Abstract
Advanced design, engineering, and manufacturing tools linked through a common digital workflow are enabling a new approach to timber construction based on parametric, component-based systems that preserve data coherence across disciplines. This is especially important for bespoke timber structures, where fragmented exchange-file workflows often separate geometric design, structural verification, fabrication, and assembly. This paper presents a new structural system as a double-curved box-beam diagrid timber wall assembled through a robotically fabricated, self-locating wood-to-wood cross-lap grammar that can be mapped onto complex curved surfaces. Assembly intent is encoded directly into the parts through embedded positional constraints, enabling measurement-free erection and reducing tolerance stacking. A co-located computer-aided design, engineering, and manufacturing workflow is implemented to reduce drift between analyzed, fabricated, and assembled states. Validation through a 1:1 prototype includes 116 structural web elements, 624 cross-lap joints, and 200 non-structural flanges assembled in 4 hours using nominal zero-gap joints. Fabrication results show 78% average sheet utilization from 2.0 m × 4.0 m stock, with joint openings within ±0.5 to 1.0 mm of nominal. The study demonstrates a reproducible pathway for engineering-integrated design for manufacture and assembly of complex timber structures.
1 Introduction
There is a growing interest in integrating design, engineering, and digital manufacturing in the construction industry, as this addresses labor shortages while increasing construction speed, quality, and productivity. However, there remain challenges associated with design space fragmentation, construction’s complex nature with emerging materials and fabrication techniques, and challenging on-site conditions. Within this context, component-based timber elements (), engineered via off-site digital fabrication, offer a pathway to reorganize precision, tolerances, structural performance, and assembly logistics, and thus to address these challenges.
1.1 Lightweight structures: robotic fabrication, timber construction, and Co-located digital design
Digital fabrication integrates computational design methods with computer numerical control (CNC) machinery to create structural components through milling and shaping of materials (; ; ; ). This integration links geometric design, building data management, manufacturing, and construction assembly into a coherent workflow (; Weinand, 2021; ; ). CNC milling with articulated multi-axis robots offers adaptive cutting, milling, sawing, profiling, and drilling that are tailored to the geometric complexity, scale, and operational constraints of building components.
Robotic fabrication for building components has matured from one-off demonstrators to reproducible cell workflows in which offline programming and digital twins govern reachable poses, collision-free paths, and tool-axis orientation during 3- to 5-axis operations (; ; ; ). Milling robots extend the reachable workspace for 1:1 construction, while parametric controllers inside Computer-Aided Design (CAD) environments make cell kinematics legible to designers and allow explicit checks for singularity, self-collision, and end-effector clearance before code export (; ; Yang et al., 2024). Based on these developments, recent research by Gamerro et al. (), , and demonstrates that digital fabrication equipment can interface robustly with a spectrum of CAD ecosystems and collaborate with Computer-Aided Manufacturing (CAM) software to streamline geometry and fabrication workflows for timber construction. These include tool-path definition, G-code generation, and direct machine control, alongside simulation tasks. In machining applications, spindle orientation and path planning are jointly optimized to ensure curvature-driven tool alignment and to prevent collisions in recessed areas, similar to the approach developed by , , and . These constraints are directly relevant to inclined cross-lap milling on curved timber elements ().
While not yet widely adopted in mainstream robotic construction research, recent pilot studies show that digital fabrication can embed structural timber engineering computational design and Computer-Aided Engineering (CAE) for bespoke construction. , , , and demonstrate workflows in which CAE is coupled to parametric geometry so that section sizing, joint detailing, and support conditions are iterated in tandem with fabrication logic. In these studies, Finite Element (FE) models are generated directly from the design environment and their results feed back into plate segmentation, shell thickening, and connection layout prior to robotic milling or assembly. At the same time, the CAE components are typically implemented as loosely coupled stages, relying on exchange files, external solver runs, and post-hoc result mapping rather than as a continuously active, edit-time structural gate. Taken together, these studies indicate a clear trajectory toward construction robotics in which structural performance, fabrication constraints, and assembly tolerances are increasingly co-designed rather than purely sequentially negotiated.
A powerful advantage of computer-controlled fabrication with customizable machining methods lies in its ability to realize wood-to-wood-only integral connections (; ; ). The development of such timber systems is tightly coupled to component geometry, which in turn requires a CAD-CAM-CAE integrated (; ; ). Results demonstrate that this method of joinery provides products “just in time”, improves construction consistency in a controlled factory environment, and minimizes waste and oversupply ().
Wood-to-wood integral connections have been deployed in recent industrial-scale timber projects studied by , Weinand (2021), and . These studies indicate that such connections enable improved structural integrity while reducing reliance on metal fasteners. Furthermore, it is concluded that the design and production of highly customized components represent a pivotal advancement in component-based timber construction, enabling greater flexibility in expressive architecture and structural applications. and demonstrate that fully digitally fabricated timber systems can be structurally optimized and materially efficient. Building on this, , , and argue that the shift toward prefabrication, including open-source digital design workflow development, requires a framework that circulates data among CAD, CAM, and CAE rather than passing in hand-to-hand. Within such a framework, Design for Manufacture and Assembly (DfMA) can explicitly account for structural performance measures while targeting cost reduction, improved product quality, shortened construction times with fewer suppliers, and lower waste.
DfMA in timber moves design and construction complexity upstream (), where structural elements are consolidated (), tolerances are budgeted explicitly (), assembly sequences are encoded (; ; ), and manufacturability is validated before components reach the shop floor (). When integrated with interlocking connections, DfMA in timber construction becomes more than a documentation protocol. In particularly, DfMA can become a design method, where joint geometry begins to function as a positional-constraint system in its own right. Sequencing, datum transfer, and erection logic are designed into the parts so that what is digitally analyzed corresponds to what is physically fabricated and installed. In this sense, DfMA adapts to timber’s material logic by enabling integral wood-to-wood joints and curved, laminar components to be produced and assembled measurement-free.
Recent built work demonstrates that DfMA-oriented timber construction belongs to a broader architectural lineage and does not emerge only from computational research prototypes. Shigeru Ban’s timber projects, including the Haesley Nine Bridges Golf Clubhouse in South Korea and the Swatch-Omega campus in Biel/Bienne, Switzerland (), illustrate how highly articulated timber systems can combine expressive geometry, prefabricated components, and carefully coordinated assembly logic at building scale. For the present study, Haesley Nine Bridges is particularly relevant for its grid-based spatial organization, while the Swatch-Omega campus demonstrates free-form timber construction supported by parametric planning, high-precision production, logistics, and assembly. Cambridge Central Mosque by Marks Barfield Architects provides another relevant precedent (), where timber columns join into an interwoven octagonal canopy that forms the roof structure. These precedents show that component-based timber assembly, expressive timber geometries, and the transfer of assembly information into fabricated parts are not, by themselves, new ambitions. Nevertheless, they also make clear the continuing need for frameworks that can explicitly describe, test, and evaluate how geometry, structural verification, robotic fabrication constraints, and assembly sequencing can be integrated within a reproducible design-to-construction workflow.
