Design and Structural Optimization of Topological Interlocking Assemblies

Abstract: We study assemblies of convex rigid blocks regularly arranged to approximate a given freeform surface. Our designs rely solely on the geometric arrangement of blocks to form a stable assembly, neither requiring explicit connectors or complex joints, nor relying on friction between blocks. The convexity of the blocks simplifies fabrication, as they can be easily cut from different materials such as stone, wood, or foam. However, designing stable assemblies is challenging, since adjacent pairs of blocks are restricted in their relative motion only in the direction orthogonal to a single common planar interface surface. We show that despite this weak interaction, structurally stable, and in some cases, globally interlocking assemblies can be found for a variety of freeform designs. Our optimization algorithm is based on a theoretical link between static equilibrium conditions and a geometric, global interlocking property of the assembly - that an assembly is globally interlocking if and only if the equilibrium conditions are satisfied for arbitrary external forces and torques. Inspired by this connection, we define a measure of stability that spans from single-load equilibrium to global interlocking, motivated by tilt analysis experiments used in structural engineering. We use this measure to optimize the geometry of blocks to achieve a static equilibrium for a maximal cone of directions, as opposed to considering only self-load scenarios with a single gravity direction. In the limit, this optimization can achieve globally interlocking structures. We show how different geometric patterns give rise to a variety of design options and validate our results with physical prototypes.

Authors/Presenter(s): Ziqi Wang, EPFL, Switzerland
Peng Song, EPFL, Singapore University of Technology and Design, Singapore
Florin Isvoranu, EPFL, Switzerland
Mark Pauly, EPFL, Switzerland

Extrusion-Based Ceramics Printing with Strictly-Continuous Deposition

Abstract: We propose a method for integrated tool path planning and support structure generation tailored to the specific constraints of extrusion-based ceramics printing. Existing path generation methods for thermoplastic materials rely on transfer moves to navigate between different print paths in a given layer. However, when printing with clay, these transfer moves can lead to severe artifacts and failure. As the core of our approach, we guarantee a single continuous deposition path per layer and thus eliminate the problems caused by transfer moves. To arrive at a tractable formulation, we split global path generation into a sequence of per-layer problems that we solve from top to bottom. In each layer, we detect points that require support, connect support points and model paths, and optimize the shape of the resulting continuous path with respect to length, smoothness, and distance to the model. For each of these subproblems, we propose dedicated solutions that take into account the fabrication constraints imposed by printable clay. We evaluate our method on a set of examples with multiple disconnected components and challenging support requirements. Comparisons to existing path generation methods designed for thermoplastic materials show that continuous deposition is indeed vital for successful clay printing.

Authors/Presenter(s): Jean Hergel, Université de Montréal, Canada
Kevin Hinz, Université de Montréal, Canada
Sylvain Lefebvre, National Institute for Research in Computer Science and Automation (INRIA), France
Bernhard Thomaszewski, Université de Montréal, Canada

Carpentry Compiler

Abstract: Traditional manufacturing workflows strongly decouple design and fabrication phases. As a result, fabrication-related objectives such as manufacturing time and precision are difficult to optimize in the design space, and vice versa. This paper presents HL-HELM, a high-level, domain-specific language for expressing abstract, parametric fabrication plans; it also introduces LL-HELM, a low-level language for expressing concrete fabrication plans that take into account the physical constraints of available manufacturing processes. We present a new compiler that supports the real-time, unoptimized translation of high-level, geometric fabrication operations into concrete, tool-specific fabrication instructions; this gives users immediate feedback on the physical feasibility of plans as they design them. HELM offers novel optimizations to improve accuracy and reduce fabrication time as well as material costs. Finally, optimized low-level plans can be interpreted as step-by-step instructions for users to actually fabricate a physical product. We provide a variety of example fabrication plans in the carpentry domain that are designed using our high-level language, show how the compiler translates and optimizes these plans to generate concrete low-level instructions, and present the final physical products fabricated in wood.

Authors/Presenter(s): Chenming Wu, Tsinghua University, University of Washington, China
Haisen Zhao, University of Washington, United States of America
Chandrakana Nandi, University of Washington, United States of America
Jeffrey Ian Lipton, Massachusetts Institute of Technology, United States of America
Zachary Tatlock, University of Washington, United States of America
Adriana Schulz, University of Washington, United States of America

Computational LEGO Technic Design

Abstract: We introduce a method to automatically compute LEGO Technic models from user input sketches, optionally with motion annotations. The generated models resemble the input sketches with coherently-connected bricks and simple layouts, while respecting the intended symmetry and mechanical properties expressed in the inputs. This complex computational assembly problem involves an immense search space, and a much richer brick set and connection mechanisms than regular LEGO. To address it, we first comprehensively model the brick properties and connection mechanisms, then formulate the construction requirements into an objective function, accounting for faithfulness to input sketch, model simplicity, and structural integrity. Next, we model the problem as a sketch cover, where we iteratively refine a random initial layout to cover the input sketch, while guided by the objective. At last, we provide a working system to analyze the balance, stress, and assemblability of the generated model. To evaluate our method, we compared it with four baselines and professional designs by a LEGO expert, demonstrating the superiority of our automatic designs. Also, we recruited several users to try our system, employed it to create models of varying forms and complexities, and physically built most of them.

Authors/Presenter(s): Hao Xu, The Chinese University of Hong Kong, Hong Kong
Ka-Hei Hui, The Chinese University of Hong Kong, Hong Kong
Chi-Wing Fu, The Chinese University of Hong Kong, Hong Kong
Hao (Richard) Zhang, Simon Fraser University, Canada

Redefining A in RGBA: Towards a Standard for Graphical 3D Printing

Abstract: Advances in multimaterial 3D printing have the potential to reproduce various visual appearance attributes of an object in addition to its shape. Since many existing 3D file formats encode color and translucency by RGBA textures mapped to 3D shapes, RGBA information is particularly important for practical applications. In contrast to color (encoded by RGB), which is specified by the object’s reflectance, selected viewing conditions and a standard observer, translucency (encoded by A) is neither linked to any measurable physical nor perceptual quantity. Thus, reproducing translucency encoded by A is open for interpretation. In this paper, we propose a rigorous definition for A suitable for use in graphical 3D printing, which is independent of the 3D printing hardware and software, and which links both optical material properties and perceptual uniformity for human observers. By deriving our definition from the absorption and scattering coefficients of virtual homogenous reference materials with an isotropic phase function, we achieve two important properties. First, a simple adjustment of A is possible, which preserves the translucency appearance if an object is rescaled for printing. Second, determining the value of A for a real (potentially non-homogenous) material, can be achieved by minimizing a distance function between light transport measurements of this material and simulated measurements of the reference materials. Such measurements can be conducted by commercial spectrophotometers used in graphic arts. Finally, we conduct visual experiments employing the method of constant stimuli, and derive from them an embedding of A into a nearly perceptually uniform scale of translucency for the reference materials.

Authors/Presenter(s): Philipp Urban, Fraunhofer IGD, Norwegian University of Science and Technology, Germany
Tejas Madan Tanksale, Fraunhofer IGD, Germany
Alan Brunton, Fraunhofer IGD, Germany
Bui Minh Vu, Toyohashi University of Technology, Japan
Shigeki Nakauchi, Toyohashi University of Technology, Japan