Abstract

Design strategies for foldable mechanisms have been developed with inspiration from origami. In this study, we investigate a new direction that blocks are folded in a way that origami folds as the ori-blocks to generate a new type of foldable mechanisms consisting of multiple blocks. During the investigation, we propose a design approach to construct ori-blocks dissected from cylinders and cones, where “ori” is derived from the word “origami” in its original meaning as “folding”. In this way, we cut the solids into six portions and assign rotation axes to assemble the portions into movable blocks. Interestingly, this connects the Bricard classical linkages developed in 1897 to these ori-blocks with coincidence of the position and orientation of the axes when the blocks are replaced by links. The study bridges the gap between ori-blocks, origami, and mechanisms, which proposes a set of novel reconfigurable mechanisms as ori-blocks. As spatial linkages have been widely used in a broad range of technical fields, we anticipate that ori-blocks will find several potential applications owing to their kinematics in reconfigurability.

References

References
1.
Greenwood
,
J.
,
Avila
,
A.
,
Howell
,
L.
, and
Magleby
,
S.
,
2020
, “
Conceptualizing Stable States in Origami-Based Devices Using an Energy Visualization Approach
,”
ASME J. Mech. Des.
,
142
(
9
), p.
093302
. 10.1115/1.4046437
2.
Gillman
,
A. S.
,
Fuchi
,
K.
, and
Buskohl
,
P. R.
,
2019
, “
Discovering Sequenced Origami Folding Through Nonlinear Mechanics and Topology Optimization
,”
ASME J. Mech. Des.
,
141
(
4
), p.
041401
. 10.1115/1.4041782
3.
Pehrson
,
N. A.
,
Bilancia
,
P.
,
Magleby
,
S.
, and
Howell
,
L.
,
2020
, “
Load-Displacement Characterization in Three Degrees-of-Freedom for General Lamina Emergent Torsion Arrays
,”
ASME J. Mech. Des.
,
142
(
9
), p.
093301
. 10.1115/1.4046072
4.
Chen
,
Y.
,
Sareh
,
P.
,
Yan
,
J.
,
Fallah
,
A. S.
, and
Feng
,
J.
,
2019
, “
An Integrated Geometric-Graph-Theoretic Approach to Representing Origami Structures and Their Corresponding Truss Frameworks
,”
ASME J. Mech. Des.
,
141
(
9
), p.
091402
. 10.1115/1.4042791
5.
Chen
,
Y.
,
Yan
,
J.
,
Feng
,
J.
, and
Sareh
,
P.
,
2021
, “
Particle Swarm Optimization-Based Metaheuristic Design Generation of Non-Trivial Flat-Foldable Origami Tessellations With Degree-4 Vertices
,”
ASME J. Mech. Des.
,
143
(
1
), p.
011703
. 10.1115/1.4047437
6.
Nickels
,
P. C.
,
Wünsch
,
B.
,
Holzmeister
,
P.
,
Bae
,
W.
,
Kneer
,
L. M.
,
Grohmann
,
D.
,
Tinnefeld
,
P.
, and
Liedl
,
T.
,
2016
, “
Molecular Force Spectroscopy With a DNA Origami-Based Nanoscopic Force Clamp
,”
Science
,
354
(
6310
), pp.
305
307
. 10.1126/science.aah5974
7.
Derr
,
N. D.
,
Goodman
,
B. S.
,
Jungmann
,
R.
,
Leschziner
,
A. E.
,
Shih
,
W. M.
, and
Reck-Peterson
,
S. L.
,
2012
, “
Tug-of-War in Motor Protein Ensembles Revealed With a Programmable DNA Origami Scaffold
,”
Science
,
338
(
6107
), pp.
662
625
. 10.1126/science.1226734
8.
Han
,
D.
,
Qi
,
X.
,
Myhrvold
,
C.
,
Wang
,
B.
,
Dai
,
M.
,
Jiang
,
S.
,
Bates
,
M.
,
Liu
,
Y.
,
An
,
B.
,
Zhang
,
F.
