Kaleidocycles are continuously rotating n-jointed linkages. We consider a certain class of six-jointed kaleidocycles which have a spring at each joint. For this class of kaleidocycles, stored energy varies throughout the rotation process in a nonconstant, cyclic pattern. The purpose of this paper is to model and provide an analysis of the stored energy of a kaleidocycle throughout its motion. In particular, we will solve analytically for the number of stable equilibrium states for any kaleidocycle in this class.

References

1.
Evans
,
T. A.
,
Rowberry
,
B. G.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2015
, “
Multistable Behavior of Compliant Kaleidocycles
,”
ASME
Paper No. DETC2015-46637.
2.
Schattschneider
,
D.
,
1977
,
M. C. Escher Kaleidocycles
,
Ballantine Books
,
New York
.
3.
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. C
,
216
(
10
), pp.
959
970
.
4.
Howell
,
L. L.
, and
Midha
,
A.
,
1994
, “
A Method for the Design of Compliant Mechanisms With Small-Length Flexural Pivots
,”
ASME J. Mech. Des.
,
116
(
1
), pp.
280
290
.
5.
Baker
,
J. E.
,
1980
, “
An Analysis of the Bricard Linkages
,”
Mech. Mach. Theory
,
15
(
4
), pp.
267
286
.
6.
Bricard
,
R.
,
1897
, “
Memoire sur la thorie de l'octadre articul
,”
J. Math. Pures Appl.
,
3
, pp.
113
150
.
7.
You
,
Z.
, and
Chen
,
Y.
,
2001
,
Motion Structures
,
Taylor and Francis
,
London
.
8.
Chen
,
Y.
,
You
,
Z.
, and
Tarnai
,
T.
,
2005
, “
Threefold-Symmetric Bricard Linkages for Deployable Structures
,”
Int. J. Solids Struct.
,
42
(
8
), pp.
2287
2301
.
9.
Song
,
C. Y.
,
Chen
,
Y.
, and
Chen
,
I. M.
,
2014
, “
Kinematic Study of the Original and Revised General Line-Symmetric Bricard 6R Linkages
,”
ASME J. Mech. Rob.
,
6
(
3
), p.
031002
.
10.
Wei
,
G.
, and
Dai
,
J. S.
,
2014
, “
Origami-Inspired Integrated Planar-Spherical Overconstrained Mechanisms
,”
ASME J. Mech. Des.
,
136
(
5
), p.
051003
.
11.
Chen
,
Y.
,
Peng
,
R.
, and
You
,
Z.
,
2015
, “
Origami of Thick Panels
,”
Science
,
349
(
6246
), pp.
396
400
.
12.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley
,
New York
.
13.
Howell
,
L. L.
,
Magleby
,
S. P.
, and
Olsen
,
B. O.
, eds.,
2013
,
Handbook of Compliant Mechanisms
,
Wiley
,
New York
.
14.
Vogtmann
,
D. E.
,
Gupta
,
S. K.
, and
Bergbreiter
,
S.
,
2013
, “
Characterization and Modeling of Elastomeric Joints in Miniature Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
5
(
4
), p.
041017
.
15.
Venkiteswaran
,
V. K.
, and
Su
,
H. J.
,
2015
, “
A Parameter Optimization Framework for Determining the Pseudo-Rigid-Body Model of Cantilever-Beams
,”
Precis. Eng.
,
40
, pp.
46
54
.
16.
Dado
,
M. H.
,
2001
, “
Variable Parametric Pseudo-Rigid-Body Model for Large-Deflection Beams With End Loads
,”
Int. J. Nonlinear Mech.
,
36
(
7
), pp.
1123
1133
.
17.
Yu
,
Y. Q.
,
Feng
,
Z. L.
, and
Xu
,
Q. P.
,
2012
, “
A Pseudo-Rigid-Body 2R Model of Flexural Beam in Compliant Mechanisms
,”
Mech. Mach. Theory
,
55
, pp.
18
33
.
18.
Dai
,
J. S.
, and
Cannella
,
F.
