Research Papers

Facilitating Deployable Mechanisms and Structures Via Developable Lamina Emergent Arrays

[+] Author and Article Information
Todd G. Nelson

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: toddgn@byu.edu

Robert J. Lang

Lang Origami,
Alamo, CA 94507

Nathan A. Pehrson, Spencer P. Magleby, Larry L. Howell

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602

1Corresponding author.

Manuscript received June 30, 2015; final manuscript received October 14, 2015; published online March 7, 2016. Assoc. Editor: Mary Frecker.

J. Mechanisms Robotics 8(3), 031006 (Mar 07, 2016) (10 pages) Paper No: JMR-15-1169; doi: 10.1115/1.4031901 History: Received June 30, 2015; Revised October 14, 2015

A method is presented utilizing networks of lamina emergent joints, known as lamina emergent arrays, to accommodate large-curvature developable structures suited to deployable applications. By exploiting the ruling lines in developable surfaces, this method enables developable structures and mechanisms that can be manufactured with two-dimensional geometry and yet have a greater range of elastic motion than is possible with a solid sheet of material. Aligning the joints to the ruling lines also biases the structure to a specific deployment path. A mathematical model is developed to describe the resulting stiffness of the structure employing the lamina emergent arrays and equations are derived to facilitate stress analysis of the structure. Finite element results show the sensitivity of alignment of the elements in the array to the stress present in the developed structure. A specific technique for creating an array pattern for conical developable surfaces is described. Examples of developable structures and mechanisms, including curved-fold origami models transitioned to thick materials and two origami-inspired mechanisms, are examined.

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Fig. 1

The three classes of developable surfaces: cylinder (left), cone (middle), and tangent developed (right)

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Fig. 2

Example of a general developable surface in an unfolded and folded configuration with ruling lines shown

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Fig. 3

A sample of joints suitable for constructing developable surfaces

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Fig. 4

Geometric parameters for the outside LET and mixed tension resistant joints

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Fig. 5

Discretized surface model using hinges and panels

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Fig. 6

Illustration of the method of aligning the axes of the joints to the ruling lines in a Mobius strip: (a) before alignment and (b) after alignment

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Fig. 7

Computer-aided design (CAD) model used in FEA to determine the sensitivity of hinge axis alignment to parallel ruling lines

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Fig. 8

Von Mises stress sensitivity to hinge axis alignment for parallel ruling lines

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Fig. 9

Von Mises stress contours of the (a) 0 degree offset model, (b) 10 degree offset model, and (c) 20 degree offset model

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Fig. 10

Definition of the total angular displacement of a partially formed cone

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Fig. 11

Parameters of the planar undeveloped cone

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Fig. 15

Examples of lamina emergent arrays to create developable surfaces in materials other than paper: (a) cylinder, (b) cone, and (c) cone in the flat state with labeled parameters

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Fig. 16

Crashing volcanoes transitioned from paper (origami model is shown in the inset) to acrylic with a fabric backing in its (a) flat state and (b) deployed state

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Fig. 17

Elliptic infinity transitioned from paper (origami model is shown in the inset) to particle board in its (a) flat state and (b) deployed state

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Fig. 18

3D printed curved-fold oriceps in its (a) flat printed state (origami model which provided inspiration is shown in the inset) and (b) folded, functional state

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Fig. 19

3D printed D-CORES in (a) flat printed state and (b) folded state connecting two panels with nearly 360 degrees of rotation



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