,
Yan
,
H.
, and
Yin
,
P.
,
2017
, “
Single-Stranded DNA and RNA Origami
,”
Science
,
358
(
6369
), p.
eaao2648
. 10.1126/science.aao2648
9.
Lang
,
R. J.
,
Tolman
,
K. A.
,
Crampton
,
E. B.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2018
, “
A Review of Thickness-Accommodation Techniques in Origami-Inspired Engineering
,”
ASME Appl. Mech. Rev.
,
70
(
1
), p.
010805
. 10.1115/1.4039314
10.
Zirbel
,
S. A.
,
Lang
,
R. J.
,
Thomson
,
M. W.
,
Sigel
,
D. A.
,
Walkemeyer
,
P. E.
,
Trease
,
B. P.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2013
, “
Accommodating Thickness in Origami-Based Deployable Arrays1
,”
ASME J. Mech. Des.
,
135
(
11
), p.
111005
. 10.1115/1.4025372
11.
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
. 10.5194/ms-4-371-2013
12.
Morgan
,
M. R.
,
Lang
,
R. J.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2016
, “
Towards Developing Product Applications of Thick Origami Using the Offset Panel Technique
,”
Mech. Sci.
,
7
(
1
), pp.
69
77
. 10.5194/ms-7-69-2016
13.
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
. 10.1115/1.4030875
14.
Delimont
,
I. L.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2015
, “
Evaluating Compliant Hinge Geometries for Origami-Inspired Mechanisms
,”
ASME J. Mech. Rob.
,
7
(
1
), p.
011009
. 10.1115/1.4029325
15.
Dai
,
J. S.
, and
Rees Jones
,
J.
,
2002
, “
Kinematics and Mobility Analysis of Carton Folds in Packing Manipulation Based on the Mechanism Equivalent
,”
J. Mech. Eng. Sci.
,
216
(
10
), pp.
959
970
. 10.1243/095440602760400931
16.
Dai
,
J. S.
, and
Rees-Jones
,
J.
,
1999
, “
Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds
,”
ASME J. Mech. Des.
,
121
(
3
), pp.
375
382
. 10.1115/1.2829470
17.
Overvelde
,
J. T. B.
,
Weaver
,
J. C.
,
Hoberman
,
C.
, and
Bertoldi
,
K.
,
2017
, “
Rational Design of Reconfigurable Prismatic Architected Materials
,”
Nature
,
541
(
7637
), pp.
347
352
. 10.1038/nature20824
18.
Felton
,
S.
,
Tolley
,
M.
,
Demaine
,
E.
,
Rus
,
D.
, and
Wood
,
R.
,
2014
, “
A Method for Building Self-Folding Machines
,”
Science
,
345
(
6197
), pp.
644
646
. 10.1126/science.1252610
19.
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.
674
650
. 10.1126/science.1252876
20.
Kim
,
S. J.
,
Lee
,
D. Y.
,
Jung
,
G. P.
, and
Cho
,
K. J.
,
2018
, “
An Origami-Inspired, Self-Locking Robotic Arm That Can be Folded Flat
,”
Sci. Rob.
,
3
(
16
), p.
eaar2915
. 10.1126/scirobotics.aar2915
21.
Dai
,
J. S.
,
Wang
,
D.
, and
Cui
,
L.
,
2009
, “
Orientation and Workspace Analysis of the Multifingered Metamorphic Hand-Metahand
,”
IEEE Trans. Rob.
,
25
(
4
), pp.
942
947
. 10.1109/TRO.2009.2017138
22.
Zhang
,
C.
,
Zhang
,
C.
,
Dai
,
J. S.
, and
Qi
,
P.
,
2019
, “
Stability Margin of a Metamorphic Quadruped Robot With a Twisting Trunk
,”
ASME J. Mech. Rob.
,
11
(
6
), p.
064501
. 10.1115/1.4044600
23.
Zhang
,
C.
, and
Dai
,
J.
,
2018
, “
Trot Gait with Twisting Trunk of a Metamorphic Quadruped Robot
,”
J. Bio. Eng.
,
15
(
6
), pp.
