrication. In other words, how to define the outer shape of a sawlog and manage its position in space. For a typical fabrication setup, for instance, when CNC-milling a construction part from a block of wood, the definition of the material is straightforward and often repetitive. Just the three dimensions of the block and a single point defining its position in the machine are needed. When using an irregular piece of wood, a whole range of complex information is required. The first challenge is obtaining a digital representation of the sawlog that can be used as the basis for matching the sawlog with a specific component design, positioning it during fabrication, and generating the machining toolpaths.

We explored various 3D scanning methods for producing point clouds representing the outer shape of the logs. See Fig. 6. A Faro Focus scanner on a tripod allowed scanning of several logs simultaneously. A Faro Arm made it possible to make a scan with high precision but without the colours. A hand-held Faro Freestyle 2 scanner provided the most efficient scanning workflow. None of these methods is nearly as efficient as the scanning technology used at the sawmills, but they, to some degree, simulate an industrial approach.

Fig. 6
figure 6

Top: A Faro Focus Lidar scanner was used for scanning multiple logs. Bottom: A Faro Arm metrology scanner was used for high-precision capturing of a single log

The point cloud of a log is data-wise heavy and difficult to engage directly in a digital workflow, so it must be translated into some form of rationalised geometry. Software for working with point clouds can be used for creating mesh geometry from the point clouds. Still, we were interested in a representation with NURBS geometry, both to have as lightweight data as possible and ensure that all sawlog geometries were constructed in the same way.

Once we had the digital representation in place, we could start to test ways of processing the sawlogs that reflected their initial shapes. We fabricated a sample where a CNC machine would follow lines on the log’s surface, similar to isocurves in a 3D modelling environment. This would be relatively simple when using a hand-held milling tool but a complex problem for automated fabrication. A similar experiment was done, where layers of the sawlog were removed. Some of the experiments used a bandsaw mounted on a robotic arm. This made it possible to produce curved boards that correspond with the curvature of the log. In this way, the fibres were kept intact, so the boards maintained their strength. See Fig. 7. This series of experiments formed the basis for imagining a complete workflow using curved sawlogs.

Fig. 7
figure 7

Top: A grid pattern is applied to the surface of a log with automated processing. Mid: An automated removal of material in specific depths corresponds to the log’s initial surface. Bottom: A bandsaw end-effector on a robot arm was used for slicing a log into boards following the curved shape of the log

A workflow for using curved natural wood

Early on in the experimentation, a partnership with a local sawmill was established. It turned out that the company had a pile of sawlogs of various species that were too irregular for production at the sawmill. The sawlogs were at best sold as firewood. A large part was oak wood, which usually has a high value. Due to oak wood’s typical irregularity, only 40% of the wood volume appears in the timber products. Up to the nineteenth century, oak was a widely used building material in Denmark, not least for its resilience to the climate with long cold periods of high humidity. Today, oak is mainly used for furniture and floorboards. With access to a cheap resource of irregular sawlogs, it is worth exploring the possibility of using the material in constructions while considering the various curvatures of the logs. One approach could be to integrate irregular wood parts in buildings where some elements do not necessarily need to be straight. The concept shown here is directed towards timber structures intended to be characterised by curvature. By considering the irregularities of the sawlogs as the basis for the design of the construction, it would be possible to make expressive curved constructions without having to slice standard timber into thin layers and turn them into glulam beams. Instead, such a construction could be based on the curvatures already present in natural wood. The concept is shown in Fig. 8.

Fig. 8
figure 8

The diagram shows the general concept of matching curved logs with curvature in the structure. The green and red curves indicate adjustments in the design to match the available sawlogs

As a basis for making a fabrication workflow with curved sawlogs, we imagine a database with information on many available sawlogs. A dataset for each log is already produced at the modern sawmills, but here they are used for specific operations leading to the production of straight cut timber. When the construction is designed, a 3D model is compared with the logs available in the database. A series of success criteria could then inform an adjustment of the design, manually or automatically, to fit with the available material. These criteria could, for instance, be a deviation in shape or location, price and quality of the sawlogs. The precise data on each log and building component could then be combined into an automated fabrication workflow for making the different building parts consisting of natural wood with various curvatures. Figure 9 is shown a diagram of the complete workflow, which, if it turns out to be relevant on a larger scope, could support forestry with a much higher diversity of species and tree shapes than in the typical plantation forest. In the following, the individual steps of the workflows are explained.