,
2008
, “
Stiffness Characteristics of Carton Folds for Packaging
,”
ASME J. Mech. Des.
,
130
(
2
), p.
022305
.
19.
Wang
,
D. A.
,
Chen
,
J. H.
, and
Pham
,
H. T.
,
2014
, “
A Tristable Compliant Micromechanism With Two Serially Connected Bistable Mechanisms
,”
Mech. Mach. Theory
,
71
, pp.
27
39
.
20.
Chen
,
G.
,
Gou
,
Y.
, and
Zhang
,
A.
,
2011
, “
Synthesis of Compliant Multistable Mechanisms Through Use of a Single Bistable Mechanism
,”
ASME J. Mech. Des.
,
133
(
8
), p.
081007
.
21.
Williams
,
M. D.
,
van Keulen
,
F.
, and
Sheplak
,
M.
,
2012
, “
Modeling of Initially Curved Beam Structures for Design of Multistable MEMS
,”
ASME J. Appl. Mech.
,
79
(
1
), p.
011006
.
22.
Dellaert
,
D.
, and
Doutreloigne
,
J.
,
2014
, “
Design and Characterization of a Thermally Actuated Latching MEMS Switch for Telecommunication Applications
,”
J. Micromech. Microeng.
,
24
(
7
), p.
075022
.
23.
Beharic
,
J.
,
Lucas
,
T. M.
, and
Harnett
,
C. K.
,
2014
, “
Analysis of a Compressed Bistable Buckled Beam on a Flexible Support
,”
ASME J. Appl. Mech.
,
81
(
8
), p.
081011
.
24.
Gomm
,
T.
,
Howell
,
L. L.
, and
Selfridge
,
R. H.
,
2002
, “
In-Plane Linear-Displacement Bistable Microrelay
,”
J. Micromech. Microeng.
,
12
(
3
), pp.
257
264
.
25.
Pucheta
,
M. A.
, and
Cardona
,
A.
,
2010
, “
Design of Bistable Compliant Mechanisms Using Precision-Position and Rigid-Body Replacement Methods
,”
Mech. Mach. Theory
,
45
(
2
), pp.
304
326
.
26.
Tanner
,
J. D.
, and
Jensen
,
B. D.
,
2013
, “
Power-Free Bistable Threshold Accelerometer Made From a Carbon Nanotube Framework
,”
J. Mech. Sci.
,
4
(
2
), pp.
397
405
.
27.
Silverberg
,
J.
,
Na
,
J.
,
Evans
,
A.
,
Liu
,
B.
,
Hull
,
T.
,
Santangelo
,
C.
,
Lang
,
R.
,
Hayward
,
R.
, and
Cohen
,
I.
,
2015
, “
Origami Structures With a Critical Transition to Bistability Arising From Hidden Degrees of Freedom
,”
Nat. Mater.
,
14
(
4
), pp.
389
393
.
28.
Hanna
,
B. H.
,
Magleby
,
S. P.
,
Lang
,
R. J.
, and
Howell
,
L. L.
,
2015
, “
Force-Deflection Modeling for Generalized Origami Waterbomb-Base Mechanisms
,”
ASME J. Appl. Mech.
,
82
(
8
), p.
081001
.
29.
Waitukaitis
,
S.
,
Menaut
,
R.
,
Chen
,
B. G.
, and
van Hecke
,
M.
,
2015
, “
Origami Multistability: From Single Vertices to Metasheets
,”
Phys. Rev. Lett.
,
114
(
5
), p.
055503
.
30.
Yasuda
,
H.
, and
Yang
,
J.
,
2015
, “
Reentrant Origami-Based Metamaterials With Negative Poisson's Ratio and Bistability
,”
Phys. Rev. Lett.
,
114
(
18
), p.
185502
.
31.
Lang
,
R. J.
,
2011
,
Origami Design Secrets: Mathematical Methods for an Ancient Art
,
CRC Press
,
Boca Raton, FL
.
32.
Greenberg
,
H. C.
,
Gong
,
M. L.
,
Howell
,
L. L.
, and
Magleby
,
S. P.
,
2011
, “
Identifying Links Between Origami and Compliant Mechanisms
,”
Mech. Sci.