1.2 Research gap, problem statement, and novelty of the work
Co-located CAD, CAE, and CAM workflows offer one pathway for operationalizing DfMA in timber construction. Their value lies in maintaining a close relationship between geometry, structural assumptions, fabrication constraints, and assembly information throughout design development. Open, Python-based ecosystems have already demonstrated how geometry kernels, model builders, and solver backends can return field data to the authoring environment for design decision-making (). The challenge is not the use of exchange files, since solver-native input and output files often remain necessary. Rather, the challenge lies in uncontrolled translation, repeated remodeling, loss of entity provenance, and the separation of analysis assumptions from the geometry that is ultimately fabricated and assembled.
Despite advances in digital fabrication for bespoke timber construction, there are still few full-scale studies that examine how measurement-free assembly, self-locating timber joinery, structural verification, robotic fabrication, and fabrication-aware data management can be integrated and evaluated within a single design-to-construction workflow. This gap is especially important for non-developable timber systems, where local curvature, joint orientation, insertion logic, and fabrication accessibility must be coordinated before material is cut.
The specific contribution of the present study is therefore framed around the development and evaluation of a robotically fabricated double-curved timber diagrid in which a self-locating cross-lap grammar, structural verification, fabrication data, kitting, and full-scale measurement-free assembly are coordinated within a single co-located analysis-to-fabrication workflow. Accordingly, the study has three objectives. The first is to develop a component grammar for a double-curved timber diagrid that preserves part identity, joint logic, and assembly sequence. The second is to integrate structural verification within the CAD-based design model so that joint geometry, fabrication constraints, and assembly logic can be evaluated together during design development. The third is to evaluate the workflow through robotic fabrication and full-scale assembly, using structural stress verification, fabrication quality, material utilization, and assembly productivity as performance measures.
The empirical work is guided by four research questions.
How can computational design support the generation of expressive, adaptive, component-based timber systems on double-curved surfaces?
How can a self-locating wood-to-wood cross-lap grammar reduce field measurement during the assembly of a non-developable timber structure?
How can structural simulation be brought upstream so that geometric exploration, joint design, and fabrication preparation remain linked to ultimate limit state criteria? And
How can the resulting system be fabricated and assembled at full scale while preserving part identity, assembly sequence, tolerance control, and construction efficiency?
By addressing these questions, the study evaluates a workflow in which geometric complexity is shifted upstream into computational design, structural verification, and robotic fabrication. The work contributes a full-scale case study for engineering-integrated DfMA in timber construction while identifying assumptions and limitations that must be addressed before similar workflows can be transferred to other structural systems or building-scale applications.
2 Materials and methods
The proposed structural system is examined through a deliberately constrained double-curved configuration in plan and elevation. The design is demanding in terms of geometry, assembly tolerances, and structural performance, while still satisfying prescribed design limit states. The study adopts a co-design approach framed within a design science research (DSR) stance, using a single-case design following Yin (2018). The case is built and evaluated in use, not to claim historical uniqueness, but to test the coordination of three interdependent challenges: (a) combining component-based assembly logic with double curvature, (b) managing a high number of individually indexed parts and joints, and (c) reducing on-site measurement through self-locating geometry. These challenges are examined within a reproducible design-to-construction workflow.
This methodological stance is motivated by the “how” nature of the research questions, the need to investigate a contemporary digital timber design workflow within its real-world construction context, and the tight coupling between fabrication, assembly, and structural response that shapes the final product. The unit of analysis is the end-to-end computational workflow (Figure 1), rather than any single software component or isolated test. This workflow spans parametric design, integrated FE simulator, robotic manufacturing, material nesting, and off-site/on-site operations, including kitting, labeling, and assembly. Performance is evaluated by tracing how decisions made in the design environment propagate through CAE verification, robotic toolpath generation, sheet utilization, and on-site erection metrics, and by assessing whether the realized structure complies with the intended geometric, structural, and assembly-logistics criteria.
FIGURE 1
2.1 Proposed structural system design
The case is built and evaluated in use, not to claim historical uniqueness, but to test the coordination of three interdependent challenges: (a) combining component-based assembly logic with double curvature, (b) managing a high number of individually indexed parts and joints, and (c) reducing on-site measurement through self-locating geometry. These challenges are examined within a reproducible design-to-construction workflow.
2.1.1 Geometry development and definition of sequential assembly logic
The base module of the structural system is a three-sided box-beam consisting of two parallel webs and a single connecting flange (Figure 2a). Structurally, the box-beam behaves analogously to a W-section, where material is concentrated in the flange, away from the centroid, to provide bending stiffness against out-of-plane loading. Identical modules are first arrayed along reference lines in plan (Figure 2b). Their individual flanges are then merged into a continuous flange strip spanning across all webs (Figure 2c). This one-dimensional box-beam strip is the starting typology that is later mapped, in diagrid directions, onto the double-curved target surface.
FIGURE 2
The webs of the box beams are planar in order to cut them from plywood. For a target surface curved on its plan, the webs are geometrically created by cutting sections through the curved surface with a plane (Figure 3). The plane which cuts the section is taken in the center of the box beam and perpendicular to the tangent of the surface curvature at the control point. It is then moved out according to the desired separation of the webs. The two planes which create the webs of each box beams are thus parallel. The box beams accordingly intersect each other in a diagrid pattern, where its webs are following the curvature along the structure and can be cut from plywood. The flanges, on the other hand, are perpendicular to the webs and parallel to the double curved surface (Figure 3). Thus, these elements follow the curvature of the surface. This is achieved by using the elastic bending range of the wood and bending the flanges into place, securing them with the wood-to-wood dowel connections.
FIGURE 3
Using section lines to create the three-sided box beams can lead to over-crossing or overly dense regions in the diagrid, depending on the curvature and boundary conditions of the target surface. The method is therefore most applicable to double-curved surfaces whose curvature variation, web spacing, member intersection angles, and insertion paths remain compatible with planar web extraction, cross-lap geometry, and robotic tool accessibility. When local curvature changes rapidly, or when the mapping produces dense intersections, steep joint angles, or inaccessible tool orientations, the guide geometry must be adjusted to avoid pathological clustering and unbuildable joint conditions. To control this, a parametric module is introduced that allows the origin of the diagrid propagation to be shifted across the height of the surface (Figure 4a). The local density of control points can also be adjusted so that regions are densified or loosened as required.
FIGURE 4
Given the two curvatures involved in the global geometric design, as well as the number of interlocking connections used to sequentially assemble the components, proper labelling of all the individual members is essential in the design process. Moreover, the design of sequential assemblies should ensure that each member has sufficient connections so that their position is maintained relative to the other members for the sake of stability during the construction phase. These two constraints are addressed when the basic grid-shell control lines are designed to be mapped onto the control surface, and thus the webs are propagated across the surface (Figure 4b). The depth of the webs and the thickness of the material are parametric, as can be the distance between the webs. The webs are connected to each other by conventional lap joints, and each web has lap joints only on one side of the web so that the webs can slide into each other, and web intersections are then computed (Figure 4c).