Fig. 9
figure 9

The diagram shows the complete workflow where first irregular logs are detected, scanned, and saved in a database. The structure design directs the assignment of the logs that are subsequently processed into specific components in a robotic fabrication facility

We gradually implemented different parts of a possible workflow by experimenting with technology and material. We chose to develop a system that could be used for constructing a lamella roof, also known as a Zollinger system. This choice came mainly because it enables a large span to be made of small beams, which we could handle in our lab facilities. Also, the principle is often related to construction with curvature. We also were interested in minimising the use of steel connectors, and this pointed towards timber joints found in traditional timber frame constructions.

The complete design-to-production workflow comprises connected manoeuvres where digital information is crucial for binding the different parts together. Firstly, the database of sawlogs needs to be established. We picked up several irregular oak logs at a local sawmill, as shown in Fig. 10. The sawlogs were debarked manually, as seen in Fig. 11. This usually is an automated process at the sawmill, even for relatively curved logs. We used a hand-held laser scanner to obtain point clouds for each sawlog. Some time is necessary to clean the point cloud in the scanning software. This is easier handled automatically at the sawmill, where the logs are placed in a well-defined chamber during the scanning that only takes a second. Every log is marked with red dots that can later be used for positioning. See Fig. 12.

Fig. 10
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A pile of irregular logs is collected at the sawmill

Fig. 11
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The logs are debarked manually before the scanning

Fig. 12
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A hand-held scanner is used for digitising the logs for the database

Establishing the digital model

A customised Grasshopper/Python script running in the 3D modelling software Rhinoceros was developed for translating the point clouds into more well-defined and lightweight geometry. The script makes use of the Volvox plugin for Grasshopper. A significant problem is defining the centre curve of the sawlogs since it is the basis for the later matching with the component design. For solving this, the end planes are first found from marks on the log. Alternatively, this could be done with a RANSAC algorithm [22]. (Fig. 13A). The two planes are connected with a straight line that guides the first sequence of extracting parallel cross-sections from the point cloud (Fig. 13B). The centroid of each cross-section is found to ensure that the preliminary centre points lie inside the log volume. A set of radial lines is defined for each of the centroids. The points in the point cloud closest to these radial lines are then used to determine the section curves (Fig. 13C). These section curves can then be used for reconstructing the centre curve more precisely. (Fig. 13D) And because the radial lines are ordered in the same way, it is possible to use the new section curves for defining the outer shape of the log as NURBS geometry (Fig. 13E). Together with the points for positioning, the centre line and the NURBS surface form the information initially linked to each sawlog in the database. Rhinoceros was used as the general environment for handling the data. We used the Elefront plugin for Grasshopper to transfer object-related information from the overall design model to the individual files for the fabrication of each component.

Fig. 13
figure 13

A) Point Cloud of a log. B) Vertical sections orthogonal to the straight line. C) Centroid points for each section. D) New section rings are constructed and used for defining the log’s centre curve. E) The section curves are the basis for a NURBS surface representation of the log volume

Design of the construction with the available logs

At this stage, a digital model of each log is available. Here begins the design process that includes information on the available material. We have worked with subdivision of a surface as input for the design since this is a typical approach to this type of parametric design. As mentioned earlier, we have worked with a lamella roof principle. We subdivided the isocurves to define each curve segment as the centre curve of each member of the reticulated structure. We developed a search algorithm that compares each member’s centre curve with the centre curves found in the database. With a resolution of 50 mm in length and 5 degrees rotation, every possible position of the member inside the log is tested. The sawlog with the smallest deviation is then assigned to the member. Figure 14 shows how a sawlog has been assigned to a specific member. Here we could presume that all logs had the necessary dimension in cross-section, but a generalised solution should address changes in each sawlog’s radius. Eventually, the search could take several parameters into account, such as how much excess material is lost, the humidity of the wood, its location (distance to storage and grouping of logs), and the wood’s quality. Considering a situation with a limited number of logs available and various parameters that need to be weighted, the search quickly becomes a complex problem that has not been pursued in depth in this research.

