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ORI* On the Aesthetics of Folding and Technology
Abstract and Figures
The art of oribotics involves a process of imagining and creating geometry for static and kinetic origami structures to fit a desired form. It is a two-fold difficult task. Firstly, tools for calculating the geometry are few, and those existing lack key aesthetic and functional criteria specific to my artistic practice. Secondly, material issues, such as durability and complex foldability, compound the issues for fabrication. Existing methods, even those applying digital fabrication, pose complex folding problems that confound origami experts.
Case studies are provided of leading origamists working with software, fabrication and materials to analyse and summarise processes. Analysis of these led to the synthesis and identification of differentiating criteria that inspired the invention of two key methods: Fold-Mapping and Fold-Printing. Fold-Mapping abstracts naturally occurring origami patterns into fold-molecules for tessellation across target geometric surfaces. It allows an artist to prioritise the sculptural shape of the result while seeking a kinetic solution through experimentation with different fold-molecules. A developability algorithm then flattens the crease pattern into geometry for fabrication. Fold-Printing allows the fabrication of Fold-Mapping results. It includes results of high-order complex-foldability by 3D printing whereby polymers are deposited onto textiles forming a durable polymer plate-structure separated by perfect textile hinges.
Evaluation of the methods is two-fold. Firstly, the methods were continuously evaluated and refined through invention based trial-and-error. Secondly, the artefacts were evaluated according to a set of aesthetic criteria which in this thesis are collectively called ORI* theory. ORI* theory includes origami and oribotic criteria, and a metric for complex-foldability.
For proof of concept, the methods are presented as an evaluated set of successful traits and developed solutions. These produce developable crease patterns from target geometries and afford the fabrication and foldability of complex ORI* objects. Fold-Printing allows near impossible-to-fold patterns to become foldable objects. The methods do not succeed in all circumstances, and that success is additionally dependent on the author’s experience of origami structures. The aesthetic qualities and material properties of the artistic results have distinct qualities that qualify them to meet the particular criteria required for ORI* objects.
The thesis concludes with the proposing of future work: 1) in the direction of soft-robotic applications using both Fold-Mapping and Fold-Printing methods, and 2) the creation of enhanced aesthetic and technical ORI* objects across many disciplinary domains.
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... The pattern is critically important in origami technology as it significantly influences the size, shape, deployment behavior, and structural characteristics of a structure. Most research related to origami utilizes or applies major existing patterns (Kresling, Yoshimura, Miura, Flasher, Waterbomb), leading to limitations in storage efficiency and design aspects [10,14]. To overcome these limitations, it can be considered to combine or modify patterns in various ways, or even incorporate Kirigami techniques by cutting parts of the pattern [15]. ...
... The rapidly developing field of structural origami investigates the correlation between forms emerging from sheet folding and their structural performance [12]. Numerous pioneers have made substantial contributions to the field of structural origami, including mathematicians [13], computer scientists [14], physicists [15], astrophysicists [16], architects and engineers [17,18], as well as origami artists and designers [19,20]. ...
The demand for adaptable structures is steadily increasing in contemporary architectural practice. Deployable structures, characterized by their flexibility and versatility, offer innovative solutions across demanding engineering and architectural contexts. Among the various types of deployable structures, two main categories emerge: lattice deployable structures and continuous surface deployable structures. This paper explores the creation of hybrid deployable vaulted structures by incorporating kinetic elements from both deployable structure categories. A combination of rigid thick origami surfaces and retractable structural frames composed of four-bar and scissor-hinged linkages is examined, while both direct and inverse design methodologies are explored. To facilitate the parameterization and kinematic study of the proposed structures, an algorithm is developed within the Rhino Grasshopper visual programming environment, which is then utilized for form-finding and design optimization of the generated deployable vaults. The present study aims to contribute to the evolution of lightweight, kinetic elements for versatile architectural applications. The proposed hybrid deployable structures are designed to adjust to evolving spatial and functional requirements while maintaining structural integrity.
This paper presents original research developed during PhD research. It proposes a multidisciplinary process as a methodology for the construction of thick, rigid origami surfaces to be used for kinetic architectural purposes. Origami surfaces that fold rigidly allow for strict geometry-based simulations that can reproduce rigorous rigid kinematics from the unfolded to the completely folded state, which is particularly important in large scale structures where motion must be predictable. The considered surfaces are regularly tessellated and have planar initial and final states. Through movement, these can assume a cycle of folding states with different three-dimensional configurations. The proposed method departs from concept, moves to geometry definition, kinematic simulation, structural evaluation, construction, and implementation for folding surfaces. It includes steps for evaluation and correction of issues as well as strategies for construction through digital fabrication with planar, thick materials. Its validity is demonstrated by its application in a constructed case study.