Once the web geometry is defined, connection points for the flanges are established (Figure 4d). The connections are designed to “pull” the top flange downward onto the crossing bottom flange and secure interaction between flanges and webs. Further consideration is also given so as not to have excessive connectors that would compromise the material integrity of the flanges. Connection geometry is iterated to introduce curved corners and tapers that ease installation (Figure 4e). The connector corners are then mapped onto the flanges to locate the openings where webs pass through (Figure 4f). The design logic is summarized in Figure 5 and implemented through the computational workflow described in Section 2.1.1.1.
FIGURE 5
2.1.1.1 Implementation
To implement the conceptual design, a computational workflow is developed to translate a curved target geometry into indexed timber components. Although the prototype was implemented in a Rhino/Grasshopper environment (), the workflow is described here through general computational operations rather than software-specific commands. It begins with parametric inputs that define the design space, including the target surface or guide curves, web spacing, web depth, material thickness, flange offset, joint tolerance, minimum tool radius, and assembly-sequence constraints. These parameters establish the geometric boundary of the system and define the limits within which the diagrid can be adjusted.
The algorithm then generates indexed families of web components across the target geometry. Each component is assigned a persistent identifier and a local coordinate frame derived from its position on the guiding geometry. This indexing preserves correspondence between the global diagrid, individual web elements, local joint features, fabrication files, and assembly sequence. As a result, each part remains linked to its geometric origin, its neighboring components, and its downstream fabrication and assembly information.
Intersections between web families are evaluated to generate the cross-lap features. At each intersection, the algorithm establishes a local joint frame from the relative position and orientation of the mating members. This frame defines the location, orientation, opening size, and insertion logic of the lap. The joint geometry is then checked against structural, fabrication, and assembly constraints, including residual section depth, opening width, spacing between adjacent openings, minimum tool radius, tool accessibility, and insertion clearance. This allows local connection geometry to be adjusted during design development rather than after the global form has been fixed.
Fabrication and assembly metadata are attached to the generated components and joint features. Each part carries information such as part ID, joint ID, mating part ID, local orientation, assembly wave, insertion direction, and fabrication operation. This metadata structure allows the same component to be traced from the three-dimensional design model to the structural analysis model, fabrication profile, nested sheet layout, and physical assembly sequence. Maintaining this chain of correspondence is one of the main computational requirements of the workflow.
The generated geometry is regularized before fabrication. Boundary curves are checked for closure and consistent orientation, short edges and sliver regions are removed, and corner conditions are adjusted to satisfy minimum tool-radius requirements. These operations reduce the risk that small geometric artifacts in the design model become invalid toolpaths, ambiguous assembly features, or stress-concentrating joint details. Finally, the three-dimensional component geometry is transformed into fabrication-ready two-dimensional profiles. The output includes cut boundaries, cross-lap openings, drilling points, orientation marks, grain direction, part labels, and nesting information. Because all fabrication features retain their parent-part identifiers, the flattened profiles remain traceable to the original design model, the corresponding structural-analysis entities, and the intended assembly sequence. Software-specific implementation details for the Rhino/Grasshopper workflow are provided in Appendix 1.
2.2 Design of integral connections
The joinery between adjacent web elements detailed in Section 2.1.1 is achieved through interlocking cross-lap connections. Each joint is defined by the intersection of two curved webs, accounting for their local radii and orientation. Neighboring elements connect along their edges and near their center lines, forming a flush surface that maximizes wood-to-wood contact for direct material embedment and compression (Figure 6).
FIGURE 6
When the centroidal axes of intersecting webs do not coincide, the intersection locus is computed as the shortest segment between the two space curves, introducing an “eccentricity” parameter. This geometric relationship results in the closest points on each curve and thus the local intersection frame. The orientation of each web at the joint is derived from the tangent vector at this frame, while the local radius informs the square cross-section of the lap volume. These resulting connections appear as orthogonal blocks generated by enclosing the intersection region with rectilinear solids.
2.2.1 Structural design considerations for cross-lap joints
The distribution of the bending stress along the depth of each web element is not linear. This is because the web elements in the proposed structural system are curved (i.e., Figure 7) and the wood grain on the tension side is thus shorter than on the compression side. Therefore, the efficiency of the joint depends on three critical geometric parameters: (a) eccentricity, which refers to the offset between the centroidal axes of intersecting members; (b) contact angle, determining how elements intersect; and (c) the tilt of cross-sections, which affects overall stability.
FIGURE 7
The DIN 1052 standard (
) outlines procedures for designing timber elements with unreinforced openings–an approach that is adopted for the cross-lap connections in this study. According to NCI NA.6.7 of DIN 1052 (
), such openings are permitted in laminated veneer lumber, provided that they are not placed in regions subject to transverse tensile stresses. To address this design criterion, the cross-lap connections are designed to effectively meet the following six criteria according to DIN 1052 (
):
The vertical position of the opening shall ensure that the remaining cross-section retains sufficient load-bearing capacity, as expressed in Equation 1.where, “h” is total beam height, and “” is remaining cross-section height below the opening, shown in Figure 7c.
The maximum opening width should be limited to prevent excessive perpendicular-to-grain tension and splitting at the opening’s corners, as expressed in Equation 2.where, “” is the opening width, shown in Figure 7c.
The maximum opening height is limited to prevent grain-parallel cracks and sudden strength loss from splitting, as shown in Equation 3.where, “” is the opening height, shown in Figure 7c.
The clear span between adjacent openings should be long enough to prevent overlapping tension stresses perpendicular to grain around the hole periphery of the neighboring openings, as expressed in Equation 4. These stresses typically dissipate along approximately 45° trajectories (triangular zones) extending about one beam depth from each opening ().where, “” is the clear span between adjacent openings, shown in Figure 7c.
The minimum spacing between the opening and beam support should be sufficient to prevent progressive shear propagation from the support to the connection, as shown in Equation 5.where, “” is the spacing between the opening and the beam support, shown in Figure 7c.
To ensure the opening is within an adequately supported region, the beam depth at the opening location must equal the full beam height, as expressed in Equation 6.where, “” is the spacing between the opening and the end grain of the beam, shown in Figure 7c.
2.3 Engineering integrated and simulation-based computational design
The FE model is compiled directly from the same parametric geometry that drives nesting and robotic toolpaths. Each web and opening carries a unique identifier and attribute set in the CAD model, and the integrated CAE Algorithm maps these attributes to FE sets and metadata. This “single source of truth” ensures that any edit to a web in the design graph is reflected in both the structural model and fabrication data, so that the configuration that is analyzed is exactly the configuration that is cut and assembled.