Fig. 14
figure 14

The algorithm searches the database to find the best match for each beam centre curve

Geometric detailing

As for similar constructions designed parametrically, the underlying model allows all geometric information needed for fabrication to be extracted. For each member, the outer shape of the beam is defined and combined with information about the connected beams, the geometries of the joints can be defined. What is unique in this workflow is that we allow the original centre curve of the sawlog to define the profile of the beams. This helps to ensure that sufficient width of the beams is maintained, but it also means that we can avoid weakening of the material, which would happen if many of its fibres are cut. [23]. The oak logs have a sapwood layer of 2–4 cm thickness that will deteriorate over time and cannot be considered structurally. The sapwood is largely removed when shaping the beams into partly rectangular sections. With attention to the assembly process, an adjustment of the centre curve is needed to make the beams orthogonal to each other where they meet in the joints when seen as projected on the control surface. The joints are defined as a standard orthogonal geometry applied to each beam according to their relative position on the control surface. The bottom surface of the beams is made as an offset surface of the overall control surface, which gives a visually smooth transition between the beams. The top is left unaltered, meaning that the original shape of the sawlog remains intact on the outside of the construction. We imagine that this side would be cladded when used as a climate screen. The complete set of beam surfaces and joint index is saved with each beam to be able to process them individually.

Processing the logs

As mentioned earlier, an industrialised version of the workflow would use a series of processing methods, such as a CNC-controlled bandsaw for processing the sides of the beams and milling for making the joint details. In the industry, multiple combinations of different machining types are used. In our lab facility, it turned out to be most efficient to do all the processing with a CNC-milling end-effector mounted on a six-axis robot arm. For machining the beams, a set of toolpaths needs to be generated. Working with a base material with an irregular shape, such as a curved sawlog, demands additional steps than working with standard box dimensions. The most straightforward approach would be defining a bounding box and gradually removing layers of material until the component's outer shape emerges. This would be unnecessarily slow since much of the milling would happen outside the sawlog. Instead, we use the known geometry of the sawlog and subtract the individual cut surfaces of the beam. Each of these operations results in a slice that is partly defined by the shape of the sawlog and partly by the geometry of the beam. This slice can then be sliced into thinner layers corresponding with the depth that can be milled away for each milling step. See Fig. 15.

Fig. 15
figure 15

A) Alightweight NURBS surface representation of a log. B) Cut surface for one side of the beam C) subdivision of the removed log part into layers. D) Milling pattern that corresponds with the volume of the log

To get the sawlog’s precise position in the robot cell, the marked dots on the sawlog are detected using the real-time tracking system OptiTrack. The system is based on camera calibration and makes it possible to translate the point positions through the Motive software to Grasshopper in Rhinoceros. The located points can then be used for placing the beam geometry with the toolpaths for processing correctly according to the coordinate system of the robot arm (Fig. 16). A rotary table integrated into data handling for the robotic fabrication makes it possible to reach all parts of the sawlog without repositioning the log. The joints in this particular workflow are made as mortice and tenon connections, as seen on an early prototype shown in Fig. 21. Through discussions with the specialist in traditional craft Nikolaj Kirk at Hjerl Hede Museum, a joint more similar to those seen in traditional Danish timber frame buildings emerged – as seen in Fig. 22. When considering using the system on a building scale, we found it difficult to find proper documentation of the strength of such wood connections, in particular when considering it as implemented in the form of a lamella roof structure rather than as in traditional buildings where the walls are filled with bricks providing stability. This led us to carry out experimental testing of the joint to get an indication of the viability of the construction principle.

Fig. 16
figure 16

An OptiTrack motion tracking system is used to locate the marked dots on the log’s surface. These are then used for matching the position and orientation of the log with the coordinate system of the robot arm

Structural implications of curved timber

The system shown is intended for curved construction such as gridshells. The standard procedure dictates that the grid elements are discretised into linear members on the freeform surface. This simplification will increase bending stresses as the truss elements deviate from the ideal, sometimes funicular freeform surface. Using naturally curved members and fitting them into the target gridshell alleviates this issue and increases the structural capacity from a global perspective. From a more local perspective, this methodology also enables more effective use of the wood log’s cross-section as it does not have to be cut into a standardised linear shape. However, some loss of excess wood is inevitable. The outer sapling layer has not yet hardened and cannot be included in the structural calculations. Without detailed MRI scanners, the milling algorithm must use an approximate depth with a safety margin to remove this layer. This procedure results in complex geometry, which must be considered in structural calculations. However, because a digital model of the log is available, the varying cross-sections can be calculated using computational methods. The digital log can be discretised into smaller segments and inserted into a global FE-model with the correct corresponding cross-sections.

