Compliant kaleidocycles can be widely used in a variety of applications, including deployable structures, origami structures, and metamorphic robots, due to their unique features of continuous rotatability and multistability. Inspired by origami kaleidocycles, a type of symmetric multistable compliant mechanism with an arbitrary number of units is presented and analyzed in this paper. First, the basic dimension constraints are developed based on mobility analysis using screw theory. Second, the kinematic relationships of the actual rotation angle are obtained. Third, a method to determine the number of stabilities and the position of stable states, including the solution for the parameterized boundaries of stable regions, is developed. Finally, experimental platforms are established, and the validity of the proposed multistable mechanisms is verified.

References

References
1.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley
, New York.
2.
Howell
,
L. L.
,
Magleby
,
S. P.
, and
Olsen
,
B. M.
,
2013
,
Handbook of Compliant Mechanisms
,
Wiley
, Oxford, UK.
3.
Tran
,
A. V.
,
Zhang
,
X.
, and
Zhu
,
B.
,
2017
, “
The Development of a New Piezoresistive Pressure Sensor for Low Pressures
,”
IEEE Trans. Ind. Electron.
,
65
(
8
), pp.
6487
6496
.
4.
Wang
,
R.
, and
Zhang
,
X.
,
2018
, “
Parameters Optimization and Experiment of a Planar Parallel 3-Dof Nanopositioning System
,”
IEEE Trans. Ind. Electron.
,
65
(
3
), pp.
2388
2397
.
5.
Gan
,
J.
,
Zhang
,
X.
,
Li
,
H.
, and
Wu
,
H.
,
2017
, “
Full Closed-Loop Controls of Micro/Nano Positioning System With Nonlinear Hysteresis Using Micro-Vision System
,”
Sens. Actuators A: Phys.
,
257
, pp.
125
133
.
6.
Li
,
H.
,
Zhang
,
X.
,
Zhu
,
B.
,
Lu
,
Y.
, and
Wu
,
H.
,
2017
, “
Micro-Motion Detection of the 3-Dof Precision Positioning Stage Based on Iterative Optimized Template Matching
,”
Appl. Optics
,
56
(
34
), pp.
9435
9443
.
7.
Chen
,
W.
,
Zhang
,
X.
,
Li
,
H.
,
Wei
,
J.
, and
Fatikow
,
S.
,
2017
, “
Nonlinear Analysis and Optimal Design of a Novel Piezoelectric-Driven Compliant Microgripper
,”
Mech. Mach. Theory
,
118
, pp.
32
52
.
8.
Zhan
,
Z.
,
Zhang
,
X.
,
Jian
,
Z.
, and
Zhang
,
H.
,
2018
, “
Error Modelling and Motion Reliability Analysis of a Planar Parallel Manipulator With Multiple Uncertainties
,”
Mech. Mach. Theory
,
124
, pp.
55
72
.
9.
Yao
,
S.
,
Li
,
H.
,
Zeng
,
L.
, and
Zhang
,
X.
,
2018
, “
Vision-Based Adaptive Control of a 3-RRR Parallel Positioning System
,”
Sci. China Technol. Sci.
,
61
(
8
), pp.
1
12
.
10.
Li
,
H.
,
Zhang
,
X.
,
Wu
,
H.
, and
Gan
,
J.
,
2017
, “
Line-Based Calibration of a Micro-Vision Motion Measurement System
,”
Opt. Lasers Eng.
,
93
, pp.
40
46
.
11.
Li
,
H.
,
Zhang
,
X.
,
Zhu
,
B.
, and
Fatikow
,
S.
,
2018
, “
Online Precise Motion Measurement of 3-Dof Nanopositioners Based on Image Correlation
,”
IEEE Trans. Instrum. Meas.
(epub).
12.
Opdahl
,
P. G.
,
Jensen
,
B. D.
, and
Howell
,
L. L.
,
1998
, “
An Investigation Into Compliant Bistable Mechanisms
,”
ASME
Paper No. MECH-5914
.https://www.et.byu.edu/~bdjensen/publications/byubistablepaper.pdf
13.
Jensen
,
B. D.
, and
Howell
,
L. L.
,
2004
, “
Bistable Configurations of Compliant Mechanisms Modeled Using Four Links and Translational Joints
,”
ASME J. Mech. Des.
,
126
(
4
), pp.
657
666
.
14.
Jacobsen
,
J. O.
,
Chen
,
G.
