Abstract

Connecting beam (CB) mandala is a kind of planar deployable mechanism with the ability of scaling up and down like a mandala flower. It is constructed by many-component connecting beams, which are identical circle arcs with specific arc angle and three revolving joints (one middle joint and two end joints) located symmetrically. In this paper, a detailed geometrical analysis of CB mandala is reported. Some basic concepts and parameters are proposed to describe CB mandala's geometry. Based on them, the scaling motion of CB mandala is analyzed, and its five morphologies and their unique features are presented. CB mandala's application is also discussed and illustrated with a simple case.

References

1.
You
,
Z.
,
2007
, “
Motion Structures Extend Their Reach
,”
Mater. Today
,
10
(
12
), pp.
52
57
. 10.1016/S1369-7021(07)70308-5
2.
Kempe
,
A. B.
,
1877
, “
On Conjugate Four-Piece Linkages
,”
Proc. London Math. Soc.
,
1
(
1
), pp.
133
149
. 10.1112/plms/s1-9.1.133
3.
Li
,
B.
,
Wang
,
S. M.
,
Zhi
,
C. J.
,
Xue
,
X. Z.
, and
Makis
,
V.
,
2017
, “
Analytical and Numerical Study of the Buckling of Planar Linear Array Deployable Structures Based on Scissor-Like Element Under Its Own Weight
,”
Mech. Syst. Signal Process.
,
83
(
Jan.
), pp.
474
488
. 10.1016/j.ymssp.2016.06.025
4.
Zhao
,
J. S.
,
Chu
,
F.
, and
Feng
,
Z. J.
,
2009
, “
The Mechanism Theory and Application of Deployable Structures Based on SLE
,”
Mech. Mach. Theory
,
44
(
2
), pp.
324
335
. 10.1016/j.mechmachtheory.2008.03.014
5.
Hoberman
,
C.
,
1990
, “
Reversibly Expandable Doubly-Curved Truss Structure
,” U.S. Patent No. 4,942,700.
6.
Hoberman
,
C.
,
2008
, “
Geared Expanding Structures
,” U.S. Patent No. 7,464,503.
7.
You
,
Z.
, and
Pellegrino
,
S.
,
1997
, “
Foldable Bar Structures
,”
Int. J. Solids Struct.
,
34
(
15
), pp.
1825
1847
. 10.1016/S0020-7683(96)00125-4
8.
Jensen
,
F.
, and
Pellegrino
,
S.
,
2005
, “
Expandable ‘Blob’ Structures
,”
J. Int. Assoc. Shell Spat. Struct.
,
46
(
149
), pp.
151
158
.
9.
Nassar
,
I. T.
,
Weller
,
T. M.
, and
Lusk
,
C. P.
,
2013
, “
Radiating Shape-Shifting Surface Based on a Planar Hoberman Mechanism
,”
IEEE Trans. Antennas Propag.
,
61
(
5
), pp.
2861
2864
. 10.1109/TAP.2013.2243094
10.
Faist
,
K. A.
, and
Wiens
,
G. J.
,
2010
, “
Parametric Study on the Use of Hoberman Mechanisms for Reconfigurable Antenna and Solar Arrays
,”
2010 IEEE Aerospace Conference
,
Big Sky, MT
,
Mar. 6–13
, pp.
1
8
.
11.
Dai
,
J. S.
,
Li
,
D.
,
Zhang
,
Q.
, and
Jin
,
G.
,
2004
, “
Mobility Analysis 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
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