971
981
. 10.1007/s42235-018-0085-x
24.
Salerno
,
M.
,
Zhang
,
K.
,
Menciassi
,
A.
, and
Dai
,
J. S.
,
2016
, “
A Novel 4-DOF Origami Grasper With an SMA-Actuation System for Minimally Invasive Surgery
,”
IEEE Trans. Rob.
,
32
(
3
), pp.
484
498
. 10.1109/TRO.2016.2539373
25.
Han
,
D.
,
Pal
,
S.
,
Nangreave
,
J.
,
Deng
,
Z.
,
Liu
,
Y.
, and
Yan
,
H.
,
2011
, “
DNA Origami With Complex Curvatures in Three-Dimensional Space
,”
Science
,
332
(
6027
), pp.
342
346
. 10.1126/science.1202998
26.
Ke
,
Y.
,
Lindsay
,
S.
,
Chang
,
Y.
,
Liu
,
Y.
, and
Yan
,
H.
,
2008
, “
Self-Assembled Water-Soluble Nucleic Acid Probe Tiles for Label-Free RNA Hybridization Assays
,”
Science
,
319
(
5860
), pp.
180
183
. 10.1126/science.1150082
27.
Acuna
,
G. P.
,
Möller
,
F. M.
,
Holzmeister
,
P.
,
Beater
,
S.
,
Lalkens
,
B.
, and
Tinnefeld
,
P.
,
2012
, “
Fluorescence Enhancement at Docking Sites of DNA-Directed Self-Assembled Nanoantennas
,”
Science
,
338
(
6106
), pp.
506
510
. 10.1126/science.1228638
28.
Zion
,
M. Y. B.
,
He
,
X.
,
Maass
,
C. C.
,
Sha
,
R.
,
Seeman
,
N. C.
, and
Chaikin
,
P. M.
,
2017
, “
Self-Assembled Three-Dimensional Chiral Colloidal Architecture
,”
Science
,
358
(
6363
), pp.
633
636
. 10.1126/science.aan5404
29.
Lei
,
D. S.
,
Marras
,
A. E.
,
Liu
,
J. F.
,
Huang
,
C. M.
,
Zhou
,
L. F.
,
Castro
,
C. E.
,
Su
,
H. J.
, and
Ren
,
G.
,
2018
, “
Three-Dimensional Structural Dynamics of DNA Origami Bennett Linkages Using Individual-Particle Electron Tomography
,”
Nat. Commun.
,
9
(
1
), pp.
592
599
. 10.1038/s41467-018-03018-0
30.
Thubagere
,
A. J.
,
Li
,
W.
,
Johnson
,
R. F.
,
Chen
,
Z.
,
Doroudi
,
S.
,
Lee
,
Y. L.
,
Izatt
,
G.
,
Wittman
,
S.
,
Srinivas
,
N.
,
Woods
,
D.
,
Winfree
,
E.
, and
Qian
,
L.
,
2017
, “
A Cargo-Sorting DNA Robot
,”
Science
,
357
(
6356
), p.
eaan6558
. 10.1126/science.aan6558
31.
Chen
,
Y.
,
Peng
,
R.
, and
You
,
Z.
,
2015
, “
Origami of Thick Panels
,”
Science
,
349
(
6246
), pp.
396
400
. 10.1126/science.aab2870
32.
Zhang
,
X.
, and
Chen
,
Y.
,
2018
, “
The Diamond Thick-Panel Origami and the Corresponding Mobile Assemblies of Plane-Symmetric Bricard Linkages
,”
Mech. Mach. Theory
,
130
, pp.
585
604
. 10.1016/j.mechmachtheory.2018.09.005
33.
Chen
,
Y.
,
Feng
,
H.
,
Ma
,
J.
,
Peng
,
R.
, and
You
,
Z.
,
2016
, “
Symmetric Waterbomb Origami
,”
Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci.
,
472
(
2190
), p.
20150846
. 10.1098/rspa.2015.0846
34.
