System and method for designing and fabricating a three-dimensional reciprocal lattice structure

Abstract

A system and method for designing and fabricating a three-dimensional lattice structure includes providing a voxel-based design for the 3D lattice structure, extracting each angled edge of the voxel-based design as a linear structural member, extracting each horizontal surface of the voxel-based design as a horizontal panel or each curved surface of the voxel-based design as a curved panel, offsetting all intersections of the linear structural members with the horizontal or curved panels by a horizontal displacement in opposing directions to eliminate collisions of the linear structural members with one another, and controlling one or more programmable or computer- controlled machines to fabricate the horizontal or curved panels. The 3D lattice structure includes linear structural members connected to horizontal or curved panels in accordance with the voxel-based design

Description

SYSTEM AND METHOD FOR DESIGNING AND FABRICATING A THREE- DIMENSIONAL RECIPROCAL LATTICE STRUCTURECROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Application Serial No. 63 / 662,495, filed June 21, 2024, the entire contents of which are incorporated herein by reference.TECHNICAL FIELD OF THE INVENTION

[0002] The present invention relates in general to the field of architecture and construction, and more particularly, to a system and method for designing and fabricating a three-dimensional lattice structure.STATEMENT OF FEDERALLY FUNDED RESEARCH

[0003] None.BACKGROUND OF THE INVENTION

[0004] Without limiting the scope of the invention, its background is described in connection with lattice structures, timber dowel systems, reciprocal structures, and advanced fabrication and assembly.

[0005] Lattice structures, characterized by their topological order and three-dimensional (3D) open-cell composition, consist of one or more repeating unit cells [1]. Also recognized as 3D space frame systems in architecture and engineering, their lightweight nature and ease of assembly and disassembly have been acknowledged by researchers and design pioneers [2,3]. Recent advancements in digital design and fabrication, such as 3D printing and robotic production, have facilitated the construction of customized lattice structures with non-repetitive modules and elements [4-6,31].

[0006] Lattice structures are notable for their structural integrity and lightness, yet traditional assembly methods often rely on secondary materials for connections, which complicates both the assembly and disassembly processes. Lattice structures have valuable outcomes, including fewer defects and the prevention of excessive stress buildup. In the context of the present disclosure, ‘defects’ refer to imperfections or flaws that manifest on the surface of the exterior of a structure and within the internal structure of the materials or components used to form the structure. Thesedefects, which may include scratches, dents, pits, or irregularities, have the potential to compromise the structural integrity, aesthetic quality, or functionality of the material. The incorporation of lattice structures having a reduced mass and profde compared to the original structure significantly reduces these defects, thereby enhancing the performance of the structure. This reduction suggests that both the manufacturing process and the intrinsic properties of lattice designs contribute to a smoother or more uniformly high-quality outcome. This outcome is crucial in preventing the buildup of stresses that could worsen such defects or imperfections, a consideration that becomes especially important when working with anisotropic materials, such as wood, where directional properties can influence the manifestation of defects.

[0007] The associated benefit of less material and volume extends to saving initial and subsequent costs and achieving high performance with less embodied energy, thereby reducing overall costs and the carbon footprint of the building processes. The background encompasses various fields of study, including computational design and automation in construction and assembly. This wealth of understanding spans key sub-disciplines such as reciprocal systems [7], timber dowels structures, lattice systems, automation in construction, design for assembly and disassembly, augmented reality-enabled assembly, and human-robot collaboration in building processes.

[0008] Architectural timber structures use standard joint techniques for stability and load-bearing capabilities. These methods often involve metal fasteners or complex woodworking joints, or 3D printed elements, which can be limiting in terms of design flexibility and sustainability in construction. Traditional assembly methods, which heavily rely on adhesives, binding elements, or metal connections, pose sustainability challenges in disassembly and recycling.

[0009] Numerous scholarly works delve into optimizing timber structures, leveraging diverse computational approaches. Villar et al. employed genetic algorithms to optimize heavy timber trusses incorporating dowel joints, meticulously considering geometry, cross-sectional dimensions, and dowel requirements [8]. Silih et al. prioritized optimizing timber trusses while factoring in joint flexibility, utilizing mixed-integer nonlinear programming [9,10]. Tang et al. investigated an innovative hybrid joint comprising dowels and bonding steel plates for timber structures, analyzing load-bearing capacity, shear stress, and slip stiffness characteristics

[0011] . Notably, accounting for joint flexibility in optimization has demonstrated substantial impact on design outcomes, underscoring its criticality in ensuring structural efficiency and costeffectiveness [9].

[0010] In the field of reciprocal frame structures, also known as nexorades, a variety of research has been conducted to explore their geometric intricacies, form-finding methodologies, and structural behavior. Douthe and Baverel employed dynamic relaxation techniques to derive the form of nexorades and perform structural analyses, addressing the inherent geometric constraints

[0012] . Senechai et al. developed analytical solutions to navigate the geometrical complexities of elementary nexorade structures

[0013] . Mesnil et al. presented the design and fabrication of complex timber structures that combined shell and nexorade geometries, highlighting their innovative structural systems and the challenges associated with their fabrication

[0014] . Gelez et al. aimed to understand the structural behavior of nexorades through analytical methods, comparing their bending resistance and stiffness to that of flat grids

[0015] . Several studies concentrated on computational tools and methods tailored for designing and optimizing reciprocal frame (RF) structures. Song et al. developed interactive computational tools for RF structure design, accentuating aesthetic considerations, generating coherent RF tessellations, and optimizing rod collinear contacts 16,17]. Parigi and Kirkegaard propounded a computational approach for predicting and governing the geometry of extensive reciprocal element networks, resolving unique fabrication problems

[0018] .

[0011] The synergy of robotic fabrication and advanced manufacturing techniques has demonstrated substantial potential in constructing timber structures. Apolinarska et al. spotlighted a computational approach employed in ETH Zurich’s “Sequential Roof’ project, involving the creation of immense 2D Trusses as freeform timber structure assembled robotically

[0019] . They developed algorithms for nail connections and strategies to surmount fabrication constraints.

[0012] Willmann et al. explored leveraging robotic fabrication to upscale additive digital fabrication techniques for industrial-scale timber assembly, optimizing structural design and efficiency

[0020] . Ruan and Adel showcased a case study on the robotic fabrication of nail-laminated timber structures, unveiling a human-robot collaborative assembly process for this innovative construction method

[0021] .

[0013] In the context of assembly design and evaluation for reciprocal architectural systems, Torghabehi et al. proposed a computational method integrating parametric assembly design with structural analysis and optimization

[0022] . Additionally, augmented reality (AR) technologies have been explored to guide and evaluate assembly sequences. Raghavan et al. examined an AR tool for evaluating assembly sequences, permitting manipulation of virtual and physical prototype components

[0023] . Molineros et al. introduced a computer vision-based AR system for visualizing and guiding assembly steps

[0024] . Wang et al. focused on utilizing AR for manual assembly design,incorporating 3D bare-hand interaction for natural manipulation of virtual components

[0025] . Kousi et al. presented an AR framework to support operators in robotic assembly lines, enhancing human-robot communication

[0026] .

[0014] Studies have explored robotic fabrication and human-robot collaboration (HRCA) for unique timber construction

[0027] . Researchers have examined HRCA's application, aiming to develop effective construction processes, robotic assembly systems, and integrated design-to- fabrication methods. Adel et al. delved into robotic timber structure fabrication, highlighting a multi-story building project as a case study

[0028] . Thoma et al. discussed a novel construction system employing wood and cooperative robotic fabrication processes, expanding dowel- laminated timber (DLT) design possibilities beyond planar geometries to complex, curved structures

[0029] .

[0015] Accordingly, there is a need for a system and method for designing and fabricating a 3D reciprocal lattice structure.SUMMARY OF THE INVENTION

[0016] In one embodiment in accordance with the present disclosure, a computerized method for designing and fabricating a three-dimensional (3D) lattice structure includes providing a voxelbased design for the 3D lattice structure stored in a memory or database of a computer comprising one or more processors communicab ly coupled to an input / output interface and the memory or database. The one or more processors extract each angled edge of the voxel-based design as a linear structural member, and each horizontal surface of the voxel-based design as a horizontal panel or each curved surface of the voxel-based design as a curved panel. The one or more processors offset all intersections of the linear structural members with the horizontal or curved panels by a horizontal displacement in opposing directions to eliminate collisions of the linear structural members with one another. The one or more processors control one or more programmable or computer-controlled machines via the input / output interface to fabricate the horizontal or curved panels.

[0017] In one aspect, the method includes providing the linear structural members or fabricating the linear structural members using the one or more programmable or computer controlled machines. In another aspect, the method includes assembling the 3D lattice structure using the fabricated linear structural members and horizontal or curved panels. In another aspect, the method includes modifying a profde of one or more of the horizontal or curved panels or one or more of the linear structural elements. In another aspect, the one or more processors identify a plurality ofpanels that partially enclose or fully enclose the linear structural members, the horizontal or curved panels, or both, and control one or more programmable or computer-controlled machines via the input / output interface to fabricate the plurality of panels. In another aspect, the method includes assembling the 3D lattice structure using the fabricated linear structural members, the horizontal or curved panels and the plurality of panels. In another aspect, the one or more processors extract each intersection of the linear structural members that is not connected to any horizontal surface of the voxel-based design as another one of the horizontal or curved panels or an extension of one of the horizontal or curved panels. In another aspect, the one or more processors control the one or more programmable or computer-controlled machines via the input / output interface to fabricate the horizontal or curved panels further comprises creating a hole in the horizontal or curved panels at each intersection of the linear structural members with the horizontal or curved panels. In another aspect, the one or more processors merge any of the horizontal or curved panels that are adjacent to and level with another horizontal or curved panel.

[0018] In another aspect, the one or more processors analyze one or more structural characteristics of the 3D lattice structure, optimize the 3D lattice structure to satisfy one or more parameters, and allocate a material profde to each linear structural member and each horizontal or curved panel based on the optimized 3D lattice structure. In another aspect, the forgoing analyzing, optimizing and allocating steps are repeated until the optimized 3D lattice structure satisfies a set of criteria. In another aspect, the linear structural members penetrate the horizontal or curved panels. In another aspect, the one or more processors assign a diameter to each linear structural member based on a structural analysis of the 3D lattice structure. In another aspect, the diameter is substantially the same or varies along a length of the linear structural member. In another aspect, the one or more processors categorize each linear structural member by a last horizontal planar member that the linear structural member pierces, and sort the categorized linear structural members into lists based on a radius and a length, wherein the lists provide guidance on assembling the 3D lattice structure. In another aspect, the voxel-based design comprises two or more solid voxels connected to one another, and each solid voxel comprises a half or whole tetrahedron, a half or whole octahedron, a half or whole polygon having six or more sides, a cumulated cuboctahedron, a uniform tetrahedron, a triangular pyramid or a non-uniform polyhedral tessellation. In another aspect, the 3D lattice structure does not contain any joint fittings, joint fasteners or adhesives. In another aspect, each linear structural member comprises a dowel or any other elongated structural element, and each horizontal or curved panel comprises a timber or any other planar and flat structural element. In another aspect, the linear structural members andhorizontal or curved panels are made of wood, plastic, plexiglass, metal, metal alloys, composite materials, bioplastics, engineered wood products, or a combination thereof. In another aspect, the 3D lattice structure comprises a slab, column, wall, arch, other building element, furniture or furniture element.

