Invertible Paradoxic Loop Structures for Transformable Design
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Date
2020
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
We present an interactive tool compatible with existing software (Rhino/Grasshopper) to design ring structures with a paradoxic mobility, which are self-collision-free over the complete motion cycle. Our computational approach allows non-expert users to create these invertible paradoxic loops with six rotational joints by providing several interactions that facilitate design exploration. In a first step, a rational cubic motion is shaped either by means of a four pose interpolation procedure or a motion evolution algorithm. By using the representation of spatial displacements in terms of dual-quaternions, the associated motion polynomial of the resulting motion can be factored in several ways, each corresponding to a composition of three rotations. By combining two suitable factorizations, an arrangement of six rotary axes is achieved, which possesses a 1-parametric mobility. In the next step, these axes are connected by links in a way that the resulting linkage is collision-free over the complete motion cycle. Based on an algorithmic solution for this problem, collision-free design spaces of the individual links are generated in a post-processing step. The functionality of the developed design tool is demonstrated in the context of an architectural and artistic application studied in a master-level studio course. Two results of the performed design experiments were fabricated by the use of computer-controlled machines to achieve the necessary accuracy ensuring the mobility of the models.
Description
@article{10.1111:cgf.13928,
journal = {Computer Graphics Forum},
title = {{Invertible Paradoxic Loop Structures for Transformable Design}},
author = {Li, Zijia and Nawratil, Georg and Rist, Florian and Hensel, Michael},
year = {2020},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.13928}
}