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Cited by 274

The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.

Second-Order Rigidity and Prestress Stability for Tensegrity Frameworks

Connelly, Robert, Whiteley, Walter·1996·SIAM Journal on Discrete Mathematics
DOI 10.1137/s0895480192229236
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Abstract

This paper defines two concepts of rigidity for tensegrity frameworks (frameworks with cables, bars, and struts): prestress stability and second-order rigidity. We demonstrate a hierarchy of rigidity—first-order rigidity implies prestress stability implies second-order rigidity implies rigidity—for any framework. Examples show that none of these implications are reversible, even for bar frameworks. Other examples illustrate how these results can be used to create rigid tensegrity frameworks. This paper also develops a duality for second-order rigidity, leading to a test which combines information on the self stresses and the first-order flexes of a framework to detect second-order rigidity. Using this test, the following conjecture of Roth is proven: a plane tensegrity framework, in which the vertices and bars form a strictly convex polygon with additional cables across the interior, is rigid if and only if it is first-order rigid.

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Cites

Show all 10 references

Research works printed but not linked: 21

  1. 10.1007/BF01404753 · doi:10.1007/bf01404753
  2. Connelly R., 1988, Structural Topology, 14, 43
  3. Connelly R., 1991, Structural Topology, 16, 57
  4. Connelly R., 1992, J. Space Structures, 7, 153, 10.1177/026635119200700208 · DOI
  5. Crapo Henry, 1982, Structural Topology, 43
  6. 10.1007/978-1-4613-9447-1 · doi:10.1007/978-1-4613-9447-1
  7. Grünbaum Branko, 1967, Convex polytopes
  8. Grünbaum B., 1975, Lectures on Lost Mathematics
  9. Grünbaum B., 1978, Lectures on Lost Mathematics
  10. N. H. Kuiper , Spheres polyhedriques flexible dans E3, d'àpres Robert Connelly, Seminaire Bourbaki, Vol. 541, 1978, 1–22
  11. E. Kötter , Über die Möglichkeit n Punkte in der Ebene oder im Raume durch weniger als 2n−3 oder 3n−6 Stäbe von ganz unveränderlicher Länge universchieblich miteinander zu verbinden, Festschrift Heinrich Müller-Breslau, 1912, pp. 61–80
  12. 10.1016/0020-7683(88)90026-1 · doi:10.1016/0020-7683(88)90026-1
  13. 10.1115/1.3176051 · doi:10.1115/1.3176051
  14. 10.1016/0020-7683(91)90138-6 · doi:10.1016/0020-7683(91)90138-6
  15. 10.1115/1.2897214 · doi:10.1115/1.2897214
  16. 10.1115/1.2897215 · doi:10.1115/1.2897215
  17. 10.1007/978-1-4612-3176-9 · doi:10.1007/978-1-4612-3176-9
  18. Szabo J., 1984, Structural Design of Cable-Suspended Roofs
  19. Tarnai Tibor, 1980, Structural Topology, 61
  20. 10.1137/0608001 · doi:10.1137/0608001
  21. 10.2140/pjm.1984.110.233 · doi:10.2140/pjm.1984.110.233

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Metadata

Authors
Connelly, R., & Whiteley, W.
Venue
SIAM Journal on Discrete Mathematics
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
1996-08
Volume
9
Issue
3
Pages
453-491
ISSN
  • 0895-4801 (ISSN-L)
  • 1095-7146
DOI
10.1137/s0895480192229236
OpenAlex
W1971255824
Cited by
274
References
10
FWCI
13.57
Type
journal article
Language
en
Open access
closed

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CoChat. (2026). Citation check: Second-Order Rigidity and Prestress Stability for Tensegrity Frameworks. https://app.cochat.ai/papers/10.1137/s0895480192229236
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Connelly, R., & Whiteley, W. (1996). Second-Order Rigidity and Prestress Stability for Tensegrity Frameworks. SIAM Journal on Discrete Mathematics. https://doi.org/10.1137/s0895480192229236

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