[0019] In another embodiment in accordance with the present disclosure, a 3D lattice structure is fabricated in accordance with the methods described above.

[0020] In another embodiment in accordance with the present disclosure, a system includes a memory or database that contains a voxel-based design for a 3D lattice structure, an input / output interface, one or more programmable or computer-controlled machines communicably coupled to the input / output interface, and one or more processors communicably coupled to the input / output interface and the memory or database. The one or more processors extract each angled edge of the voxel-based design as a linear structural member, extract each horizontal surface of the voxelbased design as a horizontal panel or each curved surface of the voxel-based design as a curved panel, offset all intersections of the linear structural members with the horizontal or curved panels by a horizontal displacement in opposing directions to eliminate collisions of the linear structural members with one another, and control the one or more programmable or computer-controlled machines to fabricate the horizontal or curved panels.

[0021] In one aspect, the one or more processors control the one or more programmable or computer-controlled machines to fabricate the linear structural members. In another aspect, the one or more processors control the one or more programmable or computer-controlled machines to assemble the 3D lattice structure using the fabricated linear structural members and horizontal or curved panels. In another aspect, the one or more processors or the one or more programmable or computer-controlled machines modify a profde of one or more of the horizontal or curved panels or one or more of the linear structural elements. In another aspect, the one or more processors further identify a plurality of panels that partially enclose or fully enclose the linear structural members, the horizontal or curved panels, or both, and control the one or more programmable or computer-controlled machines to fabricate the plurality of panels. In another aspect, the one or more processors further control the one or more programmable or computer- controlled machines to assemble the 3D lattice structure using the fabricated linear structural members, the horizontal or curved panels and the plurality of panels. In another aspect, the one or more processors further extract each intersection of the linear structural members that is not connected to any horizontal surface of the voxel-based design as another one of the horizontal or curved panels or an extension of one of the horizontal or curved panels. In another aspect, the oneor more processors further control the one or more programmable or computer-controlled machines to fabricate the horizontal or curved panels further comprises creating a hole in the horizontal or curved panels at each intersection of the linear structural members with the horizontal or curved panels. In another aspect, the one or more processors further merge any of the horizontal or curved panels that are adjacent to and level with another horizontal or curved panel.

[0022] In another aspect, the one or more processors further analyze one or more structural characteristics of the 3D lattice structure, optimize the 3D lattice structure to satisfy one or more parameters, and allocate a material profde to each linear structural member and each horizontal or curved panel based on the optimized 3D lattice structure. In another aspect, the analyzing, optimizing and allocating steps are repeated until the optimized 3D lattice structure satisfies a set of criteria. In another aspect, the linear structural members penetrate the horizontal or curved panels. In another aspect, the one or more processors further assign a diameter to each linear structural member based on a structural analysis of the 3D lattice structure. In another aspect, the diameter is substantially the same or varies along a length of the linear structural member. In another aspect, the one or more processors further categorize each linear structural member by a last horizontal planar member that the linear structural member pierces, and sort the categorized linear structural members into lists based on a radius and a length, wherein the lists provide guidance on assembling the 3D lattice structure. In another aspect, the voxel-based design comprises two or more solid voxels connected to one another, and each solid voxel comprises a half or whole tetrahedron, a half or whole octahedron, a half or whole polygon having six or more sides, a cumulated cuboctahedron, a uniform tetrahedron, a triangular pyramid or a non-uniform polyhedral tessellation. In another aspect, the 3D lattice structure does not contain any joint fittings, joint fasteners or adhesives. In another aspect, each linear structural member comprises a dowel or any other elongated structural element, and each horizontal or curved panel comprises a timber or any other planar and flat structural element. In another aspect, the linear structural members and horizontal or curved panels are made of wood, plastic, plexiglass, metal, metal alloys, composite materials, bioplastics, engineered wood products, or a combination thereof. In another aspect, the 3D lattice structure comprises a slab, column, wall, arch, other building element, furniture or furniture element.

[0023] In another embodiment in accordance with the present disclosure, a 3D lattice structure includes a linear structural member for each angled edge of a voxel-based design of the 3D lattice structure, and a horizontal panel for each horizontal surface of the voxel-based design or a curved panel for each curved surface of the voxel-based design. The linear structural members areconnected to the horizontal or curved panels substantially in accordance with the voxel-based design. All intersections of the linear structural members with the horizontal or curved panels are offset by a horizontal displacement to eliminate collisions of the linear structural members with one another.

[0024] In one aspect, a profde of one or more of the horizontal or curved panels or one or more of the linear structural elements is modified. In another aspect, the 3D lattice structure includes a plurality of panels that partially enclose or fully enclose the linear structural members, the horizontal or curved panels, or both. In another aspect, the 3D lattice structure includes another one of the horizontal or curved panels or an extension of one of the horizontal or curved panels corresponding to each intersection of the linear structural members that is not connected to any horizontal surface of the voxel-based design. In another aspect, the horizontal or curved panels have a hole at each intersection of the linear structural members with the horizontal or curved panels. In another aspect, the linear structural members penetrate the horizontal or curved panels. In another aspect, a diameter of the linear structural member is substantially the same or varies along a length of the linear structural member. In another aspect, the voxel-based design comprises two or more solid voxels connected to one another, and each solid voxel comprises a half or whole tetrahedron, a half or whole octahedron, a half or whole polygon having six or more sides, a cumulated cuboctahedron, a uniform tetrahedron, a triangular pyramid or a non-uniform polyhedral tessellation. In another aspect, the 3D lattice structure does not contain any joint fittings, joint fasteners or adhesives. In another aspect, each linear structural member comprises a dowel or any other elongated structural element, and each horizontal or curved panel comprises a timber or any other planar and flat structural element. In another aspect, the linear structural members and horizontal or curved panels are made of wood, plastic, plexiglass, metal, metal alloys, composite materials, bioplastics, engineered wood products, or a combination thereof. In another aspect, the 3D lattice structure comprises a slab, column, wall, arch, other building element, furniture or furniture element.

[0025] Note that the invention is not limited to the embodiments described herein, instead it has the applicability beyond the embodiments described herein. The brief and detailed descriptions of this disclosure are given in the following.BRIEF DESCRIPTION OF THE DRAWINGS

[0026] For a more complete understanding of the features and advantages of the present invention, reference is now made to the detailed description of the invention along with the accompanying figures and in which:

[0027] FIG. 1 depicts a flowchart of a method for the design and fabrication of a three-dimensional (3D) lattice structure in accordance with one embodiment of the present disclosure;

[0028] FIG. 2 depicts a block diagram of a system in accordance with one embodiment of the present disclosure;

[0029] FIGS. 3A and 3B depict a non-limiting example of a voxel-based design and a 3D reciprocal lattice structure in accordance with one embodiment of the present disclosure;

[0030] FIG. 4 depicts a flowchart of the design, fabrication and assembly of a 3D reciprocal lattice structure, such as a timber-dowel reciprocal lattice system, in accordance with another embodiment of the present disclosure;

[0031] FIG. 5 A depicts an overview voxelization to materialization in accordance with one embodiment of the present disclosure;

[0032] FIG. 5B depicts a materialized prototype with plywood in accordance with one embodiment of the present disclosure;

[0033] FIG. 5C depicts a materialized prototype with varied dowel thicknesses in accordance with one embodiment of the present disclosure;

[0034] FIGS. 6A-6D depicts reciprocalization shown on a horizontal section of four voxels in which the reciprocalization factor is increasing from left to right in accordance with one embodiment of the present disclosure;

[0035] FIGS. 6E and 6F show isometric views of the prototyped system before and after reciprocalization in accordance with one embodiment of the present disclosure;

[0036] FIG. 7 depicts prototype photos of a timber dowel reciprocal lattice system, horizontal elements are robotically produced, dowels are cut by miter saw and the assembly done manually following the 3D model in accordance with one embodiment of the present disclosure;

[0037] FIG. 8 depicts a non-limiting example of applying the integrated design to production workflow of timber-dowel reciprocal lattice systems to an arch configuration in accordance with one embodiment of the present disclosure;

[0038] FIGS. 9A-9D depict side, front, top and isometric views, respectively, of a timber-dowel reciprocal lattice arch prototype in accordance with another embodiment of the present disclosure;

[0039] FIG. 10A depicts a demonstration of early phases of a robotic production workflow, with the simulated phases on the left and the corresponding phases on the right in accordance with another embodiment of the present disclosure;

[0040] FIG. 10B depicts a demonstration of later phases of a robotic production workflow, with the simulated phases on the left and the corresponding phases on the right in accordance with another embodiment of the present disclosure;

[0041] FIG. 11A is a top view of designed and assembled prototypes utilizing the timber-dowel reciprocal lattice structure system in accordance with one embodiment of the present disclosure in which the prototype on the left side corresponds to the middle prototype, featuring the same lattice structure with 3D printed joints;

[0042] FIG. 1 IB is a front view of designed and assembled prototypes utilizing the timber-dowel reciprocal lattice structure system in accordance with one embodiment of the present disclosure in which the prototype on the left side corresponds to the middle prototype, featuring the same lattice structure with 3D printed joints;

[0043] FIG. 12 is a photograph of the manufactured and assembled prototype featuring oak dowels of various dimensions in accordance with one embodiment of the present disclosure;

[0044] FIGS. 13A-13D depict the timber-dowel reciprocal lattice system used to construct typical building elements including a slab, column, wall and arch, respectively, in accordance with one embodiment of the present disclosure;

[0045] FIGS. 14A-14B depict the parametric capabilities of the timber-dowel reciprocal lattice system illustrating its flexibility in accommodating free-form structures through customized configurations in accordance with one embodiment of the present disclosure;

[0046] FIG. 15 depicts five column topologies from left to right: straight, compound, V-shape, concave, and convex in accordance with one embodiment of the present disclosure;

[0047] FIG. 16 depicts a table of column prototypes showing voxel geometries, reciprocal lattices, principal stresses, and corresponding weight and displacement for five topologies in accordance with one embodiment of the present disclosure;

[0048] FIG. 17 depicts a reciprocal timber dowel column with four thicknesses of allocated dowels in accordance with one embodiment of the present disclosure;

[0049] FIG. 18 depicts a sample of a double-sided milled 20 mm topologically optimized timber (TOT) plate component in accordance with one embodiment of the present disclosure;

[0050] FIG. 19 depicts plates with TOT method applied and order of assembly and a digital model of Jointless Reciprocal Lattice (JRL) column and labeled plates in accordance with one embodiment of the present disclosure;

[0051] FIG. 20 depicts an assembled scaled column prototype of the JRL and nine 3D printed plates using TOT method in accordance with one embodiment of the present disclosure;

[0052] FIG. 21 depicts a column prototype of the JRL system assembled using TOT method and an augmented reality-assisted assembly of the JRL column in accordance with one embodiment of the present disclosure;

[0053] FIG. 22 depicts a comparative demonstration between two column systems at a larger scale (3x3x6 feet): the Timber Dowel Reciprocal Lattice (TDRL) column without mechanical joints (left), and the Joint-Based Lattice System (right), assembled one-to-one using identical components in accordance with one embodiment of the present disclosure;

[0054] FIG. 23 depicts the one-to-one TDRL column positioned on the ground, demonstrating the system’s inherent compression load-bearing capacity without the use of joints in accordance with one embodiment of the present disclosure; and

[0055] FIG. 24 depicts the one-to-one TDRL column suspended from a crane and hovering above the ground, demonstrating the system’s inherent tension load-bearing capacity without the use of joints in accordance with one embodiment of the present disclosure.DETAILED DESCRIPTION OF THE INVENTION

[0056] While the making and using of various embodiments of the present invention are discussed in detail below, it should be appreciated that the present invention provides many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific embodiments discussed herein are merely illustrative of specific ways to make and use the invention and do not delimit the scope of the invention.