Zhang
,
K.
,
Qiu
,
C.
, and
Dai
,
J. S.
,
2016
, “
An Extensible Continuum Robot With Integrated Origami Parallel Modules
,”
J. Mech. Rob.
,
8
(
3
), p.
031010
. 10.1115/1.4031808
35.
Wei
,
G.
, and
Dai
,
J. S.
,
2014
, “
Origami-Inspired Integrated Planar-Spherical Overconstrained Mechanisms
,”
ASME J. Mech. Des.
,
136
(
5
), p.
051003
. 10.1115/1.4025821
36.
Teschemacher
,
P. E.
, and
Godfrey
,
J. O.
,
1880
,
U.S. Patent No. 232140
.
37.
Schatz
,
P.
,
1934
,
C.H. Patent No. 173832A
.
38.
Baker
,
J. E.
,
Duclong
,
T.
, and
Khoo
,
P. S. H.
,
1982
, “
On Attempting to Reduce Undesirable Inertial Characteristics of the Schatz Mechanism
,”
ASME J. Mech. Des.
,
104
(
1
), pp.
192
205
. 10.1115/1.3256310
39.
Bhoite
,
K.
,
Kakandikar
,
G. M.
, and
Nandedkar
,
V. M.
,
2015
, “
Schatz Mechanism With 3D-Motion Mixer—A Review
,”
Mater. Today Proc.
,
2
(
4–5
), pp.
1700
1706
. 10.1016/j.matpr.2015.07.003
40.
Cui
,
L.
,
Dai
,
J. S.
, and
Lee
,
C. C.
,
2015
, “
Characteristics of the Double-Cycled Motion-Ruled Surface of the Schatz Linkage With Differential Geometry
,”
J. Mech. Eng. Sci.
,
229
(
5
), pp.
957
964
. 10.1177/0954406214541430
41.
Stevens
,
K. V.
,
1994
,
U.S. Patent No. 5299804
.
42.
Cornelius
,
B.
, and
Sligh
,
J. P.
,
1999
,
A.U. Patent No. WO 99/10059
.
43.
Cornelius
,
B.
, and
Sligh
,
J. P.
,
2004
,
U.S. Patent No. 6796560 B1
.
44.
Dai
,
J. S.
,
Li
,
D.
,
Zhang
,
Q.
, and
Jin
,
G.
,
2004
, “
Mobility of a Complex Structured Ball Based on Mechanism Decomposition and Equivalent Screw-System Analysis
,”
Mech. Mach. Theory
,
39
(
4
), pp.
445
458
. 10.1016/j.mechmachtheory.2003.12.004
45.
Wei
,
G.
,
Ding
,
X.
, and
Dai
,
J. S.
,
2010
, “
Mobility and Geometry of the Hoberman Switch-Pitch Ball and Its Variants
,”
J. Mech. Rob.
,
2
(
3
), p.
031010
. 10.1115/1.4001730
46.
Wei
,
G.
, and
Dai
,
J. S.
,
2014
, “
A Spatial Eight-Bar Linkage and Its Association With the Deployable Platonic Mechanisms
,”
J. Mech. Rob.
,
6
(
2
), p.
021010
. 10.1115/1.4025472
47.
Xiu
,
H.
,
Wang
,
K.
,
Wei
,
G.
,
Ren
,
L.
, and
Dai
,
J. S.
,
2020
, “
A Sarrus-Like Overconstrained Eight-Bar Linkage and Its Associated Fulleroid-Like Platonic Deployable Mechanisms
,”
J. Mech. Eng. Sci.
,
234
(
1
), pp.
241
262
. 10.1177/0954406218816343
48.
Seo
,
J.
,
Gray
,
S.
,
Kumar
,
V.
, and
Yim
,
M.
,
2010
,
Algorithmic Foundations of Robotics Ix
, Vol.
68
,
Springer-Verlag Berlin Heidelberg
, pp.
105
120
.
49.
Zhou
,
Y.
,
Sueda
,
S.
,
Matusik
,
W.
, and
Shamir
,
A.