The 2.1FE modeling begins with the web surfaces (Figure 8a). Mid-surfaces are derived these solids (Figure 8b), and intersections between crossing webs are determined to identify overlaps and the extent of the cross-lap regions (Figure 8c). The global surface is then segmented into discrete sub-domains (Figure 8d) so that opening edges, lap boundaries, and support regions form explicit topological entities. Finally, the segmented geometry is converted into a consistent, integrated shell mesh suitable for FE analysis (Figure 8e). In the numerical model, only the load-bearing webs are represented as homogenized shell elements; flanges are omitted from stiffness but included in self-weight. The mesh uses a target edge length of 20 mm, with automatic local refinement of 5 mm in a 200-mm band around openings, cross-lap edges, and supports to resolve stress gradients with sufficient fidelity while maintaining tractable model size and run time. The structure uses conventional linear 3-node triangular shell elements with linear interpolation, selected because of insignificant through-thickness strains and small thickness-to-length ratio of the web elements. Due to this small thickness, transverse shear strains are also neglected.
FIGURE 8
2.3.1 Development of an integrated CAE algorithm
To shift structural verification upstream, this study contributes a software layer that provides solver-backed structural evaluation in a single Python runtime. Rather than offering “real-time FEA” in the abstract, the implementation embeds an in-line CAE gate inside the CAD ecosystem that controls parametric edits before CAM. The module is implemented on top of COMPAS, an open-source Python-based framework (). Building on compas_fea, the proposed in-line, assembly-aware CAE pipeline is organized as a compact set of object-oriented classes that together provide a deterministic compiler from CAD layers to CAE input and back to CAD-embedded results. The module constructs a numerical FE model associated with the geometry developed in Rhino (i.e., CAD), runs analysis with ABAQUS as the chosen backend (i.e., CAE) directly inside Rhino, returns results to the same CAD scene, and binds design metrics against pre-declared structural criteria, including the and ultimate limit states.
Algorithm 1
Require: Geometry from Rhino, node coordinates, material properties, load,
boundary conditions, element definitions, output data
1: Import core COMPAS, CAD, and COMPAS FEA modules
2: from compas fea.cad import rhino
3: from compas fea.structure import (Structure, ElasticIsotropic,
ShellSection, ElementProperties, PointLoad, PinnedDisplacement,
GeneralStep)
4: Initialize Structure Object
5: model = Structure(name=’model_name’, path=’/folder/’)
6: Extract Geometry from Rhino Layers
6: rhino.add_nodes_elements_from_layers (model,
mesh_type=’ShellElement’, layers=’element_set mesh’)
8: Create Sets for Nodes and Elements from Layers
9: rhino.add_sets_from_layers (model, layers=[’element_set mesh’,
’node_set load’, ’node_set support’])
10: Define Material and Section Properties
11: model.add_material(ElasticIsotropic (name=’material_linear’, E, v,
density))
12: model.add_section (ShellSection(name=’section_shell’, t))
13: Assign Element Properties
14: model.add_element_properties (ElementProperties (name=’shell’,
material=’material_linear’, section=’section_shell’,
element_set=’element set mesh’))
15: Apply Loads
16: model.add_load (PointLoad(name=’load_point’, nodes=’node_set
load’, intensity_x, intensity_y, intensity_z))
17: Apply Boundary Conditions
18: model.add_displacements(PinnedDisplacement(name=’displacement_pinned’, nodes=’node_set support’))
19: Define Analysis Steps
20: model.add_steps([GeneralStep(name=’step_boundary_conditions’, displacements=[’displacement_pinned’]),
GeneralStep(name=’step_load’, loads=[’load_point’])])
21: model.steps_order = [’step_boundary_conditions’, ’step_load’]
22: Run Analysis and Extract Results
23: model.analyze_and_extract(software=’abaqus’,
fields=[’displacement’, ’stress’, ’reaction_forces’, ’section_forces’])
24: Post-processing and Visualization
25: rhino.plot_data (model, step=’step_load’,
field=[’nodal_displacement’, ‘stress’, ‘section_forces’])
26: rhino.plot_reaction_forces(model, step=’step load’)
The proposed CAE algorithm provides a deterministic compiler from CAD edits to a “Structure” instance, which is a class that orchestrates the structural simulation and design flow. To allow this class to act as an interface between the CAD and CAE platforms for the proposed structural system, four service objects are developed and detailed in Algorithm 1.
2.3.1.1 GeometryAdapter
This object presents an adapter interface to the CAD model. It maps CAD layer names and object identifiers to typed selections (i.e., node sets, element sets, layer tags, meshes, and per-object metadata such as local axes). This adapter normalizes CAD inputs into immutable data transfer objects (DTOs) and leverages a set of core modules from the COMPAS libraries, including the compas.datastructures and compas.geometry packages, to construct and manipulate geometric input data, and the compas_fea.cad.rhino module as a dedicated CAD integration module for extracting geometry from the Rhino workspace.
2.3.1.2 ModelBuilder
This object compiles the DTOs from GeometryAdapter into a Structure instance by materializing FE entities, including nodes, elements, sets, materials, sections, loads, and boundary conditions. Sections are defined via compas_fea.structure.section, and shell elements are instantiated with unique integer keys.
Constitutive behavior is assigned through the. materials dictionary from compas_fea.structure.material. Plywood, using APA Marine Grade, is chosen due to its resilience in moisture-prone environments. The material is made with waterproof glue and Douglas-Fir veneers. The mechanical and layup properties of the panels used in this study are detailed in Table 1. The ElementProperties object then associates the elements module with both materials and section modules. The add_nodes_elements_from_layers () utility creates nodes from mesh vertices and records local coordinate axes in an. axes dictionary for material orientation.
TABLE 1
| Description | Value | Unit |
|---|---|---|
| Mean modulus | ||
| Modulus of elasticity, long-grain | 5,200 | N/mm2 |
| Modulus of elasticity, cross-grain | 4,560 | N/mm2 |
| Mean strength | ||
| Bending, long-grain | 42.0 | N/mm2 |
| Bending, cross-grain | 37.0 | N/mm2 |
| Geometric properties | ||
| Nominal thickness | 15 | mm |
| Layers | 7 | N/A |
Mechanical and geometrical properties of plywood ().
Load objects are defined via compas_fea.structure.load and associated with node sets. The design loads for the baseline structure are established in accordance with the National Building Code of Canada (NBCC) standard (). Toronto Metropolitan City Hall Region in the Province of Ontario, Canada is the reference location for climatic data, based on Ontario’s Ministry of Municipal Affairs and Housing (MMAH) Supplementary Standard SB-1 (). The structure is classified as having “Normal Importance.” The reference height and wind pressures are taken at the top height of the structure, assuming the structure is located on flat terrain with urban exposure conditions. The effective pressure is accordingly computed using Equation 7.
Where “” is the Importance Factor for Wind Load, “q” is the reference velocity pressure for a return period of 50 years, “” is the Exposure Factor for external pressure, “” is the Topographic Factor, “” is the Gust Effect Factor, and “” is the External Pressure Coefficient. Values associated with these wind load parameters are detailed in Table 2.
