One of the drawbacks of conventional mechanisms is the significant inertia of their moving parts. Tensegrity mechanisms, which have a reduced mass because of their extensive use of cables and springs, represent a potential alternative to these mechanisms for certain types of applications. In this paper a new spatial three-degree-of-freedom tensegrity mechanism is developed and analyzed. Mathematical models of the kinematics, statics, and dynamics of the mechanism are generated. These models reveal several characteristics of the fundamental behavior of tensegrity mechanisms that make them rather unique.

1.
Fuller
,
B.
, 1975,
Synergetics: The Geometry of Thinking
,
MacMillan
, New York.
2.
Motro
,
R.
, 1992, “
Tensegrity Systems: The State of the Art
,”
Int. J. Space Struct.
0956-0599,
7
, pp.
75
83
.
3.
Pugh
,
A.
, 1976,
An Introduction to Tensegrity
,
1st ed.
,
University of California Press
, Los Angeles, CA.
4.
Duffy
,
J.
,
Rooney
,
J.
,
Knight
,
B.
, and
Crane
,
C. D.
, III
, 2000, “
Review of a Family of Self-Deploying Tensegrity Structures with Elastic Ties
,”
Shock Vib. Dig.
0583-1024,
32
, pp.
100
106
.
5.
Sultan
,
C.
, and
Skelton
,
R. E.
, 1998, “
Tendon Control Deployment of Tensegrity Structures
,” in
Proceedings of SPIE - The International Society for Optical Engineering
, Vol.
3323
, pp.
455
466
.
6.
Tibert
,
G.
, 2002, “
Deployable Tensegrity Structures for Space Applications
,” Ph.D. thesis, Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden.
7.
Furuya
,
H.
, 1992, “
Concept of Deployable Tensegrity Structures in Space Application
,”
Int. J. Space Struct.
0956-0599,
7
, pp.
143
152
.
8.
Calladine
,
C. R.
, and
Pellegrino
,
S.
, 1991, “
First-Order Infinitesimal Mechanisms
,”
Int. J. Solids Struct.
0020-7683,
27
, pp.
505
515
.
9.
Pellegrino
,
S.
, 1993, “
Structural Computations with the Singular Value Decomposition of the Equilibrium Matrix
,”
Int. J. Solids Struct.
0020-7683,
30
, pp.
3025
3035
.
10.
Pellegrino
,
S.
, 1990, “
Analysis of Prestressed Mechanisms
,”
Int. J. Solids Struct.
0020-7683,
26
, pp.
1329
1350
.
11.
Vassart
,
N.
, and
Motro
,
R.
, 1999, “
Multiparametered Formfinding Method: Application to Tensegrity Systems
,”
Int. J. Space Struct.
0956-0599,
14
, pp.
147
154
.
12.
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
.
13.
Pellegrino
,
S.
, 1986, “
Mechanics of Kinematically Indeterminate Structures
,” Ph.D. thesis, University of Cambridge, United Kingdom.
14.
Motro
,
R.
, 1984, “
Forms and Forces in Tensegrity Systems
,” in
Proceedings of the 3rd International Conference on Space Structures
, pp.
180
185
.
15.
Tibert
,
A. G.
, and
Pellegrino
,
S.
, 2003, “
Review of Form-Finding Methods for Tensegrity Structures
,”
Int. J. Space Struct.
0956-0599,
18
, pp.
209
223
.
16.
Sultan
,
C.
,
Corless
,
M.
, and
Skelton
,
R. E.
, 1999, “
Reduced Prestressability Conditions for Tensegrity Structures
,” in
Proceedings of 40th AIAA/ASME/ASCE/AHS/ASC Structures
, Structural Dynamics and Materials Conference.
17.
Kebiche
,
K.
,
Kazi-Aoual
,
M.
, and
Motro
,
R.
, 1999, “
Geometrical Non-Linear Analysis of Tensegrity Systems
,”
Eng. Struct.
0141-0296,
21
, pp.
864
876
.
18.
Crane
,
C. D.
, III
,
Duffy
,
J.
, and
Correa
,
J. C.
, 2005, “
Static Analysis of Prestressed Tensegrity Structures
,”
ASME J. Mech. Des.
1050-0472,
127
, pp.
257
268
.
19.
Skelton
,
R. E.
,
Adhikari
,
R.
,
Pinaud
,
J.-P.
,
Chan
,
W.
, and
Helton
,
J. W.
, 2001, “
An Introduction to the Mechanics of Tensegrity Structures
,” in
Proceedings of the IEEE Conference on Decision and Control
, Vol.
5
, pp.
