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Produktentwicklung und Produktionsgestaltung
Produktentwicklung und Produktionsgestaltung - Spezialisierung Inhalt Industrial Origami • • • • • • (Historical) roots State of the art and basic operations Make a fold Make another fold and learn about - mathematical origami, - computational origami and - technological origami - applications, applications and more applications… Benefits Main Sources Prof. Dr.-Ing. C. Hentschel PEPG_Origami 0 What is Origami? Paper folding associated mostly with Japan (origami means paper folding in Japanese) but concurrent invention in different parts of the world USA China Spain hobby, craft, art form mathematical aspects mathematics is not just numbers, also patterns and shapes basic mathematics to current research (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 1 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Basic forms (to be verified) (Historical) roots 1. Triangle 2. Rectangle 3. Dragon 4. Mill 5. Double square State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 2 Bull moose, rattle snake and mule deer (by Robert J. Lang) (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits http://www.langorigami.com Prof. Dr.-Ing. C. Hentschel PEPG_Origami 3 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Orchestra and organist (by Robert J. Lang) (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits http://www.langorigami.com Prof. Dr.-Ing. C. Hentschel PEPG_Origami 4 Irish Elk with crease pattern (by Robert J. Lang) (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits http://www.langorigami.com Prof. Dr.-Ing. C. Hentschel PEPG_Origami 5 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Tarantula (by Robert J. Lang) (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 6 The six operations of Huzita‘s Axioms I/II (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 7 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung The six operations of Huzita‘s Axioms II/II and Hatori‘s 7th Axiom (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Source: Origami and geometric constructions; by Robert J. Lang, Prof. Dr.-Ing. C. Hentschel PEPG_Origami 8 Make a fold… (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 9 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Make another one… (Historical) roots State of the Art … and unfold! Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits PEPG_Origami Prof. Dr.-Ing. C. Hentschel 10 4 simple Rules of Origami (by courtesy of Robert J. Lang) 1. 2-colorability of crease patterns (Historical) roots 2. Look at the directions of the folds at any given vertex: the numer of mountain folds and the number of valley folds always differ by 2 M – V ±2 State of the Art Make a fold Learn about 3. If you number the angles around a vertex, alternate angles, all even numbered angles add up to a straight line, and all odd numbered angels add up to a straight line (always sum up to a straight line) Mathematical Origami Computational Origami Technological Origami 4. Look how the layers stack: a sheet can never penetrate a fold. Benefits TED Conference February, 2008 Prof. Dr.-Ing. C. Hentschel Applications PEPG_Origami 11 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Properties of Crease Patterns - Rule 1: 2-colorability (by courtesy of Robert J. Lang) 2-colorability (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications TED Conference February, 2008 Benefits PEPG_Origami Prof. Dr.-Ing. C. Hentschel 12 Properties of Crease Patterns – Rule 3: Angles around vertex (by courtesy of Robert J. Lang) Alternate angles around a vertex sum to a straight line (Historical) roots State of the Art Make a fold Learn about 3 2 4 1 6 5 1 2 5 6 4 3 Mathematical Origami Computational Origami Technological Origami Applications TED Conference February, 2008 Prof. Dr.-Ing. C. Hentschel Benefits PEPG_Origami 13 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Properties of Crease Patterns – Rule 4: No self-intersection (by courtesy of Robert J. Lang) No self-intersection at overlaps. (Historical) roots CCFO Ci Fi,1 Fi,2 Fj Ci Fi,1 Fi,2 Fj CUUCO Make a fold Cj Learn about CFFCO Ci Fi,1 Fj,1 State of the Art CFUCO Fi ,2 Fj ,2 Cj Mathematical Origami Ci Fi,1 Fi,2 Fi,1 Fi,2 Cj Fi,1 Fi,1 Fi,2 Fi,2 Cj Ci Computational Origami Technological Origami Applications Benefits TED Conference February, 2008 PEPG_Origami Prof. Dr.-Ing. C. Hentschel 14 Abstraction of the process: Subject --- Tree figure --- Base --- Model Subject Tree Base Model (Historical) roots State of the Art easy Hard easy Make a fold Learn about Mathematical Origami How do you make a bunch of flaps? Computational Origami Technological Origami Applications Benefits (by courtesy of Robert J. Lang) TED Conference, February 2008 Prof. Dr.-Ing. C. Hentschel PEPG_Origami 15 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung An exact folding sequence for dividing a square into thirds (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Source: Origami and geometric constructions; by Robert J. Lang, Prof. Dr.-Ing. C. Hentschel PEPG_Origami 16 Folding sequence for dividing the central 90º angle into sevenths (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Source: Origami and geometric constructions; by Robert J. Lang, Prof. Dr.-Ing. C. Hentschel PEPG_Origami 17 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung First 2 steps of Lang‘s scorpion, which entails a division of an angle into sevenths (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Source: Origami and geometric constructions; by Robert J. Lang, Prof. Dr.