A set of procedures was presented for characterizing static and dynamic response of tensegrity modules. The procedures were applied to two tensegrity modules: a six-bar spherical module and a two-stage cylindrical module with three bars at each stage. The singular value decomposition of the initial equilibrium matrix revealed prestress and infinitesimal mechanism modes. The prestress stiffening effect of infinitesimal mechanism modes was found to be isotropic at each node. In the initial quasi-static loading, infinitesimal mechanisms exhibited soft response. As the deformation advanced, the stiffness of tensegirty modules increased almost quadratically with infinitesimal mechanism amplitudes. Modal analyses revealed that the lowest modes were those of infinitesimal mechanism modes and their natural frequencies were an order of magnitude smaller than those of higher deformation modes.

Issue Section:
Technical Papers
Keywords:
singular value decomposition, classical mechanics, differential geometry, stress analysis, deformation
Topics:
Equilibrium (Physics), Tensegrity, Cables
1.
Schultz, D. G., 1981, Kenneth Snelson, an Exhibition, Albright-Knox Art Gallery, Buffalo, NY, Thorney-Sidney Press Inc., Buffalo, NY.
2.
Marks, R., and Fuller, R. B., 1973, The Dymaxion World of Buckminster Fuller, Anchor Books, Garden City, NY.
3.
Pugh, A., 1976, An Introduction to Tensegrity, University of California Press, Berkeley, CA.
4.
Kenner, H., 1976, Geodesic Math and How to Use It, University of California Press, Berkeley, CA.
5.
Skelton, R. E., and Sultan, C., 1997, “Controllable Tensegrity, a New Class of Smart Structures,” Proceedings of the International Society for Optical Engineers, 4th Symposium on Smart Structures and Materials, Vol. 3039, V. V. Varadan and J. Chandra, eds., San Diego, CA, Mar. 3–7, SPIE, Bellingham, WA, pp. 166–177.
6.
Motro
,
R.
,
1990
, “
Tensegrity Systems and Geodesic Domes
,”
Int. J. Space Struct.
,
5
, pp.
341
–
351
.
7.
Furuya
,
H.
,
1992
, “
Concept of Deployable Tensegrity Structures in Space Application
,”
Int. J. Space Struct.
,
7
, pp.
143
–
151
.
8.
Hanaor
,
A.
,
1993
, “
Double-Layer Tensegrity Grids as Deployable Structures
,”
Int. J. Space Struct.
,
8
, pp.
135
–
143
.
9.
Hanaor, A., 1997, “Tensegrity: Theory and Application,” Beyond the Cube: The Architecture of Space Frames and Polyhedra, J. F. Gabriel, ed., John Wiley and Sons, New York, pp. 385–408.
1.
Maxwell
,
J. C.
,
1864
, “
On the Calculation of the Equilibrium and Stiffness of Frames
,”
Philos. Mag.
,
27
, p.
250
250
;
2.
also 1890 in The Scientific Papers of James Clerk Maxwell, W. D. Niven, ed., Dover New York, pp. 598–604.
1.
Calladine
,
C. R.
,
1978
, “
Buckminster Fuller’s “Tensegrity” Structures and Clerk Maxwell’s Rules for the Construction of Stiff Frames
,”
Int. J. Solids Struct.
,
14
, pp.
161
–
172
.
2.
Argyris
,
J. H.
, and
Scharpf
,
D. W.
,
1972
, “
Large Deflection Analysis of Prestressed Networks
,”
J. Struct. Div. ASCE
,
98
, No.
ST3
, pp.
633
–
654
.
3.
Bathe, K.-J., 1982, Finite Element Procedure in Engineering Analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ, Chapter 11.
4.
Underwood, P., 1983, “Dynamic Relaxation,” Computational Methods for Transient Analysis, T. Belytschko and T. J. R. Hughes, eds., Elsevier, New York, Chapter 5.
5.
Barnes
,
M.
,
1994
, “
Form and Stress Engineering of Tension Structures
,”
Structural Engineering Review
,
6
, No.
3–4
, pp.
175
–
202
.
6.
Murakami, H., 2000, “Static and Dynamic Analysis of Tensegrity Structures, Part 1. Nonlinear Equations of Motion,” Int. J. Solids Struct., in press.
7.
Hughes, T. J. R., 1987, The Finite Element Method, Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ.
8.
Malvern, L., 1969, Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Englewood Cliffs, NJ.
9.
Murakami, H., 2000, “Static and Dynamic Analysis of Tensegrity Structures, Part 2. Quasi-Static Analysis,” Int. J. Solids Struct., in press.
10.
Tarnai
,
T.
,
1980
, “
Simultaneous Static and Kinematic Indeterminancy of Space Trusses With Cyclic Symmetry
,”
Int. J. Solids Struct.
,
16
, pp.
347
–
359
.
11.
Tobie, R. S., 1967, “A Report on an Inquiry into the Existence, Formation and Representation of Tensile Structures,” Masters’ thesis, Pratt Institute, Brooklyn, NY.
12.
Williamson, D., and Skelton, R. E., 1998, “A General Class of Tensegrity Systems: Geometric Definition,” Engineering Mechanics: A Force for the 21st Century, the Proceedings of the 12th ASCE Engineering Mechanics Conference, H. Murakami and J. E. Luco, eds., La Jolla, CA, May 17–20, ASCE, Reston, VA, pp. 732–735.
13.
Sultan, C., 1999, “Modeling, Design and Control of Tensegrity Structures with Applications,” Ph.D. dissertation, Purdue University, West Lafayette, IN.
14.
Sokolnikoff, I. S., 1956, Mathematical Theory of Elasticity, 2nd Ed., McGraw-Hill, New York, Section 26.
15.
Naylor, A. W., and Sell, G. R., 1971, Linear Operator Theory in Engineering and Science, Holt, Rinehart and Winston, New York, Chapter 5.
16.
Pellegrino
,
S.
, and
Calladine
,
C. R.
,
1986
, “
Matrix Analysis of Statically and Kinematically Indeterminate Frameworks
,”
Int. J. Solids Struct.
,
22
, pp.
409
–
428
.
17.
Noble, B., and Daniel, J. W., 1977, Applied Linear Algebra, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ.
18.
Skelton, R. E., and Akhikari, R., 1998, “An Introduction to Smart Tensegrity Structures,” Engineering Mechanics: A Force for the 21st Century, the Proceedings of the 12th ASCE Engineering Mechanics Conference, H. Murakami and J. E. Luco, eds., La Jolla, CA, May 17–20, ASCE, Reston, VA, pp. 24–27.
1.
Koiter, W. T., 1945, “On the Stability of Elastic Equilibrium,” thesis, Delft University, Amsterdam, The Netherlands (in Dutch);
2.
also 1970, AFFDL-TR-70-25, (English Translation).
1.
Budiansky, B., 1974, “Theory of Buckling and Post-Buckling Behavior of Elastic Structures,” Advances in Applied Mechanics, Vol. 14, C.-H. Yih, ed., Academic Press, San Diego, pp. 1–65.
2.
Hanaor
,
A.
,
1988
, “
Prestressed Pin-Jointed Structures—Flexibility Analysis and Prestress Design
,”
Comput. Struct.
,
28
, pp.
757
–
769
.
3.
Frankel, T., 1997, The Geometry of Physics, an Introduction, Cambridge University Press, Cambridge, MA, Chapter 6.
Copyright © 2001
 by ASME
You do not currently have access to this content.