Non-Euclidean Origami

Non-Euclidean Origami

Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how non-Euclidean 4-vertices overcome these limitations by lifting th...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2019-09
Hauptverfasser: Waitukaitis, Scott, Dieleman, Peter, Martin van Hecke
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Elasticity
Flat surfaces
Physics - Soft Condensed Matter
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Waitukaitis, Scott
Dieleman, Peter
Martin van Hecke
description Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how non-Euclidean 4-vertices overcome these limitations by lifting this degeneracy, and that when the elasticity of the hinges is taken into account, non-Euclidean 4-vertices permit higher-order multistability. We harness these advantages to design an origami inverter that does not suffer from misfolding and to physically realize a tristable vertex.
doi_str_mv 10.48550/arxiv.1909.13674
format Article
fullrecord <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_1909_13674</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2299621509</sourcerecordid><originalsourceid>FETCH-LOGICAL-a529-59fb3d31c24bfceb624e91426899f4f89e15439868c914565548d9ea66974e243</originalsourceid><addsrcrecordid>eNotzsFLwzAUBvAgCBtzRw87KXhOTV7eS_OOMqYThrvsXtI2lYytnakV_e-tm6cPPj4-fkIstMrQEalHn77jV6ZZcaaNzfFKTMEYLR0CTMS87_dKKbA5EJmpuH3rWrkaqkOsg2_vtym--2O8EdeNP_Rh_p8zsXte7ZZrudm-vC6fNtITsCRuSlMbXQGWTRVKCxhYI1jH3GDjOGhCw866aqzJEqGrOXhrOccAaGbi7nJ7NhenFI8-_RR_9uJsHxcPl8UpdR9D6D-LfTekdjQVAMwWNCk2v8VNQ3o</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2299621509</pqid></control><display><type>article</type><title>Non-Euclidean Origami</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Waitukaitis, Scott ; Dieleman, Peter ; Martin van Hecke</creator><creatorcontrib>Waitukaitis, Scott ; Dieleman, Peter ; Martin van Hecke</creatorcontrib><description>Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how non-Euclidean 4-vertices overcome these limitations by lifting this degeneracy, and that when the elasticity of the hinges is taken into account, non-Euclidean 4-vertices permit higher-order multistability. We harness these advantages to design an origami inverter that does not suffer from misfolding and to physically realize a tristable vertex.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1909.13674</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Apexes ; Elasticity ; Flat surfaces ; Physics - Soft Condensed Matter</subject><ispartof>arXiv.org, 2019-09</ispartof><rights>2019. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,780,881,27902</link.rule.ids><backlink>$$Uhttps://doi.org/10.1103/PhysRevE.102.031001$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.1909.13674$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Waitukaitis, Scott</creatorcontrib><creatorcontrib>Dieleman, Peter</creatorcontrib><creatorcontrib>Martin van Hecke</creatorcontrib><title>Non-Euclidean Origami</title><title>arXiv.org</title><description>Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how non-Euclidean 4-vertices overcome these limitations by lifting this degeneracy, and that when the elasticity of the hinges is taken into account, non-Euclidean 4-vertices permit higher-order multistability. We harness these advantages to design an origami inverter that does not suffer from misfolding and to physically realize a tristable vertex.</description><subject>Apexes</subject><subject>Elasticity</subject><subject>Flat surfaces</subject><subject>Physics - Soft Condensed Matter</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><sourceid>GOX</sourceid><recordid>eNotzsFLwzAUBvAgCBtzRw87KXhOTV7eS_OOMqYThrvsXtI2lYytnakV_e-tm6cPPj4-fkIstMrQEalHn77jV6ZZcaaNzfFKTMEYLR0CTMS87_dKKbA5EJmpuH3rWrkaqkOsg2_vtym--2O8EdeNP_Rh_p8zsXte7ZZrudm-vC6fNtITsCRuSlMbXQGWTRVKCxhYI1jH3GDjOGhCw866aqzJEqGrOXhrOccAaGbi7nJ7NhenFI8-_RR_9uJsHxcPl8UpdR9D6D-LfTekdjQVAMwWNCk2v8VNQ3o</recordid><startdate>20190930</startdate><enddate>20190930</enddate><creator>Waitukaitis, Scott</creator><creator>Dieleman, Peter</creator><creator>Martin van Hecke</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>GOX</scope></search><sort><creationdate>20190930</creationdate><title>Non-Euclidean Origami</title><author>Waitukaitis, Scott ; Dieleman, Peter ; Martin van Hecke</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a529-59fb3d31c24bfceb624e91426899f4f89e15439868c914565548d9ea66974e243</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Apexes</topic><topic>Elasticity</topic><topic>Flat surfaces</topic><topic>Physics - Soft Condensed Matter</topic><toplevel>online_resources</toplevel><creatorcontrib>Waitukaitis, Scott</creatorcontrib><creatorcontrib>Dieleman, Peter</creatorcontrib><creatorcontrib>Martin van Hecke</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Waitukaitis, Scott</au><au>Dieleman, Peter</au><au>Martin van Hecke</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Non-Euclidean Origami</atitle><jtitle>arXiv.org</jtitle><date>2019-09-30</date><risdate>2019</risdate><eissn>2331-8422</eissn><abstract>Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how non-Euclidean 4-vertices overcome these limitations by lifting this degeneracy, and that when the elasticity of the hinges is taken into account, non-Euclidean 4-vertices permit higher-order multistability. We harness these advantages to design an origami inverter that does not suffer from misfolding and to physically realize a tristable vertex.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1909.13674</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2019-09
issn 2331-8422
language eng
recordid cdi_arxiv_primary_1909_13674
source arXiv.org; Free E- Journals
subjects Apexes
Elasticity
Flat surfaces
Physics - Soft Condensed Matter
title Non-Euclidean Origami
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-09T23%3A18%3A06IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Non-Euclidean%20Origami&rft.jtitle=arXiv.org&rft.au=Waitukaitis,%20Scott&rft.date=2019-09-30&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1909.13674&rft_dat=%3Cproquest_arxiv%3E2299621509%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2299621509&rft_id=info:pmid/&rfr_iscdi=true