Kinematic Design of Miura-Ori-Based Folding Structures Using the Screw Axis of a Relative Displacement

Abdul-Sater, Kassim; Lueth, Tim C.; Irlinger, Franz

doi:10.1007/978-3-319-06698-1_25

Advances in Robot Kinematics 2014

DOI: 10.1007/978-3-319-06698-1_25

|View full text |Cite

Kinematic Design of Miura-Ori-Based Folding Structures Using the Screw Axis of a Relative Displacement

Kassim Abdul-Sater

Tim C. Lueth

Franz Irlinger

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2015

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By patterning creases, hinges, or folds into an otherwise flat sheet (be it composed of paper, metal or polymer gel), the bulk material is imbued with an effective mechanical response. In contrast to conventional com-posites engineering, wherein methods generally rely on designing response based on the interaction between the constituent parts that compose the material, origamibased design injects novelty at the "atomic" level; even single vertices of origami behave as engineering mechanisms [14], providing novel functionality such as complicated bistability [15][16][17] and auxetic behavior [6,[11][12][13]. This generic property inspires the identification of origami tessellations with mechanical metamaterials, or a composite whose effective properties arise from the structure of the unit cell.…”

mentioning

confidence: 99%

Lattice mechanics of origami tessellations

2015

View full text Add to dashboard Cite

Origami-based design holds promise for developing materials whose mechanical properties are tuned by crease patterns introduced to thin sheets. Although there has been heuristic developments in constructing patterns with desirable qualities, the bridge between origami and physics has yet to be fully developed. To truly consider origami structures as a class of materials, methods akin to solid mechanics need to be developed to understand their long-wavelength behavior. We introduce here a lattice theory for examining the mechanics of origami tessellations in terms of the topology of their crease pattern and the relationship between the folds at each vertex. This formulation provides a general method for associating mechanical properties with periodic folded structures, and allows for a concrete connection between more conventional materials and the mechanical metamaterials constructed using origami-based design.While for hundreds of years origami has existed as an artistic endeavor, recent decades have seen the application of folding thin materials to the fields of architecture, engineering, and material science [1][2][3][4][5][6][7]. Controlled actuation of thin materials via patterned folds has led to a variety of self-assembly strategies in polymer gels [8] and shape-memory materials [4], as well elastocapillary self-assembly [9], leading to the design of a new category of shape-transformable materials inspired by origami design. The origami repertoire itself, buoyed by advances in the mathematics of folding and the burgeoning field of computational geometry [10], is no longer limited to designs of animals and children's toys that dominate the art in popular consciousness, but now includes tessellations, corrugations, and other non-representational structures whose mechanical properties are of interest from a scientific perspective. These properties originate from the confluence of geometry and mechanical constraints that are an intrinsic part of origami, and ultimately allow for the construction of mechanical meta-materials using origami-based design [1-4, 6, 11-13]. In this paper we formulate a general theory for periodic lattices of folds in thin materials, and combine the language of traditional lattice solid mechanics with the geometric theory underlying origami.A distinct characteristic of all thin materials is that geometric constraints dominate the mechanical response of the structure. Because of this strong coupling between shape and mechanics, it is far more likely for a thin sheet to deform by bending without stretching. Strategically weakening a material with a crease or fold, and thus lowering the energetic cost of stretching, allows complex deformations and re-ordering of the material for negligible elastic energy cost. This vanishing energy cost, especially combined with increased control over micro-and nanoscopic material systems, indicates the great promise for structures whose characteristics depend primarily on geometry, rather than material composition.By patterning creases, hinges, or fold...

show abstract

mentioning

confidence: 99%

Lattice mechanics of origami tessellations

2015

View full text Add to dashboard Cite

show abstract

Three-Position Synthesis of Origami-Evolved, Spherically Constrained Spatial Revolute–Revolute Chains

Abdul-Sater

Winkler

Irlinger

et al. 2015

Journal of Mechanisms and Robotics

View full text Add to dashboard Cite

This paper presents a finite position synthesis (f.p.s.) procedure of a spatial single-degree-of-freedom linkage that we call origami-evolved, spherically constrained spatial revolute–revolute (RR) chain here. This terminology is chosen because the linkage may be found from the mechanism equivalent of an origami folding pattern, namely, known as the Miura-ori folding. As shown in an earlier work, the linkage under consideration has naturally given slim shape and essentially represents two specifically coupled spherical four-bar linkages, whose links may be identified with spherical and spatial RR chains. This provides a way to apply the well-developed f.p.s. theory of these linkage building blocks in order to design the origami-evolved linkage for a specific task. The result is a spherically constrained spatial RR chain, whose end effector may reach three finitely separated task positions. Due to an underspecified spherical design problem, the procedure provides several free design parameters. These can be varied in order to match further given requirements of the task. This is shown in a design example with particularly challenging space requirements, which can be fulfilled due to the naturally given slim shape.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Kinematic Design of Miura-Ori-Based Folding Structures Using the Screw Axis of a Relative Displacement

Cited by 2 publications

References 3 publications

Lattice mechanics of origami tessellations

Lattice mechanics of origami tessellations

Three-Position Synthesis of Origami-Evolved, Spherically Constrained Spatial Revolute–Revolute Chains

Contact Info

Product

Resources

About