Rolling joints, which are created by attaching two cylindrical surfaces of equal radius using two or more thin tapes or cable, are used for rigid origami considering the panel thickness. First, the concept and two implementation methods of this joint are given. Then planar linkages are chosen to study the mobility and kinematics of foldable plate structures with rolling joints. It can be found that the rolling joints preserve the full-cycle-motion of foldable plate structures. From the closure equations of linkages, the results show that the outputs of linkages with rolling joints are the same as that with traditional revolute joints if the lengths of links are equal. However, the results are different when the lengths of links are unequal. Moreover, the difference between linkages with rolling joints and revolute joints increases with an increase of the size of rolling joints.

References

References
1.
Guest
,
S. D.
,
1996
, “
Deployable Structures: Concepts and Analysis
,” Ph.D. thesis, Cambridge University, Cambridge, UK.
2.
Tachi
,
T.
,
2009
, “
Simulation of Rigid Origami
,”
Origami 4: Fourth International Meeting of Origami Science, Mathematics, and Education
, Taylor & Francis, Natick, MA.
3.
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 Arrays
,”
ASME J. Mech. Des.
,
135
(
11
), p.
111005
.
4.
Tachi
,
T.
,
2011
, “
Rigid Foldable Thick Origami
,”
Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education
, Taylor & Francis, Natick, MA.
5.
Hoberman
,
C.
,
1991
, “
Reversibly Expandable Structures
,” U.S. Patent No. 4,981,732.
6.
Hoberman
,
C.
,
2010
, “
Folding Structures Made of Thick Hinged Sheets
,” U.S. Patent No. 7,794,019.
7.
Faist
,
K. A.
, and
Wiens
,
G. J.
,
2010
, “
Parametric Study on the Use of Hoberman Mechanisms for Reconfigurable Antenna and Solar Arrays
,”
IEEE Aerospace Conference
, Big Sky, MT, Mar. 6–13, Paper No. 1172.
8.
Chen
,
Y.
,
Peng
,
R.
, and
You
,
Z.
,
2015
, “
Origami of Thick Panels
,”
Science
,
349
(
6246
), pp.
396
400
.
9.
Hilberry
,
B. M.
, and
Hall
,
A. S.
,
1974
, “
Rolling Contact Prosthetic Knee Join
,” U.S. Patent No. 3,945,053.
10.
Wilkes
,
D. F.
,
1969
, “
Roller-Band Devices
,” U.S. Patent No. 3,452,175.
11.
Schioler
,
T.
,
2005
, “
Multi-Stable Structural Elements
,” Ph.D. dissertation, Cambridge University, Cambridge, UK.
12.
Pellegrino
,
S.
,
Green
,
C.
,
Guest
,
S. D.
, and
Watt
,
A.
,
2000
, “
SAR Advanced Deployable Structure
,” Cambridge University, Cambridge, UK, Project Report No. CUED/D-STRUCT/TR191.
13.
Page
,
Á.
,
de Rosario
,
H.
,
Gálvez
,
J. A.
, and
Mata
,
V.
,
2011
, “
Representation of Planar Motion of Complex Joints by Means of Rolling Pairs Application to Neck Motion
,”
J. Biomech.
,
44
(
4
), pp.
747
750
.
14.
Halverson
,
P. A.
,
Howell
,
L. L.
, and
Magleby
,
S. P.
,
2010
, “
Tension-Based Multi-Stable Compliant Rolling-Contact Elements
,”
Mech. Mach. Theory
,
45
(
2
), pp.
147
156
.
15.
Halverson
,
P. A.
,
Bowden
,
A. E.
, and
Howell
,
L. L.
,
2012
, “
A Compliant-Mechanism Approach to Achieving Specific Quality of Motion in a Lumbar Total Discreplacement
,”
Int. J. Spine Surg.
,
6
(
1
), pp.
78
86
.
16.
Nai
,
T. Y.
,
Herder
,
J. L.
, and
Tuijthof
,
G. J.
,
2011
, “
Steerable Mechanical Joint for High Load Transmission in Minimally Invasive Instruments
,”
ASME J. Med. Devices
,
5
(
3
), p.
034503
.
17.
Cai
,
J. G.
, and
Feng
,
J.
,
2014
, “
Concept and Behavior of Rolling Joints for Multistable Plate Structures
,”
Smart Mater. Struct.
,
23
(
4
), p.
045011
.
18.
Dai
,
J. S.
, and
Jones
,
J. R.
,
1999
, “
Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds
,”
ASME J. Mech. Des.
,
121
(
3
), pp.
375
382
.
19.
Hunt
,
K. H.
,
1990
,
Kinematic Geometry of Mechanisms
,
Clarendon Press
,
Oxford, UK
.
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