Worst‐Case Rigidity Analysis and Optimization for Assemblies with Mechanical Joints

Stripe patterns are ubiquitous in nature and everyday life. While the synthesis of these patterns has been thoroughly studied in the literature, their potential to control the mechanics of structured materials remains largely unexplored. In this work, we introduce Differentiable Stripe Patterns---a computational approach for automated design of physical surfaces structured with stripe-shaped bi-material distributions. Our method builds on the work by Knöppel and colleagues [2015] for generating globally-continuous and equally-spaced stripe patterns. To unlock the full potential of this design space, we propose a gradient-based optimization tool to automatically compute stripe patterns that best approximate macromechanical performance goals. Specifically, we propose a computational model that combines solid shell finite elements with XFEM for accurate and fully-differentiable modeling of elastic bi-material surfaces. To resolve non-uniqueness problems in the original method, we furthermore propose a robust formulation that yields unique and differentiable stripe patterns. We combine these components with equilibrium state derivatives into an end-to-end differentiable pipeline that enables inverse design of mechanical stripe patterns. We demonstrate our method on a diverse set of examples that illustrate the potential of stripe patterns as a design space for structured materials. Our simulation results are experimentally validated on physical prototypes.

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Differentiable Stripe Patterns for Inverse Design of Structured Surfaces

Maestre

Hinchet

et al. 2023

ACM Trans. Graph.

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Computational Design of LEGO ^® Sketch Art

Zhou,

Ge,

et al. 2023

ACM Trans. Graph.

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This paper presents computational methods to aid the creation of LEGO ®1 sketch models from simple input images. Beyond conventional LEGO ® mosaics, we aim to improve the expressiveness of LEGO ® models by utilizing LEGO ® tiles with sloping and rounding edges, together with rectangular bricks, to reproduce smooth curves and sharp features in the input. This is a challenging task, as we have limited brick shapes to use and limited space to place bricks. Also, the search space is immense and combinatorial in nature. We approach the task by decoupling the LEGO ® construction into two steps: first approximate the shape with a LEGO ® -buildable contour then filling the contour polygon with LEGO ® bricks. Further, we formulate this contour approximation into a graph optimization with our objective and constraints and effectively solve for the contour polygon that best approximates the input shape. Further, we extend our optimization model to handle multi-color and multi-layer regions, and formulate a grid alignment process and various perceptual constraints to refine the results. We employ our method to create a large variety of LEGO ® models and compare it with humans and baseline methods to manifest its compelling quality and speed.

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Optimal Design of Robotic Character Kinematics

Maloisel,

Schumacher,

Knoop

et al. 2023

ACM Trans. Graph.

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The kinematic motion of a robotic character is defined by its mechanical joints and actuators that restrict the relative motion of its rigid components. Designing robots that perform a given target motion as closely as possible with a fixed number of actuated degrees of freedom is challenging, especially for robots that form kinematic loops. In this paper, we propose a technique that simultaneously solves for optimal design and control parameters for a robotic character whose design is parameterized with configurable joints. At the technical core of our technique is an efficient solution strategy that uses dynamic programming to solve for optimal state, control, and design parameters, together with a strategy to remove redundant constraints that commonly exist in general robot assemblies with kinematic loops. We demonstrate the efficacy of our approach by either editing the design of an existing robotic character, or by optimizing the design of a new character to perform a desired motion.

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Worst‐Case Rigidity Analysis and Optimization for Assemblies with Mechanical Joints

Cited by 3 publications

References 57 publications

Differentiable Stripe Patterns for Inverse Design of Structured Surfaces

Differentiable Stripe Patterns for Inverse Design of Structured Surfaces

Computational Design of LEGO ^® Sketch Art

Optimal Design of Robotic Character Kinematics

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About

Worst‐Case Rigidity Analysis and Optimization for Assemblies with Mechanical Joints

Cited by 3 publications

References 57 publications

Differentiable Stripe Patterns for Inverse Design of Structured Surfaces

Differentiable Stripe Patterns for Inverse Design of Structured Surfaces

Computational Design of LEGO ® Sketch Art

Optimal Design of Robotic Character Kinematics

Contact Info

Product

Resources

About

Computational Design of LEGO ^® Sketch Art