TABLE 2
| Design parameter | Symbol | Value | Reference |
|---|---|---|---|
| Reference wind pressure | 0.44 kPa | MMAH SB-1 | |
| Importance factor for wind load | 1.0 | MMAH SB-1 | |
| Exposure factor for heights shorter than 20 meters | 0.9 | Cl. 4.1.7.1 (5) | |
| Gust effect factor | 2.00 | Cl. 4.1.7.3 (8) | |
| Topographic factor | 1.0 | Cl. 4.1.7.4 (1) | |
| External pressure coefficient | 0.8 | Cl 4.1.7.5(a) | |
| Internal pressure coefficient | −0.7 – 0.7 | Cl 4.1.7.6 | |
| Area of surface | A | 12.6 m2 | Cl 14.1 |
| External wind pressure for zone “e” as per NBCC | −1.23 kPa | Cl. 4.1.7.3 | |
| External wind pressure for zone “w” as per NBCC | 1.13 kPa | Cl. 4.1.7.3 |
Building wind load parameters for Toronto Metropolitan City Hall region.
Next, the boundary conditions of the structure are defined, where a displacement object is created to instantiate a class from compas_fea.structure.displacement in order to specify the nodes and relevant degrees-of-freedom to be restrained. Displacement objects are stored in the. displacements dictionary. Analysis steps are then assembled by combining load and displacement objects into a step sequence.
2.3.1.3 SolverRunner
This object writes the native input file from the populated Structure object developed in ModelBuilder, invokes the backend solver, and manages result extraction. This adapter provides a backend-agnostic execution interface by writing solver input files (i.e., .inp files), serializing structure representations (i.e., .obj files), and launching the analysis in no-Graphical User Interface (GUI) mode. The implementation of this step does not modify ABAQUS itself, and it simply guarantees that a given CAD state produces a unique, reproducible input file.
The use of solver-native input and output files is therefore not eliminated in this workflow. Instead, these files are generated and read through a controlled translation layer that preserves entity correspondence between the CAD model, FE model, and fabrication model. Each generated node set, element set, opening, joint region, and support condition is derived from the indexed design geometry rather than from a manually rebuilt analysis model. As a result, the ABAQUS input file functions as a deterministic representation of the current design state, while the extracted results are mapped back to the originating components for visualization and design feedback. In this context, the contribution is not the avoidance of exchange files, but the reduction of uncontrolled model drift through automated generation, persistent identifiers, and traceable result mapping.
The SolverRunner object generates a. inp file where Python-based zero-indexed nodes and elements are automatically adjusted to the one-based indexing used by ABAQUS. Individual element sets are created per element for detailed referencing. The input file is passed to the solver in the background by calling the launch_job.py script from compas_fea’s ABAQUS module. Upon completion, ABAQUS writes an. odb file, which is parsed using extract_odb_data () to populate structure. results. This includes creation of a results. json file in the designated project path.
2.3.1.4 ResultsBroker
This object maps displacements, stresses, and base reaction forces back into the CAD scene so that structural feedback remains co-located with the design model. ABAQUS. odb output is parsed, and the resulting fields are stored in Structure. results as JSON and Pickle artifacts. To handle large datasets using NumPy and SciPy, the data processing is executed using the CFunc in compas.utilities.
2.4 Robotic fabrication
The fabrication strategy translates the component grammar into operations for two production streams: (1) milled web elements and (2) routed flange elements. Web elements require 5-axis access because the cross-lap pockets vary with local member orientation and surface curvature. Flange elements, by contrast, remain planar and are therefore fabricated through 3-axis routing. Web elements are fabricated using a 6-axis KUKA KR150 R2700 robot mounted on a 4.5 m linear rail, while flange elements are fabricated using a 3-axis AXYZ Pacer 4008 CNC router.
2.4.1 Fabrication of web elements
In the first step, screw locations are computed per web and drilled first to mechanically fix the sheet to the sub-bed using a 90° V-groove endmill. Screws are placed inside the final profile and away from cross-lap regions as illustrated in Figure 9, and the pattern is generated from the unrolled geometry as part of the nesting logic. These 3-axis operations are simulated for reachability and visibility within the nesting layout, with collision risk limited to the spindle body modelled in the digital cell. Next, a series of helical spiral cutting paths are run in a minimum distance order of operations to cut the dowel locations with a ¼-inch downcutting endmill. Figure 10 shown a typical cutting path adopted for fabricating dowel hole profiling.
FIGURE 9
FIGURE 10
The final web operation is a continuous hybrid 3-/5-axis pass cutting outer profiles and inclined cross-lap pockets. Three endmills are utilized at this stage: (1) a 0.25-inch V-groove for etching, (2) a 0.25-inch two-flute down-cut for the inner profiles, and (3) a 0.375-inch down-cut for the outer profile cuts. Using KUKA Parametric Robotic Control (PRC), the robot and spindle are encoded in a digital cell, and a custom C# component pushes KUKA code to the controller. This ecosystem functions as a simulation-based digital twin for path planning, kinematics simulation, and rapid error visualization against the design geometry (Figure 11). These are calculated through two profile curves; i.e., one at the top level and one at the bottom level of the plywood sheet with the thickness provided in Table 1.
FIGURE 11
A no-collision rotation rule is enforced, where the workpiece is only rotated when the tool is safely retracted clear of the part. All 5-axis repositioning moves occur at a safe height above the material to ensure nothing collides during rotation. Before any index of the A/B axis, the tool moves to a clearance plane to ensure that the spindle and tool have sufficient clearance, satisfying our no-collision rotation criterion. Furthermore, the cutter enters the material along a tangent arc outside the final geometry and exits similarly, which prevents gouging the part edges.
Five to six profiles per 4 by 8-foot plywood sheet are nested within each plywood sheet (Figure 12a). Profile frames are calculated through point sampling across the bottom and top chord of each profile, and a two-point vector path (Figure 12b) is generated to represent the direction axis of the milling spindle. The 90-degree X-axis from this Z-axis is generated along the chord direction (Figure 12c), and rotation around the Z-axis of the generated drive frame is adjusted to prevent collisions between the milling spindle and plywood surface during steep 5-axis joint cutting (Figure 12d).
FIGURE 12
2.4.2 Fabrication of flange elements
Flange components enable the active bending of the 3-sided diagrid system shown in Figures 2, 3. They are nested algorithmically using the OpenNest plugin (), and each part receives a single-line engraved label encoding its bay, wave, and orientation, as shown in Figure 13. This label schema aligns with the kitting and assembly logic and ensures that parts cut on the 3-axis machine remain fully compatible with the 5-axis-milled webs.
FIGURE 13
3 Results and discussion
This section presents results and discussions regarding digital fabrication, construction sequencing, and structural design automation and performance associated with the proposed structural system and its computational design workflow. To demonstrate the self-aligning typology, sequential assembly logic, and constructability of the structural system with the proposed robot-assisted cross-lap joints, a full-scale 1:1 prototype is designed and constructed based on the structural system outlined in Section 2.