[0057] To facilitate the understanding of this invention, a number of terms are defined below. Terms defined herein have meanings as commonly understood by a person of ordinary skill in the areas relevant to the present invention. Terms such as “a”, “an” and “the” are not intended to refer to only a singular entity but include the general class of which a specific example may be used forillustration. The terminology herein is used to describe specific embodiments of the invention, but their usage does not limit the invention, except as outlined in the claims.

[0058] Various methods are described below to provide an example of each claimed embodiment. They do not limit any claimed embodiment. Any claimed embodiment may cover methods that are different from those described above and below. The drawings and descriptions are for illustrative, rather than restrictive, purposes.

[0059] Various embodiments of the present disclosure provide a lightweight, highly configurable building method and three-dimensional (3D) lattice structure that maximizes the reusability and recyclability of its constituent pieces. The present disclosure addresses the challenge of creating stable, load-bearing structures using sustainable materials while avoiding conventional joint-based lattice structures. It offers an innovative approach to architectural design that combines aesthetics with practical functionality, focusing on renewable materials, advanced fabrication techniques, and automation in construction.

[0060] In addition, the 3D lattice structures described herein diverge from space frames as they do not rely on nodes for load transfer or connection, which facilitates fabrication through subtractive manufacturing and promotes reuse with no additional elements for connection. The distinctive half or whole polygon geometric structure eliminates traditional joints and adhesives, utilizing linear structural members or dowels to reciprocally traverse horizontal panels or timber elements. This approach, rooted in physics, generates counterbalancing forces in reciprocal elements, obviating the need for nodes, joints, connectors or adhesives, which saves both time and cost during fabrication and assembly. Nodes compose the majority of the mass in existing lattice systems, and reciprocal systems are usually challenging to construct, so the present disclosure addresses both of these problems. Due to the modular nature of the developed system, innovative technologies like computational design, robotic manufacturing, and augmented reality can be easily utilized in the design, production, and assembly of the disclose system, method and structures.

[0061] For example, almost any shape or building configuration can be modularized into smaller 3D elements referred to as voxels. These voxels take the form of half or whole polyhedron geometric elements, such as tetrahedra and octahedra, among space-filling tessellation systems. In this proposed method and presented case, the tetrahedral -octahedral honeycomb is chosen as the foundational geometry, selected for its rectangular base topology in horizontal sections and triangular facets in oblique directions. A robotic production process can be used to createhorizontal panels or timber elements with placeholders for linear structural members or dowels at specific spatial angles. Subsequently, the linear structural members or dowels are reciprocally displaced, generating counterbalancing force vectors that obviate the necessity for adhesive materials as the forces inherently self-balance the assembly. Varying degrees of automation can be used in both fabrication and assembly. An additional layer of technological sophistication can be introduced with the possibility of augmented reality-enabled assembly. The degree of automation used is flexible, accommodating various needs based on technological availability, targeted efficiency in production time and material consumption, or particular demands of the construction process. In the illustrated examples, robotic fabrication offers a high degree of precision, yet the designed system can be adjusted for production through alternative methods. The inherent modularity of the system enables this versatility, accommodating various technological landscapes and preferences in fabrication and assembly methodologies. Moreover, this modular design allows it to function seamlessly across a range of scales, from small to large. This adaptability enhances operational efficiency, minimizes production costs, and delivers a robust solution for the fabrication of spatial lattice structures incorporating horizontal panels or timber elements and linear structural members or dowels.

[0062] The embodiments described herein span various scales from interior and exterior building components to large-scale design and assembly of spatial structures. Moreover, the present disclosure can be used for furniture design and construction (e.g., self-balancing shelves, etc.) or any other type of structure or component. The focus is on wood architecture, emphasizing applications in both temporary scaffolds and permanent structures that possess both lightweight and high strength. Additionally, the geometric system introduced in this invention can be adapted to other industries where the demand for optimum structural strength and efficiency of material assembly is crucial, ensuring minimal material consumption. This versatile and modular approach extends the applicability of the inventive system beyond the realm of architecture, building and automation in construction. Moreover, the geometric system can be applied to diverse industries where the imperative is to achieve optimal structural strength and efficiency in material assembly while minimizing material consumption.

[0063] Now referring to FIG. 1, a flowchart of a method 100 for the design and fabrication of a three-dimensional (3D) lattice structure in accordance with one embodiment of the present disclosure is shown. A voxel-based design for the 3D lattice structure stored in a memory or database of a computer comprising one or more processors communicably coupled to an input / output interface and the memory or database is provided in block 102. An example of anapparatus, such as a computer, is shown in FIG. 2. The one or more processors extract each angled edge of the vox el -based design as a linear structural member in block 104, and each horizontal surface of the voxel-based design as a horizontal panel or each curved surface of the voxel-based design as a curved panel in block 106. The linear structural member can be a dowel or any other elongated structural element having a suitable cross-sectional profile (e.g., circular, oval, polygonal, I-Beam, etc.). The horizontal or curved panel can be a timber or any other planar and flat structural element. In some embodiments, the linear structural members and horizontal or curved panels are made of wood, plastic, plexiglass, metal, metal alloys, composite materials, bioplastics, engineered wood products, or a combination thereof. Moreover, the linear structural members and horizontal or curved panels can be solid, hollow, contain voids, or a combination thereof. Non-limiting examples of the 3D lattice structure may include a slab, column, wall, arch, other building element, furniture or furniture element. The one or more processors offset all intersections of the linear structural members with the horizontal or curved panels by a horizontal displacement in opposing directions to eliminate collisions of the linear structural members with one another in block 108. The one or more processors control one or more programmable or computer-controlled machines via the input / output interface to fabricate the horizontal or curved panels in block 110.

[0064] In one aspect, the method includes providing the linear structural elements or fabricating the linear structural elements using the one or more programmable or computer-controlled machines. In another aspect, the method includes assembling the 3D lattice structure using the fabricated linear structural members and horizontal or curved panels. In another aspect, the method includes modifying a profile of one or more of the horizontal or curved panels or one or more of the linear structural elements, which can reduce weight, increase structural strength, improve aesthetics, or improve other characteristics. In another aspect, the one or more processors identify a plurality of panels that partially enclose or fully enclose the linear structural members, the horizontal or curved panels, or both, and control one or more programmable or computer- controlled machines via the input / output interface to fabricate the plurality of panels. In another aspect, the method includes assembling the 3D lattice structure using the fabricated linear structural members, the horizontal or curved panels and the plurality of panels. In another aspect, the one or more processors extract each intersection of the linear structural members that is not connected to any horizontal surface of the voxel -based design as another one of the horizontal or curved panels or an extension of one of the horizontal or curved panels. In another aspect, the one or more processors control the one or more programmable or computer-controlled machines viathe input / output interface to fabricate the horizontal or curved panels further comprises creating a hole in the horizontal or curved panels at each intersection of the linear structural members with the horizontal or curved panels. In another aspect, the one or more processors merge any of the horizontal or curved panels that are adjacent to and level with another horizontal or curved panel.

[0065] In another aspect, the one or more processors analyze one or more structural characteristics of the 3D lattice structure, optimize the 3D lattice structure to satisfy one or more parameters, and allocate a material profile to each linear structural member and each horizontal or curved panel based on the optimized 3D lattice structure. In another aspect, the forgoing analyzing, optimizing and allocating steps are repeated until the optimized 3D lattice structure satisfies a set of criteria. In another aspect, the linear structural members penetrate the horizontal or curved panels. In another aspect, the one or more processors assign a diameter to each linear structural member based on a structural analysis of the 3D lattice structure. In another aspect, the diameter is substantially the same or varies along a length of the linear structural member. In another aspect, the one or more processors categorize each linear structural member by a last horizontal planar member that the linear structural member pierces, and sort the categorized linear structural members into lists based on a radius and a length, wherein the lists provide guidance on assembling the 3D lattice structure. In another aspect, the voxel-based design comprises two or more solid voxels connected to one another, and each solid voxel comprises a half or whole tetrahedron, a half or whole octahedron, a half or whole polygon having six or more sides, a cumulated cuboctahedron, a uniform tetrahedron, a triangular pyramid or a non-uniform polyhedral tessellation. In another aspect, the 3D lattice structure does not contain any joint fittings, joint fasteners or adhesives.

[0066] Various 3D lattice structures can be fabricated in accordance with the methods described above.

[0067] Referring now to FIG. 2, block diagram of a system 200 in accordance with one embodiment of the present disclosure is shown. The system 200 includes an apparatus 202 that includes one or more processors 204 communicably coupled to a memory 206 and an input / output interface 208, which is communicably coupled to a display 210. Note that the apparatus 202, such as a computer or other processing device, may include other components not specifically described herein. The memory 206 can be local, remote or distributed. Likewise, the one or more processors 204 can be local, remote or distributed. The input / output interface 208 is also communicably coupled to one or more databases 212 and one or more programmable or computer-controlled machines or other devices 214 via one or more communication links 216. The one or moredatabases 212 can also be local, remote or distributed. The input / output interface 208 can be any mechanism for facilitating the input and / or output of information (e.g., web-based interface, touchscreen, keyboard, mouse, display, printer, etc.) Moreover, the input / output interface 208 can be a remote device communicably coupled to the one or more processors 204 via one or more communication links 216 (e.g., network(s), cable(s), wireless, satellite, etc.). The one or more communication links 216 can communicably couple the apparatus 202 to other devices (e.g., remote devices, controllers, sensors, etc.).