Structural performance of the joints

The structural concept is developed with a top-down approach, where the joints are designed to fit the requirements of a given global structure. The global topology pattern is based on a reciprocal logic, similar to Zollinger roof structures [24] and the ceiling systems developed by Serlio. The latter’s performance is discussed, for example, in [25]. The motivation behind the development of these systems was to enable larger span structures with elements of limited length.

The Zollinger principle was chosen as the global topology pattern with elements that interlock with an almost 90-degree angle. These angles were chosen because of practical considerations regarding the manufacturing process and the assembly. However, the orthogonal angles in the structure also create some issues, as the structure cannot break down the affecting forces into normal forces. Instead, it has to carry the forces as bending moments. This is the same problem as seen in frame structures.

Consequently, the joints have to be designed with a rotational capacity to ensure the stability of the structure. The chosen connection design can be described as a pocketed mortise-tenon joint with two dowels that lock the elements together. This creates a rather rigid joint, as the dowels and contact area can be used to absorb forces that arise from rotational- and shear forces. Figure 17 illustrates the geometrical principle of the joint.

Fig. 17
figure 17

Illustration of principal forces in the joint, using local coordinate axes as a reference

The strength of the joint typology was investigated through experimental testing. As there were only a limited number of specimens available for testing, it was decided to focus on the most dominant section forces expected to occur in the joint. These forces include tension, bending around the y- and z-axis, and shear forces in the z- and y-direction, as illustrated in Fig. 17. Compression is not included as the effect of this force can be easily calculated by comparing the force pressure with the compression capacity perpendicular to the grain direction of the specified type of wood. Furthermore, if the compression force only transfers through the dowel, the capacity is equal to the tension capacity. Torsion is not examined as it is not expected to be a dominant force in the structures. The experimental examinations are carried out four times for each of the five test setups. This number of tests is far too small to draw any statistical conclusions on the capacity. There are also several other uncertainties to consider, such as material homogeneity, moisture content, splits and other defects. However, the tests do provide an indication of the structural validity of the joint typology and information on the mechanical behaviour of the joint. This data can then be used to examine why a specific failure mechanism occurred and how to possible reinforce the joint. The experimental setups are illustrated in Fig. 18 with an image of the corresponding failure mechanism and data on the average failure load.

Fig. 18
figure 18

Illustration of the typical failure mechanism in each test setup. Fmax is the maximum force measured in kN or kNm just before failure occurs. Fmin is the minimum achieved value, and Favr is the average value

The analytical calculations predicted that the failure mechanism in all test subjects would manifest either as a shear failure in the dowel or as a splitting failure from forces acting perpendicular to the grain direction. This is also evident in Fig. 18. The numeric distribution of the test results is relatively large, which is typical for solid wood elements, as the homogeneity of the material varies far more than in glue-laminated timber and other engineered wood products. The average maximum capacity does indicate that the joint type performs structurally well, as the joint can transfer a significant amount of load—the exception though being examination 4A: bending around the z-axis. A possible way to improve the performance of this load case could be to move the dowels in to increase the thickness of the part of the beam that is sensible to splitting failure.

Prototypes in workflow development

The proposed workflow has been developed by producing a series of prototypes. The 1:1 testing gave indispensable knowledge on the oak logs’ fabrication constraints and material behaviour. Besides the CMS Antares machine used for the initial experiments, we tested end-effectors mounted on a six-axis robot arm, such as a chainsaw, bandsaw and spindle. See Fig. 19 and Fig. 20. The bandsaw corresponds directly to the way timber is manufactured at sawmills. For implementation at an industrial scale, it would be the logical choice of tool for cutting the sides of the beams. In a sawmill, straight oak timber can be sawn at impressive speeds of around 50 m/min [26]. Even for an optimised industrial workflow, this would be slower for curved wood, and with our lab equipment, the speed was as low as around 0.1 m/min. A component produced with a bandsaw would often need a subsequent finishing procedure, for instance, with CNC-milling, and this part happens at a much slower pace—also in the industry. We were already relying on CNC milling for processing the joint details, and during the fabrication of prototypes, it became clear that a workflow entirely based on milling would be easier to control than a workflow with combined processing tools.

