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Research Papers

Kinematic Representations of Pop-Up Paper Mechanisms

[+] Author and Article Information
Brian G. Winder

Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602b.winder@byu.edu

Spencer P. Magleby1

Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602magleby@byu.edu

Larry L. Howell

Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602lhowell@byu.edu

1

Corresponding author.

J. Mechanisms Robotics 1(2), 021009 (Jan 12, 2009) (10 pages) doi:10.1115/1.3046128 History: Received June 27, 2008; Revised October 29, 2008; Published January 12, 2009

Pop-up paper mechanisms use techniques similar to the well-studied paper folding techniques of origami. However, pop-ups differ in both the manner of construction and the target uses, warranting further study. This paper outlines the use of planar and spherical kinematics to model commonly used pop-up paper mechanisms. A survey of common joint types is given, including folds, interlocking slots, bends, pivots, sliders, and rotating sliders. Also included is an overview of common one-piece and layered mechanisms, including single-slit, double-slit, V-fold, tent, tube strap, and arch mechanisms. Each mechanism or joint is shown using both a paper representation and either a rigid-body or pseudo-rigid-body representation. In addition, this paper shows that more complex mechanisms may be created by combining simple mechanisms in various ways. The principles presented are applied to the creation of new pop-up joints and mechanisms. The new mechanisms employ both spherical and spatial kinematic chains. Understanding pop-up mechanism kinematics could lead to new applications in deployable structures, packaging, and instruments for minimally invasive surgery.

Copyright © 2009 by American Society of Mechanical Engineers
Topics: Mechanisms
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References

Figures

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Figure 1

A pop-up mechanism from Sabuda (5), shown in three stages of opening

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Figure 2

The relationship between pop-up books, collapsible products, and movable products (adapted from Ref. 17)

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Figure 3

Planar topology (above) versus spherical topology. The left images show slider-cranks and the right images show four-bar mechanisms.

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Figure 4

Spatial topology. The left image shows a RSSR and the right image shows a RCCC. The spheres shown represent spherical joints.

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Figure 5

A simple paper pop-up mechanism

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Figure 6

The required cuts and folds for making a simple paper pop-up mechanism

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Figure 7

Linkage topology conventions used in this paper. Paper folds are modeled as pin joints with some amount of stiffness.

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Figure 8

A fold (crease) and its PRBM representation

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Figure 9

An interlocking slot and its kinematic representation

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Figure 10

A bend and its PRBM representation

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Figure 11

A pivot and its kinematic representation

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Figure 12

A slider and its kinematic representation

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Figure 13

A rotating slider and its kinematic representation

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Figure 14

A double-slit device and its PRBM representation

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Figure 15

A tent and its PRBM representation

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Figure 16

A tube strap and its PRBM representation

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Figure 17

An arch and its PRBM representation

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Figure 18

A single-slit device and its PRBM representation

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Figure 19

A V-fold and its PRBM representation. The PRBM shows the traditional representation of a spherical mechanism to emphasize the spherical motion characteristics of the V-fold.

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Figure 20

A floating layer and its PRBM representation

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Figure 21

A solid shape and its PRBM representation

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Figure 22

A 45 deg fold and its PRBM representation

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Figure 23

A mechanism with a complex link shape and its PRBM representation

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Figure 24

A paper cylindric joint and its kinematic representation

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Figure 25

A paper spherical joint and its PRBM representation.

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Figure 26

Photographs of a paper spherical joint in two positions

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Figure 27

A simplified representation of the spherical joint PRBM

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Figure 28

A circular arch and its PRBM representation

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Figure 29

A photograph of a circular arch

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Figure 30

A photograph of a circular arch in the flat-folded position

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Figure 31

A figure-8 (paper RSSR mechanism) and its PRBM representation

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Figure 32

A figure-8 folded flat (left), and a photograph of a figure-8 in the raised position. The flat-folded figure-8 has the left base page removed to show the link shapes

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