[0068] The memory 206 or database 212 contains a voxel-based design for a 3D lattice structure. The one or more processors 204 extract each angled edge of the voxel-based design as a linear structural member, extract each horizontal surface of the voxel-based design as a horizontal panel or each curved surface of the voxel-based design as a curved panel, offset all intersections of the linear structural members with the horizontal or curved panels by a horizontal displacement in opposing directions to eliminate collisions of the linear structural members with one another, and control the one or more programmable or computer-controlled machines 214 to fabricate the horizontal or curved panels. The linear structural member can be a dowel or any other elongated structural element having a suitable cross-sectional profile (e.g., circular, oval, polygonal, I-Beam, etc.). The horizontal or curved panel can be a timber or any other planar and flat structural element. In some embodiments, the linear structural members and horizontal or curved panels are made of wood, plastic, plexiglass, metal, metal alloys, composite materials, bioplastics, engineered wood products, or a combination thereof. Moreover, the linear structural members and horizontal or curved panels can be solid, hollow, contain voids, or a combination thereof. Non-limiting examples of the 3D lattice structure may include a slab, column, wall, arch, other building element, furniture or furniture element.

[0069] In one aspect, the one or more processors control the one or more programmable or computer-controlled machines to fabricate the linear structural elements. In another embodiment, the one or more processors control the one or more programmable or computer-controlled machines to assemble the 3D lattice structure using the fabricated linear structural members and horizontal or curved panels. In another aspect, the one or more processors or the one or more programmable or computer-controlled machines modify a profile of one or more of the horizontal or curved panels or one or more of the linear structural elements, which can reduce weight, increase structural strength, improve aesthetics, or improve other characteristics. In another aspect, the one or more processors further identify a plurality of panels that partially enclose or fully enclose the linear structural members, the horizontal or curved panels, or both, and control the oneor more programmable or computer-controlled machines to fabricate the plurality of panels. In another aspect, the one or more processors further control the one or more programmable or computer-controlled machines to assemble the 3D lattice structure using the fabricated linear structural members, the horizontal or curved panels and the plurality of panels. In another aspect, the one or more processors further extract each intersection of the linear structural members that is not connected to any horizontal surface of the voxel-based design as another one of the horizontal or curved panels or an extension of one of the horizontal or curved panels. In another aspect, the one or more processors further control the one or more programmable or computer- controlled machines to fabricate the horizontal or curved panels further comprises creating a hole in the horizontal or curved panels at each intersection of the linear structural members with the horizontal or curved panels. In another aspect, the one or more processors further merge any of the horizontal or curved panels that are adjacent to and level with another horizontal or curved panel.

[0070] In another aspect, the one or more processors further analyze one or more structural characteristics of the 3D lattice structure, optimize the 3D lattice structure to satisfy one or more parameters, and allocate a material profile to each linear structural member and each horizontal or curved panel based on the optimized 3D lattice structure. In another aspect, the analyzing, optimizing and allocating steps are repeated until the optimized 3D lattice structure satisfies a set of criteria. In another aspect, the linear structural members penetrate the horizontal or curved panels. In another aspect, the one or more processors further assign a diameter to each linear structural member based on a structural analysis of the 3D lattice structure. In another aspect, the diameter is substantially the same or varies along a length of the linear structural member. In another aspect, the one or more processors further categorize each linear structural member by a last horizontal planar member that the linear structural member pierces, and sort the categorized linear structural members into lists based on a radius and a length, which can be further optimized considering the availability of material types and diameters, wherein the lists provide guidance on assembling the 3D lattice structure. In another aspect, the voxel-based design comprises two or more solid voxels connected to one another, and each solid voxel comprises a half or whole tetrahedron, a half or whole octahedron, a half or whole polygon having six or more sides, a cumulated cuboctahedron, a uniform tetrahedron, a triangular pyramid or a non-uniform polyhedral tessellation. In another aspect, the 3D lattice structure does not contain any joint fittings, joint fasteners or adhesives.

[0071] Now referring to FIGS. 3A and 3B, a non-limiting example of a voxel-based design 300 and a 3D reciprocal lattice structure 350 in accordance with one embodiment of the present disclosure is shown. The 3D reciprocal lattice structure 350 includes a linear structural member 352 for each angled edge 302 of the voxel -based design 300 of the 3D reciprocal lattice structure 350, and a horizontal panel 354 for each horizontal surface 304 of the voxel-based design 300 or a curved panel for each curved surface of the voxel-based design. The linear structural members 352 are connected to the horizontal panels 354 substantially in accordance with the voxel-based design 300. All intersections of the linear structural members 352 with the horizontal panels 354 are offset by a horizontal displacement to eliminate collisions of the linear structural members 352 with one another (see also FIGS. 5B and 6A-6D). The linear structural members 352 and horizontal panels 354 can be made of any building material or combination of building materials as long as the structural requirements of the 3D reciprocal lattice structure are satisfied. In addition, robotic or automated fabrication and assembly of the 3D reciprocal lattice structure are not required for small scale assemblies.

[0072] In one aspect, a profile of one or more of the horizontal or curved panels or one or more of the linear structural elements is modified, which can reduce weight, increase structural strength, improve aesthetics, or improve other characteristics. In another aspect, the 3D reciprocal lattice structure 350 includes a plurality of panels that partially enclose or fully enclose the linear structural members, the horizontal panels, or both. In another aspect, the 3D reciprocal lattice structure 350 includes another one of the horizontal panels 356 or an extension of one of the horizontal panels 354 corresponding to each intersection of the linear structural members 352 that is not connected to any horizontal surface 304 of the voxel-based design 300, such as the peaks 306 of the voxel-based design 300. For example, a separate horizontal panel could be initially placed at each peak 306 of the voxel -based design 300, or the initial separate horizontal panels 354 can be joined together like horizontal panel 356 since they are at the same level. In another aspect, the horizontal panels 354 have a hole (see FIG. 5B) at each intersection of the linear structural members 352 with the horizontal panels 354. In another aspect, the linear structural members 352 penetrate the horizontal panels 354. The portion of the linear structural members 352 that extend above the upper horizontal panels or below the base horizontal panel can be trimmed or otherwise removed. In another aspect, a diameter of the linear structural member 352 is substantially the same or varies along a length of the linear structural member 352. In another aspect, the voxel-based design 300 comprises two or more solid voxels connected to one another, and each solid voxel comprises a half or whole tetrahedron, a half or whole octahedron, a half orwhole polygon having six or more sides, a cumulated cuboctahedron, a uniform tetrahedron, a triangular pyramid or a non-uniform polyhedral tessellation. In another aspect, the 3D reciprocal lattice structure 350 does not contain any joint fittings, joint fasteners or adhesives. The linear structural member 352 can be a dowel or any other elongated structural element having a suitable cross-sectional profile (e.g., circular, oval, polygonal, I-Beam, etc.). The horizontal panel 354 can be a timber or any other planar and flat structural element. In some embodiments, the linear structural members 352 and horizontal panels 354 are made of wood, plastic, plexiglass, metal, metal alloys, composite materials, bioplastics, engineered wood products, or a combination thereof. Moreover, the linear structural members 352 and horizontal panels 354 can be solid, hollow, contain voids, or a combination thereof. Non-limiting examples of the 3D reciprocal lattice structure 350 may include a slab, column, wall, arch, other building element, furniture or furniture element.

[0073] Various non-limiting examples of the design, fabrication and assembly of 3D reciprocal lattice structures are described below.

[0074] The progress in computer-based design and robot-assisted manufacturing methods has allowed designers and engineers to develop construction solutions based on data and resource considerations. The methods described herein provide a comprehensive approach to facilitate the process from design to assembly, customized for creating timber-dowel lattice structures focusing on efficient use of resources and data-driven decisions. The examples involve establishing a computational design system within CAD / CAM software, such as Rhinoceros 3D, and add-on plug-ins of Grasshopper for graphical algorithmic modeling as its implementation platform. As will be described in more detail below, the workflow initiates with the voxelization of a free-form volume serving as the design input. Subsequently, material profiles are allocated based on parametric structural analysis considering the support and load case conditions, the topologically optimized horizontal elements are generated, and production files are automatically generated through a developed file-to-factory workflow. This workflow seamlessly translates the 3D model results into production files, enhancing the efficiency and precision of the overall design and manufacturing process.

[0075] Now referring to FIG. 4, a flowchart of a method 400 for the design, fabrication and assembly of a 3D reciprocal lattice structure, such as a Timber-Dowel Reciprocal Lattice (TDRL), in accordance with another embodiment of the present disclosure is shown. Although the examples described below involve a timber-dowel reciprocal lattice system, the present disclosureis applicable to any 3D lattice structure. The three stages of the method 400 are: Design Computation 402, Material and Structure 404, and Fabrication and Assembly 406.

[0076] Design Computation Stage 402

[0077] The design computation stage 402 will now be described. The use of the 3D lattice system, such as a TDRL system, developed through an integrated computational design workflow, can be facilitated as described below. The system is designed to accept any input surface or volumetric geometry. Initially, the system generates voxels; then, timber and dowels are sorted. In the subsequent reciprocalization phase, the dowels are shifted to opposing directions to create the reciprocal system. It is important to highlight that while the primary innovation involves advanced computation, the same procedural steps can be applied on a smaller scale using manual digital 3D design for creating and assembling the 3D lattice structures. The key phases of the design computation process 402 include voxelization and the development of the reciprocal system.

[0078] The voxel-based design is provided in block 450. Thereafter, angled edges are extracted as linear structural elements (e.g., dowels, etc.) in block 452, and the horizontal surfaces are extracted as horizontal panels or the curved surfaces are extracted as curved panels (e.g., timber elements) in block 454. The linear structural elements are sorted in block 456 and reciprocation is performed in block 458. Reciprocation moves linear structural elements in opposing directions as explained below. The outer borders of the horizontal panels are offset in block 460, and the long and short linear structural members are found in block 462. These steps will be further described below.

[0079] Voxelization

[0080] A voxel can be understood as the 3D equivalent of a pixel in two-dimensional space, representing the smallest distinct unit of a 3D obj ect or space in the context of octree representation

[0030] , This embodiment of the present disclosure harnesses the voxel-based design methodology using tetrahedral -octahedral honeycomb geometry. This integration facilitates 3D space-filling tessellation. The methodology empowers users to input freeform shapes or geometries, which are subsequently transformed into 3D voxelated structures. This output, in turn, serves as a foundational input for the reciprocation system, illustrating the versatility and applicability of the voxel-based and modular approach in architectural design processes.

[0081] The starting point for the design can be a surface or volume to be voxelated. Alternatively, the designer can directly populate the space with the voxels by aggregating the voxel modules next to each other, or the distribution of the voxels can be computed with methods such as topologyoptimization. FIG. 5A demonstrates the process of generating the initial voxel-based abstract geometry, which will subsequently be transformed into the 3D lattice or TDRL structure using the horizontal panels in FIG. 5B and the dowels or linear elements in FIG. 5C.

[0082] Reciprocalization 458

[0083] Reciprocalization 458 begins with the identification of sets of voxels, from which oblique elements are extracted and represented as lines, known as linear structural members or dowels. The remaining edges form rectangular profiles, which are joined as surfaces and termed as horizontal panels or timber elements. The reciprocalization process 458 commences with these two sets of geometric data: lines and surfaces.

