The umbrella linkage is one of the most classical deployable mechanisms. This paper concentrates on topological structural design of a family of umbrella-shaped deployable mechanisms based on new two-layer and two-loop spatial linkage units. First, deployable units are developed systematically from two-layer and two-loop linkage with four revolute pair (4R) coupling chains. Then, mobile connection modes of the deployable units are established based on the conditions of one degree-of-freedom (DOF) and structural symmetry. Finally, umbrella-shaped deployable mechanisms are constructed based on the developed deployable units and the established mobile connection modes. Like umbrellas, the designed deployable mechanisms can be actuated in a simple and reliable way, and those mechanisms have good potential applications in the fields of architecture, manufacturing, space exploration, and recreation.

References

References
1.
Escrig
,
F.
, and
Valcarcel
,
J. P.
,
1993
, “
Geometry of Expandable Space Structures
,”
Int. J. Space Struct.
,
8
(
1–2
), pp.
71
84
.
2.
Puig
,
L.
,
Barton
,
A.
, and
Rando
,
N.
,
2010
, “
A Review on Large Deployable Structures for Astrophysics Missions
,”
Acta Astronaut.
,
67
(
1–2
), pp.
12
26
.
3.
Deng
,
Z.
,
Huang
,
H.
,
Li
,
B.
, and
Liu
,
R.
,
2011
, “
Synthesis of Deployable/Foldable Single Loop Mechanisms With Revolute Joints
,”
J. Mechanisms Rob.
,
3
(
3
), p.
031006
.
4.
Hanaor
,
A.
, and
Levy
,
R.
,
2001
, “
Evaluation of Deployable Structures for Space Enclosures
,”
Int. J. Space Struct.
,
16
(
4
), pp.
211
229
.
5.
Kiper
,
G.
,
Söylemez
,
E.
, and
Kişisel
,
A. U. Ö.
,
2008
, “
A Family of Deployable Polygons and Polyhedra
,”
Mechanism Mach. Theory
,
43
(
5
), pp.
627
640
.
6.
Li
,
R.
,
Yao
,
Y.-A.
, and
Kong
,
X.
,
2016
, “
A Class of Reconfigurable Deployable Platonic Mechanisms
,”
Mechanism Mach. Theory
,
105
, pp.
409
427
.
7.
St-Onge
,
D.
, and
Gosselin
,
C.
,
2016
, “
Synthesis and Design of a One Degree-of-Freedom Planar Deployable Mechanism With a Large Expansion Ratio
,”
ASME J. Mech. Rob.
,
8
(
2
), p.
021025
.
8.
Zhao
,
D.-J.
,
Zhao
,
J.-S.
, and
Yan
,
Z.-F.
,
2016
, “
Planar Deployable Linkage and Its Application in Overconstrained Lift Mechanism
,”
ASME J. Mech. Rob.
,
8
(
2
), p.
021022
.
9.
Chen
,
Y.
,
Fan
,
L.
, and
Feng
,
J.
,
2017
, “
Kinematic of Symmetric Deployable Scissor-Hinge Structures With Integral Mechanism Mode
,”
Comput. Struct.
,
191
, pp.
140
152
.
10.
Li
,
B.
,
Huang
,
H.
, and
Deng
,
Z.
,
2015
, “
Mobility Analysis of Symmetric Deployable Mechanisms Involved in a Coplanar 2-Twist Screw System
,”
ASME J. Mech. Rob.
,
8
(
1
), p.
011007
.
11.
Chen
,
Y.
, and
You
,
Z.
,
2008
, “
An Extended Myard Linkage and Its Derived 6R Linkage
,”
ASME J. Mech. Des.
,
130
(
5
), p.
052301
.
12.
Chen
,
Y.
, and
You
,
Z.
,
2009
, “
Two-Fold Symmetrical 6R Foldable Frame and Its Bifurcations
,”
Int. J. Solids Struct.
,
46
(
25–26
), pp.
4504
4514
.
13.
Chen
,
Y.
, and
You
,
Z.
,
2008
, “
On Mobile Assemblies of Bennett Linkages
,”
Proc. R. Soc. A: Math., Phys. Eng. Sci.
,
464
(
2093
), pp.
1275
1293
.
14.
Liu
,
S. Y.
, and
Chen
,
Y.
,
2009
, “
Myard Linkage and Its Mobile Assemblies
,”
Mech. Mach. Theory
,
44
(
10
), pp.
1950
1963
.
15.
Baker
,
J. E.
,
2006
, “
Kinematic Investigation of the Deployable Bennett Loop
,”
ASME J. Mech. Des.
,
129
(
6
), pp.
602
610
.
16.
Huang
,
H.
,
Deng
,
Z.
,
Qi
,
X.
, and
Li
,
B.
,
2013
, “
Virtual Chain Approach for Mobility Analysis of Multiloop Deployable Mechanisms
,”
ASME J. Mech. Des.
,
135
(
11
), p.
111002
.
17.
Huang
,
H.
,
Li
,
B.
,
Zhu
,
J.
, and
Qi
,
X.
,
2016
, “
A New Family of Bricard-Derived Deployable Mechanisms
,”
ASME J. Mech. Rob.