,
2014
, “
Boxelization
,”
ACM Trans. Graph.
,
33
(
4
), pp.
1
8
. 10.1145/2601097.2601173
50.
Yuan
,
Y.
,
Zheng
,
C.
, and
Coros
,
S.
,
2018
, “
Computational Design of Transformables
,”
Comput. Graph. Forum
,
37
(
8
), pp.
103
113
. 10.1111/cgf.13516
51.
Nelson
,
T. G.
,
Zimmerman
,
T. K.
,
Magleby
,
S. P.
,
Lang
,
R. J.
, and
Howell
,
L. L.
,
2019
, “
Developable Mechanisms on Developable Surfaces
,”
Sci. Rob.
,
4
(
27
), p.
eaau5171
. 10.1126/scirobotics.aau5171
52.
Hyatt
,
L. P.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2020
, “
Developable Mechanisms on Right Conical Surfaces
,”
Mech. Mach. Theory
,
149
, p.
103813
. 10.1016/j.mechmachtheory.2020.103813
53.
Greenwood
,
J. R.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2019
, “
Developable Mechanisms on Regular Cylindrical Surfaces
,”
Mech. Mach. Theory
,
142
, p.
103584
. 10.1016/j.mechmachtheory.2019.103584
55.
Chen
,
Y.
,
You
,
Z.
, and
Tarnai
,
T.
,
2005
, “
Threefold-Symmetric Bricard Linkages for Deployable Structures
,”
Int. J. Solids Struct.
,
42
(
8
), pp.
2287
2301
. 10.1016/j.ijsolstr.2004.09.014
56.
Lyu
,
S. N.
,
Zlatanov
,
D.
,
Zoppi
,
M.
,
Ding
,
X. L.
,
Chirikjian
,
G. S.
, and
Guest
,
S. D.
,
2020
, “
Bundle Folding Type III Bricard Linkages
,”
Mech. Mach. Theory
,
144
, p.
103663
. 10.1016/j.mechmachtheory.2019.103663
57.
Abbott
,
T. G.
,
Abel
,
Z.
,
Charlton
,
D.
,
Demaine
,
E. D.
,
Demaine
,
M. L.
, and
Kominers
,
S. D.
,
2008
, “
Hinged Dissections Exist
,”
Proceedings of the Twenty-Fourth Annual Symposium on Computational Geometry (Sgg'08)
,
College Park, MD
,
June 9–11
. http://dx.doi.org/10.1145/1377676.1377695
58.
Viquerat
,
A. D.
,
Hutt
,
T.
, and
Guest
,
S. D.
,
2013
, “
A Plane Symmetric 6R Foldable Ring
,”
Mech. Mach. Theory
,
63
, pp.
73
88
. 10.1016/j.mechmachtheory.2012.12.004
59.
Kang
,
X.
,
Ma
,
X.
,
Dai
,
J. S.
, and
Yu
,
H.
,
2020
, “
Bifurcation Variations and Motion-Ruled-Surface Evolution of a Novel Schatz Linkage Induced Metamorphic Mechanism
,”
Mech. Mach. Theory
,
150
, pp.
103867
. 10.1016/j.mechmachtheory.2020.103867
60.
Jia
,
G.
,
Li
,
B.
,
Huang
,
H.
, and
Zhang
,
D.
,
2020
, “
Type Synthesis of Metamorphic Mechanisms With Scissor-Like Linkage Based on Different Kinds of Connecting Pairs
,”
Mech. Mach. Theory
,
151
, p.
103848
. 10.1016/j.mechmachtheory.2020.103848
61.
Jia
,
G. L.
,
Huang
,
H. L.
,
Li
,
B.
,
Wu
,
Y. L.
,
Cao
,
Q. D.
, and
Guo
,
H. W.
,
2018
, “
Synthesis of a Novel Type of Metamorphic Mechanism Module for Large Scale Deployable Grasping Manipulators
,”
Mech. Mach. Theory
,
128
, pp.
544
559
. 10.1016/j.mechmachtheory.2018.06.017
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