4254
4259
.
20.
Oppenheim
,
I. J.
, and
Williams
,
W. O.
, 2000, “
Geometric Effects in an Elastic Tensegrity Structure
,”
J. Elast.
0374-3535,
59
, pp.
51
65
.
21.
Sultan
,
C.
, 1999, “
Modeling, Design and Control of Tensegrity Structures With Applications
,” Ph.D. thesis, Purdue University.
22.
Sultan
,
C.
,
Corless
,
M.
, and
Skelton
,
R. E.
, 2002, “
Linear Dynamics of Tensegrity Structures
,”
Eng. Struct.
0141-0296,
24
, pp.
671
685
.
23.
Oppenheim
,
I. J.
, and
Williams
,
W. O.
, 2001, “
Vibration of an Elastic Tensegrity Structure
,”
Eur. J. Mech. A/Solids
0997-7538,
20
, pp.
1023
1031
.
24.
Oppenheim
,
I. J.
, and
Williams
,
W. O.
, 2001, “
Vibration and Damping in a Three-Bar Tensegrity Structure
,”
J. Aerosp. Eng.
0893-1321,
14
, pp.
85
91
.
25.
Tran
,
T. M.
, 2002, “
Reverse Displacement Analysis for Tensegrity Structures
,” Master’s thesis, University of Florida, 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
,” in
Proceedings of SPIE—The International Society for Optical Engineering
, Vol.
3039
, pp.
166
177
.
28.
Arsenault
,
M.
, and
Gosselin
,
C. M.
, 2005, “
Kinematic, Static and Dynamic Analysis of a Planar 1-DoF Tensegrity Mechanism
,”
ASME J. Mech. Des.
1050-0472,
127
, pp.
1152
1160
.
29.
Arsenault
,
M.
, and
Gosselin
,
C. M.
, 2005, “
Kinematic, Static and Dynamic Analysis of a Planar 2-DoF Tensegrity Mechanism
,”
Mech. Mach. Theory
0094-114X,
41
(
9
), pp.
1071
1089
.
30.
Bayat
,
J.
, and
Crane
,
C. D.
, III
, 2004, “
Closed-Form Equilibrium Analysis of a Planar Tensegrity Structure
,” in
Proceedings of the 9th International Symposium on Advances in Robot Kinematics
.
31.
Marshall
,
M.
, and
Crane
,
C. D.
, III
, 2004, “
Design and Analysis of a Hybrid Parallel Platform that Incorporates Tensegrity
,” in
Proceedings of the ASME 2004 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, pp.
535
540
.
32.
Sultan
,
C.
, and
Corless
,
M.
, 2000, “
Tensegrity Flight Simulator
,”
J. Guid. Control Dyn.
0731-5090,
23
, pp.
1055
1064
.
33.
Sultan
,
C.
,
Corless
,
M.
, and
Skelton
,
R. E.
, 1999, “
Peak to Peak Control of an Adaptive Tensegrity Space Telescope
,” in
Proceedings of SPIE - The International Society for Optical Engineering
, Vol.
3667
, pp.
190
201
.
34.
Sultan
,
C.
, and
Skelton
,
R. E.
, 2004, “
A Force and Torque Tensegrity Sensor
,”
Sens. Actuators, A
0924-4247,
112
, pp.
220
231
.
35.
Snelson
,
K.
, 1965, “
Continuous Tension, Discontinuous Compression Structures
,” United States Patent No. 3,169,611, February 16.
36.
Fuller
,
B.
, “
Tensile-Integrity Structures
, United States Patent No. 3,063,521, November 13, 1962.
37.
Knight
,
B.
,
Zhang
,
Y.
,
Duffy
,
J.
, and
Crane
,
C. D.
, III
, 2000, “
On the Line Geometry of a Class of Tensegrity Structures
,” in
Proceedings of a Symposium Commemorating the Legacy, Works, and Life of Sir Robert Stawell Ball
.
38.
Gosselin
,
C. M.
, 1999, “
Static Balancing of Spherical 3-DoF Parallel Mechanisms and Manipulators
,”
Int. J. Robot. Res.
0278-3649,
18
, pp.
819
829
.
39.
Connelly
,
R.
, and
Whiteley
,
W.
, 1996, “
Second-Order Rigidity and Prestress Stability for Tensegrity Frameworks
,”
SIAM J. Discrete Math.
0895-4801,
9
, pp.
453
491
.
40.
Arsenault
,
M.
, and
Gosselin
,
C. M.
, 2005, “
Static Balancing of Tensegrity Mechanisms
,” in
Proceedings of the 2005 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE)
.
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