,
2
(
2
), pp.
217
225
.
33.
Winder
,
B. G.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2009
, “
Kinematic Representations of Pop-Up Paper Mechanisms
,”
ASME J. Mech. Rob.
,
1
(
2
), pp.
217
225
.
34.
Silverberg
,
J. L.
,
Evans
,
A. A.
,
McLeod
,
L.
,
Hayward
,
R. C.
,
Hull
,
T.
,
Santangelo
,
C. D.
, and
Cohen
,
I.
,
2014
, “
Using Origami Design Principles to Fold Reprogrammable Mechanical Metamaterials
,”
Science
,
345
(
6197
), pp.
647
650
.
35.
Schenk
,
M.
, and
Guest
,
S. D.
,
2012
, “
Geometry of Miura-Folded Metamaterials
,”
Proc. Natl. Acad. Sci. U.S.A.
,
110
(
9
), pp.
3276
3281
.
36.
Miura
,
K.
,
1985
, “
Method of Packaging and Deployment of Large Membranes in Space
,” The Institute of Space and Astronautical Science, Tokyo, Tech. Report 618.
37.
Zirbel
,
S. A.
,
Lang
,
R. J.
,
Magleby
,
S. P.
,
Thomson
,
M. W.
,
Sigel
,
D. A.
,
Walkemeyer
,
P. E.
,
Trease
,
B. P.
, and
Howell
,
L. L.
,
2013
, “
Accommodating Thickness in Origami-Based Deployable Arrays
,”
ASME J. Mech. Des.
,
135
(
11
), p.
111005
.
38.
Ma
,
J.
, and
You
,
Z.
,
2013
, “
Energy Absorption of Thin-Walled Square Tubes With a Prefolded Origami Pattern—Part I: Geometry and Numerical Simulation
,”
ASME J. Appl. Mech.
,
81
(
1
), p.
011003
.
39.
Guest
,
S. D.
, and
Pellegrino
,
S.
,
1994
, “
The Folding of Triangulated Cylinders—Part I: Geometric Considerations
,”
ASME J. Appl. Mech.
,
61
(
4
), pp.
773
777
.
40.
Hawkes
,
E.
,
An
,
B.
,
Benbernou
,
N. M.
,
Tanaka
,
H.
,
Kim
,
S.
,
Demaine
,
E. D.
,
Rus
,
D.
, and
Wood
,
R. J.
,
2010
, “
Programmable Matter by Folding
,”
Proc. Natl. Acad. Sci. U.S.A.
,
107
(
28
), pp.
12441
12445
.
41.
Felton
,
S.
,
Tolley
,
M.
,
Demaine
,
E.
,
Rus
,
D.
, and
Wood
,
R.
,
2014
, “
A Method for Self-Folding Machines
,”
Science
,
345
(
6197
), pp.
644
646
.
42.
Quaglia
,
C. P.
,
Dascanio
,
A. J.
, and
Thrall
,
A. P.
,
2014
, “
Bascule Shelters: A Novel Erection Strategy for Origami-Inspired Deployable Structures
,”
Eng. Struct.
,
75
, pp.
276
287
.
43.
Francis
,
K. C.
,
Blanch
,
J. E.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2013
, “
Origami-Like Creases in Sheet Materials for Compliant Mechanism Design
,”
Mech. Sci.
,
4
(
2
), pp.
371
380
.
44.
Delimont
,
I. L.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2015
, “
A Family of Dual-Segment Compliant Joints Suitable for Use as Surrogate Folds
,”
ASME J. Mech. Des.
,
137
(
9
), p.
092302
.
45.
Evans
,
T.
,
2015
, “
Deployable and Foldable Arrays of Spatial Mechanisms
,” M.S. thesis, Brigham Young University, Provo, UT.
46.
Rowberry
,
B. G.
,
2013
, “
Stability of n = 6 Normal and Right-Angled Kaleidocycles Under the Influence of Energy Elements
,” B.S. honors thesis, Brigham Young University, Provo, UT.
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