The use of tensegrity systems as structures has been extensively studied. However, their development for use as mechanisms is quite recent even though they present such advantages as reduced mass and a deployment capability. The object of this paper is to apply analysis methods usually reserved for conventional mechanisms to a planar one-degree-of-freedom tensegrity mechanism. This mechanism is obtained from a three-degree-of-freedom tensegrity system by adding actuation to the latter as well as by making some assumptions of symmetry. Analytical solutions are thus developed for the mechanism’s direct and inverse static problems. Furthermore, the working curve, singularities, and stiffness of the mechanism are detailed. Finally, a dynamic model of the mechanism is developed and a preliminary control scheme is proposed.

1.
Motro
,
R.
, 1992, “
Tensegrity Systems: The State of the Art
,”
Int. J. Space Struct.
0956-0599,
7
(
2
), pp.
75
83
.
2.
Pugh
,
A.
, 1976,
An Introduction to Tensegrity
,
1st Ed.
,
University of California Press
, Los Angeles.
3.
Calladine
,
C. R.
, and
Pellegrino
,
S.
, 1991, “
First-Order Infinitesimal Mechanisms
,”
Int. J. Solids Struct.
0020-7683,
27
(
4
), pp.
505
515
.
4.
Pellegrino
,
S.
, 1993, “
Structural Computations With the Singular Value Decomposition of the Equilibrium Matrix
,”
Int. J. Solids Struct.
0020-7683,
30
(
21
), pp.
3025
3035
.
5.
Pellegrino
,
S.
, 1990, “
Analysis of Prestressed Mechanisms
,”
Int. J. Solids Struct.
0020-7683,
26
(
12
), pp.
1329
1350
.
6.
Vassart
,
N.
, and
Motro
,
R.
, 1999, “
Multiparametered Formfinding Method: Application to Tensegrity Systems
,”
Int. J. Space Struct.
0956-0599,
14
(
2
), pp.
147
154
.
7.
Schek
,
H.-J.
, 1974, “
The Force Density Method for Form Finding and Computation of General Networks
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
3
, pp.
115
134
.
8.
Pellegrino
,
S.
, 1986, “
Mechanics of Kinematically Indeterminate Structures
,” Ph.D. thesis, University of Cambridge, United Kingdom.
9.
Motro
,
R.
, 1984, “
Forms and Forces in Tensegrity Systems
,”
Proc. of Third International Conference on Space Structures
, pp.
180
185
.
10.
Crane
III,
C. D.
,
Duffy
,
J.
, and
Correa
,
J. C.
, 2005, “
Static Analysis of Prestressed Tensegrity Structures
,”
ASME J. Mech. Des.
1050-0472,
127
(
2
),
257
268
.
11.
Tibert
,
A.
, and
Pellegrino
,
S.
, 2003, “
Review of Form-Finding Methods for Tensegrity Structures
,”
Int. J. Space Struct.
0956-0599,
18
(
4
), pp.
209
223
.
12.
Kebiche
,
K.
,
Kazi-Aoual
,
M.
, and
Motro
,
R.
, 1999, “
Geometrical Non-Linear Analysis of Tensegrity Systems
,”
Eng. Struct.
0141-0296,
21
(
9
), pp.
864
876
.
13.
Crane
III,
C. D.
,
Duffy
,
J.
, and
Correa
,
J. C.
, 2002, “
Static Analysis of Tensegrity Structures Part 1: Equilibrium Equations
,”
Proc. of 2002 ASME Design Engineering Technical Conf.
,
ASME
, New York, pp.
671
680
.
14.
Crane
III,
C. D.
,
Duffy
,
J.
, and
Correa
,
J. C.
, 2002, “
Static Analysis of Tensegrity Structures Part 2: Numerical Examples
,”
Proc. of 2002 ASME Design Engineering Technical Conf.
,
ASME
, New York, pp.
681
687
.
15.
Skelton
,
R. E.
,
Adhikari
,
R.
,
Pinaud
,
J.-P.
,
Chan
,
W.
, and
Helton
,
J. W.
, 2001, “
An Introduction to the Mechanics of Tensegrity Structures
,”
Proc. of the 40th IEEE Conf. on Decision and Control
.
16.
Oppenheim
,
I. J.
, and
Williams
,
W. O.
, 2000, “
Geometric Effects in an Elastic Tensegrity Structure
,”
J. Elast.
0374-3535,
59
(
1
), pp.
51
65
.
17.
Sultan
,
C.
, 1999, “
Modeling, Design and Control of Tensegrity Structures With Applications
,” Ph.D. thesis, Purdue University.
18.
Sultan
,
C.
,
Corless
,
M.
, and
Skelton
,
R. E.
, 2002, “
Linear Dynamics of Tensegrity Structures
,”
Eng. Struct.
0141-0296,
24
(
6
), pp.
671
685
.
19.
Oppenheim
,
I. J.
, and
Williams
,
W. O.
, 2001, “
Vibration of an Elastic Tensegrity Structure
,”
Eur. J. Mech. A/Solids
0997-7538,
20
(
6
), pp.
1023
1031
.
20.
Oppenheim
,
I. J.
, and
Williams
,
W. O.
, 2001, “
Vibration and Damping in a Three-Bar Tensegrity Structure
,”
J. Aerosp. Eng.
0893-1321,
14
(
3
), pp.
85
91
.
21.
Duffy
,
J.
,
Rooney
,
J.
,
Knight
,
B.
, and
Crane
III,
C. D.
, 2000, “
Review of a Family of Self-Deploying Tensegrity Structures With Elastic Ties
,”
Shock Vib. Dig.
0583-1024,
32
(
2
), pp.
100
106
.
22.
Sultan
,
C.
, and
Skelton
,
R. E.
, 1998, “
Tendon Control Deployment of Tensegrity Structures
,”
Proc. SPIE
0277-786X,
3323
, pp.
455
466
.
23.
Tibert
,
G.
, 2002, “
Deployable Tensegrity Structures for Space Applications
,” Ph.D. thesis, Department of Mechanics, Royal Institude of Technology, Stockholm, Sweden.
24.
Furuya
,
H.
, 1992, “
Concept of Deployable Tensegrity Structures in Space Applications
,”
Int. J. Space Struct.
0956-0599,
7
(
2
), pp.
143
152
.
25.
Tran
,
T. M.
, 2002, “
Reverse Displacement Analysis for Tensegrity Structures
,” Master’s thesis, University of Florida.
26.
Oppenheim
,
I. J.
, and
Williams
,
W. O.
, 1997, “
Tensegrity Prisms as Adaptive Structures
,”
ASME Adaptive Structures and Material Systems
,
54
, pp.
113
120
.
27.
Skelton
,
R. E.
, and
Sultan
,
C.
, 1997, “
Controllable Tensegrity, a New Class of Smart Structures
,”
Proc. SPIE
0277-786X,
3039
, pp.
166
177
.
28.
Sultan
,
C.
, and
Corless
,
M.
, 2000, “
Tensegrity Flight Simulator
,”
J. Guid. Control Dyn.
0731-5090,
23
(
6
), pp.
1055
1064
.
29.
Sultan
,
C.
,
Corless
,
M.
, and
Skelton
,
R. E.
, 1999, “
Peak to Peak Control of an Adaptive Tensegrity Space Telescope
,”
Proc. SPIE
0277-786X,
3667
, pp.
190
201
.
30.
Gosselin
,
C. M.
, 1999, “
Static Balancing of Spherical 3-DOF Parallel Mechanisms and Manipulators
,”
Int. J. Robot. Res.
0278-3649,
18
(
2
), pp.
819
829
.
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