This paper presents the design methodology for a single-mobility, large surface-deployable mechanism using irregularly shaped triangular prismoid units. First, we demonstrate that the spherical shell, as the deployed profile of the large deployable mechanism, cannot be filled with identical regular-shaped triangular prismoids (truncated pyramid) without gaps, which makes the design challenging because a large set of nonidentical modules should be moved synchronously. Second, we discuss the design of a novel deployable mechanism that can be deployed onto irregularly shaped triangular prismoids, which will be used as the basic module to fill the spherical shell. Owing to high stiffness and ease of actuation, a planar scissor-shape deployable mechanism is applied. Third, we study the mobile assemblies of irregularly shaped modules in large surface-deployable mechanisms. We discover that hyper kinematic redundant constraints exist in a multiloop mechanism, making the design even more difficult. In order to address this issue, a methodology for reducing these redundant constraints is also discussed. Finally, a physical prototype is fabricated to demonstrate the feasibility of the proposed design methodology.

References

References
1.
Hu
,
K.
, and
Zhang
,
Y. J.
,
2016
, “
Centroidal Voronoi Tessellation Based Polycube Construction for Adaptive All-Hexahedral Mesh Generation
,”
Comput. Methods Appl. Mech. Eng.
,
305
(
15
), pp.
405
421
.
2.
Lacey
,
P. M.
, and
Fenney
,
S.
,
2016
, “
Tessellation Method Using Recursive Sub-Division of Triangles
,” U.S. Patent No. US20160358375.
3.
Sugimoto
,
T.
,
2017
, “
Convex Polygons for Aperiodic Tiling
,” eprint
arXiv:1602.06372
.https://arxiv.org/abs/1602.06372
4.
Mathar
,
R. J.
,
2016
, “
Tiling Hexagons With Smaller Hexagons and Unit Triangles
,” eprint
viXra:1608.0380
.http://www.rxiv.org/abs/1608.0380
5.
Chen
,
Y.
,
2003
, “
Design of Structural Mechanisms
,” Ph.D. dissertation, University of Oxford, Oxford, UK.
6.
Liu
,
S. Y.
, and
Chen
,
Y.
,
2009
, “
Myard Linkage and Its Mobile Assemblies
,”
Mech. Mach. Theory
,
44
(
10
), pp.
1950
1963
.
7.
Chen
,
Y.
, and
You
,
Z.
,
2008
, “
On Mobile Assemblies of Bennett Linkages
,”
Proc. R. Soc. A
,
464
(
2093
), pp.
1275
1283
.
8.
Chen
,
Y.
, and
You
,
Z.
,
2007
, “
Square Deployable Frame for Space Application—Part II: Realization
,”
Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng.
,
221
(
1
), pp.
37
45
.
9.
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.
Wang
,
J.
, and
Kong
,
X.
,
2018
, “
Deployable Polyhedron Mechanisms Constructed by Connecting Spatial Single-Loop Linkages of Different Types and/or in Different Sizes Using S Joints
,”
Mech. Mach. Theory
,
124
, pp.
211
225
.
11.
Cao
,
W-A.
,
Yang
,
D.
, and
Ding
,
H.
,
2018
, “
Topological Structural Design of Umbrella-Shaped Deployable Mechanisms Based on New Spatial Closed-Loop Linkage Units
,”
ASME J. Mech. Des.
,
140
(
6
), p.
062302
.
12.
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
.
13.
Qi
,
X.
,
Huang
,
H.
,
Miao
,
Z.
, and
Li
,
B.
,
2017
, “
Design and Mobility Analysis of Large Deployable Mechanisms Based on Plane-Symmetric Bricard Linkage
,”
ASME J. Mech. Des.
,
139
(
2
), p.
022302
.
14.
Sattar
,
M.
, and
Wei
,
C.
,
2016
, “
Analytical Kinematics and Trajectory Planning of Large Scale Hexagonal Modular Mesh Deployable Antenna
,”
Third International Conference on Mechanics and Mechatronics Research
, Chongqing, China, June 15–17, p. 01012.
15.
Wei
,
G.
,
Chen
,
Y.
, and
Dai
,
J.
,
2014
, “
Synthesis, Mobility, and Multifurcation of Deployable Polyhedral Mechanisms With Radially Reciprocating Motion
,”
ASME J. Mech. Des.
,
136
(
9
), p.
091003
.
16.
Cui
,
J.
,
Huang
,
H.
,
Li
,
B.
, and
Deng
,
Z.
,
2012
, “
A Novel Surface Deployable Antenna Structure Based on Special Form of Bricard Linkages
,”
The Second ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots
, Tianjin, China, July 8–11, pp. 783–792.
17.
Guest
,
S. D.
, and
Pellegrino
,
S.
,
1996
, “
A New Concept for Solid Surface Deployable Antennas
,”
Acta Astronaut.
,
38
(
2
), pp.
103
113
.
18.
Nelson
,
T. G.
,
Lang
,
R. J.
,
Pehrson
,
N. A.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2016
, “
Facilitating Deployable Mechanisms and Structures Via Developable Lamina Emergent Arrays
,”
ASME J. Mech. Rob.
,
8
(
3
), p.
031006
.
19.
Wohlhart
,
K.
,
2008
, “
Double-Ring Polyhedral Linkages
,”
Conference on Interdisciplinary Applications of Kinematics
, Lima, Peru, Jan. 9–11, pp. 1–17.
20.
Wei
,
G.
, and
Dai
,
J.
,
2014
, “
A Spatial Eight-Bar Linkage and Its Association With the Deployable Platonic Mechanisms
,”
ASME J. Mech. Rob.
,
6
(
2
), p.
021010
.
21.
Huang
,
H.
,
Zhu
,
J.
,
Li
,
B.
, and
Qi
,
X.
,
2016
, “
A New Family of Bricard-Derived Deployable Mechanisms
,”
ASME J. Mech. Rob.
,
8
(
3
), p.
034503
.
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