Polyhedral Single Degree-of-freedom Expanding Structures: Design and Prototypes

[+] Author and Article Information
Sunil K. Agrawal, Saravana Kumar

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716e-mail: Agrawal@me.udel.edu

Mark Yim

Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, CA 94304e-mail: Yim@parc.xerox.com

J. Mech. Des 124(3), 473-478 (Aug 06, 2002) (6 pages) doi:10.1115/1.1480413 History: Received October 01, 2000; Online August 06, 2002
Copyright © 2002 by ASME
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The five regular polyhedra: (a) tetrahedron, (b) octahedron, (c) cube, (d) icosahedron, (e) pentagonal dodecahedron
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The edges of a regular tetrahedron are replaced by prismatic joints to form a single degree-of-freedom expandable unit
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Photographs of planar and spatial lattices fabricated at University of Delaware
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The net diagrams for the regular tetrahedron, octahedron and icosahedron can be used to show that these are single degree-of-freedom
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Single degree-of-freedom cube actuated by the edges or the inscribing tetrahedron. A pentagonal dodecahedron module actuated.
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Vertex, edge and face joining modules
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A 3-dimensional lattice formed by cubic modules. The actuation could be either through the edges or through the edges of an inscribed tetrahedron.
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An icosahedron/dodecahedron placed inside a cube so that an edge touches each face of the cube
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A prototype tetrahedral-octahedral lattice in two configurations
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A tetrahedron is a set of four nodes, each consisting of three prongs which slide with respect to adjacent nodes
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The coordinate axes to identify a node on a tetrahedral lattice
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A lattice with 40 cubic elements that approximates a car-like exterior shape
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A lattice that approximates a chair. The diagonal members on the side face ensure propagation of equal expansion along the three mutually orthogonal directions of the cubes forming the lattice.
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An alternative lattice that approximates a chair. An expanding tetrahedron is inscribed within every cube forming the skeleton of the chair.



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