0
Technical Brief

Kinematic Analysis of Congruent Multilayer Tessellations

[+] Author and Article Information
Yves Klett

Institute of Aircraft Design,
University of Stuttgart,
Pfaffenwaldring 31,
Stuttgart 70569, Germany
e-mail: klett@ifb.uni-stuttgart.de

Peter Middendorf

Institute of Aircraft Design,
University of Stuttgart,
Pfaffenwaldring 31,
Stuttgart 70569, Germany
e-mail: middendorf@ifb.uni-stuttgart.de

Manuscript received June 2, 2015; final manuscript received November 30, 2015; published online March 7, 2016. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(3), 034501 (Mar 07, 2016) (7 pages) Paper No: JMR-15-1125; doi: 10.1115/1.4032203 History: Received June 02, 2015; Revised November 30, 2015

Rigidly foldable origami tessellations exhibit interesting kinematic properties. Several tessellation types (most prominently Miura-ori) have shown potential for technical usage in aerospace and general lightweight construction. In addition to static (e.g., as core structures for sandwich components) and single-layer kinematic (e.g., deployable) applications, new possibilities arise from the combination of several layers of tessellations with congruent kinematics. This paper presents an analytical description of the kinematics of multilayered, or stacked, globally plane tessellations which retain rigid/isometric foldability by congruent, compatible movement.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Multilayer Miura-ori stack [12]

Grahic Jump Location
Fig. 2

Miura unit cell dimensions: Developed cell, 3D state, and stack of two congruent unit cells with different heights

Grahic Jump Location
Fig. 3

Folding sequence of three stacked Miura unit cells

Grahic Jump Location
Fig. 4

Miura stack with plane outer layers. Top: perspective view, each image scaled to maximize detail. Bottom: side views with fixed scale to show height differences.

Grahic Jump Location
Fig. 5

The configuration from Fig. 4 with inverted outer layer crease assignment/folding direction. The first state is identical to the first state from Fig. 4.

Grahic Jump Location
Fig. 6

Miura stack with plane inner layer (darker)

Grahic Jump Location
Fig. 7

Combined normalized stack height Hcn as functions of S and the ratio of outer and inner height Ho/Hi for unit cells with design parameters SD = 1, V D = 1, LD = 1, and HD = 1. All curves pass through the design point.

Grahic Jump Location
Fig. 8

Two stack setups, featuring L=S=V=10  mm and a design height of HD=40  mm. For the upper stack, the height ratio rH=1.3 results in HiD=25  mm and HoD=32.5  mm, for the lower one with rH = 3 in HiD=8  mm and HoD=24  mm.

Grahic Jump Location
Fig. 9

Overall height Hc as a function of the innermost dihedral folding angle θ (see Fig. 2) of two stacks with differing rH as detailed in Fig. 8. The stack unit cells show the corresponding folding state.

Grahic Jump Location
Fig. 10

Two asymmetric cell stacks shown in different folding states with a design height of HD = 1. The conjoined vertices are marked as spheres, and the accumulated distance between corresponding points on the lower and higher layer is shown below each subfigure. The top configuration features 6, the bottom one 128 coinciding vertices.

Grahic Jump Location
Fig. 11

Miura-type stack with differing cell sizes

Grahic Jump Location
Fig. 12

A stack with biarc-based unit cells. In fact, the geometry used here is #6 from Ref. [17].

Grahic Jump Location
Fig. 13

Conical tessellation stack

Grahic Jump Location
Fig. 14

A spiral stack that winds in on itself during folding

Grahic Jump Location
Fig. 15

Another strip-based stack that results in a 3 × 3 hexagonal grid

Grahic Jump Location
Fig. 16

Stacked Barreto-ori. Top to bottom: perspective, front, side, and top (wireframe) view. The stack is not flat-foldable: the rightmost image shows intersection between the outer and inner layers. The major crease lines stay congruent and aligned in the plane.

Grahic Jump Location
Fig. 17

The stack from Fig. 16 with inverted outer layer folding direction. The left and the right folding states both feature planar face sheets (developed versus flat-folded).

Grahic Jump Location
Fig. 18

Yet another Barreto stack, this time shown for the complete possible kinematic range. This configuration exhibits a flat-foldable state for all layers on the left, and a blocking state on the right.

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