,
8
(
3
), p.
034503
.
18.
Song
,
X.
,
Deng
,
Z.
,
Guo
,
H.
,
Liu
,
R.
,
Li
,
L.
, and
Liu
,
R.
,
2017
, “
Networking of Bennett Linkages and Its Application on Deployable Parabolic Cylindrical Antenna
,”
Mech. Mach. Theory
,
109
, pp.
95
125
.
19.
Qi
,
X.
,
Huang
,
H.
,
Miao
,
Z.
,
Li
,
B.
, and
Deng
,
Z.
,
2016
, “
Design and Mobility Analysis of Large Deployable Mechanisms Based on Plane-Symmetric Bricard Linkage
,”
ASME J. Mech. Des.
,
139
(
2
), p.
022302
.
20.
Qi
,
X.
,
Huang
,
H.
,
Li
,
B.
, and
Deng
,
Z.
,
2016
, “
A Large Ring Deployable Mechanism for Space Satellite Antenna
,”
Aerosp. Sci. Technol.
,
58
, pp.
498
510
.
21.
Ding
,
X.
,
Yang
,
Y.
, and
Dai
,
J. S.
,
2013
, “
Design and Kinematic Analysis of a Novel Prism Deployable Mechanism
,”
Mech. Mach. Theory
,
63
, pp.
35
49
.
22.
Lu
,
S.
,
Zlatanov
,
D.
,
Ding
,
X.
,
Molfino
,
R.
, and
Zoppi
,
M.
,
2015
, “
Novel Deployable Mechanisms With Decoupled Degrees-of-Freedom
,”
ASME J. Mech. Rob.
,
8
(
2
), p.
021008
.
23.
Lu
,
S.
,
Zlatanov
,
D.
, and
Ding
,
X.
,
2017
, “
Approximation of Cylindrical Surfaces With Deployable Bennett Networks
,”
ASME J. Mech. Rob.
,
9
(
2
), p.
021001
.
24.
Wei
,
G.
,
Chen
,
Y.
, and
Dai
,
J. S.
,
2014
, “
Synthesis, Mobility, and Multifurcation of Deployable Polyhedral Mechanisms With Radially Reciprocating Motion
,”
ASME J. Mech. Des.
,
136
(
9
), p.
091003
.
25.
Wei
,
G.
, and
Dai
,
J. S.
,
2014
, “
A Spatial Eight-Bar Linkage and Its Association With the Deployable Platonic Mechanisms
,”
ASME J. Mech. Rob.
,
6
(
2
), p.
021010
.
26.
Chen
,
Y.
,
Feng
,
J.
, and
Qian
,
Z.
,
2016
, “
A Self-Equilibrated Load Method to Locate Singular Configurations of Symmetric Foldable Structures
,”
Acta Mech.
,
227
(
10
), pp.
2749
2763
.
27.
Chen
,
Y.
, and
Feng
,
J.
,
2015
, “
Mobility of Symmetric Deployable Structures Subjected to External Loads
,”
Mechanism Mach. Theory
,
93
, pp.
98
111
.
28.
Wei
,
G.
,
Ding
,
X.
, and
Dai
,
J. S.
,
2010
, “
Mobility and Geometric Analysis of the Hoberman Switch-Pitch Ball and Its Variant
,”
ASME J. Mech. Rob.
,
2
(
3
), p.
031010
.
29.
Hasanzade
,
V.
,
Sedighy
,
S. H.
, and
Shahravi
,
M.
,
2017
, “
Compact Deployable Umbrella Antenna Design With Optimum Communication Properties
,”
J. Spacecr. Rockets
,
54
(
3
), pp.
782
788
.
30.
Huang
,
H.
,
Deng
,
Z.
, and
Li
,
B.
,
2012
, “
Mobile Assemblies of Large Deployable Mechanisms
,”
J. Space Eng.
,
5
(
1
), pp.
1
14
.
31.
Korkmaz
,
K.
,
2005
, “
Generation of a New Type of Architectural Umbrella
,”
Int. J. Space Struct.
,
20
(
1
), pp.
35
41
.
32.
Ding
,
H.
,
Cao
,
W.-A.
,
Chen
,
Z.
, and
Kecskemethy
,
A.
,
2015
, “
Structural Synthesis of Two-Layer and Two-Loop Spatial Mechanisms With Coupling Chains
,”
Mech. Mach. Theory
,
92
, pp.
289
313
.
33.
Cao
,
W.-A.
,
Ding
,
H.
,
Chen
,
Z.
, and
Zhao
,
S.
,
2016
, “
Mobility Analysis and Structural Synthesis of a Class of Spatial Mechanisms With Coupling Chains
,”
Robotica
,
34
(
11
), pp.
2467
2485
.
34.
Cao
,
W.-A.
,
Yang
,
D.
, and
Ding
,
H.
,
2017
, “
A New Family of Deployable Mechanisms Derived From Two-Layer and Two-Loop Spatial Linkages With Five Revolute Pair Coupling Chains
,”
ASME J. Mech. Rob.
,
9
(
6
), p.
061016
.
You do not currently have access to this content.