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Abstract Swarm manufacturing is an emerging manufacturing paradigm that employs a heterogeneous swarm of robots to accomplish complex hybrid manufacturing tasks. Cooperative 3D printing (C3DP), a specialized form of swarm manufacturing, enables multiple printers to collaboratively produce large-scale parts, addressing key tradeoffs in additive manufacturing, such as size, speed, quality, and cost. A fundamental challenge in C3DP is ensuring collision-free, time-optimal printing in a shared workspace. This is a complex problem that can be influenced by factors such as the number of printers, part geometry, printer positioning, mobility, and kinematics. In this article, we present SafeZone*, a collision-free and scalable C3DP framework that optimizes printing time by co-considering the geometry (area and shape) and topology (space-connectivity) of a shared workspace during layer partitioning. We first establish a conceptual framework to mathematically represent the topology of a layer through partition graphs. Then, we use a Voronoi tessellation within a constrained optimization framework to control the partition graph and minimize makespan. The Voronoi sites are associated with printer locations, allowing the framework to integrate physical constraints and facilitating solutions for systems with robotic manipulators. Physical testing in a four-printer scenario with robotic arms confirms that SafeZone* enables collision-free printing, resulting in a printing time reduction of 44.63% when compared to the single-printer scenario. Finally, numerical studies reveal trends in the optimal solutions concerning the chromatic number of their resulting partition graphs and the distribution of the printing areas among printers. 

Abstract We present a novel methodology to generate mechanical structures based on fractal geometry using the chaos game, which generates self-similar point-sets within a polygon. Using the Voronoi decomposition of these points, we are able to generate groups of self-similar structures that can be related back to their chaos game parameters, namely, the polygonal domain, fractional distance, and number of samples. Our approach explores the use of forward design of generative structures, which in some cases can be easier to use for designing than inverse generative design techniques. To this end, the central hypothesis of our work is that structures generated using the chaos game can generate families of self-similar structures that, while not identical, exhibit similar mechanical behavior in a statistical sense. We present a systematic study of these self-similar structures through modal analysis and tensile loading and demonstrate a preliminary confirmation of our hypothesis. 

Abstract Swarm manufacturing (SM) is an emerging manufacturing paradigm that employs a heterogeneous swarm of robots to accomplish complex hybrid manufacturing tasks. Cooperative 3D Printing (C3DP), a special form of swarm manufacturing, uses multiple printers to print large-scale parts cooperatively and aims to tackle key challenges in the additive manufacturing industry, such as trade-offs among size, speed, quality, and cost. A fundamental challenge in C3DP is how to achieve collision-free, time-efficient printing when multiple printers operate in a shared workspace. This is a complex problem since the solution may depend on a myriad of factors, such as the number of printers, part geometry, printer positioning, mobility, and kinematics, or whether the printing path pre-determined. In this paper, we present SafeZone, a collision-free and scalable C3DP framework that aims to minimize printing time by considering both the geometry and topology (space-connectivity) of the resulting workspace when segmenting the part layer. To achieve this, we use a guided Voronoi tessellation that can only produce degree-3 partitions, which we show to have optimal scheduling properties based on the chromatic number of the resulting partition graph. The sites of the Voronoi tessellation are constrained to only lie on the boundary of their convex hull, thus facilitating collision-free operation in C3DP systems with robotic arms. We demonstrate through physical testing in a 4-printer scenario with SCARA arms that SafeZone can produce collision-free prints, resulting in a printing time reduction of 44.63% when compared to the single-printer scenario. Finally, we show how the partition created by our methodology has a printing time reduction of 22.83% when compared to a naive choice which does not consider workspace topology. 

Abstract We present a novel methodology to generate mechanical structures based on the idea of fractal geometry as described by the chaos game. Chaos game is an iterative method that generates self-similar point-sets in the limiting case within a polygonal domain. By computing Voronoi tessellations on these point-sets, our method generates mechanical structures that adopts the self-similarity of the point-sets resulting in fractal distribution of local stiffness. The motivation behind our approach comes from the observation that a typical generative structural design workflow requires the ability to generate families of structures that possess shared behavioral (e.g. thermal, mechanical, etc.) characteristics making each structure distinct but feasible. However, the generation of the alternatives, almost always, requires solving an inverse structural problem which is both conceptually and computationally challenging. The objective of our work is to develop and investigate a forward-design methodology for generating families of structures that, while not identical, exhibit similar mechanical behavior in a statistical sense. To this end, the central hypothesis of our work is that structures generated using the chaos game can generate families of self-similar structures that, while not identical, exhibit similar mechanical behavior in a statistical sense. Furthermore, each family is uniquely identifiable from the parameters of the chaos game, namely, the polygonal domain, fractional distance, and number of samples. We present a systematic study of these self-similar structures through modal analysis and demonstrate a preliminary confirmation of our hypothesis. 