[0084] The steps to create timber-dowel reciprocal lattice structure are as follows: The lines or linear elements are grouped into four sets based on their spatial orientation. Each of these sets undergoes horizontal displacement in opposing directions (-x, +x, -y, +y) to create a reciprocal system. The reciprocalization 458 is illustrated in FIGS. 6A-6D as the horizontal offset is increased from FIG. 6 A to 6D until the lines or linear elements do not intersect with one another or certain material and / or fabrication requirements and constraints are met. The displacement factor plays a crucial role in determining the extent of reciprocalization. The more elements are shifted in the x and y directions, the greater the offset in vertices of the lines compared to their original positions on the vertices of the original voxels.

[0085] Simultaneously, the horizontal elements are assembled into groups to form surfaces that represent horizontal panels or timber elements. As the lines undergo displacement for reciprocalization 458, an offset becomes necessary to accommodate all oblique elements materialized with dowels in block 460. This offset ensures that the dowels can penetrate the horizontal elements without encountering collisions. This process is visually illustrated in FIGS. 6A-6E, where FIGS. 6A-6D shows the horizontal section of the four modules and FIGS. 6E and 6F show isometric views of the prototyped system before and after reciprocalization.

[0086] At this stage, there are elements that connect one or more levels together. Depending on the linear structural member or dowel lengths, it becomes feasible to filter out elements exceeding the available resource material and then divide them into smaller lengths. Subsequently, all lines in the subsystem are extended in both directions, ensuring they penetrate the top and bottom faces of the timber elements once they are placed. However, care is taken to avoid intersections with elements above or below themselves.

[0087] Linear structural members or dowels are subsequently created along the lengths of each line, utilizing a specified radius parameter. The prototype showcased in FIGS. 5 A and 7 incorporates a structural analysis routine that assigns radius to each line within the system. Following this, the intersection points between the linear structural members or dowels and horizontal panels or timbers are subtracted from the horizontal panels or timbers through robotic milling, creating holes designed to securely hold the linear structural members or dowels at the designated angle.

[0088] Eventually, the horizontal panels or horizontal timber elements enhance the structural integrity of the entire 3D lattice or TDRL system by supporting the linear structural members or dowels through tension. The linear structural members or dowels, primarily working under compression, transfer the load from top to bottom. Simultaneously, as the linear structural members or dowels reciprocate spatially, the opposing forces hold the horizontal panels or timbers in their designated special coordinates.

[0089] Material and Structure Stage 404

[0090] The material and structure stage 404 includes analyzing one or more structural characteristics of the 3D lattice structure in block 464, optimizing the 3D lattice structure to satisfy one or more parameters in block 466, and allocating a material profile to each linear structural member and each horizontal panel based on the optimized 3D lattice structure in block 468. The analyzing, optimizing and allocating steps 464-468 can be repeated until the optimized 3D lattice structure satisfies a set of criteria. These steps will be described in more detail below.

[0091] The TDRL system uses a resource- and data-driven design strategy for material allocation and eliminates the need for secondary materials in joints and connections through an integrated computational design approach. This is done by incorporating reciprocal geometry and structural optimization, which enhance structural performance by minimizing the mass and displacement at the same time. The key innovation lies in the jointless reciprocal lattice design, achieved through the integration of tetrahedral-octahedral geometry where each linear element moves at the same angle but in different vectors, creating a consistent geometry that avoids the complexities of typical space frame structure connections, as shown in FIGS. 11A-11B. Underpinning the structural system is a multi-objective optimization process, utilizing computational algorithms to evaluate load and support cases, material properties, and geometric configurations to achieve efficient material usage and load transfer, including distributed or point loads as needed in the design as well as the weight of the structure. This is further enhanced by dynamically allocating customizedstructural profiles within the lattice, optimizing each component based on the load each element receives. This approach marks an advancement in the materialization of lattice systems, opening new avenues for efficient and circular design and construction of wood structures.

[0092] Structural Model: from a joint based to jointless lattice system.

[0093] The design and fabrication approach described herein in the construction of reciprocal structures provides a jointless lattice system. This tailored feature stems from the pursuit of a structural system which benefits from counter balancing force vectors of the voxels in opposing directions. Moreover, the system is not only cost-effective and environmentally sustainable but also simplifies the fabrication process. The decision to eliminate conventional joints and structural connections marks a significant shift in design and construction of lattice structures.

[0094] Incorporating the reciprocal system approach into the horizontal panel or timber and linear structural member or dowel structure allows for jointless fabrication and assemble. This approach is underpinned by the ingenious integration of tetrahedral-octahedral geometry with the reciprocal system, presenting an unprecedented solution to avoid the complexities of designing and fabricating joints and connections. This integration is not just a structural choice but a radical rethinking of architectural design and construction methodologies.

[0095] The essence of this reciprocal process is demonstrated by the uniform movement of all linear elements, with each one moving at precisely the same angle but in different, orthogonal vectors - namely x, -x, y, and -y. This consistent angular movement across different vectors is key in achieving a self-balancing reciprocal system. In one embodiment, a tetrahedral-octahedral honeycomb voxelization with rectangular horizontal profiles is utilized, aligning the movement of the dowels with the x and y vectors. In scenarios involving different polyhedral topologies, a similar approach can be applied, provided the movements align with the directionalities of the base voxels

[0096] The numeric value of reciprocation is intricately linked to the linear distribution of loads, introducing a novel approach to managing structural forces. This method ingeniously leverages the XY plane to distribute forces, effectively eliminating the necessity for complex structural joints. Such a strategy not only simplifies construction but also enhances the structural integrity of the design.

[0097] This approach marks a significant advancement in architectural design, particularly with reciprocal structures. By moving beyond traditional joints and connections, it opens possibilities for more efficient, sustainable, and aesthetically refined designs. This method exemplifies theimpact of creative engineering, showing how traditional construction challenges can be addressed through thoughtful design and engineering. The work stands as a pioneering example of how contemporary Architecture, Engineering, and Construction (AEC) industry can evolve to meet the demands of efficiency, sustainability, and aesthetic elegance.

[0098] Structural Analysis 464, Structural Optimization 466 and Profile Allocation 468 and Topologically Optimized Timber

[0099] In the 3D lattice or TDRL system, the framework uses advanced computational algorithms for optimization, focusing on the most efficient material usage and structural form utilization. This involves iterative simulations to evaluate various load scenarios, material properties, and geometric configurations, aiming to trade-off between structural stability and material usage. This optimization enhances performance and supports circularity by minimizing waste and maximizing resource efficiency. A key aspect of this process is the dynamic allocation of profiles within the lattice, facilitated by the development of an integrated computational design workflow using Karamba3D as a structural analysis add-on plugin. This system assigns profiles of varying radii and lengths to elements based on structural analyses, leading to performance differentiation of structural elements where each component is tailored for its structural function. The profiles may also include material specifications and other information. The profile allocation is dynamic, allowing adjustments in real-time during the design process, which provides a significant flexibility and adaptability to meet varying project requirements, site conditions, and available material palettes.

[0100] The next step introduces material optimization, where principal stress lines extracted from Karamba3D structural analysis are analyzed to guide the redistribution of material within the timber elements, enhancing structural stability while reducing overall weight. FIG. 3 summarizes the first three steps of the workflow in a table, showing the progression from voxel input to material optimization. The column on principal stresses highlights how material is distributed across the timber components to improve structural performance.

[0101] Initially, using the millipede plugin, topology optimization tool was employed to investigate the performance of timber structures under axial forces generated by dowels. However, the resulting mesh lacked the coherence necessary for the integrated system to function cohesively, as it produced a dense mesh primarily around nodal region. Consequently, principal stress distribution on the timber mid-planes is analyzed to better understand material behavior under gravity combined with axial forces which are transferred from the dowels to the plates. Buildingon this, the method is progressed toward the generation of printable and millable meshes using the Marching Cubes algorithm via the Cocoon plugin, focusing on columns composed of 88 voxels. The raw discrete lines which is derived as a data set for compression and tension representing the principal stress analysis on the plates are then used to inform both the material redistribution and the local refinement of mesh geometry. FIG. 5 shows a CNC double-sided milled timber and robotically milled using KUKA | PRC plugin.

[0102] Fabrication and Assembly Stage 406

[0103] The fabrication and assembly stage 406 includes fabricating the linear structural members and the horizontal panels in block 470, assembling the 3D lattice structure using the fabricated linear structural members and horizontal panels in block 472. The fabrication the materials and assembly of the 3D reciprocal lattice structure can be accomplished with a variety of programmable or computer-controlled machines depending on the characteristics of the materials being fabricated, and the size and complexity of the 3D reciprocal lattice structure. These steps will be described in more detail below.

[0104] In one embodiment, the method that has been developed utilizes robotic milling, incorporating multi-directional milling to eliminate the intersection between dowels and timbers. Other types of robotic machines can be used depending on the materials being used. Linear structural members or dowels can be cut numerically using CNC machines, manual tools, or augmented reality enabled cutting setups. Assembly can be automated or assisted through augmented reality, with the choice dependent on the complexity and density of the structure

[0029] , Additionally, given the modular structure, human-robot collaborative design and assembly workflows can be utilized in the assembly of the developed 3D lattice or TDRL system

[0027] ,

[0105] Computer-controlled manufacturing systems with 5 or more axes can be used for multidirectional milling to produce horizontal panels. Implementing programmable production systems with additional axes, such as an 8-axis robotic setup (6 axis robotic arm with a 2-axis positioner holding the horizontal panels to be milled), will notably enhance robotic production flexibility and allow for the milling of steeper angles with reduced singularity, thereby providing increased design freedom compared to a 5-axis machine. Additionally, users can seamlessly customize the size of dowels or linear elements at no additional cost using numerically controlled systems. The implementation of augmented reality-enabled workflows for the cutting and assembly processes, leverages the modular nature of the reciprocal lattice system and further enhances efficiency. Furthermore, fully automated assembly of the reciprocal lattice structures can be achieved usinga sophisticated robotic setup adapted for automated production and assembly. Alternatively, a collaborative approach involving human and programmed robotic setups can effectively execute the production and assembly of the reciprocal lattice structure.

[0106] Robotic Fabrication

[0107] Using robotic multi -directional milling, the process is programmable and customized for different dimensions and configuration of voxels where milling angles are aligned with the angle of linear structural elements or dowels (i.e., the required angles for linear structural member or dowel insertion in horizontal panel or timber structures). FIGS. 10A and 10B illustrate the simulation process of robotic production next to real photos of the process in different stages applying the holes in four different angles. The simulation is conducted using the KUKA|PRC add-on plugin within the Rhino-Grasshopper interface. This system is adaptable to work with a variety of dowel diameters. In the presented prototypes, the dowel diameters span from 3 / 8 inch to one inch. This variation requires an adjustment in the drilled hole diameters, a factor systematically addressed during the design phase, considering various parameters such as structural considerations and resource availability. This flexibility highlights the approach's adaptability and the system's focus on performative customization and circularity in construction. Consequently, the project employs a resource-driven design approach from the outset, mirroring practical adaptations to the availability of material sources. The fabrication process integrates a six-axis industrial robotic arm into the sequence, serving as a key component of the integrated design-to-production. The milling head is equipped with a 6 mm diameter drill bit. Oak wood is chosen for dowels, with 3 / 8-, 1 / 2-, 3 / 4-, and 1-inch diameters (9.5 to 25.4 mm).

