Design and simulation of origami structures with smooth folds

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 473, Issue 2200, 2017, Pages

  Peraza Hernandez, E A ^a   Hartl, D J ^a   Lagoudas, D C ^a  

^a Department of Electrical and Computer Engineering   (United States)

Author keywords

Design; Origami; Smooth folds

Indexed keywords

GEOMETRY; MESH GENERATION;

DESIGN AND SIMULATION; DESIGN PROBLEMS; GEOMETRIC CONTINUITY; MULTIPLE STRUCTURES; ORIGAMI; PARAMETRIZATIONS; POLYGONAL MESHES; SMOOTH FOLDS;

DESIGN;

EID: 85034824589     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2016.0716     Document Type: Conference Paper

References (47)

1. Demaine ED, O’Rourke J. 2007 Geometric folding algorithms. Cambridge, UK: Cambridge University Press.
2. Lang RJ. 2007 The science of origami. Phys. World 20, 30–31. (doi:10.1088/2058-7058/20/2/31)
3. Lang RJ. 2009 Computational origami: from flapping birds to space telescopes. In Proc. of the Twenty-fifth Annual Symp. on Computational Geometry, Aarhus, Denmark, 8–10 June, pp. 159–162. New York, NY: ACM.
4. Turner N, Goodwine B, Sen M. 2015 A review of origami applications in mechanical engineering. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 230, 0954406215597713. (doi:10.1177/0954406215597713)
5. Peraza Hernandez EA, Hartl DJ, Malak Jr RJ, Lagoudas DC. 2014 Origami-inspired active structures: a synthesis and review. Smart Mater. Struct. 23, 094001. (doi:10.1088/0964-1726/ 23/9/094001)
6. Cromvik C, Eriksson K. 2006 Airbag folding based on origami mathematics. In Origami 4, Fourth Int. Meeting of Origami Science, Mathematics, and Education, Pasadena, CA, 8–10 September, pp. 129–139. Natick, MA: AK Peters.
7. Peraza Hernandez EA, Hu S, Kung HW, Hartl D, Akleman E. 2013 Towards building smart self-folding structures. Computers Graphics 37, 730–742. (doi:10.1016/j.cag.2013.05.022)
8. Shaar NS, Barbastathis G, Livermore C. 2015 Integrated folding, alignment, and latching for reconfigurable origami microelectromechanical systems. J. Microelectromech. Syst. 24, 1043–1051. (doi:10.1109/JMEMS.2014.2379432)
9. Filipov ET, Paulino GH, Tachi T. 2016 Origami tubes with reconfigurable polygonal cross-sections. Proc. R. Soc. A 472, 20150607. (doi:10.1098/rspa.2015.0607)
10. Saintsing CD, Cook BS, Tentzeris MM. 2014 An origami inspired reconfigurable spiral antenna. In Proc. of ASME 2014 IDETC/CIE, Buffalo, NY, 17–20 August, pp. V05BT08A050. New York, NY: American Society of Mechanical Engineers.
11. Bassik N, Stern GM, Gracias DH. 2009 Microassembly based on hands free origami with bidirectional curvature. Appl. Phys. Lett. 95, 091901. (doi:10.1063/1.3212896)
12. Shin B, Felton SM, Tolley MT, Wood RJ. 2014 Self-assembling sensors for printable machines. In Proc. of the 2014 IEEE Int. Conf. on Robotics and Automation (ICRA), Hong Kong, 31 May–5 June, pp. 4417–4422. Piscataway, NJ: IEEE.
13. Early JT, Hyde R, Baron RL. 2004 Twenty-meter space telescope based on diffractive Fresnel lens. In Proc. of the SPIE’s 48th Annual Meeting, Optical Science and Technology. Int. Soc. for Optics and Photonics, San Diego, CA, pp. 148–156. Bellingham, WA: SPIE.
14. Song Z et al. 2014 Origami lithium-ion batteries. Nat. Commun. 5, 3140. (doi:10.1038/ ncomms4140)
15. Miyashita S, Guitron S, Ludersdorfer M, Sung CR, Rus D. 2015 An untethered miniature origami robot that self-folds, walks, swims, and degrades. In Proc. of the 2015 IEEE Int. Conf. on Robotics and Automation (ICRA), Seattle, WA: 26–30 May, pp. 1490–1496. Piscataway, NJ: IEEE.
16. Martínez-Martín FJ, Thrall AP. 2014 Honeycomb core sandwich panels for origami-inspired deployable shelters: multi-objective optimization for minimum weight and maximum energy efficiency. Eng. Struct. 69, 158–167. (doi:10.1016/j.engstruct.2014.03.012)
17. Kuribayashi K, Tsuchiya K, You Z, Tomus D, Umemoto M, Ito T, Sasaki M. 2006 Self-deployable origami stent grafts as a biomedical application of Ni-rich TiNi shape memory alloy foil. Mater. Sci. Eng. A 419, 131–137. (doi:10.1016/j.msea.2005.12.016)
18. Lebée A. 2015 From folds to structures, a review. Int. J. Space Struct. 30, 55–74. (doi:10.1260/ 0266-3511.30.2.55)
19. Tachi T. 2009 Simulation of rigid origami. In Origami 4, Fourth Int. Meeting of Origami Science, Mathematics, and Education, Pasadena, CA, 8–10 September, pp. 175–187. Natick, MA: AK Peters.
20. Belcastro SM, Hull TC. 2002 Modelling the folding of paper into three dimensions using affine transformations. Linear Algebra and its Applications 348, 273–282. (doi:10.1016/ S0024-3795(01)00608-5)