3.1 Construction sequencing and robotic fabrication
Design requirements dictated by DIN 1052 () in Equation 1 yield the admissible geometric range for the cross-lap joints, summarized in Table 3. Together with the structural design requirements detailed in Section 2.2.1, these provisions are checked concurrently with non-structural constraints, namely, (1) the sequential interlocking requirements, (2) robotic fabrication limitations, and (3) target surface approximation of the target double-curved surface.
TABLE 3
| Description | Symbol as per DIN1052 () | (Min-Max) Value [mm] |
|---|---|---|
| Total beam height | h | 85 – 107 |
| Opening height | 30 – 37 | |
| Remaining cross-section height below the opening | 55 – 70 | |
| Opening width | a | 14 – 18 |
| Spacing between the opening and beam support | 50 – 290 | |
| Spacing between the opening and the end grain of beam | 55 – 295 | |
| Clear span between adjacent openings | 95 – 515 |
Geometrical dimension of the cross-lap connections.
The overall geometry of the prototype is shown in Figure 14. For each web element, the resulting 2D geometry embeds not only the cross-lap locations and dimensions, but also curvature and assembly vectors used to verify that local joint cuts do not hinder insertion of the curved components during construction. Web elements are cut to nominal zero tolerance (slot width equal to mating thickness) to keep the erected geometry as close as possible to the design surface. The subsequent on-site assembly metrics quantify the effect of encoding assembly constraints in the parts themselves.
FIGURE 14
Table 4 summarizes the build scale and the observed on-site installation effort. The prototype comprises a large number of repeatable elements and joints, yet the assembly is completed rapidly with a standard crew and without tape-measure layout lines, indicating that alignment and placement are primarily governed by the embedded joinery logic rather than field measurement. The normalized labour metrics reported in Table 4 (person-minutes per joint and per web) provide a transferable measure of constructability and allow comparison against alternative connection typologies or assembly strategies independent of crew size and total duration. Furthermore, the maximum surface curvature, shown in Figure 15, correlates to a maximum milling angle of 30°. This limit is achievable without any collisions or complications in the simulated path planning for the given endmills.
TABLE 4
| Metric | Value | Unit | Note |
|---|---|---|---|
| Structural web elements | 116 | Elements | - |
| Cross-lap joints (total) | 624 | Joints | - |
| Non-structural flanges | 200 | Elements | - |
| Crew size | 20 | People | - |
| Installation duration | 4 | Hours | On-site assembly time |
| Total labour input | 80 | Person-hours | 20 × 4 = 80 person-hours |
| Average labour per joint | 7.7 | Person-min/joint | Averaged over the build |
| Average labour per web | 41.4 | Person-min/web | Averaged over the build |
Prototype scale and on-site assembly productivity metrics.
FIGURE 15
Table 5 reports production efficiency and dimensional quality outcomes. Material utilization is consistently high, with a narrow percentile band, and waste is limited through nesting strategies that exploit remnant regions and grain-aligned cutting layouts. In parallel, quality assurance results indicate that the cross-lap openings track the digital nominal dimension closely. The measured distribution exhibits a small mean bias relative to the model and most joints fall within ±0.5–1.0 mm of the target. Importantly, none of the joints required dressing, shimming, or dimensional rework during assembly, supporting the conclusion that the achieved fabrication variability is compatible with the intended friction-fit, self-locating joint behavior. Off-cut area is also minimized by nesting short web segments into remnant “islands,” and by aligning long edges with the stock grain.
TABLE 5
| Metric | Value | Unit | Note |
|---|---|---|---|
| Average sheet utilization | 78 | % | (5th–95th percentile: 68%–84%) |
| Stock sheet size | 2.0 × 4.0 | m | |
| Average off-cut per sheet | 0.6 | m2/sheet | ≈7.5% of an 8.0 m2 sheet |
| Opening width audit sample size | 102 | # | Completed webs |
| Nominal opening width | 14.0 | mm | Digital model nominal |
| Measured range | 12.5–16.1 | Mm | |
| Mean/median/SD | 13.9/13.8/0.6 | Mm | |
| Mean offset vs. nominal | 0.06 | mm | |
| Within ±0.5 mm of nominal | 63.7 | % | |
| Within ±1.0 mm of nominal | 91.2 | % | |
| Stated variability band | ±0.5–1.0 | mm | |
Material utilization and fabrication quality summary.
The results indicate that the most influential parameter in determining the geometry of the connections is the capability of the milling machine, along with its end effector, to avoid collision. This parameter determines the ultimate degree of rotation about the machine’s Axis X and Axis Y (Figures 12d,e) on joint inclination and hence on local lap geometry. Furthermore, nesting yield and sheet counts indicate that adding “instruction-in-part” features (keys, stops, marks) does not materially degrade stock utilization.
The erection sequence builds directly on the DfMA logic encoded in the CAD model. Web pieces are kitted by wave and bay clusters, and each element arrives on site with a unique ID, orientation path, and mating codes for the two cross-lap families, all derived from the parametric model. This one-to-one mapping between digital identifiers and physical parts collapses layout into a retrieval problem rather than a measurement task. On site, a single datum bay is established at the base using only the self-locating laps. Each joint incorporates a keyed lead-in and a stop-depth shoulder, so once a tongue is rolled into its slot and seated, in-plane position and axial registration are fixed without tapes, chalk lines, or ad-hoc jigging.
A deterministic, four-wave sequence, shown in Figures 16a–d, translates the diagrid pattern into field operations. Waves 1 and 2 (Figures 16a,b) place every other web in one family to establish a diamond cell that both defines curvature and provides access for Waves 3 and 4. Each piece is handled by a two-person crew to retrieve from the kit, orient by the printed arrow, engage the lower cheek of the lap, then roll the part about its own edge until the stop-depth shoulder contacts. At each intersection, mating order is encoded in the lap geometry (i.e., Wave 1’s lap first, Wave 2’s lap second) so joints cannot be assembled in the wrong order or at the wrong depth. Waves 3 and 4 (Figures 16c,d) continue the same odd–even logic, advancing the diagrid in continuous bands rather than isolated ribs. The results indicate that this banded progression limits cumulative mismatch.
FIGURE 16
Crew leads perform fast, non-instrumented checks at every cross-lap (i.e., shoulder flushness, full tongue engagement, and absence of rocking) to detect any deviation before it propagates. In practice, these checks function as a low-tech quality gate layered on top of the high-information parts. Any residual fabrication or handling tolerances are absorbed by the keyed lead-ins and stop-depths rather than by site cutting or shimming. This approach shows how a formally simple grammar of self-locating joints, when coupled with kitting and wave-based deployment, provides a measurement-free, repeatable erection process consistent with the DfMA assumptions made upstream. Following the successful installation of the webs, flanges are installed from bottom to top, with lapping of the upper over the lower, and from left to right, with lapping of the flanges heading to the upper left over the flanges heading to the upper right. After completing the flange assembly on the web components, wood dowels are installed.
