0
Design Innovation Paper

Reconfigurable Modular Chain: A Reversible Material for Folding Three-Dimensional Lattice Structures

[+] Author and Article Information
Zhe Xu

Mem. ASME
Department of Mechanical Engineering,
Yale University,
New Haven, CT 06511
e-mail: zhe.xu@yale.edu

Connor McCann

Department of Mechanical Engineering,
Yale University,
New Haven, CT 06511
e-mail: connor.mccann@yale.edu

Aaron M. Dollar

Mem. ASME
Department of Mechanical Engineering,
Yale University,
New Haven, CT 06511
e-mail: aaron.dollar@yale.edu

Manuscript received October 7, 2016; final manuscript received January 13, 2017; published online March 9, 2017. Assoc. Editor: Hai-Jun Su.

J. Mechanisms Robotics 9(2), 025002 (Mar 09, 2017) (11 pages) Paper No: JMR-16-1298; doi: 10.1115/1.4035863 History: Received October 07, 2016; Revised January 13, 2017

A wide range of engineering applications, ranging from civil to space structures, could benefit from the ability to construct material-efficient lattices that are easily reconfigurable. The challenge preventing modular robots from being applied at large scales is mainly the high level of complexity involved in duplicating a large number of highly integrated module units. We believe that reconfigurability can be more effectively achieved at larger scales by separating the structural design from the rest of the functional components. To this end, we propose a modular chainlike structure of links and connector nodes that can be used to fold a wide range of two-dimensional (2D) or three-dimensional (3D) structural lattices that can be easily disassembled and reconfigured when desired. The node geometry consists of a diamondlike shape that is one-twelfth of a rhombic dodecahedron, with magnets embedded on the faces to allow a forceful and self-aligning connection with neighboring links. After describing the concept and design, we demonstrate a prototype consisting of 350 links and experimentally show that objects with different shapes can be successfully approximated by our proposed chain design.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Neubert, J. , Rost, A. , and Lipson, H. , 2014, “ Self-Soldering Connectors for Modular Robots,” IEEE Trans. Rob., 30(6), pp. 1344–1357. [CrossRef]
Rubenstein, M. , Cornejo, A. , and Nagpal, R. , 2014, “ Programmable Self-Assembly in a Thousand-Robot Swarm,” Science, 345(6198), pp. 795–799. [CrossRef] [PubMed]
Becker, A. , Habibi, G. , Werfel, J. , Rubenstein, M. , and McLurkin, J. , 2013, “ Massive Uniform Manipulation: Controlling Large Populations of Simple Robots With a Common Input Signal,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Nov. 3–8, Tokyo, pp. 520–527.
Balkcom, D. J. , and Mason, M. T. , 2008, “ Robotic Origami Folding,” Int. J. Rob. Res., 27(5), pp. 613–627. [CrossRef]
Schenk, M. , and Guest, S. D. , 2011, “ Origami Folding: A Structural Engineering Approach,” Fifth International Meeting of Origami Science, Mathematics, and Education (Origami 5), Singapore, July 14–15, pp. 293–305.
Mueller, S. , Im, S. , Gurevich, S. , Teibrich, A. , Pfisterer, L. , Guimbretière, F. , and Baudisch, P. , 2014, “ WirePrint: 3D Printed Previews for Fast Prototyping,” 27th Annual ACM Symposium on User Interface Software and Technology (UIST), Honolulu, HI, Oct. 5–8.
Goldstein, S. C. , Campbell, J. D. , and Mowry, T. C. , 2005, “ Invisible Computing: Programmable Matter,” Computer, 38(6), pp. 99–101. [CrossRef]
Kodama, S. , 2008, “ Dynamic Ferrofluid Sculpture: Organic Shape-Changing Art Forms,” Commun. ACM, 51(6), pp. 79–81. [CrossRef]
Wakita, A. , Nakano, A. , and Kobayashi, N. , 2011, “ Programmable Blobs: A Rheologic Interface for Organic Shape Design,” Fifth International Conference on Tangible, Embedded, and Embodied Interaction (TEI), Funchal, Portugal, Jan. 22–26, pp. 273–276.
Cheung, K. C. , and Gershenfeld, N. , 2013, “ Reversibly Assembled Cellular Composite Materials,” Science, 341(6151), pp. 1219–1221. [CrossRef] [PubMed]
Groß, R. , and Dorigo, M. , 2008, “ Self-Assembly at the Macroscopic Scale,” Proc. IEEE, 96(9), pp. 1490–1508. [CrossRef]
Fuller, R. B. , 1961, “ Octet Truss,” U.S. Patent No. 2,986,241.
Conway, J. H. , Jiao, Y. , and Torquato, S. , 2011, “ New Family of Tilings of Three-Dimensional Euclidean Space by Tetrahedra and Octahedra,” Proc. Natl. Acad. Sci., 108(27), pp. 11009–11012. [CrossRef]
Li, Z. , Balkcom, D. J. , and Dollar, A. M. , 2013, “ Rigid 2D Space-Filling Folds of Unbroken Linear Chains,” IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, May 6–10, pp. 551–557.
Deshpande, V. S. , Ashby, M. F. , and Fleck, N. A. , 2001, “ Foam Topology: Bending Versus Stretching Dominated Architectures,” Acta Mater., 49(6), pp. 1035–1040. [CrossRef]
Griffith, S. T. , 2004, “ Growing Machines,” Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA.
Pevzner, P. A. , Tang, H. , and Waterman, M. S. , 2001, “ An Eulerian Path Approach to DNA Fragment Assembly,” Proc. Natl. Acad. Sci. U.S.A., 98(17), pp. 9748–9753. [CrossRef] [PubMed]
Hawkes, E. , An, B. , Benbernou, N. M. , Tanaka, H. , Kim, S. , Demaine, E. D. , Rus, D. , and Wood, R. J. , 2010, “ Programmable Matter by Folding,” Proc. Natl. Acad. Sci., 107(28), pp. 12441–12445. [CrossRef]
Overvelde, J. T. B. , de Jong, T. A. , Shevchenko, Y. , Becerra, S. A. , Whitesides, G. M. , Weaver, J. C. , Hoberman, C. , and Bertoldi, K. , 2016, “ A Three-Dimensional Actuated Origami-Inspired Transformable Metamaterial With Multiple Degrees of Freedom,” Nat. Commun., 7.
Nigl, F. , Li, S. , Blum, J. E. , and Lipson, H. , 2013, “ Structure-Reconfiguring Robots: Autonomous Truss Reconfiguration and Manipulation,” IEEE Rob. Autom. Mag., 20(3), pp. 60–71. [CrossRef]
Gershenfeld, N. , Carney, M. , Jenett, B. , Calisch, S. , and Wilson, S. , 2015, “ Macrofabrication With Digital Materials: Robotic Assembly,” Archit. Des., 85(5), pp. 122–127.
Cheung, K. C. , Demaine, E. D. , Bachrach, J. R. , and Griffith, S. , 2011, “ Programmable Assembly With Universally Foldable Strings (Moteins),” IEEE Trans. Rob., 27(4), pp. 718–729. [CrossRef]
Sproewitz, A. , Asadpour, M. , Bourquin, Y. , and Ijspeert, A. J. , 2008, “ An Active Connection Mechanism for Modular Self-Reconfigurable Robotic Systems Based on Physical Latching,” IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, May 19–23, pp. 3508–3513.
Eckenstein, N. , and Yim, M. , 2014, “ Design, Principles, and Testing of a Latching Modular Robot Connector,” IEEE International Conference on Intelligent Robots and Systems (IROS), Chicago, IL, Sept 14–18, pp. 2846–2851.
Swensen, J. P. , Nawroj, A. I. , Pounds, P. E. I. , and Dollar, A. M. , 2014, “ Simple, Scalable Active Cells for Articulated Robot Structures,” IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, China, May 31–June 7, pp. 1241–1246.
Deshpande, V. S. , Fleck, N. A. , and Ashby, M. F. , 2001, “ Effective Properties of the Octet-Truss Lattice Material,” J. Mech. Phys. Solids, 49(8), pp. 1747–1769. [CrossRef]
Dong, L. , Deshpande, V. , and Wadley, H. , 2015, “ Mechanical Response of Ti–6Al–4V Octet-Truss Lattice Structures,” Int. J. Solids Struct., 60, pp. 107–124. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Pictures of our proof-of-concept design: (a) 293 links are used in the folding of the pyramid shape and (b) a spool of the modular chain