[0108] This system is adaptable to work with a variety of linear structural member diameters or dowel diameters within a project. In the prototypes outlined in this disclosure, the dowel diameters span from 3 / 8 inch to one inch. The type of wood in the present prototype is oak or pine wood. This variation requires an adjustment in the drilled hole diameters, a factor systematically addressed during the design phase, considering various parameters such as structural considerations and resource availability. This flexibility not only showcases the adaptability of the approach but also emphasizes the method’s dedication to automation, purposeful customization, and circularity in construction.

[0109] The fabrication process integrates a six-axis industrial robotic arm seamlessly into the sequence, serving as a critical component of design and construction. This machinery, equipped with a 6 mm diameter drill bit and a milling head, enables precision drilling that would bechallenging using conventional methods. However, since the angles are fixed it is still possible to drill the holes manually in case one does not have access to advanced machinery. Additionally, the method adopts a resource-driven design approach from the initial stages, reflecting practical responses to material availability. Oak wood was chosen for dowels, with diameters of 3 / 8, 1 / 2, 3 / 4, and 1 inch, maintaining a balance between resource availability and design necessities. This methodology, blending robotic precision with computational design, sets a new standard in construction of invented type of structural system, showcasing the potential of advanced robotics fabrication. FIGS. 10A and 10B show an overview of robotic fabrication of timber elements.

[0110] Assembly and Sequencing

[0111] The implemented fabrication and assembly process follows a methodologically rigorous series of steps. Linear structural members or dowels are cut to predetermined lengths and radii, ensuring alignment with the structurally analyzed model. Horizontal panels or timber elements are robotically milled to remove holes in varying angles and diameters to hold timber elements or dowels. For example, the horizontal panels or timber elements undergo shaping with a CNC milling machine and perforation using a robotic milling production with an end effector, ensuring accurate correspondence to desired dowel specifications. The assembly method adopts a systematic approach, commencing with the longest dowels that connect three or more horizontal timbers and progressing to the shortest, which only connect two layers of timbers. The placement of the first four opposing direction dowels stabilizes each timber layer, allowing subsequent dowels to fortify the overall structure. Linear structural member or dowel lengths are determined by structural requirements, each having a fabricated counterpart hole with an identical radius in the timber structure. Holes in the timber elements match corresponding dowels with different thicknesses. Horizontal panels or timber elements are crafted using a subtractive method to match system specifications in size, shape, and thickness. Precision milling of holes in timbers is executed by a robotic arm with a milling attachment, following a scripted path to create holes of exact dimensions and orientations.

[0112] In preparation for assembly, horizontal panels or timber elements are prioritized based on removal difficulty, with emphasis on those closest to the ground or support structures. Simultaneously, linear structural members or dowels are categorized by the last element they pierce and sorted into lists based on radius and length, providing guidance for the assembly process. In this documented prototype development, an augmented reality workflow is implemented to tag and organize layers of timbers and sets of dowels according to the assembly sequence. This enables the assembly team to interactively navigate through the list, revealing theposition, orientation, and specific details of each element. Such an approach ensures an efficient and precise assembly process (see FIGS. 8, 9, 10A-10B, 11 A-l IB and 12A-12C).

[0113] FIG. 8 depicts a non-limiting example of applying the integrated design to production workflow of timber-dowel reciprocal lattice systems to an arch configuration in accordance with one embodiment of the present disclosure. The illustrated process is tetrahedron geometry as solid voxels in 802, generating dowels by extracting the angled edges of Tetrahedron voxels in 804, finding the horizontal surfaces of each voxel in 806, using offset to find the optimum configuration of the timber elements in 808, sorting the dowels by the angle to have reciprocal geometry in xy plane of the timber and dowel structure in 810, and extension of dowel elements and profile allocation based on the structural analysis and finding the optimized cross section of each element in 812.

[0114] Resource Driven Design / Circularity

[0115] The 3D reciprocal lattice structure, such as the TDRL system, is grounded in Resource Driven Design, emphasizing sustainable, renewable, and locally resourced or repurposed materials to minimize environmental impact. Timber and dowels are chosen for their biodegradable and renewable qualities, and the approach applies to all materials and processes in the project. The system also incorporates circularity in construction, focusing on design for disassembly. This allows for easy disassembling and recycling or reusing components, supported by the lattice's jointless, glue-less nature and modular design. This approach facilitates component reuse in various configurations or new projects, extending material lifecycles and reducing waste.

[0116] FIGS. 11 A-l IB and 12 showcase a one-to-one prototype utilizing the 3D lattice or TDRL system, demonstrating its practical application. Meanwhile, FIGS. 13A-13D highlight the versatility of the developed method, showcasing its adaptability to a variety of standard building elements, including walls, columns, beams, and slabs. Furthermore, FIGS. 14A-14B explore the parametric capabilities of the 3D lattice or TDRL system, illustrating its flexibility in accommodating free-form structures through customized configurations, thereby underlining the innovative potential of this approach in design and construction.

[0117] Recent research and practical endeavors have highlighted the significance of circular design and construction within the AEC sectors [32,33], Building on the principles of circular thinking, the TDRL System emphasizes a resource-driven design that prioritizes sustainable, renewable, and locally sourced materials to minimize environmental impact. Timber and dowels are specifically selected for their biodegradable and renewable properties, although the system'smethodology could be applied to other material sets. Additionally, the system incorporates design for disassembly, enabling easy dismantling and facilitating the recycling or reuse of components. This enables easy disassembly and the recycling or reuse of components, supported by the fact that the developed method facilitates the design and assembly of jointless, glue-less, and modular structures. This approach promotes the reuse of components in various configurations or new projects, thereby extending material lifecycles and reducing waste.

[0118] The Timber-Dowel Reciprocal Lattice (TDRL) system presented herein introduces a bespoke design to production workflow for resources driven discrete assembly of spatial structures. By developing integrated computational design methodologies, robotic fabrication, and augmented reality-enabled assembly workflows, this approach addresses several key challenges associated with state-of-the-art design, fabrication and assembly of lattice systems.

[0119] One of the central advantages of the TDRL system is its ability to eliminate the need for secondary materials or adhesives in the construction process. This is achieved through the purposeful use of reciprocally displaced timber dowels, which generate counterbalancing forces that stabilize the overall structure. The self-supporting nature of this system not only streamlines the construction process but also aligns with principles of sustainability and material efficiency, as it minimizes the embodied energy and waste associated with additional connectors or fasteners.

[0120] Moreover, the modular design of the TDRL system facilitates adaptability across different scales and densities, enabling its application in a wide range of architectural projects. The structurally informed variation of dowel profiles further enhances this flexibility, allowing for resource- and data-driven design workflows that optimize material usage based on structural requirements and material availability. This aspect of the system is particularly significant in the context of circular construction practices, as it promotes the efficient utilization of resources and minimizes waste.

[0121] The integration of robotic fabrication techniques into the TDRL system is crucial for ensuring precision during the production phase. Multi-directional robotic milling creates precise placeholders for dowels at calculated angles, enabling seamless assembly of the structure. Additionally, the implementation of augmented reality workflows enhances the assembly process by allowing for sequential assembly of the structure and facilitating human-robot collaboration. By providing interactive navigation and real-time visualization of element positions, orientations, and details, the AR-enabled approach streamlines construction and minimizes the potential for errors. This integration of emerging technologies showcases the possibilities for blendingtraditional construction techniques with advanced digital tools, paving the way for innovative building practices.

[0122] In conclusion, this disclosure demonstrates the development and implementation of a novel timber-dowel reciprocal lattice system for architectural applications. Some key aspects lie in the elimination of commonly used joints and connections, the integration of computational optimization, and the adoption of degradable, reusable materials. This disclosure highlights the potential of this approach to streamline fabrication, enhance structural performance, and promote environmentally responsible design and construction practices. The final prototype as shown in FIGS. 11 A-l IB, and the evaluation of the system suggest its applicability in various architectural and construction contexts.

[0123] The timber-dowel reciprocal lattice (TDRL) system can be applied to curved surfaces and freeform volumetric systems as illustrated in FIGS. 14A-14B. Adapting the TDRL system to complex freeform geometries offers the potential to extend its application beyond standard configurations like the arches presented herein. Integration of computational design tools with advanced simulation capabilities will facilitate the design and fabrication of structures with organic, continuous surfaces. Additionally, the development of freeform volumetric systems is expected to enable dynamic spatial arrangements that optimize environmental parameters such as light and sound, as well as overall embodied energy efficiency. Furthermore, other topological types of voxelization systems using polyhedral tessellations beyond the used tetrahedral- octahedral honeycomb — such as cumulated cuboctahedron, uniform tetrahedrons or triangular pyramids, and non-uniform polyhedral tessellations — can extend the functionality of the developed methods.

[0124] Jointless Reciprocal Lattice (JRL) System

[0125] The JRL system integrates computational design, robotic fabrication, and augmented assembly techniques to create modular and jointless timber components. It employs two primary elements: Topologically Optimized Timber-Plates (TOT) and Varied Profile Dowels (VPD). The TOT components are fabricated using multi -axis CNC methods, such as robotic milling with more than five axes, to interlock seamlessly with the dowels, forming a structurally stable lattice without the need for additional fasteners.

[0126] The methodology combines principles of reciprocal frames and topological optimization, enabling the system to distribute forces efficiently while minimizing material use. The integration of tailor-made computational workflows facilitates the optimization of timbercomponents and the variation of dowel sizes based on specific load conditions, contributing to both structural performance and material efficiency. Furthermore, the modular nature of the JRL system allows for scalability and adaptability across a range of architectural applications.

[0127] Building on previous research on the TDRL structural system previously described, the Jointless Reciprocal Lattice (JRL) system will be described through a column case study. The approach focuses on improving material efficiency and structural performance. Central to the system is the jointless assembly of two key components: topologically optimized timber-plates (TOT) and varied profile dowels (VPD).

[0128] FIG. 15 presents five selected voxel configurations and volumetric designs of column topologies, including straight, compound, V-shape, concave, and convex types. The first three configurations consist of 88 voxels, while the concave and convex types are composed of 56 voxels. While these configurations were initially modeled manually, a parametric system was later developed to convert any given input surface or boundary representation into a customizable voxelized framework. In the next phase of the workflow, the output voxel geometry is used as input for generating the elements of the lattice. The following three interconnected steps of the workflow — reciprocalization, structural analysis, and material optimization — are applied to all five column configurations. Together, these steps extend the voxel -based framework into a system for developing modular, lightweight, and resource-efficient timber structures.

[0129] In the creation of the timber-dowel system, input voxel geometries are defined to establish the modular framework of the lattice. A tetrahedral-octahedral honeycomb configuration is used for its ability to expand uniformly in three-dimensional space, enabling distributed force flow and structural stability. This step is followed by reciprocalization, in which dowels are offset from the intersection points on the plates to meet stabilizing requirements, forming a selfbalancing structure.