-Ing. C. Hentschel PEPG_Origami 18 Screen shot of the Origami Simulation after one fold has been performed by dragging the top left corner to the bottom edge of the paper (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits http://www.langorigami.com Prof. Dr.-Ing. C. Hentschel PEPG_Origami 19 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Computer-generated folding sequences from ReferenceFinder 4 for locating the point (0,1/3) within a unit square. (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications http://www.langorigami.com Prof. Dr.-Ing. C. Hentschel Benefits PEPG_Origami 20 The scorpion: folded base, finished model folded from this base and photograph of the origami figure (by R. J. Lang) (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits http://www.langorigami.com Prof. Dr.-Ing. C. Hentschel PEPG_Origami 21 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung The scorpion crease pattern (by Robert J. Lang) (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 22 A screen shot of the design screen for a scorpion using TreeMaker 4. (Historical) roots The light blue lines define the tree; the desired lengths are entered as numerical values State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits http://www.langorigami.com Prof. Dr.-Ing. C. Hentschel PEPG_Origami 23 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung A screen shot of the computed crease pattern for a scorpion using TreeMaker 4. Circles corresponding to leaf nodes (terminal flaps) are shown to aid intuition (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits http://www.langorigami.com Prof. Dr.-Ing. C. Hentschel PEPG_Origami 24 Screen shot of TreeMaker 5, showing the full crease pattern, folded form, and the new Inspector for editing the design (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits http://www.langorigami.com Prof. Dr.-Ing. C. Hentschel PEPG_Origami 25 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung What can Origami be used for in Industry? (Historical) roots State of the Art Make a fold … collect solutions, in groups, please! Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 26 BMW-STUDIE COUPÉ MILLE MIGLIA "Industrial Origami" im Innenraum der Studie Zwar wurde das Auto als Held für 1000 Meilen nur für die paar Stunden in Brescia gebaut, doch so ein ganz klein wenig Hintersinn hat die Studie doch – zumindest was die Produktionstechnik angeht. "Insbesondere im Innenraum haben wir viel ausprobiert", sagt Bangle und spricht von "Industrial Origami". Ähnlich wie bei der japanischen Papierbastelei wurde das gesamte Interieur der Studie, vom Instrumententräger bis zum Mitteltunnel, aus einem einzigen Edelstahlblech hergestellt, das vorher von einem Laserstrahl angeritzt und dann von Hand gefaltet wurde. So spart man laut Bangle teure Presswerke, die insbesondere eine Kleinserienproduktion oft unrentabel machen. Und man gewinnt eine ausgesprochen attraktive http://www.spiegel.de/fotostrecke/fotostreckeOberflächengestaltung. 13764-2.html#backToArticle=415904 Prof. Dr.-Ing. C. Hentschel PEPG_Origami (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits 27 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung BMW-STUDIE COUPÉ MILLE MIGLIA http://www.spiegel.de/fotostrecke/fotostrecke13764-2.html#backToArticle=415904 PEPG_Origami Prof. Dr.-Ing. C. Hentschel 28 Applications (Historical) roots State of the Art Make a fold Learn about Mathematical Origami … see also: http://www.langorigami .com/science/airbag/air bag.php4 Computational Origami Technological Origami Applications Benefits http://ttr.blog-city.com/origami__automobile_airbags.htm Prof. Dr.-Ing. C. Hentschel PEPG_Origami 29 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Application: Airbag (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 30 Origami: Crash-Strukturen im Fahrzeugbau Quelle: Unveröffentlichte Ideensammlung Czinki-Hentschel, 2008 (Historical) roots State of the Art Kfz-Anwendung Erprobungsträger: Crash-Box für Eisenbahn (Uni Wien) Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications unterschiedliche Realisierungsformen… Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 31 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Origami: Crash-Strukturen im Fahrzeugbau Quelle: Unveröffentlichte Ideensammlung Czinki-Hentschel, 2008 (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Deformationsprozess eines Audi A6 [34] Applications Frontschutzkonzept [59] [34] Wallrich, M., Skript zur Vorlesung Fahrzeugtechnik, FH-Koeln Prof. Dr.-Ing. C. Hentschel [59] www.azt.allianz.de Benefits PEPG_Origami 32 Applications A model for an origami stent, in stainless steel. Its width expands from 12 mm to 23 mm. In practice, flexible materials are best in place of steel, the makers say. (Courtesy K. Kuribayashi, Z. You/University of Oxford) (Historical) roots State of the Art Make a fold Learn about Origami – in den Adern… Ein weiteres Einsatzgebiet für die OrigamiTechnik findet sich in der Medizintechnik. So genannte Stents, Gebilde, die in die Blutgefäße eingeführt werden um sie zu erweitern, werden gefaltet und dehnen sich erst im Gefäß zur gewünschten Größe aus. Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 33 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Applications Origami – … und im Weltraum (Historical) roots Doch auch für die Bearbeitung größerer Dinge, die aus ziemlich festen Werkstoffen bestehen, taugt Origami. Ein Unternehmer aus Northeim in Niedersachsen nutzt die Methode, um Plexiglas in Form(en) zu bringen. Er berechnet mit Origami-Mathematik die zu faltenden Stellen, erwärmt Plexiglasscheiben mit zwei hochenergetischen Heizquellen und klappt sie an den vorgesehen Stellen um wie ein Stück Papier. Erfinder Wolf-Dietrich Hannecke hat die Methode weltweit patentieren lassen. Und es rechnet sich. Denn normalerweise braucht man zur Herstellung von Plexiglasobjekten Spritzgussformen. Eine sehr kostspielige Angelegenheit. Durch die auf Origami basierende Methode werden Formen überflüssig. Ein echt geldwerter Vorteil. State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications http://www.space.com/php/multimedia/imagedisplay/img_display.php?pic=origami_eyeglass_020220_02.gif &cap=The%20proposed%20100meter%20Eyeglass%20telescope%20could%20point%20into%20space%20 or,%20as%20this%20example%20shows,%20back%20at%20Earth. Prof. Dr.-Ing. C. Hentschel Benefits PEPG_Origami 34 Applications (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits http://www.origami-resource-center.com/origami-science.html Prof. Dr.-Ing. C. Hentschel PEPG_Origami 35 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Applications (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits http://www.origami-resource-center.com/origami-science.html Prof. Dr.-Ing. C. Hentschel PEPG_Origami 36 Applications (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 37 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Origami-House (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 38 Applications: Furniture (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits http://www.origami-resource-center.com/origami-furniture.html Prof. Dr.-Ing. C. Hentschel PEPG_Origami 39 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Origami-Table (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 40 The Industrial Origami "smiles" are stamped into an 18 gauge steel plate by turret-punching The Industrial Origami "smiles" are cut into ¼" steel plate with a high speed laser. Industrial Origami "smiles", are subsequently pulled into engagement, creating the patented load-bearing edge-to-face overlap that alternates from smile to smile. (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits http://www.industrialorigami.com Prof. Dr.-Ing. C. Hentschel PEPG_Origami 41 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Origami in der Blechumformung? Quelle: Unveröffentlichte Ideensammlung Czinki-Hentschel, 2008 (Historical) roots State of the Art Blechumformtechnik Origamitechnik Sicken =? Falzen =? Bördeln =? Make a fold Learn about usw. Computational Origami Quelle: http://images.google.de/imgres?imgurl=http://meisterschule.regionkaiserslautern.de/fst/homekb/grafiken/diagramm.jpg&imgrefurl=http://meisterschule.regio nkaiserslautern.de/fst/homekb/sicken.htm&h=400&w=410&sz=12&hl=de&start=6&um=1& usg=__c7KNqdcJi1wXpOUicF9bTTGNyCM=&tbnid=D_YjE8Iwq8tEHM:&tbnh=122&tbnw =125&prev=/images%3Fq%3DSicken%26um%3D1%26hl%3Dde%26rlz%3D1G1GGLQ _DEDE294%26sa%3DG Prof. Dr.-Ing. C. Hentschel Mathematical Origami Technological Origami Applications Benefits PEPG_Origami 42 Origami for Fast Food (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 43 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Multimedia-Origami (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 44 Origami in der Mode (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 45 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Origami in der Mode Quelle: Unveröffentlichte Ideensammlung Czinki–Hentschel, 2008 (Historical) roots Tragetuch… State of the Art Make a fold Learn about Mathematical Origami Buff… Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 46 ... and many more.......... (Historical) roots State of the Art Make a fold Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 47 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Benefits Reducing the number and cost of components and joining operations Simplifying and reducing the cost of manufacturing including stamping and assembly Simplifying and reducing the cost of shipping and storage (Historical) roots State of the Art Make a fold Increasing precision Learn about Reducing the time and cost of prototyping Mathematical Origami Reducing weight under certain circumstances Computational Origami Teaching mathematical thinking through origami Technological Origami Connections in art, music and science!!! Applications … Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 48 In case you are interested to do more reseach on Origami, …. (Historical) roots State of the Art Make a fold …please, contact Prof. Hentschel! Learn about Mathematical Origami Computational Origami Technological Origami Applications Benefits Prof. Dr.-Ing. C. Hentschel PEPG_Origami 49 Industrial_Origami, Seite Produktentwicklung und Produktionsgestaltung - Spezialisierung Main Sources (accessed in February 2010) http://www.langorigami.com/ http://www.ted.com/index.php/talks/robert_lang_folds_way_new_origami.html http://www.industrialorigami.com/home.cfm http://www.origami-resource-center.com/origami-science.html http://newmedia.purchase.edu/~Jeanine/origami … more to come… AND: I thank my elder son Moritz Wilksch for the inspiration and the support in folding about 3647 models in 2008 when he was 10 - while I did about 5….. Claudia Hentschel Prof. Dr.-Ing. C. Hentschel PEPG_Origami 50 Industrial_Origami, Seite