Grahic Jump Location
Fig. 2

Top views of the tiling patterns in 2D and 3D situations: (a) using regular triangle-lattices to construct 2D shapes and (b) using cube-lattices to construct 3D shapes

Grahic Jump Location
Fig. 3

Tessellation of 3D space with regular octahedra and tetrahedra

Grahic Jump Location
Fig. 4

Schematic drawing showing the lattice structure (left) and its unit cell after the solid-to-lattice conversion of a cube (right). Note: the arrows illustrate the loading orientations of the compressive and shear forces that act on the shaded top and bottom planes.

Grahic Jump Location
Fig. 5

Schematic drawing showing the different components at the busiest connection joint inside a large three-dimensional lattice structure (an antenna frame)

Grahic Jump Location
Fig. 6

The formation of the basic node geometry. Top row: a smaller rhombic dodecahedron is first fit into the center of the busiest connection joint. Bottom row: after a series of cutting processes, the rhombic pyramid shape is selected to form basic geometry of node design.

Grahic Jump Location
Fig. 7

The important dimensions of our node design: (a) the rhombic pyramid with four symmetrically identical faces and (b) schematic drawing of the node design showing the critical assembly angles

Grahic Jump Location
Fig. 8

Two different types of magnetic coupling used in our prototype: (a) type-I—embedding paired magnets directly at the contacting sites and (b) type-II—transmitting magnetic forces through the node made of ferrous materials. Note: the central hole is for anchoring connecting strings.

Grahic Jump Location
Fig. 9

Possible connection joints supported by type-I coupling method. Note: except for the start and the end, all the other connection joints have even number of nodes inside any folded lattice structure. Rods were removed for better visibility of the nodes.

Grahic Jump Location
Fig. 10

Two-dimensional simulation of the magnetic fields by using type-II coupling method: (a) alternating the poles at the two ends of each rod and (b) 2D simulation of the magnetic fields at different connection joints in a 3D reconfigurable lattice structure

Grahic Jump Location
Fig. 11

The prototyping process of nodes via 3D printing: (a) a tray of 110 3D-printed nodes, (b) example of a separate link, and (c)–(j) variations of 2D and 3D structures folded by a 14-link chain

Grahic Jump Location
Fig. 12

Prototyping process of nodes by using cold-casting method: (a) 3D-printed positives and the silicone rubber mold, (b) and (c) cold-casted parts made from the mixture of fine iron powder and resins, and (d) comparison of magnetic forces with nodes made of different materials. Note: each steel ball weights 8.4 g. The rod is the off-the-shelf Geomag part.

Grahic Jump Location
Fig. 13

Example of the folding process: (a) the separate folding paths for constructing different layers of a pyramid and (b) snapshots showing the demonstration of planned folding process

Grahic Jump Location
Fig. 14

Variations of folded shapes both in 2D and 3D (329-link)

Grahic Jump Location
Fig. 15

Potential applications of our proposed chain design in space exploration. Note: the frames of the antenna and solar panel are all folded by the same chain with 1554 links.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In