21. Belcastro SM, Hull TC. 2002 A mathematical model for non-flat origami. In Origami 3: Third Int. Meeting of Origami Mathematics, Science, and Education, Asiloma, CA, pp. 39–51. Natick, MA: AK Peters.
22. Tachi T. 2010 Origamizing polyhedral surfaces. IEEE Trans. Visualization Computer Graphics 16, 298–311. (doi:10.1109/TVCG.2009.67)
23. Lang RJ. 1996 A computational algorithm for origami design. In Proc. of the Twelfth Annual Symp. on Computational Geometry, Philadelphia, PA, 24–26 May, pp. 98–105. New York, NY: ACM.
24. Evans TA, Lang RJ, Magleby SP, Howell LL. 2015 Rigidly foldable origami gadgets and tessellations. R. Soc. open sci. 2, 150067. (doi:10.1098/rsos.150067)
25. Zhou X, Wang H, You Z. 2015 Design of three-dimensional origami structures based on a vertex approach. Proc. R. Soc. A 471, 20150407. (doi:10.1098/rspa.2015.0407)
26. Schlickenrieder W. 1997 Nets of polyhedra. Berlin, Germany: Technische Universität.
27. Tachi T. 2009 3D origami design based on tucking molecule. In Origami 4, Fourth Int. Meeting of Origami Science, Mathematics, and Education, Pasadena, CA, 8–10 September, pp. 259–272. Natick, MA: AK Peters.
28. Tachi T. 2013 Designing freeform origami tessellations by generalizing Resch’s patterns. J. Mech. Des. 135, 111006. (doi:10.1115/1.4025389)
29. Saito K, Tsukahara A, Okabe Y. 2016 Designing of self-deploying origami structures using geometrically misaligned crease patterns. Proc. R. Soc. A 472, 20150235. (doi:10.1098/ rspa.2015.0235)
30. Upadhe SN, Chavan AS, Shaikh TB. 2014 Industrial origami a review. Int. J. Innov. Res. Adv. Eng. 1, 265–269.
31. Peraza-Hernandez E, Hartl D, Galvan E, Malak R. 2013 Design and optimization of a shape memory alloy-based self-folding sheet. J. Mech. Des. 135, 111007. (doi:10.1115/1.4025382)
32. Mailen RW, Liu Y, Dickey MD, Zikry M, Genzer J. 2015 Modelling of shape memory polymer sheets that self-fold in response to localized heating. Soft Matter 11, 7827–7834. (doi:10.1039/C5SM01681A)
33. Peraza Hernandez EA, Hartl DJ, Lagoudas DC. 2016 Kinematics of origami structures with smooth folds. J. Mech. Robotics 8, 061019. (doi:10.1115/1.4034299)
34. Peraza Hernandez EA, Hartl DJ, Akleman E, Lagoudas DC. 2016 Modeling and analysis of origami structures with smooth folds. Computer-Aided Design 78, 93–106. (doi:10.1016/ j.cad.2016.05.010)
35. Wheeler CM, Culpepper ML. 2016 Soft origami: classification, constraint, and actuation of highly compliant origami structures. J. Mech. Robotics 8, 051012. (doi:10.1115/1.4032472)
36. Kwok TH, Wang CCL, Deng D, Zhang Y, Chen Y. 2015 Four-dimensional printing for freeform surfaces: design optimization of origami and kirigami structures. J. Mech. Design 137, 111413. (doi:10.1115/1.4031023)
37. Barsky BA, DeRose TD. 1984 Geometric continuity of parametric curves. San Francisco, CA: Computer Science Division, University of California.
38. Akleman E, Chen J. 2006 Insight for practical subdivision modeling with discrete Gauss-Bonnet theorem. In Int. Conf. on Geometric Modeling and Processing, Pittsburg, PA, 26–28 July (eds M-S Kim, K Shimada), pp. 287–298. Berlin, Germany: Springer.
39. Tachi T. 2010 Freeform variations of origami. J. Geom. Graph 14, 203–215.
40. Erickson J, Har-Peled S. 2004 Optimally cutting a surface into a disk. Discrete Comput. Geometry 31, 37–59. (doi:10.1007/s00454-003-2948-z)
41. Sullivan JM. 2008 Curvatures of smooth and discrete surfaces. In Discrete Differential Geometry. Berlin, Germany: Springer, pp. 175–188.
42. Song G, Amato NM. 2004 A motion-planning approach to folding: from paper craft to protein folding. IEEE Trans. Robotics Autom. 20, 60–71. (doi:10.1109/TRA.2003.820926)
43. Xi Z, Lien JM. 2015 Plan folding motion for rigid self-folding machine via discrete domain sampling. In 2015 IEEE Int. Conf. on Robotics and Automation (ICRA), Seattle, WA: 26–30 May, pp. 2938–2943. Piscataway, NJ: IEEE.
44. Xi Z, Lien JM. 2015 Folding and unfolding origami tessellation by reusing folding path. In 2015 IEEE Int. Conf. on Robotics and Automation (ICRA), Seattle, WA, 26–30 May, pp. 4155–4160. Piscataway, NJ: IEEE.
45. Calladine CR. 1989 Theory of shell structures. Cambridge, UK: Cambridge University Press.
46. Frey PJ, George PL. 2008 Mesh generation: application to finite elements, 2nd edn. Hoboken, NJ: ISTE/John Wiley & Sons.
47. Zheng Y, Lewis RW, Gethin DT. 1996 Three-dimensional unstructured mesh generation: Part 2. Surface meshes. Computer Methods Appl. Mech. Eng. 134, 269–284. (doi:10.1016/ 0045-7825(95)00917-5)