This study investigates the programmable strain sensing capability, auxetic behaviour, and failure modes of 3D-printed, self-monitoring auxetic lattices fabricated from in-house engineered polyetheretherketone (PEEK) reinforced with multi-walled carbon nanotubes (MWCNTs). A skeletally-parametrized geometric modelling framework, combining Voronoi tessellation with 2D wallpaper symmetries, is used to systematically explore a vast range of non-predetermined topologies beyond traditional lattice designs. A representative set of these architectures is realized via fused filament fabrication, and multiscale characterization—including macroscale tensile testing and microstructural analysis—demonstrates tuneable multifunctional performance as a function of MWCNT content and unit cell topology. Real-time resistance measurements track deformation, damage initiation, and progression, with the sensitivity factor increasing from below 1 in the elastic regime (strain sensitivity) to as high as 80 for PEEK/MWCNT at 6 wt.% under inelastic deformation (damage sensitivity). Implicit architecture-topology tailoring further allows fine-tuning of mechanical properties, achieving stiffness values ranging from 9 MPa to 63 MPa and negative Poisson’s ratios between –0.63 and –0.17 using ~3 wt.% MWCNT at a relative density of 25%. Furthermore, a novel piezoresistive finite element model, implemented in Abaqus via a user-defined subroutine, accurately captures the electromechanical response up to the onset of ligament failure, offering predictive capability. These results demonstrate how architecture-topology tuning can be leveraged to customise strain sensitivity and failure modes, enabling the development of multifunctional piezoresistive lattice composites for applications such as smart orthopaedic implants, aerospace skins, and impact-tolerant systems. 

A novel methodology is introduced for designing auxetic (negative Poisson's ratio) structures based on topological principles and is demonstrated by investigating a new class of auxetics based on two‐dimensional (2D) textile weave patterns. Conventional methodology for designing auxetic materials typically involves determining a single deformable block (a unit cell) of material whose shape results in auxetic behavior. Consequently, patterning such a unit cell in a 2D (or 3D) domain results in a larger structure that exhibits overall auxetic behavior. Such an approach naturally relies on some prior intuition and experience regarding which unit cells may be auxetic. Second, tuning the properties of the resulting structures is typically limited to parametric variations of the geometry of a specific type of unit cell. Thus, most of the currently known auxetic structures belong to a selected few classes of unit cell geometries that are explicitly defined in accordance with a specified topological (i.e., grid structure). Herein, a new class of auxetic structures is demonstrated that, while periodic, can be generated implicitly, i.e., without reference to a specific unit cell design. The approach leverages weave‐based parameters (A–B–C), resulting in a rich design space for auxetics that is previously unexplored. 

An approach for modeling topologically interlocked building blocks that can be assembled in a water‐tight manner (space filling) to design a variety of spatial structures is introduced. This approach takes inspiration from recent methods utilizing Voronoi tessellation of spatial domains using symmetrically arranged Voronoi sites. Attention is focused on building blocks that result from helical stacking of planar 2‐honeycombs (i.e., tessellations of the plane with a single prototile) generated through a combination of wallpaper symmetries and Voronoi tessellation. This unique combination gives rise to structures that are both space‐filling (due to Voronoi tessellation) and interlocking (due to helical trajectories). Algorithms are developed to generate two different varieties of helical building blocks, namely, corrugated and smooth. These varieties result naturally from the method of discretization and shape generation and lead to distinct interlocking behavior. In order to study these varieties, finite‐element analyses (FEA) are conducted on different tiles parametrized by 1) the polygonal unit cell determined by the wallpaper symmetry and 2) the parameters of the helical line generating the Voronoi tessellation. Analyses reveal that the new design of the geometry of the building blocks enables strong variation of the engagement force between the blocks.