3.2 Structural performance assessment, and design recommendation
The finite element model, shown in Figure 17, is generated automatically by the in-line CAE pipeline developed in the compas_fea ecosystem and described in Section 2.3.1. The framework integrates linear isotropic material behavior and establishes the solver parameters for small-displacement finite element analysis using a linear static solver. Base nodes of each web are pinned in translation (Ux = Uy = Uz = 0, rotations free), representing dowelled fixity to a plywood slab bed. Loads comprise self-weight and factored wind pressure derived from NBCC climatic data for Toronto (Table 2), applied as distributed pressure on the web faces. The governing Ultimate Limit State (ULS) combination 1.25D + 1.4W is implemented. The FE simulations and subsequent post-processing are conducted on a workstation equipped with a 12th Gen Intel® Core™ i7-12800H CPU operating at 2.40 GHz, supported by 32 GB of RAM. The computational time associated with modeling, analysis, output database development, and visualization, all automated in compas_fea, is provided in Table 6.
FIGURE 17
TABLE 6
| Description | Time [seconds] |
|---|---|
| Analysis time required by ABAQUS | 100.3 |
| Data extracted from abaqus.odb file | 162.8 |
| Saving data to structure.results | 10.2 |
| Processing stored data for visualization | 3.3 |
Computation time breakdown for finite element analysis and post-processing workflow.
Results demonstrate that the principal stress field is strongly disturbed in the cross-lap regions, as expected for openings that remove a significant fraction of the web depth (Figure 18). Stress amplification is also pronounced near the base and in zones of higher curvature and elevation. Under the factored ULS combination, the maximum principal stress reaches approximately 25.5 N/mm2 in the most critical web segments. When compared to the characteristic bending strength of the marine plywood used (42 N/mm2, Table 1), this corresponds to a utilization on the order of 0.6. In other words, the stress state under factored wind remains within the ULS capacity of the material, with a residual margin that is consistent with the demonstrator’s non-occupied use and the simplifying assumptions in the model.
FIGURE 18
The stress patterns clarify likely failure mechanisms. Edge-wise bending of the curved webs generates transverse tensile stresses and shear stresses concentrated around the corners of the cross-lap openings near the base, suggesting that shear cracking and perpendicular-to-grain tension in those zones are the governing local limit states. This observation is consistent with the DIN-based opening criteria used in the grammar, which constrain opening height, width, and spacing to maintain a sufficient residual section.
At global level, the stress distribution clearly demonstrates that the proposed diagrid system, with its distributed network of cross-lap connections, provides a robust force-transfer mechanism. This structural resilience predominantly arises from the redundancy created by numerous cross-lap connections, which allow force redistribution across the entire network, acting like “micro modules.” Furthermore, the relatively shallow curvature of the system maintains moderate stress concentrations across the structure. This mechanism results in reducing the risk of localized failures and improving overall structural integrity.
Figure 19 presents the total displacement under the ULS threshold. The structure exhibits a maximum displacement of 242 mm, located at the uppermost free corner where cantilever action is most pronounced and lateral restraint is weakest. Although this deformation is large compared with conventional serviceability criteria for building components, it is compatible with the pavilion’s extremely low weight (266 kg), expansive vertical surface area (22 m2), and its role as a temporary demonstrator without superimposed finishes or stiffness contributions from non-structural elements. Observations during loading and occupant interaction confirmed the predicted flexible behavior, where the structure remained safe and stable, but with perceptible sway at the high corner, consistent with the FE deformation shape.
FIGURE 19
To reduce deflection at the serviceability limit state, the following three complementary measures are recommended for future iterations of the grammar: (a) The depth of web elements could be increased such that they become deeper at the base and through the cantilever zone. This approach simultaneously increases cross-lap bearing and shear capacity by enlarging the joint shear planes. (b) Box action can be further exploited by promoting flange bands to structural members (i.e., continuous flange strips bonded to web edges), which will elevate the section’s second moment. (c) The diagrid can be locally tightened in the high-deflection region by reducing bay length and/or adding ribs, while keeping coarser spacing over mild curvature. The latter shifts more load into shorter, stiffer spans and raises both membrane and bending stiffness where needed. All three interventions preserve measurement-free assembly because they are encoded as parametric rules in the component grammar (depth grading, flange role flags, local spacing) and realized through the same self-locating cross-lap features. In this way, the FE analysis is not a one-off validation step but part of an iterative, solver-backed design loop that adjusts the grammar to balance structural performance, material use, and constructability.
Figure 20 shows the reaction forces at the base of the structure, decomposed into tension and compression. These forces are especially pronounced in areas with extensive cantilever and torsional action. Peak torsional action reaches an uplift force of approximately 4.5 kN per web element pinned to the support. Beyond planar curvature in the plan, the structure also exhibits curvature in elevation (out-of-plane with respect to the target surface). The combination of these two curvature effects, coupled with the relatively large surface area, increases the eccentricity between the center of mass and the center of rigidity. Consequently, significant torsional overturning moments are generated at the extremities of the structure in the plan. This overturning torsional behavior is evidenced by the notable uneven uplift reactions shown in Figure 21, as predicted by the FE model in Figure 20. These uplift forces are effectively counteracted by securely pinning the structure to the foundation, ensuring overall structural stability.
FIGURE 20
FIGURE 21
3.3 Limitations and transferability
The demonstrator validates the feasibility of the proposed workflow within the scope of a controlled full-scale prototype; however, the following assumptions limit direct transfer to other structural systems or occupied buildings. First, the structural model uses a simplified linear static analysis with homogenized shell elements. The flanges are included in self-weight but are not modeled as stiffness-contributing structural members, and the cross-lap joints are represented through idealized geometric continuity rather than calibrated nonlinear connection behaviour. As a result, the analysis is suitable for evaluating global stress patterns, identifying critical regions around openings, and informing design iteration; however, it should not be interpreted as a non-linear predictive model for performance-based design.
Second, the assembly and fabrication conditions are controlled relative to conventional construction sites. The prototype is fabricated with known material stock, calibrated robotic and CNC equipment, pre-defined kitting, and a coordinated assembly crew. These conditions support measurement-free assembly. However, transfer to larger buildings would require additional tolerance studies and staged-construction analysis. In particular, slip, moisture effects, and accumulated fabrication tolerances would need to be explicitly characterized before the system could be generalized to occupied structures.
Despite these limitations, the following aspects of the workflow remain transferable: the use of indexed component data, persistent part and joint identifiers, local joint-frame generation, co-located structural verification, fabrication-aware geometry checking, nesting, labeling, kitting, and assembly sequencing. The transferable contribution is therefore not the specific pavilion geometry or its simplified structural model, but the workflow logic through which geometry, structural constraints, fabrication constraints, and assembly information are coordinated before material is cut.