[0130] The third step introduces material optimization, where principal stress lines are analyzed to guide the redistribution of material within the timber elements, enhancing structural stability while reducing overall weight. FIG. 16 depicts a table of column prototypes showing voxel geometries, reciprocal lattices, principal stresses, and corresponding weight and displacement for five topologies in accordance with one embodiment of the present disclosure. The column on principal stresses highlights how material is distributed across the timber components to improve structural performance.

[0131] Under the defined boundary conditions, dowel lengths are derived directly from structural analysis. In the current system, dowels are categorized into two types: short dowels that connect two layers of timber, and long dowels that span three layers, supporting both performance and assembly requirements. The length of the dowels is determined based on two performance criteria: total structural mass and maximum displacement, with the aim of minimizing both objectives.

[0132] FIG. 16 also summarizes the first three steps of the workflow in a table, showing the progression from voxel input to material optimization. The column on principal stresses highlights how material is distributed across the timber components to improve structural performance. Initially, using the millipede plugin, topology optimization tool was employed to investigate the performance of timber structures under axial forces generated by dowels. However, the resulting mesh lacked the coherence necessary for the integrated system to function cohesively, as it produced a dense mesh primarily around nodal region. Consequently, principal stress distribution on the timber mid-planes is analyzed to better understand material behavior under gravity combined with axial forces which are transferred from the dowels to the plates. Building on this, the method is progressed toward the generation of printable and millable meshes using the Marching Cubes algorithm via the Cocoon plugin, focusing on columns composed of 88 voxels. The raw discrete lines which are derived as a data set for compression and tension representing the principal stress analysis on the plates are then used to inform both the material redistribution and the local refinement of mesh geometry.

[0133] FIG. 17 provides further detail, showing how principal stress lines from the voxel geometry are translated into continuous, closed watertight meshes. These meshes are both 3D printable and robotically millable, enabling efficient material usage and fabrication. On the right side of FIG. 17, optimized dowel profiles are allocated based on structural performance and resource availability, using four dowel thickness ranges (-13-26 mm) to meet performance requirements and material constraints.

[0134] The workflow employs parametric structural analysis using Karamba3D, while Rhino- Grasshopper supports iterative modeling and geometric refinement. Learning from the analysis and fabrication of prototypes, it was observed that thinner column configurations with 56 voxels may underperform in regions where a single voxel is responsible for distributing load — particularly at connecting layers. To address this issue, additional connecting dowels were introduced between layers to improve structural stability.

[0135] Initially, using the millipede plugin, topology optimization tool was employed to investigate the performance of timber structures under axial forces generated by dowels. However, the resulting mesh lacked the coherence necessary for the integrated system to function cohesively, as it produced a dense mesh primarily around nodal region. Consequently, principal stress distribution on the timber mid-planes is analyzed to better understand material behavior under gravity combined with axial forces which are transferred from the dowels to the plates. Building on this, the method is progressed toward the generation of printable and millable meshes using the Marching Cubes algorithm via the Cocoon plugin, focusing on columns composed of 88 voxel elements. The raw discrete lines which is derived as a data set for compression and tension representing the principal stress analysis on the plates is then used to inform both the material redistribution and the local refinement of mesh geometry. FIG. 18 shows a CNC double-sided milled timber and robotically milled holes using KUKA | PRC simulator plugin in Grasshopper.

[0136] This feedback driven integrated approach allows an iterative workflow across design, analysis, and fabrication phases, providing the opportunity for the JRL system to adapt to diverse architectural applications. The column case study demonstrates the scalability and material efficiency of the system.

[0137] FIG. 19 presents the compound column configuration, composed of nine timber elements stacked to a total height of 9 feet (-275 cm). This configuration integrates topologically optimized timber-plates (TOT) and varied profile dowels (VPD), with varied dowel thicknesses, assigned based on structural performance requirements. Material optimization is achieved through porosity informed by computational analysis, resulting in lightweight timber elements that reduces material usage while maintaining structural integrity.

[0138] The evaluation highlights how the combination of optimized material distribution and reciprocal lattice geometry contributes to self-balancing behavior by distributing forces across interconnected layers. Earlier prototypes revealed that thinner columns underperformed in areas where load transfer depended on single voxels, prompting a refinement of the compound column by increasing the number of voxels per layer. In other words, providing more options for force flow enables the system to redirect loads through alternative structural paths. These refinements lead to improved structural performance while maintaining scalability and adaptability for modular timber construction. FIG. 20 illustrates a scaled, prototyped, and assembled version of the column at 1 :6 scale, composed of nine timber elements and 154 dowels - 102 short dowels connection two layers and 52 longer dowels spanning three layers of timber.

[0139] This study validates the feasibility of the JRL system as a modular and resourceefficient approach. Through iterative testing and refinement, the compound column demonstrates the alignment of computational workflows with structural optimization, offering insights into the broader application of the JRL system in sustainable timber architecture.

[0140] The Jointless Reciprocal Lattice (JRL) system introduces a resource-driven, lightweight method for designing and constructing lattice structures, offering a scalable and modular assembly approach without the need for secondary materials. The results focus on validating this system through the compound column case study, emphasizing material efficiency, and structural performance. By focusing on the discrete assembly of topologically optimized timber plates (TOT) and varied profile dowels (VPD), the system demonstrates its potential for material efficiency, lightweight, and scalable lattice structures. This disclosure highlights the interplay between structural optimization and material efficiency, emphasizing the importance of modular and jointless assembly in advancing sustainable timber construction practices. The compound column case study serves as a validation of the system’s capability to balance structural performance, geometric adaptability, and fabrication precision, reinforcing its relevance in contemporary architectural applications.

[0141] This study evaluated five column typologies through the complete JRL workflow, including voxel-based modeling, reciprocalization, structural analysis, material optimization for both timber and dowel elements and prototyping. Future work will include improving the method for determining which dowels should be long and which should be short, with the goal of enhancing both structural performance and facilitating the assembly process. FIG. 21 illustrates a close-up view of three connected layers using a range of long and short dowels, along with a snapshot of the AR-assisted assembly process of the scaled prototype.

[0142] FIG. 22 depicts a comparative demonstration between two column systems at a larger scale (3 *3 *6 feet): the TDRL column without mechanical joints (left), and the Joint-Based Lattice System (right), assembled one-to-one using identical components. The figure illustrates the selfbalancing capacity of the jointless system through comparative structural performance.

[0143] FIG. 23 depicts the one-to-one TDRL column positioned on the ground, demonstrating the system’s inherent compression load-bearing capacity without the use of joints.

[0144] FIG. 24 depicts the one-to-one TDRL column suspended from a crane and hovering above the ground, demonstrating the system’s inherent tension load-bearing capacity without the use of joints.

[0145] It is understood that particular embodiments described herein are shown by way of illustration and not as limitations of the invention. The principal features of this invention can be employed in various embodiments without departing from the scope of the invention. Those skilled in the art will recognize or be able to ascertain using no more than routine experimentation, numerous equivalents to the specific procedures described herein. Such equivalents are considered to be within the scope of this invention and are covered by the claims.

[0146] All publications and patent applications mentioned in the specification are indicative of the level of skill of those skilled in the art to which this invention pertains. All publications and patent applications are herein incorporated by reference to the same extent as if each individual publication or patent application was specifically and individually indicated to be incorporated by reference.

[0147] The use of the word “a” or “an” when used in conjunction with the term “comprising” in the claims and / or the specification may mean “one,” but it is also consistent with the meaning of “one or more,” “at least one,” and “one or more than one.” The use of the term “or” in the claims is used to mean “and / or” unless explicitly indicated to refer to alternatives only or the alternatives are mutually exclusive, although the disclosure supports a definition that refers to only alternatives and “and / or.” Throughout this application, the term “about” is used to indicate that a value includes the inherent variation of error for the device, the method being employed to determine the value, or the variation that exists among the study subjects.

[0148] As used in this specification and claim(s), the words “comprising” (and any form of comprising, such as “comprise” and “comprises”), “having” (and any form of having, such as “have” and “has”), “including” (and any form of including, such as “includes” and “include”) or “containing” (and any form of containing, such as “contains” and “contain”) are inclusive or open- ended and do not exclude additional, unrecited features, elements, components, groups, integers, and / or steps, but do not exclude the presence of other unstated features, elements, components, groups, integers and / or steps. In embodiments of any of the compositions and methods provided herein, “comprising” may be replaced with “consisting essentially of’ or “consisting of’. As used herein, the term “consisting” is used to indicate the presence of the recited integer (e.g., a feature, an element, a characteristic, a property, a method / process step or a limitation) or group of integers (e.g., feature(s), element(s), character! stic(s), property(ies), method / process steps or limitation(s)) only. As used herein, the phrase “consisting essentially of’ requires the specified features, elements, components, groups, integers, and / or steps, but do not exclude the presence of otherunstated features, elements, components, groups, integers and / or steps as well as those that do not materially affect the basic and novel characteristic(s) and / or function of the claimed invention.

[0149] The term “or combinations thereof’ as used herein refers to all permutations and combinations of the listed items preceding the term. For example, “A, B, C, or combinations thereof’ is intended to include at least one of: A, B, C, AB, AC, BC, or ABC, and if order is important in a particular context, also BA, CA, CB, CBA, BCA, ACB, BAC, or CAB. Continuing with this example, expressly included are combinations that contain repeats of one or more item or term, such as BB, AAA, AB, BBC, AAABCCCC, CBBAAA, CABABB, and so forth. The skilled artisan will understand that typically there is no limit on the number of items or terms in any combination, unless otherwise apparent from the context.

[0150] As used herein, words of approximation such as, without limitation, “about”, “substantial” or “substantially” refers to a condition that when so modified is understood to not necessarily be absolute or perfect but would be considered close enough to those of ordinary skill in the art to warrant designating the condition as being present. The extent to which the description may vary will depend on how great a change can be instituted and still have one of ordinary skill in the art recognize the modified feature as still having the required characteristics and capabilities of the unmodified feature. In general, but subject to the preceding discussion, a numerical value herein that is modified by a word of approximation such as “about” may vary from the stated value by at least ±1, 2, 3, 4, 5, 6, 7, 10, 12 or 15%.

[0151] All of the compositions and / or methods disclosed and claimed herein can be made and executed without undue experimentation in light of the present disclosure. While the compositions and methods of this invention have been described in terms of preferred embodiments, it will be apparent to those of skill in the art that variations may be applied to the compositions and / or methods and in the steps or in the sequence of steps of the method described herein without departing from the concept, spirit and scope of the invention. All such similar substitutes and modifications apparent to those skilled in the art are deemed to be within the spirit, scope and concept of the invention as defined by the appended claims.

[0152] To aid the Patent Office, and any readers of any patent issued on this application in interpreting the claims appended hereto, applicants wish to note that they do not intend any of the appended claims to invoke paragraph 6 of 35 U.S.C. § 112, U.S.C. § 112 paragraph (f), or equivalent, as it exists on the date of filing hereof unless the words “means for” or “step for” are explicitly used in the particular claim.

