In this paper, we present a virtual chain approach for the mobility analysis of multiloop deployable mechanisms. First, the relative motion of the links of single-loop units in multiloop mechanisms are analyzed using the equivalent motion of certain types of open-loop virtual kinematic chains; these kinematic chains comprise some types of joints connected in series by flexible links. This reveals that the links in these virtual chains are not rigid when the mechanism is moving. The parameters of these virtual kinematic chains (such as the link length, the twist angle of two adjacent revolute joint axes, and so on) are variable. By using this approach that involves equivalent kinematic chains, the multiloop mechanisms can be considered equivalent to single-loop mechanisms with flexible links; the closure equations of such multiloop mechanisms can also be derived. The analytical procedures are explained using examples of multiloop mechanisms in which Myard mechanisms as used as the basic single-loop units. A prototype is also fabricated to demonstrate the feasibility of the proposed multiloop mechanism. The proposed method yields a more intuitive and straightforward insight into the mobility of complicated multiloop mechanisms.

References

References
1.
Hailin
,
H.
,
Zongquan
,
D.
, and
Bing
,
L.
,
2012
, “
Mobile Assemblies of Large Deployable Mechanisms
,”
JSME J. Space Eng.
,
5
(
1
), pp.
1
14
.10.1299/spacee.5.1
2.
Grigore
,
G.
,
2005
, “
Mobility of Mechanisms: A Critical Review
,”
Mech. Mach. Theory
,
40
(
9
), pp.
1068
1097
.10.1016/j.mechmachtheory.2004.12.014
3.
Liu
,
J.
,
Huang
,
Z.
, and
Li
,
Y.
,
2009
, “
Mobility of the Myard 5R Linkage Involved in Gogu Problem
,”
Chin. J. Mech. Eng.
,
22
(
3
), pp.
325
330
.10.3901/CJME.2009.03.325
4.
Jingfang
,
L.
, and
Zhen
,
H.
,
2008
, “
Mobility Analysis of Some Paradoxical Mechanisms Using a General Methodology
,”
ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, pp.
1421
1426
.
5.
Zongquan
,
D.
,
Hailin
,
H.
,
Bing
,
L.
, and
Rongqiang
,
L.
,
2012
, “
Synthesis of Deployable/Foldable Single Loop Mechanisms With Revolute Joints
,”
ASME J. Mech. Robot.
,
3
(
3
), p.
031006
.10.1115/1.4004029
6.
Chen
,
Y.
,
2003
, “
Design of Structural Mechanism
,” Ph.D. dissertation,
University of Oxford
,
Oxford, UK
.
7.
Song
,
C.
, and
Chen
,
Y.
,
2011
, “
A Spatial 6R Linkage Derived from Subtractive Goldberg 5R Linkages
,”
Mech. Mach. Theory
,
46
(
8
), pp.
1097
1106
.10.1016/j.mechmachtheory.2011.03.006
8.
Song
,
C.
, and
Chen
,
Y.
,
2011
, “
A Family of Mixed Double-Goldberg 6R Linkages
,”
Proc. R. Soc. London, Ser. A
,
468
(
2139
), pp.
871
890
.10.1098/rspa.2011.0345
9.
Dai
,
J. S.
, and
Jones
,
J. R.
,
1999
, “
Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds
,”
ASME Trans. J. Mech. Des.
,
121
(
3
), pp.
375
382
.10.1115/1.2829470
10.
Dai
,
J. S.
,
Huang
,
Z.
, and
Lipkin
,
H.
,
2006
, “
Mobility of Overconstrained Parallel Mechanisms
,”
ASME Trans.: J. Mech. Des.
,
128
(
1
), pp.
220
229
.10.1115/1.1901708
11.
Liu
,
S. Y.
, and
Chen
,
Y.
,
2009
, “
Myard Linkage and Its Mobile Assemblies
,”
Mech. Mach. Theory
,
44
(
10
), pp.
1950
1963
.10.1016/j.mechmachtheory.2009.05.001
12.
Qi
,
X. Z.
,
Deng
,
Z. Q.
,
Ma
,
B. Y.
,
Li
,
B.
, and
Liu
,
R. Q.
,
2011
, “
Design of Large Deployable Networks Constructed by Myard Linkages
,”
Key Eng. Mater.
,
486
, pp.
291
296
.10.4028/www.scientific.net/KEM.486.291
13.
Myard
,
F. E.
,
1931
, “
Contribution à la Géométrie des Systèmes Articulés
,”
Bull. Soc. Math. France
,
59
, pp.
183
210
.
14.
Chen
,
Y.
, and
You
,
Z.
,
2008
, “
An Extended Myard Linkage and its Derived 6R Linkage
,”
ASME J. Mech. Des.
,
130
(
5
), pp.
23011
23018
.10.1115/1.2885506
15.
Bricard
,
R.
,
1926
, “
Leçons de Cinématique
,”
Tome II Cinématique Appliquée
,
Gauthier-Villars
,
Paris
, pp.
7
12
.
You do not currently have access to this content.