4 Summary, conclusion and outlook
This research employed computational methods and a case-study experimental approach to develop and evaluate a component-based timber system, demonstrated through a full-scale pavilion and an integrated CAD–CAE–CAM framework. The study presented a bespoke, double-curved timber diagrid connected exclusively through wood-to-wood-only integral joints. Within a unified workflow, a parametric pipeline automated geometric modeling, structural simulation, robotic fabrication, and construction sequencing. The framework operationalized Design for Manufacture and Assembly (DfMA) by encoding key assembly constraints “in-part” through a component grammar of self-locating cross-laps. Mating order, axial registration, and stop-depths were implemented as geometric features within the components, reducing reliance on drawing-based layout during assembly. This shifted tolerance budgeting upstream into part geometry and enabled the prototype to be assembled without tape-measure layout, using 116 webs and 624 cross-lap joints.
As digital-to-physical workflows mature, timber is well positioned for highly specific, performance-driven structural components in expressive architecture. In this work, prefabricated bespoke parts improved assembly efficiency while reducing fabrication waste. Repeatable robotic fabrication processes provided design flexibility with predictable performance, as evidenced by the full-scale construction and 78% average sheet utilization. The research also showed how robotic path planning, nesting, and joint geometry can be coordinated to respect curvature envelopes, minimum tool radii, and collision-free access for 3-axis and 5-axis operations.
A second contribution is the design component that embeds structural verification within the same CAD-based environment used for geometric authoring and manufacturing preparation. The workflow does not eliminate solver-native exchange files, since the ABAQUS backend still requires input and output files. Instead, it controls how these files are generated, read, and mapped back to the design model. CAE model objects are constructed directly from the indexed design geometry, solver input is dispatched deterministically, and returned field data are associated with the originating components. The software contribution, implemented around COMPAS/compas_fea with an ABAQUS backend, establishes a compact CAD/CAM-integrated CAE architecture that can be reused for other timber grammars and material systems while preserving an in-line design loop. The benefit is less “real-time FEA” as a slogan and more the controlled management of translation steps that might otherwise cause drift between design intent, analysis assumptions, fabrication geometry, and physical assembly.
From a construction perspective, the proposed component grammar extends an established lineage of timber systems in which component geometry, fabrication accuracy, and assembly sequence are closely linked. In this study, the cross-lap geometry acted as a positional-constraint system for a non-developable diagrid, but the contribution lies in how this logic was coupled to structural verification, robotic fabrication limits, part indexing, and measured assembly performance. Joints were cut to nominal zero-gap dimensions, while assembly robustness was achieved by distributing fit constraints across many cross-laps, sequencing erection in bands, and encoding mating order in the joint geometry.
Empirically, the full-scale pavilion at the University of Toronto (Figure 22) physically validated the framework. The prototype demonstrated how a component-based structural system can be mapped onto free-form double-curved surfaces, offered a lightweight and efficient digital wood construction approach that eliminates reliance on conventional steel fasteners, and showed that wood-to-wood integral joints can enhance construction efficiency while reducing material consumption and on-site labor. The robotic fabrication process confirmed that high-precision milling of architecturally complex timber components with embedded cross-lap geometry is technically feasible and logistically viable, while the computational structural analysis confirmed that a tightly integrated simulation-based workflow can produce materially efficient systems whose stresses remain within ultimate limit state criteria under wind loading.
FIGURE 22
Compared with built precedents, the present work does not primarily contribute to another example of expressive prefabricated timber construction. Its main contribution lies in the integration of structural simulation and design constraints within the CAD-based geometric model itself. In the proposed workflow, structural checks are not treated as downstream validation after form generation. Instead, geometry, joint dimensions, fabrication constraints, and assembly logic are developed in parallel, allowing connection geometry to be adjusted during design and in a real-time manner. As such, structural requirements and fabrication feasibility are evaluated together. Beyond the bespoke structural system presented, the automated design framework has broader implications for construction robotics. Although applied here to a geometrically complex demonstrator, elements of the workflow may be transferable to more conventional building types and larger-scale applications, provided that structural assumptions, connection behavior, fabrication access, and construction tolerances are recalibrated for those contexts. This adaptability offers a route to scalable solutions for a sector under pressure to deliver faster, lower-carbon housing. When coupled with design intelligence, performance analysis, and material-aware detailing, the approach supports a shift toward high-performance building systems rooted in precision, explicit tolerance management, and adaptability.
Future work will extend the in-line verifier to include connection constitutive laws and staged construction effects within the same architecture, so that joint stiffness, slip, and progressive activation can be reflected directly in the design loop. From a grammar standpoint, depth-graded webs, flange bands promoted to structural action, and locally tightened diagrid spacing will be formalized as rules with automatic re-checking of stiffness, joint capacity, and assembly feasibility. At system scale, the pipeline should be evaluated under a Yin-style multiple-case design to test theoretical replication and explored at full-building scale, including elastic bending on double-curved surfaces, integration of envelope systems, and strategies for embedding services within the structural logic.
Statements
Data availability statement
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.
Author contributions
AR: Conceptualization, Data curation, Formal Analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review and editing. AM: Conceptualization, Data curation, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review and editing. NH: Conceptualization, Data curation, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Validation, Visualization, Writing – original draft, Writing – review and editing, Formal Analysis.
Funding
The author(s) declared that financial support was received for this work and/or its publication. The authors gratefully acknowledge the financial support of the John H. Daniels Faculty of Architecture, Landscape, and Design at the University of Toronto for providing resources and materials for the design and construction of the pavilion. The authors also extend their acknowledgement to the Department of Civil and Mineral Engineering within the Faculty of Applied Science and Engineering at the University of Toronto, as well as the School of Architecture and Landscape Architecture at the University of British Columbia, for their institutional support.
Acknowledgments
This research pavilion benefited greatly from the dedication and contributions of Highly Qualified Personnel (HQP) involved in construction, including: Liam Cassano, Mateusz Grabowski, Caroline Guirguis, Amirhossein Heidari, Zhelun Li, Sarah Mak, Ala Mohammadi, Julia Paulson, Nicole Quesnelle, Jagtesgwar Singh, Annie Song, Julia Song, Emily Sun, Jun Heng Tan, Eugene Wang, Jaya Xue, and Yixuan Zhang.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
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Appendix A
Figure A1 provides the software-specific implementation of the computational workflow detailed in Section 2.1.1 in Rhino/Grasshopper.
FIGURE A1
Summary
Keywords
computational design, design automation, design for manufacture and assembly, robotic fabrication, timber construction
Citation
Rezaei Rad A, Meyboom A and Hoban N (2026) Engineering-integrated robotic timber diagrids: co-located analysis-to-fabrication workflow and rapid assembly. Front. Built Environ. 12:1837367. doi: 10.3389/fbuil.2026.1837367
Received
24 March 2026
Revised
10 May 2026
Accepted
31 May 2026
Published
07 July 2026
Volume
12 - 2026
Edited by
Hüseyin Emre Ilgın, Tampere University, Finland
Reviewed by
Tom Svilans, Royal Danish Academy, Denmark
Zhigang Li, National University of Singapore, Singapore
Updates
Copyright
© 2026 Rezaei Rad, Meyboom and Hoban.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Aryan Rezaei Rad, aryan.rad@utoronto.ca
Disclaimer
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