[0153] For each of the claims, each dependent claim can depend both from the independent claim and from each of the prior dependent claims for each and every claim so long as the prior claim provides a proper antecedent basis for a claim term or element.

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Claims

CLAIMSWhat is claimed is:

1. A computerized method for designing and fabricating a three-dimensional (3D) lattice structure comprising: providing a voxel -based design for the 3D lattice structure stored in a memory or database of a computer comprising one or more processors communicably coupled to an input / output interface and the memory or database; extracting by the one or more processors, each angled edge of the voxel-based design as a linear structural member; extracting by the one or more processors, each horizontal surface of the voxel -based design as a horizontal panel or each curved surface of the voxel -based design as a curved panel; offsetting by the one or more processors, all intersections of the linear structural members with the horizontal or curved panels by a horizontal displacement in opposing directions to eliminate collisions of the linear structural members with one another; and controlling by the one or more processors via the input / output interface, one or more programmable or computer-controlled machines to fabricate the horizontal or curved panels.

2. The method of claim 1, further comprising providing the linear structural members, or fabricating the linear structural members using the one or more programmable or computer- controlled machines.

3. The method of claim 1, further comprising assembling the 3D lattice structure using the fabricated linear structural members and horizontal or curved panels.

4. The method of claim 1, further comprising modifying a profile of one or more of the horizontal or curved panels or one or more of the linear structural elements.

5. The method of claim 1, further comprising: identifying by the one or more processors, a plurality of panels that partially enclose or fully enclose the linear structural members, the horizontal or curved panels, or both; and controlling by the one or more processors, via the input / output interface, one or more programmable or computer-controlled machines to fabricate the plurality of panels.

6. The method of claim 5, further comprising assembling the 3D lattice structure using the fabricated linear structural members and the horizontal or curved panels and the plurality of panels.

7. The method of claim 1, further comprising extracting by the one or more processors, each intersection of the linear structural members that is not connected to any horizontal or curved surface of the voxel-based design as another one of the horizontal or curved panels or an extension of one of the horizontal or curved panels.

8. The method of claim 1, wherein controlling by the one or more processors via the input / output interface, the one or more programmable or computer-controlled machines to fabricate the horizontal or curved panels further comprises creating a hole in the horizontal or curved panels at each intersection of the linear structural members with the horizontal or curved panels.

9. The method of claim 1, further comprising merging by the one or more processors, any of the horizontal or curved panels that are adjacent to another horizontal or curved panel.

10. The method of claim 1, further comprising: analyzing by the one or more processors, one or more structural characteristics of the 3D lattice structure; optimizing by the one or more processors, the 3D lattice structure to satisfy one or more parameters; and allocating by the one or more processors, a material profile to each linear structural member and each horizontal or curved panel based on the optimized 3D lattice structure.

11. The method of claim 10, wherein the analyzing, optimizing and allocating steps are repeated until the optimized 3D lattice structure satisfies a set of criteria.

12. The method of claim 1, wherein the linear structural members penetrate the horizontal or curved panels.

13. The method of claim 1, further comprising assigning by the one or more processors, a diameter to each linear structural member based on a structural analysis of the 3D lattice structure.

14. The method of claim 13, wherein the diameter is substantially the same or varies along a length of the linear structural member.

15. The method of claim 1, further comprising: categorizing by the one or more processors, each linear structural member by a last horizontal or curved member that the linear structural member pierces; and sorting by the one or more processors, the categorized linear structural members into lists based on a radius and a length, wherein the lists provide guidance on assembling the 3D lattice structure.

16. The method of claim 1, wherein the voxel -based design comprises two or more solid voxels connected to one another, and one voxel comprises a half or whole tetrahedron, a half or whole octahedron, a half or whole polygon having six or more sides, a cumulated cuboctahedron, a uniform tetrahedron, a triangular pyramid or a non-uniform polyhedral tessellation.

17. The method of claim 1, wherein the 3D lattice structure does not contain any joint fittings, joint fasteners or adhesives.

18. The method of claim 1, wherein: each linear structural member comprises a dowel or any other elongated structural element; and each horizontal or curved panel comprises a timber or any other planar, flat or curved structural element.

19. The method of claim 1, wherein the linear structural members and horizontal or curved panels are made of wood, plastic, plexiglass, metal, metal alloys, composite materials, bioplastics, engineered wood products, or a combination thereof.

20. The method of claim 1, wherein the 3D lattice structure comprises a slab, column, wall, arch, other building element, furniture or furniture element.

21. A 3D lattice structure fabricated in accordance with claim 1.

22. A 3D lattice structure fabricated in accordance with claim 3.

23. A 3D lattice structure fabricated and assembled in accordance with claim 2.

24. A 3D lattice structure fabricated and assembled in accordance with claim 4.

25. A system comprising: a memory or database that contains a voxel-based design for a 3D lattice structure; an input / output interface; one or more programmable or computer-controlled machines communicably coupled to the input / output interface; one or more processors communicably coupled to the input / output interface and the memory or database; and wherein the one or more processors extract each angled edge of the voxel-based design as a linear structural member, extract each horizontal surface of the voxel-based design as a horizontal panel or each curved surface of the voxel-based design as a curved panel, offset all intersections of the linear structural members with the horizontal or curved panels by a horizontal displacement in opposing directions to eliminate collisions of the linear structural members with one another, control the one or more programmable or computer-controlled machines to fabricate the horizontal or curved panels.

26. The system of claim 25, wherein the one or more processors control the one or more programmable or computer-controlled machines to fabricate the linear structural members.

27. The system of claim 25, wherein the one or more processors control the one or more programmable or computer-controlled machines to assemble the 3D lattice structure using the fabricated linear structural members and horizontal or curved panels.

28. The system of claim 25, wherein the one or more processors or the one or more programmable or computer-controlled machines modify a profile of one or more of the horizontal or curved panels or one or more of the linear structural elements.

29. The system of claim 25, wherein the one or more processors further:identify a plurality of panels that partially enclose or fully enclose the linear structural members, the horizontal or curved panels, or both; and control the one or more programmable or computer-controlled machines to fabricate the plurality of panels.

30. The system of claim 29, wherein the one or more processors further control the one or more programmable or computer-controlled machines to assemble the 3D lattice structure using the fabricated linear structural members, the horizontal or curved panels and the plurality of panels.

31. The system of claim 25, wherein the one or more processors further extract each intersection of the linear structural members that is not connected to any horizontal or curved surface of the voxel-based design as another one of the horizontal or curved panels or an extension of one of the horizontal or curved panels.

32. The system of claim 25, wherein the one or more processors further control the one or more programmable or computer-controlled machines to fabricate the horizontal or curved panels further comprises creating a hole in the horizontal or curved panels at each intersection of the linear structural members with the horizontal or curved panels.

33. The system of claim 25, wherein the one or more processors further merge any of the horizontal or curved panels that are adjacent to another horizontal or curved panel.

34. The system of claim 25, wherein the one or more processors further: analyze one or more structural characteristics of the 3D lattice structure; optimize the 3D lattice structure to satisfy one or more parameters; and allocate a material profile to each linear structural member and each horizontal or curved panel based on the optimized 3D lattice structure.

35. The system of claim 35, wherein the analyzing, optimizing and allocating steps are repeated until the optimized 3D lattice structure satisfies a set of criteria.

36. The system of claim 25, wherein the linear structural members penetrate the horizontal or curved panels.

37. The system of claim 25, wherein the one or more processors further assign a diameter to each linear structural member based on a structural analysis of the 3D lattice structure.

38. The system of claim 25, wherein the diameter is substantially the same or varies along a length of the linear structural member.

39. The system of claim 25, wherein the one or more processors further: categorize each linear structural member by a last horizontal or curved member that the linear structural member pierces; and sort the categorized linear structural members into lists based on a radius and a length, wherein the lists provide guidance on assembling the 3D lattice structure.

40. The system of claim 25, wherein the voxel-based design comprises two or more solid voxels connected to one another, and each solid voxel comprises a half or whole tetrahedron, a half or whole octahedron, a half or whole polygon having six or more sides, a cumulated cuboctahedron, a uniform tetrahedron, a triangular pyramid or a non-uniform polyhedral tessellation.

41. The system of claim 25, wherein the 3D lattice structure does not contain any j oint fittings, joint fasteners or adhesives.

42. The system of claim 25, wherein: each linear structural member comprises a dowel or any other elongated structural element; and each horizontal or curved panel comprises a timber or any other planar, flat or curved structural element.

43. The system of claim 25, wherein the linear structural members and horizontal or curved panels are made of wood, plastic, plexiglass, metal, metal alloys, composite materials, bioplastics, engineered wood products, or a combination thereof.

44. The system of claim 25, wherein the 3D lattice structure comprises a slab, column, wall, arch, other building element, furniture or furniture element.

45. A 3D lattice structure comprising: a linear structural member for each angled edge of a voxel-based design of the 3D lattice structure; a horizontal panel for each horizontal surface of the voxel-based design, or a curved panel for each curved surface of the voxel-based design; wherein the linear structural members are connected to the horizontal or curved panels substantially in accordance with the voxel-based design; and wherein all intersections of the linear structural members with the horizontal or curved panels are offset by a horizontal displacement to eliminate collisions of the linear structural members with one another.

46. The 3D lattice structure of claim 45, wherein a profile of one or more of the horizontal or curved panels or one or more of the linear structural elements is modified.

47. The 3D lattice structure of claim 45, further comprising a plurality of panels that partially enclose or fully enclose the linear structural members, the horizontal or curved panels, or both.

48. The 3D lattice structure of claim 45, further comprising another one of the horizontal or curved panels or an extension of one of the horizontal or curved panels corresponding to each intersection of the linear structural members that is not connected to any horizontal or curved surface of the voxel-based design.

49. The 3D lattice structure of claim 45, wherein the horizontal or curved panels have a hole at each intersection of the linear structural members with the horizontal or curved panels.

50. The 3D lattice structure of claim 45, wherein the linear structural members penetrate the horizontal or curved panels.

51. The 3D lattice structure of claim 45, wherein a diameter of the linear structural member is substantially the same or varies along a length of the linear structural member.

52. The 3D lattice structure of claim 45, wherein the voxel-based design comprises two or more solid voxels connected to one another, and each solid voxel comprises a half or wholetetrahedron, a half or whole octahedron, a half or whole polygon having six or more sides, a cumulated cuboctahedron, a uniform tetrahedron, a triangular pyramid or a non-uniform polyhedral tessellation.

53. The 3D lattice structure of claim 45, wherein the 3D lattice structure does not contain any joint fittingsjoint fasteners or adhesives.

54. The 3D lattice structure of claim 45, wherein: each linear structural member comprises a dowel or any other elongated structural element; and each horizontal or curved panel comprises a timber or any other planar, flat or curved structural element.

55. The 3D lattice structure of claim 45, wherein the linear structural members and horizontal or curved panels are made of wood, plastic, plexiglass, metal, metal alloys, composite materials, bioplastics, engineered wood products, or a combination thereof.

56. The 3D lattice structure of claim 45, wherein the 3D lattice structure comprises a slab, column, wall, arch, other building element, furniture or furniture element.

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