0
Research Papers

Creating Rigid Foldability to Enable Mobility of Origami-Inspired Mechanisms

[+] Author and Article Information
Alden Yellowhorse

Compliant Mechanisms Laboratory,
Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: aldenyellowhorse@gmail.com

Larry L. Howell

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

Manuscript received November 11, 2014; final manuscript received February 19, 2015; published online August 18, 2015. Assoc. Editor: Robert J. Wood.

J. Mechanisms Robotics 8(1), 011011 (Aug 18, 2015) (8 pages) Paper No: JMR-14-1317; doi: 10.1115/1.4029923 History: Received November 11, 2014

Rigidly foldable origami crease patterns can be translated into corresponding rigid mechanisms with at least one degree of freedom. However, origami crease patterns of interest for engineering applications are not always rigidly foldable, and designers trying to adapt a crease pattern may be confronted with the need to add more mobility to their design. This paper presents design guidelines for making alterations to a crease pattern to make it rigidly foldable. Adding creases, removing panels, and splitting creases are presented as potential alterations for increasing mobility, and approaches for determining the position and number of alterations are discussed. This paper also investigates means for reducing the number of changes necessary to achieve this condition. The approach is developed in general and illustrated through a demonstrative example.

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

References

Demaine, E. , and O'Rourke, J. , 2007, Geometric Folding Algorithms, Cambridge University Press, New York.
Tachi, T. , 2009, “Generalization of Rigid-Foldable Quadrilateral-Mesh Origami,” J. Int. Assoc. Shell Spat. Struct., 50(162), pp. 173–179.
Zhang, K. , and Dai, J. S. , 2014, “A Kirigami-Inspired 8R Linkage and Its Evolved Overconstrained 6R Linkages With the Rotational Symmetry of Order Two,” ASME J. Mech. Rob., 6(2), p. 021007. [CrossRef]
Abdul-Sater, K. , Irlinger, F. , and Lueth, T. C. , 2013, “Two-Configuration Synthesis of Origami-Guided Planar, Spherical and Spatial Revolute—Revolute Chains,” ASME J. Mech. Rob., 5(3), p. 031005. [CrossRef]
Mavroidis, C. , and Roth, B. , 1995, “Analysis of Overconstrained Mechanisms,” ASME J. Mech. Des., 117(1), pp. 69–74. [CrossRef]
Wu, W. , and You, Z. , 2010, “Modelling Rigid Origami With Quaternions and Dual Quaternions,” Proc. R. Soc. A, 466(2119), pp. 2155–2174. [CrossRef]
Diaz, A. R. , and Fuchi, K. , 2013, “Origami Design by Topology Optimization,” ASME J. Mech. Des., 135(11), p. 111003. [CrossRef]
Wu, W. , and You, Z. , 2011, “A Solution for Folding Rigid Tall Shopping Bags,” Proc. R. Soc. A, 467(2133), pp. 2561–2574. [CrossRef]
Tachi, T. , and Miura, K. , 2012, “Rigid-Foldable Cylinders and Cells,” J. Int. Assoc. Shell Spat. Struct., 53(4), pp. 217–226.
Tachi, T. , 2009, “Simulation of Rigid Origami,” Origami 4, R. J. Lang , ed., A.K. Peters/CRC Press, Natick, MA, pp. 175–187.
Angeles, J. , 1988, Rational Kinematics, Springer, New York.
Wampler, C. , Larson, B. , and Erdman, A. , 2008, “A New Mobility Formula for Spatial Mechanisms,” ASME Paper No. DETC2007-35574.
Shai, O. , 2011, “The Correction to Grubler Criterion for Calculating the Degrees of Freedoms of Mechanisms,” ASME Paper No. DETC2011-48146.
Davies, T. H. , 1981, “Kirchhoff's Circulation Law Applied to Multi-Loop Kinematic Chains,” Mech. Mach. Theory, 16(3), pp. 171–183. [CrossRef]
Wohlhart, K. , 2004, “Screw Spaces and Connectivities in Multiloop Linkages,” On Advances in Robot Kinematics, J. Lenarcic , and C. Galletti , eds., Springer, Netherlands, pp. 97–104.
Xia, S. , Ding, H. , and Kecskemethy, A. , 2012, “A Loop-Based Approach for Rigid Subchain Identification in General Mechanisms,” Latest Advances in Robot Kinematics, J. Lenarcic , and M. Husty , eds., Springer, Dordrecht, pp. 19–26.
Dai, J. S. , and Jones, J. R. , 2002, “Kinematics and Mobility Analysis of Carton Folds in Packing Manipulation Based on the Mechanism Equivalent,” Proc. Inst. Mech. Eng., Part C, 216(10), pp. 959–970. [CrossRef]
Wei, G. , and Dai, J. S. , 2014, “Origami-Inspired Integrated Planar-Spherical Overconstrained Mechanisms,” ASME J. Mech. Des., 136(5), p. 051003. [CrossRef]
Winder, B. G. , Magleby, S. P. , and Howell, L. L. , 2009, “Kinematic Representations of Pop-Up Paper Mechanisms,” ASME J. Mech. Rob., 1(2), p. 021009. [CrossRef]
Howell, L. L. , 2001, Compliant Mechanisms, Wiley, New York.
Goodman, J. E. , and O'Rourke, J. , 1997, Handbook of Discrete and Computational Geometry, 2nd ed., Chapman & Hall/CRC, New York.
McCarthy, J. M. , 2000, Geometric Design of Linkages, Springer, New York.
Greenberg, H. C. , Gong, M. L. , Magleby, S. P. , and Howell, L. L. , 2011, “Identifying Links Between Origami and Compliant Mechanisms,” J. Mech. Sci., 2(2), pp. 217–225. [CrossRef]
Wang, Y. , Zhang, J. , and Wang, Y. , 2011, “Optimizational Study on Computing Method of Channel Earthwork Based on matlab ,” Intelligent Computing and Information Science (Communications in Computer and Information Science (Book 134), Vol. 1), R. Chen , ed., Springer, Berlin, pp. 69–76.
Koetsier, T. , and Ceccarelli, M. , eds., 2012, Spatial Overconstrained Linkages—The Lost Jade, Springer, Dordrecht.
Dai, J. S. , Huang, Z. , and Lipkin, H. , 2006, “Mobility of Overconstrained Parallel Mechanisms,” ASME J. Mech. Des., 128(1), pp. 220–229. [CrossRef]
Mitani, J. , 2011, “A Method for Designing Crease Patterns for Flat-Foldable Origami With Numerical Optimization,” J. Geom. Graphics, 15(2), pp. 195–201.

