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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 NoodlePrint, a generalized computational framework for maximally concurrent layer-wise cooperative 3D printing (C3DP) of arbitrary part geometries with multiple robots. NoodlePrint is inspired by a recently discovered set of helically interlocked space-filling shapes called VoroNoodles. Leveraging this unique geometric relationship, we introduce an algorithmic pipeline for generating helically interlocked cellular segmentation of arbitrary parts followed by layer-wise cell sequencing and path planning for cooperative 3D printing. Furthermore, we introduce a novel concurrence measure that quantifies the amount of printing parallelization across multiple robots. Consequently, we integrate this measure to optimize the location and orientation of a part for maximally parallel printing. We systematically study the relationship between the helix parameters (i.e., cellular interlocking), the cell size, the amount of concurrent printing, and the total printing time. Our study revealed that both concurrence and time to print primarily depend on the cell size, thereby allowing the determination of interlocking independent of time to print. To demonstrate the generality of our approach with respect to part geometry and the number of robots, we implemented two cooperative 3D printing systems with two and three printing robots and printed a variety of part geometries. Through comparative bending and tensile tests, we show that helically interlocked part segmentation is robust to gaps between segments. 

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. 

In this work, we introduce an approach to model topologically interlocked corrugated bricks that can be assembled in a water-tight manner (space-filling) to design a variety of spatial structures. Our approach takes inspiration from recently developed methods that utilize Voronoi tessellation of spatial domains by using symmetrically arranged Voronoi sites. However, in contrast to these existing methods, we focus our attention on Voronoi sites modeled using helical trajectories, which can provide corrugation and better interlocking. For symmetries, we only use affine transformations based on the Bravais lattice to avoid self-intersections. This methodology naturally results in structures that are both space-filling (owing to Voronoi tessellation) as well as interlocking by corrugation (owing to helical trajectories). The resulting shapes of the bricks appear to be similar to a variety of pasta noodles, thereby inspiring the names, Voronoi Spaghetti and VoroNoodles. 

Abstract In this paper, we introduce a novel prototyping workflow, QuickProbe, that enables a user to create quick-and-dirty prototypes taking direct inspiration from existing physical objects. Our workflow is inspired by the notion of prototyping-in-context using physical scaffolds in digital environments. To achieve this we introduce a simple kinesthetic-geometric curve representation wherein we integrated the geometric representation of the curve with the virtual kinesthetic feedback. We test the efficacy of this kinesthetic-geometric curve representation through a qualitative user study conducted with ten participants. In this study, users were asked to generate wire-frame curve networks on top of the physical shapes by sampling multiple control points along the surface. We conducted two different sets of experiments in this work. In the first set of experiments, users were tasked with tracing the physical shape of the object. In the second set of experiments, the goal was to explore different artistic designs that the user could draw using the physical scaffolding of the shapes. Through our user studies, we showed the variety of designs that the users were able to create. We also evaluated the similarities and differences we observed between the two different sets of experiments. We further discuss the user feedback and the possible design scenarios where our QuickProbe workflow can be used. 

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.