,
Howell
,
L. L.
, and
Magleby
,
S. P.
,
2009
, “
Lamina Emergent Torsional (let) Joint
,”
Mech. Mach. Theory
,
44
(
11
), pp.
2098
2109
.
15.
Zhang
,
X.
,
2003
, “
Topology Optimization of Compliant Mechanisms
,”
Chin. J. Mech. Eng.
,
39
(
11
), pp.
47
51
.
16.
Zhan
,
J.
, and
Zhang
,
X.
,
2011
, “
Topology Optimization of Compliant Mechanisms With Geometrical Nonlinearities Using the Ground Structure Approach
,”
Chin. J. Mech. Eng. (Engl. Ed.)
,
24
(
2
), pp.
257
263
.
17.
Zhu
,
B.
,
Zhang
,
X.
, and
Wang
,
N.
,
2013
, “
Topology Optimization of Hinge-Free Compliant Mechanisms With Multiple Outputs Using Level Set Method
,”
Struct. Multidiscip. Optim.
,
47
(
5
), pp.
659
672
.
18.
Jin
,
M.
,
Zhang
,
X.
, and
Zhu
,
B.
,
2014
, “
Design of Compliant Mechanisms Using a Pseudo-Rigid-Body Model Based Topology Optimization Method
,”
ASME
Paper No. DETC2014-34325.
19.
Zhu
,
B.
,
Zhang
,
X.
, and
Fatikow
,
S.
,
2014
, “
A Multi-Objective Method of Hinge-Free Compliant Mechanism Optimization
,”
Struct. Multidiscip. Optim.
,
49
(
3
), pp.
431
440
.
20.
Liu
,
M.
,
Zhang
,
X.
, and
Fatikow
,
S.
,
2015
, “
Topology Optimization of Large-Displacement Flexure Hinges
,”
ASME
Paper No. DETC2015-46444.
21.
Zhu
,
B.
,
Liu
,
M.
,
Chen
,
Q.
,
Li
,
H.
,
Zhang
,
X.
, and
Fu
,
Y.
,
2017
, “
Topology Optimization of the Flexure Hinges for Precision Engineering
,”
International Conference on Manipulation, Automation and Robotics at Small Scales
(
MARSS
), Montreal, QC, Canada, July 17–21, pp.
1
5
.
22.
Liu
,
M.
,
Zhang
,
X.
, and
Fatikow
,
S.
,
2017
, “
Design of Flexure Hinges Based on Stress-Constrained Topology Optimization
,”
Proc. Inst. Mech. Eng., Part C
,
231
(
24
), pp.
4635
4645
.
23.
Jin
,
M.
,
Zhang
,
X.
,
Yang
,
Z.
, and
Zhu
,
B.
,
2018
, “
Jacobian-Based Topology Optimization Method Using an Improved Stiffness Evaluation
,”
ASME J. Mech. Des.
,
140
(
1
), p.
011402
.
24.
Masters
,
N. D.
, and
Howell
,
L. L.
,
2003
, “
A Self-Retracting Fully Compliant Bistable Micromechanism
,”
J. Microelectromech. Syst.
,
12
(
3
), pp.
273
280
.
25.
Jensen
,
B. D.
, and
Howell
,
L. L.
,
2003
, “
Identification of Compliant Pseudo-Rigid-Body Four-Link Mechanism Configurations Resulting in Bistable Behavior
,”
ASME J. Mech. Des.
,
125
(
4
), pp.
701
708
.
26.
Chen
,
G.
,
Gao
,
H.
, and
Jia
, J.
, “
A 3-DOF Pseudo-Rigid-Body Model for Tension-Based Compliant Bistable Mechanisms
,”
Chin. J. Mech. Eng.
,
23
(
2
), pp.
149
153
.
27.
Qiu
,
J.
,
Lang
,
J. H.
, and
Slocum
,
A. H.
,
2004
, “
A Curved-Beam Bistable Mechanism
,”
J. Microelectromech. Syst.
,
13
(
2
), pp.
137
146
.
28.
Chen
,
G.
, and
Bai
,
R.
,
2016
, “
Modeling Large Spatial Deflections of Slender Bisymmetric Beams in Compliant Mechanisms Using Chained Spatial-Beam Constraint Model
,”
ASME J. Mech. Rob.
,
8
(
4
), p.
041011
.
29.
Ma
,
F.
, and
Chen
,
G.