Figures

Grahic Jump Location
Fig. 1

(a) An arbitrary crease pattern is shown with modified patterns (b) and (c). (b) With one panel split by an added crease. (c) With an edge panel split by an added crease.

Grahic Jump Location
Fig. 2

(a) and (c) An arbitrary degree-4 vertex is shown modeled with rods and ball joints and (b) and (d) its equivalent configuration when one panel has been removed

Grahic Jump Location
Fig. 3

(a) and (c) An arbitrary vertex is shown and (b) and (d) its equivalent configuration when one crease has been split. (b) General vertex with one crease split.

Grahic Jump Location
Fig. 4

(a) An arbitrary crease pattern and (b) its configuration when one crease has been split

Grahic Jump Location
Fig. 5

A situation where a crease not touching the edge is split and mobility does not increase

Grahic Jump Location
Fig. 6

(a) An arbitrary crease pattern and (b) its equivalent configuration when multiple creases have been split

Grahic Jump Location
Fig. 7

This map-fold crease pattern is calculated to have a negative degree of freedom, but symmetry allows mobility by folds along the vertical and horizontal creases

Grahic Jump Location
Fig. 8

(a) A pattern with zero degrees of freedom where (b) part of the pattern can fold rigidly

Grahic Jump Location
Fig. 9

An arbitrary polygon whose directed area is being calculated by summing the directed areas of its side triangles, where (a) each side forms a triangle with the origin and (b) the polygon's sides are shown as ωi and their directed areas

Grahic Jump Location
Fig. 10

A square twist crease pattern that has a mobility of zero but actuates with one degree of freedom

Grahic Jump Location
Fig. 11

An arbitrary crease pattern where creases have been added to one panel and to adjacent panels. (a) Creases added to a single panel and (b) creases added to adjacent panels.

Grahic Jump Location
Fig. 12

A sink fold crease pattern that is inflexible

Grahic Jump Location
Fig. 13

An over-constrained region in the crease pattern

Grahic Jump Location
Fig. 14

Creases added to the circled vertices to permit rigid folding motion

Grahic Jump Location
Fig. 15

The sequence of folded states of the modified sink fold crease pattern. (a) Flat state, (b) partially folded state, and (c) fully folded state.

Grahic Jump Location
Fig. 16

Creases split to permit rigid folding motion

Grahic Jump Location
Fig. 17

Sequence of folded states of the sink fold crease pattern with split creases. (a) Flat state, (b) partially folded state, and (c) fully folded state.

Grahic Jump Location
Fig. 18

Panels removed to permit rigid folding motion

Grahic Jump Location
Fig. 19

Sequence of folded states of the sink fold crease pattern with missing panels. (a) Flat state, (b) partially folded state, and (c) fully folded state.

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