This paper covers the brief 4 year history of Oribotics as a tangible field of study; as a hybrid field of study, with art exhibits as the end goals. I will cover my definition of Oribotics, the origin and evolution of oribotics, design problems and solutions. While thinking generally about origami and technology I realised the two fields are very similar. Origami often borrows from nature, and often highly regarded origami works are the most 'natural. The same aspirations exist in robotic behaviour and movement. Robots are programmed machines, and origami is programmed paper, that is paper coded with creases.
OMTO solves displacement objective problems where boundary conditions, force input nodes, and displacement output nodes are specified on a user-defined grid. Given this user-defined problem statement, it determines the fold lines that produce the greatest displacement, in the specified direction or directions, at the specified output nodes. The default setting requires MATLAB's optimization toolbox.
Tutorial video is available at: https://youtu.be/U68LqwRGrI4
This research is supported under the Air Force Office of Scientific Research (AFOSR) funding,
LRIR13RQ02COR.
Contributions by
Philip Buskohl, Michael Kuhn, Giorgio Bazzan,
Michael Durstock, Richard Vaia, Gregory Reich, James Joo
Air Force Research Labs, Wright-Patterson AFB, 45433
We present a design method that prioritises in-context design for origami surfaces with periodic tessellations in a parametric CAD workflow using Grasshopper 3D. The key design criteria are: target geometry surface, user-defined folding patterns as periodic tessellations, and fold resolution. Using an error minimisation solver, we generate developable crease patterns from non-developable meshes. We evaluate our method through a study of a target geometry , Fold Mapped with various fold molecules at variable resolutions, and present a visual analysis as proof of form-fit to the target. This method affords rapid development of origami surfaces, bypassing significant trial and error in by-hand design processes.
Computational Origami invents a new kind of complexity: the highly irregular crease pattern, posing a significant challenge to foldability. We design a method for digital fabrication of multi-material composites to overcome issues of foldability and durability faced when producing functional prototypes with paper. Our fabrication method, called Fold Printing, uses off-the-shelf and customised 3D printing technology, heat pressing, and elastomers to control fold memory in Folded Polymer Textile Elastomer Composites (FPTEC). Our results show that Fold-Printing affords foldability of high-irregularity crease patterns, and can produce durable advanced origami prototypes.
Oribotics is a field of research concerned with the aesthetic, biomechanic, and morphological connections among nature, origami, and robotics. In my current research, the focus is on the actuation of fold-programmed materials such as paper and synthetic fabrics. The design of the crease pattern, the precise arrangement of mountain and valley folds, and the way they fold and unfold directly inform mechanical design. Therefore, a key area of current research is focused on the discovery of patterns that have complex expressions that can be actuated repeatedly. This research has resulted in some artistic exhibitions; the largest to date was at the 2010 Ars Electronica Festival in Linz, Austria
Robert J. Lang, one of the worlds foremost origami artists and scientists, presents the never-before-described mathematical and geometric principles that allow anyone to design original origami, something once restricted to an elite few. From the theoretical underpinnings to detailed step-by-step folding sequences, this book takes a modern look at the centuries-old art of origami.
Origami, the art of paper folding, is a technologically transformative art with applications at many length scales from material microstructure design to space deployable structures. The transformation of a two-dimensional fold pattern to a three-dimensional structure makes origami a practical basis for deployability, light-weight materials, and self-actuation. In order to predict the complex motions of origami structures including path traversal of instabilities, accurate and efficient modeling techniques are required. While many approaches consider rigid facets and/or linear approximations to rotations, a truss and hinge finite element method is presented here within a global coordinate system framework to accurately capture the geometric nonlinearities while allowing for small to moderate facet deformation. Accurately capturing these modes of deformation is critical toward understanding the elastic energetic states required for design and analysis of multistable origami structures and mechanical metamaterials. Particular formulation developments that we address to solve origami mechanics problems include formulation of a continuous and differentiable fold angle, strategy for selecting fold path off the flat state, and integration of common numerical approaches important for origami (large rotation formulation, enforcement of periodic boundary conditions for tessellations, arc-length continuation method for solving highly nonlinear loading paths, and a perturbation strategy for handling bifurcations). After formulating this truss finite element method, we verify our modified finite element method on well-studied structures. The waterbomb fold pattern is studied, and the interplay of the stretching and folding energies are considered toward design of a bistable structure that exhibits a fold based snap-through instability. This study is followed by analysis of a cylindrical network of waterbombs (axial periodicity) that exhibits a stretch driven instability. Lastly, a tessellated square twist pattern, exhibiting multiple bifurcations off the flat state is presented that employs all aspects of our numerical method.
More than just simple folding
Origami involves folding two-dimensional sheets into complex three-dimensional objects. However, some shapes cannot be created using standard folds. Faber et al. studied the wing of an earwig, which can fold in ways not possible using origami and can alter its shape for flight. The authors replicated this ability by using a membrane that allows for deformations and variable stiffness. Prestretching generated energetically bistable origami patterns that exhibited passive self-folding behavior.
Science , this issue p. 1386