,
2017
, “
Bi-BCM: A Closed-Form Solution for Fixed-Guided Beams in Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
9
(
1
), p.
014501
.
30.
Chen
,
Q.
,
Zhang
,
X.
, and
Zhu
,
B.
,
2018
, “
Design of Buckling-Induced Mechanical Metamaterials for Energy Absorption Using Topology Optimization
,”
Struct. Multidiscip. Optim.
,
58
(
4
), pp.
1395
1410
.
31.
Chen
,
G.
,
Aten
,
Q. T.
,
Zirbel
,
S.
,
Jensen
,
B. D.
, and
Howell
,
L. L.
,
2010
, “
A Tristable Mechanism Configuration Employing Orthogonal Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
2
(
1
), p.
014501
.
32.
Chen
,
T.
,
Mueller
,
J.
, and
Shea
,
K.
,
2017
, “
Integrated Design and Simulation of Tunable, Multi-State Structures Fabricated Monolithically With Multi-Material 3D Printing
,”
Sci. Rep.
,
7
, p.
45671
.
33.
Greenberg
,
H.
,
Gong
,
M.
,
Magleby
,
S.
, and
Howell
,
L.
,
2011
, “
Identifying Links Between Origami and Compliant Mechanisms
,”
Mech. Sci.
,
2
(
2
), pp.
217
225
.
34.
Hanna
,
B. H.
,
Lund
,
J. M.
,
Lang
,
R. J.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2014
, “
Waterbomb Base: A Symmetric Single-Vertex Bistable Origami Mechanism
,”
Smart Mater. Struct.
,
23
(
9
), p.
094009
.
35.
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
.
36.
Waitukaitis
,
S.
,
Menaut
,
R.
,
Chen
,
B. G.-G.
,
V.
, and
Hecke
,
M.
,
2015
, “
Origami Multistability: From Single Vertices to Metasheets
,”
Phys. Rev. Lett.
,
114
(
5
), p.
055503
.
37.
Baker
,
J. E.
,
1980
, “
An Analysis of the Bricard Linkages
,”
Mech. Mach. Theory
,
15
(
4
), pp.
267
286
.
38.
Chen
,
Y.
,
2003
, “
Design of Structural Mechanisms
,” Ph.D. thesis, University of Oxford, UK.
39.
Chen
,
Y.
, and
You
,
Z.
,
2004
, “
Deployable Structures Based on the Bricard Linkages
,”
AIAA
Paper No. 2004-1604.
40.
Chen
,
Y.
,
You
,
Z.
, and
Tarnai
,
T.
,
2005
, “
Threefold-Symmetric Bricard Linkages for Deployable Structures
,”
Int. J. Solids Struct.
,
42
(
8
), pp.
2287
2301
.
41.
Chen
,
Y.
,
Peng
,
R.
, and
You
,
Z.
,
2015
, “
Origami of Thick Panels
,”
Science
,
349
(
6246
), pp.
396
400
.
42.
Shang
,
H.
,
Wei
,
D.
,
Kang
,
R.
, and
Chen
,
Y.
,
2017
, “
A Deployable Robot Based on the Bricard Linkage
,”
Asian Conference on Mechanism and Machine Science (ASIAN MMS 2016, CCMMS 2016)
, Guangzhou, China, Dec. 15–17, pp.
737
747.
43.
Dai
,
J.
,
2014
, “
Geometrical Foundations and Screw Algebra for Mechanisms and Robotics
,” High Education Press, Beijing, China, pp. 1–161.
44.
Tang
,
Z.
,
Qi
,
P.
, and
Dai
,
J.
,
2017
, “
Mechanism Design of a Biomimetic Quadruped Robot
,”
Ind. Robot: An Int. J.
,
44
(
4
), pp. 512–520.
45.
Evans
,
T. A.
,
Rowberry
,
B. G.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2015
, “
Multistable Behavior of Compliant Kaleidocycles
,”
ASME
Paper No. DETC2015-46637.
46.
Safsten
,
C.
,
Fillmore
,
T.
,
Logan
,
A.
,
Halverson
,
D.
, and
Howell
,
L.
,
2016
, “
Analyzing the Stability Properties of Kaleidocycles
,”
ASME J. Appl. Mech.
,
83
(
5
), p.
051001
.
47.
Norton
,
R. L.
,
1999
,
Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines
, Vol.
924
,
McGraw-Hill Boston
, MA.
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