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We present an algorithm that canonicalizes the algebraic representations of the topological semantics of machine knitting programs. Machine knitting is a staple technology of modern textile production where hundreds of mechanical needles are manipulated to form yarn into interlocking loop structures. Our semantics are defined using a variant of a monoidal category, and they closely correspond to string diagrams. We formulate our canonicalization as an Abstract Rewriting System (ARS) over words in our category, and prove that our algorithm is correct and runs in polynomial time. 

Storage, organizing, and decorating are important aspects of home design. Buying commercial items for many of these tasks, this can be costly, and reuse is more sustainable. An alternative is a “home hack,” i.e., a functional assembly constructed from existing household items. However, coming up with such hacks requires combining objects to make a physically valid design, which might be difficult to test if they are large, require nailing or screwing to the wall, or if the designer has mobility limitations. We present a design and visualization system, FabHacks, for cre- ating workable functional assemblies. The system is based on a new solver-aided domain-specific language (S-DSL) called FabHaL. By analyzing existing home hacks shared online, we create a design abstraction for connecting household items using predefined con- nection types. We also provide a UI for designing hack assemblies that fulfill a given specification. FabHacks leverages a physics-based solver that finds the expected physical configuration of an assembly design. Our validation includes a user study with our UI, which shows that users can easily create assemblies and explore a range of designs. 

Reducing the environmental footprint of electronics and computing devices requires new tools that empower designers to make informed decisions about sustainability during the design process itself. This is not possible with current tools for life cycle assessment (LCA) which require substantial domain expertise and time to evaluate the numerous chips and other components that make up a device. We observe first that informed decision-making does not require absolute metrics and can instead be done by comparing designs. Second, we can use domain-specific heuristics to perform these comparisons. We combine these insights to develop DeltaLCA, an open-source interactive design tool that addresses the dual challenges of automating life cycle inventory generation and data availability by performing comparative analyses of electronics designs. Users can upload standard design files from Electronic Design Automation (EDA) software and the tool will guide them through determining which one has greater carbon footprints. DeltaLCA leverages electronics-specific LCA datasets and heuristics and tries to automatically rank the two designs, prompting users to provide additional information only when necessary. We show through case studies DeltaLCA achieves the same result as evaluating full LCAs, and that it accelerates LCA comparisons from eight expert-hours to a single click for devices with ~30 components, and 15 minutes for more complex devices with ~100 components. 

Sub-gram flying robots have transformative potential in applications from search and rescue to precision agriculture to environmental monitoring. However, a key gap in achieving autonomous flight for these applications is the low lift to weight ratio of flapping wing and quadrotor designs around 1 g or less. To close this gap, we propose a helictoper-style design that minimizes size and weight by leveraging the high lift, reliability, and low-voltage of sub-gram motors. We take an important step to enable this goal by designing a light-weight, micfrofabricated flybar mechanism to passively stabilize such a robot. Our 48 mg flybar is folded from a flat carbon fiber laminate into a 3D mechanism that couples tilting of the flybar to a change in the angle of attack of the rotors. Our design uses flexure joints instead of ball-in-socket joints common in larger flybars. To expedite the design exploration and optimization of a microfabricated flat-folded flybar, we develop a novel user-in-the-loop bi-level optimization workflow that combines Bayesian optimization design tools and expert feedback. We develop four template designs and use this method to achieve a peak damping ratio of 0.528, an 18.9x improvement from our initial design. Compared to a flybar-less rotor with a near 0 damping ratio, our flybar-rotor mechanism maintains a stable roll and pitch with relative deviations < 1°. Our results show that, if combined with a counter-torque mechanism such as a tail rotor, our miniaturized flybar could mechanically provide attitude stability for a sub-gram helicopter. 

Sheet Metal (SM) fabrication is perhaps one of the most common metalworking technique. Despite its prevalence, SM design is manual and costly, with rigorous practices that restrict the search space, yielding suboptimal results. In contrast, we present a framework for the first automatic design of SM parts. Focusing on load bearing applications, our novel system generates a high-performing manufacturable SM that adheres to the numerous constraints that SM design entails: The resulting part minimizes manufacturing costs while adhering to structural, spatial, and manufacturing constraints. In other words, the part should be strong enough, not disturb the environment, and adhere to the manufacturing process. These desiderata sum up to an elaborate, sparse, and expensive search space. Our generative approach is a carefully designed exploration process, comprising two steps. In Segment Discovery connections from the input load to attachable regions are accumulated, and during Segment Composition the most performing valid combination is searched for. For Discovery, we define a slim grammar, and sample it for parts using a Markov-Chain Monte Carlo (MCMC) approach, ran in intercommunicating instances (i.e, chains) for diversity. This, followed by a short continuous optimization, enables building a diverse and high-quality library of substructures. During Composition, a valid and minimal cost combination of the curated substructures is selected. To improve compliance significantly without additional manufacturing costs, we reinforce candidate parts onto themselves --- a unique SM capability called self-riveting. we provide our code and data in https://github.com/amir90/AutoSheetMetal. We show our generative approach produces viable parts for numerous scenarios. We compare our system against a human expert and observe improvements in both part quality and design time. We further analyze our pipeline's steps with respect to resulting quality, and have fabricated some results for validation. We hope our system will stretch the field of SM design, replacing costly expert hours with minutes of standard CPU, making this cheap and reliable manufacturing method accessible to anyone. 

Illusion-knit fabrics reveal distinct patterns or images depending on the viewing angle. Artists have manually achieved this effect by exploiting microgeometry, i.e., small differences in stitch heights. However, past work in computational 3D knitting does not model or exploit designs based on stitch height variation. This paper establishes a foundation for exploring illusion knitting in the context of computational design and fabrication. We observe that the design space is highly constrained, elucidate these constraints, and derive strategies for developing effective, machine-knittable illusion patterns. We partially automate these strategies in a new interactive design tool that reduces difficult patterning tasks to familiar image editing tasks. Illusion patterns also uncover new fabrication challenges regarding mixed colorwork and texture; we describe new algorithms for mitigating fabrication failures and ensuring high-quality knit results. 

3D Computer-Aided Design (CAD) modeling is ubiquitous in mechanical engineering and design. Modern CAD models are programs that produce geometry and can be used to implement high-level geometric changes by modifying input parameters. While there has been a surge of recent interest in program-based tooling for the CAD domain, one fundamental problem remains unsolved. CAD programs pass geometric arguments to operations using references, which are queries that select elements from the constructed geometry according to programmer intent. The challenge is designing reference semantics that can express programmer intent across all geometric topologies achievable with model parameters, including topologies where the desired elements are not present. In current systems, both users and automated tools may create invalid models when parameters are changed, as references to geometric elements are lost or silently and arbitrarily switched. While existing CAD systems use heuristics to attempt to infer user intent in cases of this undefined behavior, this best-effort solution is not suitable for constructing automated tools to edit and optimize CAD programs. We analyze the failure modes of existing referencing schemes and formalize a set of criteria on which to evaluate solutions to the CAD referencing problem. In turn, we propose a domain-specific language that exposes references as a first-class language construct, using user-authored queries to introspect element history and define references safely over all paths. We give a semantics for fine-grained element lineage that can subsequently be queried; and show that our language meets the desired properties. Finally, we provide an implementation of a lineage-based referencing system in a 2.5D CAD kernel, demonstrating realistic referencing scenarios and illustrating how our system safely represents models that cause reference breakage in existing CAD systems.