Digital origami from geometrically frustrated tiles

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harnettlab.org Digital Origami from Geometrically Frustrated Tiles C. K. Harnett University of Louisville C. J. Kimmer Indiana University Southeast

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From http://harnettlab.org Our presentation from the 2013 ASME meeting explains how to build up 2-D and 3-D shapes from curved tiles that can pop up or down. Even though the tiles' shapes are limited to only 2 options, the proper tile sequence can create a larger, much more interesting shape. In 2-D we describe how to create arbitrary contours from strings of identical curved segments. (Imagine trying to decorate a squiggle drawn on paper by gluing pieces of macaroni on top.) The problem becomes finding the right binary sequence to follow the line with the fewest errors. In 3D we show a video of a self-consistency algorithm to generate a shape from a 2D tile array.

Transcript of Digital origami from geometrically frustrated tiles

  • 1. harnettlab.org Digital Origami from Geometrically Frustrated Tiles C. K. Harnett University of Louisville C. J. Kimmer Indiana University Southeast

2. harnettlab.org Toward a digital material for origami Goal: a membrane that can be programmed for a given shape using two-state cells Geometric frustration is the key to a simple, digital shape sensor element Threshold-based bistable systems require power only when switching/reading. We can microfabricate these devices or make them on a larger size scale. 3. harnettlab.org Is digital origami a real possibility? There are also 3D printed multistable structures. Lets apply concept to a wider range of materials and over a larger range of size scales. http://home.earthlink.net/~barkingpo/bistabledome.html YES, multistable structures have been made from spring steel sheets with dimples. 4. harnettlab.org 2-D arrays can be made by inserting pieces a little too large to stay in plane 5. harnettlab.org Manipulating a 2-D array 6. harnettlab.org Geometrical frustration key to making a multistable structure It costs energy to bend or compress a sheet Geometrical frustration: not all parts of the material can be at the minimum energy state at the same time because of constraints. Geometrical frustration can happen if parts of the sheet are tied together. The material responds by bending out of plane Examples can be found from micro to macroscale 7. harnettlab.org Geometrical frustration creates two stable states for a doubly clamped compressed beam 8. harnettlab.org Describing a shape with up-or-down pieces: 1-D example Important: the tangent is continuous between neighbors. This coupling makes the global shape depend on local conditions. We can easily recreate a curve from a given bit sequence (next slide). The inverse problem is more challenging: How can we come up with a bit sequence to describe a known shape? 9. harnettlab.org Convert a curve to 1-bit digital by making a sequence of macaroni arcs Each sequence of up-or- down orientations of the 8 segments produces a different curve. Rotate to an accumulated angle, translate the new arc to the latest endpoint, and repeat. Heres a byte of macaroni 10. harnettlab.org Manipulating a 1-D array equipped with sensors 11. harnettlab.org Shape-matching problem: Metropolis algorithm explores a large territory by allowing mistakes Smarten it by gradually increasing cost of mistakes Or try a different approach: curvature matching Using 60 identical arcs to fit a circle 12. harnettlab.org Local curvature depends on local bit distribution 13. harnettlab.org Challenge: Find a 1-bit, length 96 sequence to match a test shape 14. harnettlab.org Dithering finds a fast solution 15. harnettlab.org Back to the 2D arrays Instead of arcs, we have dimpled tiles in an array. Its still a 1-bit depth system with dimples facing up or down. A binary array of tile orientations is used to generate a shape. Its a curvature map like the macaroni sequence. Recovering a shape from a 2D bit array is not as straightforward as 1D because of constraints. You need to evolve a surface where each tile satisfies boundary conditions with its neighbor on each of 4 sides. 16. harnettlab.org 17. harnettlab.org Our 2D solver generates some self- consistent shapes from bit arrays 18. harnettlab.org More folded tile arrays 19. harnettlab.org Are the structures truly stable? Bistability is lost at a critical angle 20. harnettlab.org In a clamped beam, the critical angle is controlled by the amount of compression. 40 20 0 20 40 0.5 0 0.5 0 0.5 1 Initial angle, degrees Vertical displacement of center in units of trench width Relativestrainenergy 20 0 20 0 gle de placement f tre 0 (stable) 0 (unstable) 0 (stable) 40 (unstable) 40 (stable) -40 (unstable) -40 (stable) 21. harnettlab.org Digital origami as a shape sensor Imagine flexible materials that report their own 3-dimensional shape. Track the unfolding of inflatable structures or the changing shapes of body parts. Make a soft robot skin that recognizes the shape of objects it contacts. These systems can already be made with fiber optics or strain gauge arrays. The big advantage of bistable sensors is power savings. 22. harnettlab.org Geometrical frustration: Microfabricated Structures Released bilayers have a preferred radius of curvature, about 200 microns shown here. Serpentine layouts cannot all attain the preferred radius at the same time. Goessling, et al. J. Micromech. Microeng. 21 065030, 2011 23. harnettlab.org This serpentine structure is bistable a b c d e f 200 microns Rest state on right (0 mA) Right side energized (1.9 mA) Rest state on left (0 mA) Left side energized (1.4 mA) Return to rest on right (0 mA) Switches to right side (1.4 mA) 24. harnettlab.org Will it bend? Silicon, glass and other brittle materials can bend in thin-film form. Microelectronics on flexible substrates is a fast moving research area. Kim et al.: Researchers have transferred functional semiconductor electronics onto silicone films. www.pnas.org/cgi/doi/10.1073/pnas.0807476105 25. harnettlab.org Summary/Acknowledgments We demonstrated digital origami cells made from compressed inserts. Other fabrication methods: smocking, microfabrication, origami New folding and analysis techniques are needed for materials that let you continuously vary local curvature With 2 cell orientations (horizontal/vertical), the existing origami techniques could apply. We acknowledge NSF grant 0814194 and U of L/IUS for support. Smocked structure and origami structure by J. Mosely, photo by B. Webb 26. harnettlab.org Sensors with discrete on/off states are good for low-power systems No amplification of a small analog signal No analog-to-digital conversion needed. But theres not much bit depth (1 bit). 27. harnettlab.org One-bit sensors? xkcd.com/271 28. harnettlab.org One-bit sensors? Arrays of 1 bit switches are still interesting for shape sensing, feedback, and control. xkcd.com/271 29. harnettlab.org A discrete shape sensor application Rolatube bistable mast has a discrete shape change that matches well with threshold sensors. Put shape-sensing stickers periodically along the tube. Is it flat or curved? Use passive wireless to poll the switches. 30. harnettlab.org What about electronic readout? Microswitches on silicon are well known from RF MEMS Ohmic contact switches are a RF MEMS device Another RF MEMS device, a variable capacitor AC switch, uses less power than an ohmic contact RF MEMS capacitive switch, memtronics.com 31. harnettlab.org Look at power constraints of one reprogrammable RFID tag WISP: Wireless Identification and Sensing Platform Open source microcontroller board powered and read by commercial UHF RFID readers Started at Intel, now at University of Washington. Mainly academic users Wisp.wikispaces.com Typical power budget: 1 mW for 1 ms. commercial UHF RFID reader WISP 4.0 sensor tag Wisp.wikispaces.com 32. harnettlab.org LOTS of switches need to be read in a low-power manner. Software/hardware problem http://www.ti.com/litv/pdf/slaa139