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.
Issue Section:
Research Papers
References
1.
Demaine
, E.
, and O'Rourke
, J.
, 2007
, Geometric Folding Algorithms
, Cambridge University Press
, New York.2.
Tachi
, T.
, 2009
, “Generalization of Rigid-Foldable Quadrilateral-Mesh Origami
,” J. Int. Assoc. Shell Spat. Struct.
, 50
(162
), pp. 173
–179
.3.
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
.4.
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
.5.
Mavroidis
, C.
, and Roth
, B.
, 1995
, “Analysis of Overconstrained Mechanisms
,” ASME J. Mech. Des.
, 117
(1
), pp. 69
–74
.6.
Wu
, W.
, and You
, Z.
, 2010
, “Modelling Rigid Origami With Quaternions and Dual Quaternions
,” Proc. R. Soc. A
, 466
(2119
), pp. 2155
–2174
.7.
Diaz
, A. R.
, and Fuchi
, K.
, 2013
, “Origami Design by Topology Optimization
,” ASME J. Mech. Des.
, 135
(11
), p. 111003
.8.
Wu
, W.
, and You
, Z.
, 2011
, “A Solution for Folding Rigid Tall Shopping Bags
,” Proc. R. Soc. A
, 467
(2133
), pp. 2561
–2574
.9.
Tachi
, T.
, and Miura
, K.
, 2012
, “Rigid-Foldable Cylinders and Cells
,” J. Int. Assoc. Shell Spat. Struct.
, 53
(4
), pp. 217
–226
.10.
Tachi
, T.
, 2009
, “Simulation of Rigid Origami
,” Origami 4
, R. J.
Lang
, ed., A.K. Peters/CRC Press
, Natick, MA
, pp. 175
–187
.11.
Angeles
, J.
, 1988
, Rational Kinematics
, Springer
, New York.12.
Wampler
, C.
, Larson
, B.
, and Erdman
, A.
, 2008
, “A New Mobility Formula for Spatial Mechanisms
,” ASME
Paper No. DETC2007-35574.13.
Shai
, O.
, 2011
, “The Correction to Grubler Criterion for Calculating the Degrees of Freedoms of Mechanisms
,” ASME
Paper No. DETC2011-48146.14.
Davies
, T. H.
, 1981
, “Kirchhoff's Circulation Law Applied to Multi-Loop Kinematic Chains
,” Mech. Mach. Theory
, 16
(3
), pp. 171
–183
.15.
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
.16.
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
.17.
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
.18.
Wei
, G.
, and Dai
, J. S.
, 2014
, “Origami-Inspired Integrated Planar-Spherical Overconstrained Mechanisms
,” ASME J. Mech. Des.
, 136
(5
), p. 051003
.19.
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
.20.
Howell
, L. L.
, 2001
, Compliant Mechanisms
, Wiley
, New York
.21.
Goodman
, J. E.
, and O'Rourke
, J.
, 1997
, Handbook of Discrete and Computational Geometry
, 2nd ed., Chapman & Hall/CRC
, New York
.22.
McCarthy
, J. M.
, 2000
, Geometric Design of Linkages
, Springer
, New York
.23.
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
.24.
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
.25.
Koetsier
, T.
, and Ceccarelli
, M.
, eds., 2012
, Spatial Overconstrained Linkages—The Lost Jade
, Springer
, Dordrecht
.26.
Dai
, J. S.
, Huang
, Z.
, and Lipkin
, H.
, 2006
, “Mobility of Overconstrained Parallel Mechanisms
,” ASME J. Mech. Des.
, 128
(1
), pp. 220
–229
.27.
Mitani
, J.
, 2011
, “A Method for Designing Crease Patterns for Flat-Foldable Origami With Numerical Optimization
,” J. Geom. Graphics
, 15
(2
), pp. 195
–201
.Copyright © 2016 by ASME
You do not currently have access to this content.