Fig. 19
figure 19

A bandsaw end-effector mounted on a robot arm. Bandsaws are efficiently employed at sawmills. In the available lab facility, the method was slow and unstable

Fig. 20
figure 20

CNC-milling of a log where a spindle end-effector is mounted on a robot arm. Combined with the rotary table, three sides of the log and the joint details could be processed without reorienting the log

In the prototype with two beams, seen in Fig. 21, we focused on the joint solution and the visual transition between the beams. We found that the smooth transition between the most visible beam surfaces was sufficient to express a sense of continuity. We also deduced that the joint solution with two dowels placed in the beam direction became too challenging to implement in terms of material dimensions and tolerances. Both this prototype and a later prototype with three components revealed the importance of controlled wood drying. Since we did not have a supply chain that could provide this, we experienced significant cracks in many logs. Still, we could counteract some of these problems by storing the wood outdoors except during processing, making it possible to produce prototypes with more beams. In the prototype in Fig. 22, we wanted to study how well the traditional timber frame joint could be implemented in the robotic workflow. The tolerances were within a few mm and allowed the beams to be joined successfully. Assembling the prototype highlighted for us the fact that the system functions best for the relatively orthogonal meeting between the joints and that the sequence of assembly needs to be taken into account. To make a more thorough test of the workflow and demonstrate its viability, we produced a larger prototype of 15 components with an approximate size of 3 m in width and 4 m in height. See Fig. 23. Figure 24 shows how the prototype can be considered part of a larger structure. We wanted to study tolerances and the effects of changing humidity and begin to discuss possible assembly strategies. We designed the prototype to express itself as part of a larger construction. Therefore, we limited the curvature to appear mainly in the cross-section. The curvature increases towards the top to allow a differentiated selection of logs. We decided on an assembly method where each vertical row of beams was assembled first and then pushed together on the ground and tightened with straps before being lifted. This is not very dissimilar from how traditional timber frame buildings are constructed. Still, the process demonstrated that the individual joints would need to allow for more flexibility in a larger construction, which is also the case in traditional systems. Alternatively, other joints solutions could be considered.

Fig. 21
figure 21

A prototype with two beams joined together with dowels. The joint was too intricate for fabrication and assembly. A shared surface defines the top surfaces of the beams

Fig. 22
figure 22

A prototype with four beams. A traditional timber frame joint was suitable for the available fabrication setup and made steel connectors unnecessary

Fig. 23
figure 23

Prototype with 15 beams. The fabricated prototype follows a single-curved control surface with an increasing curvature towards the top

Fig. 24
figure 24

Visualisation of how the prototype of 15 beams could appear in a larger structure

Reflections on the experimental workflow

The design-to-production workflow described here is proposed to demonstrate how the properties and irregularities that characterise natural wood can be embedded and utilised in architecture. It is explained how the employed technologies correspond with existing workflows in the wood industry. This indicates that the industry is technically prepared to embrace a wider variety of wood types than is currently the case. However, to scale up irregular wood in sawmills and obtain the same efficiency as straight wood, scanning and sawing technologies would need to be reconfigured to meet more considerable variations and more complex geometries. Even though it is more to be seen as one of many possible ways of engaging deeper with natural wood, the specific workflow and prototypes suggest issues that could be further pursued. It would be possible to make better use of the individual log’s dimension and shape by using CT-scanning methods to define the interior layers of the wood, particularly the division between heartwood and sapwood, and including this information in the distribution of the material. The size and shape of the beams are to a high degree result of the constraints from the machinery, such as the reach of the robot arm, the proportions of the workshop spaces and limited weight so humans can carry the material. The decision on using a traditional mortice and tenon joint led to the need for a particular beamwidth, which would probably not be the structurally optimised solution when considering a complete roof construction. Here, a more rectangular beam section corresponds typically better with the flow of forces. A robotic workstation with a track and cranes for moving the logs and construction parts would allow producing longer beams and using sawlogs with larger dimensions more similar to the typical size found at sawmills. It could be considered to divide the logs and make several components from each. The joint solution could be altered to give more flexibility during assembly and better absorb tolerances in beam dimensions. Beyond developing the method further, other construction types could be explored. The general approach could be transferred to other wood species and variations other than curvature in a broad perspective.

We hope that the workflow can help to broaden the view on natural materials and encourage the building industry to reconsider the general tendency to strive for standardisation. Gradually, as the need for sustainable solutions increases, perhaps the success criteria will begin to include biodiversity, greenhouse gas emission levels and resource scarcity. By introducing new construction types and implementing irregular wood materials, architects can help develop and support a more diverse marketplace for natural materials.