This paper presents a one-degree-of-freedom network of Bennett linkages which can be deployed to approximate a cylindrical surface. The geometry of the unit mechanism is parameterized and its position kinematics is solved. The influence of the geometric parameters on the deployed shape is examined. Further kinematic analysis isolates those Bennett geometries for which a cylindrical network can be constructed. The procedure for connecting the unit mechanisms in a deployable cylinder is described in detail and used to gain insight into, and formulate some general guidelines for, the design of linkage networks which unfold as curved surfaces. Case studies of deployable structures in the shape of circular and elliptical cylinders are presented. Modeling and simulation validate the proposed approach.

References

References
1.
Escrig
,
F.
,
Valcarcel
,
J. P.
, and
Sanchez
,
J.
,
1996
, “
Deployable Cover on a Swimming Pool in Seville
,”
Bull. Int. Assoc. Shell Spat. Struct.
,
37
(
1
), pp.
39
70
.
2.
Zhao
,
J. S.
,
Wang
,
J. Y.
,
Chu
,
F. L.
,
Feng
,
Z. J.
, and
Dai
,
J. S.
,
2012
, “
Mechanism Synthesis of a Foldable Stair
,”
ASME J. Mech. Rob.
,
4
(
1
), p.
014502
.
3.
Durand
,
G.
,
Sauvage
,
M.
,
Bonnet
,
A.
,
Rodriguez
,
L.
,
Ronayette
,
S.
,
Chanial
,
P.
,
Scola
,
L.
,
Révéret
,
V.
,
Aussel
,
H.
,
Carty
,
M.
,
Durand
,
M.
,
Durand
,
L.
,
Tremblin
,
P.
,
Pantin
,
E.
,
Berthe
,
M.
,
Martignac
,
J.
,
Motte
,
F.
,
Talvard
,
M.
,
Minier
,
V.
, and
Bultel
,
P.
,
2014
, “
TALC: A New Deployable Concept for a 20-m Far-Infrared Space Telescope
,”
SPIE
Astronomical Telescopes+ Instrumentation, International Society for Optics and Photonics, Montreal, Quebec, Canada, June 22, p.
91431A
.
4.
Maden
,
F.
,
Korkmaz
,
K.
, and
Akgün
,
Y.
,
2011
, “
A Review of Planar Scissor Structural Mechanisms: Geometric Principles and Design Methods
,”
Archit. Sci. Rev.
,
54
(
3
), pp.
246
257
.
5.
Zhao
,
J. S.
,
Chu
,
F. L.
, and
Feng
,
Z. J.
,
2009
, “
The Mechanism Theory and Application of Deployable Structures Based on SLE
,”
Mech. Mach. Theory
,
44
(
2
), pp.
324
335
.
6.
O'brian
,
E. D.
, and
Phelan
,
C.
,
1984
, “
Folding Structure Employing a Sarrus Linkage
,”
U.S. Patent No. 4,437,413
.
7.
Lu
,
S. N.
,
Zlatanov
,
D.
,
Ding
,
X. L.
,
Molfino
,
R.
, and
Zoppi
,
M.
,
2016
, “
Novel Deployable Mechanisms With Decoupled Degrees-of-Freedom
,”
ASME J. Mech. Rob.
,
8
(
2
), p.
021008
.
8.
Deng
,
Z.
,
Huang
,
H.
,
Li
,
B.
, and
Liu
,
R.
,
2011
, “
Synthesis of Deployable/Foldable Single Loop Mechanisms With Revolute Joints
,”
ASME J. Mech. Rob.
,
3
(
3
), p.
031006
.
9.
Li
,
B.
,
Huang
,
H.
, and
Deng
,
Z.
,
2016
, “
Mobility Analysis of Symmetric Deployable Mechanisms Involved in a Coplanar 2-Twist Screw System
,”
ASME J. Mech. Rob.
,
8
(
1
), p.
011007
.
10.
Chen
,
Y.
, and
You
,
Z.
,
2008
, “
On Mobile Assemblies of Bennett Linkages
,”
Proc. R. Soc. London, Ser. A
,
464
(
2093
), pp.
1275
1293
.
11.
Chen
,
Y.
,
2003
, “
Design of Structural Mechanisms
,”
Ph.D. thesis
, University of Oxford, Oxford, UK.
12.
Liu
,
S. Y.
, and
Chen
,
Y.
,
2009
, “
Myard Linkage and Its Mobile Assemblies
,”
Mech. Mach. Theory
,
44
(
10
), pp.
1950
1963
.
13.
Qi
,
X. Z.
,
Deng
,
Z. Q.
,
Li
,
B.
,
Liu
,
R. Q.
, and
Guo
,
H. W.
,
2013
, “
Design and Optimization of Large Deployable Mechanism Constructed by Myard Linkages
,”
CEAS Space J.
,
5
(
3–4
), pp.
147
155
.
14.
Lu
,
S. N.
,
Zlatanov
,
D.
,
Ding
,
X. L.
,
Zoppi
,
M.
, and
Guest
,
S. D.
,
2015
, “
A Network of Type III Bricard Linkages
,”
ASME
Paper No. DETC2015-47139.
15.
Chu
,
Z. R.
,
Deng
,
Z. Q.
,
Qi
,
X. Z.
, and
Li
,
B.
,
2014
, “
Modeling and Analysis of a Large Deployable Antenna Structure
,”
Acta Astronaut.
,
95
, pp.
51
60
.
16.
Rahmat-Samii
,
Y.
,
Huang
,
J.
,
Lopez
,
B.
,
Lou
,
M.
,
Im
,
E.
,
Durden
,
S. L.
, and
Bahadori
,
K.
,
2005
, “
Advanced Precipitation Radar Antenna: Array-Fed Offset Membrane Cylindrical Reflector Antenna
,”
IEEE Trans. Antennas Propag.
,
53
(
8
), pp.
2503
2515
.
17.
Hoberman
,
C.
, and
Davis
,
M.
,
2010
, “
Synchronized Four-Bar Linkages
,”
U.S. Patent No. 7,644,721
.
18.
Hoberman
,
C.
,
2006
, “
Transformation in Architecture and Design
,”
Transportable Environments 3
, Vol.
3
,
Taylor & Francis
,
New York
, pp.
70
73
.
19.
Lu
,
S. N.
,
Zlatanov
,
D.
, and
Ding
,
X. L.
,
2016
, “
Approximation of Cylindrical Surfaces With Deployable Bennett Networks
,”
ASME
Paper No. DETC2016-59817.
20.
Bennett
,
G.
,
1903
, “
A New (Four-Piece Skew) Mechanism
,”
Engineering
,
76
, pp.
777
778
.
21.
Waldron
,
K.
,
1979
, “
Overconstrained Linkages
,”
Environ. Plann. B
,
6
(
4
), pp.
393
402
.
22.
Phillips
,
J.
,
2007
,
Freedom in Machinery
, Vol.
1
,
Cambridge University Press
,
New York
.
You do not currently have access to this content.