Skip to main content
Search
Search
Quick Search anywhere
Quick Search fdjslkfh
Advanced search
Cart
Join AIAA Institution Login
Skip main navigation
AIAA Journal logo
Skip to article control options
No AccessFull-Length Paper

Double-Helix Tensegrity Structures

Published Online:12 Aug 2014https://doi.org/10.2514/1.J053264

Abstract

This paper describes a class of tensegrity systems that are formed from a common type of connectivity, having a double-helix configuration. Structures made from such internal patterns will be called a double-helix tensegrity. This paper derives the connectivity matrix for the double-helix tensegrity class of structures. This generalized common mathematical formulation will allow efficient computations for a large class of tensegrity systems, which can have many different configurations, albeit employing the same rules for connecting components. Special cases of these configurations include torus, cylinders, paraboloids, spheres, ellipsoids, and other configurations.

References

  • [1] Fuller R. B., “Tensile-Integrity Structures,” U.S. Patent 3,063,521, 1962. Google Scholar

  • [2] Sadao S., “Fuller on Tensegrity,” International Journal of Space Structures, Vol. 11, Nos. 1–2, 1996, pp. 37–42. ISSTER Google Scholar

  • [3] Miura K. and Miyazaki Y., “Concept of the Tension Truss Antenna,” AIAA Journal, Vol. 28, No. 6, 1990, pp. 1098–1104. doi:https://doi.org/10.2514/3.25172 AIAJAH 0001-1452 LinkGoogle Scholar

  • [4] Schmit L. A., “Structural Synthesis—Its Genesis and Development,” AIAA Journal, Vol. 19, No. 10, 1981, pp. 1249–1263. doi:https://doi.org/10.2514/3.7859 AIAJAH 0001-1452 LinkGoogle Scholar

  • [5] You Z. and Pellegrino S., “Cable-Stiffened Pantographic Deployable Structures Part 1: Triangular Mast,” AIAA Journal, Vol. 34, No. 4, 1996, pp. 813–820. doi:https://doi.org/10.2514/3.13144 AIAJAH 0001-1452 LinkGoogle Scholar

  • [6] Sultan C. and Skelton R. E., “Deployment of Tensegrity Structures,” International Journal of Solids and Structures, Vol. 40, No. 18, 2003, pp. 4637–4657. doi:https://doi.org/10.1016/S0020-7683(03)00267-1 IJSOAD 0020-7683 CrossrefGoogle Scholar

  • [7] Pellegrino S. (ed.), Deployable Structures, Springer-Verlag, Wien, Austria, 2001, pp. 1–35, 179–238. CrossrefGoogle Scholar

  • [8] Puig L., Barton A. and Rando N., “A Review on Large Deployable Structures for Astrophysics Missions,” Acta Astronautica, Vol. 67, Nos. 1–2, 2010, pp. 12–26. AASTCF 0094-5765 CrossrefGoogle Scholar

  • [9] Aldrich J. B., “Control Synthesis for a Class of Light and Agile Robotic Tensegrity Structures,” Ph.D. Thesis, Dept. of Mechanical and Aerospace Engineering, Univ. of California, San Diego, San Diego, CA, 2004. Google Scholar

  • [10] Paul C., Valero-Cuevas F. J. and Lipson H., “Design and Control of Tensegrity Robots for Locomotion,” IEEE Transactions on Robotics, Vol. 22, No. 5, Oct. 2006, pp. 944–957. doi:https://doi.org/10.1109/TRO.2006.878980 IRAUEZ 1042-296X CrossrefGoogle Scholar

  • [11] Masic M. and Skelton R. E., “Open-Loop Control of Class-2 Tensegrity Towers,” Proceedings of the SPIE Smart Structures and Materials: Modeling, Signal Processing, and Control, edited by Smith R. C., Vol. 5383, SPIE, Bellingham, Washington, March 2004, pp. 298–308. Google Scholar

  • [12] Fraternali F., Senatore L. and Daraio C., “Solitary Waves on Tensegrity Lattices,” Journal of the Mechanics and Physics of Solids, Vol. 60, No. 6, 2012, pp. 1137–1144. doi:https://doi.org/10.1016/j.jmps.2012.02.007 JMPSA8 0022-5096 CrossrefGoogle Scholar

  • [13] Ingber D. E., “The Architecture of Life,” Scientific American, Vol. 278, Jan. 1998, pp. 48–57. doi:https://doi.org/10.1038/scientificamerican0198-48 SCAMAC 0036-8733 CrossrefGoogle Scholar

  • [14] Vera C., Skelton R. E., Bossens F. and Sung L. A., “3-D Nanomechanics of an Erythrocyte Junctional Complex in Equibiaxial and Anisotropic Deformations,” Annals of Biomedical Engineering, Vol. 33, No. 10, 2005, pp. 1387–1404. doi:https://doi.org/10.1007/s10439-005-4698-y ABMECF 0090-6964 CrossrefGoogle Scholar

  • [15] Hanaor A., “Prestressed Pin-Jointed Structures—Flexibility Analysis and Prestress Design,” Computers & Structures, Vol. 28, No. 6, 1988, pp. 757–769. CrossrefGoogle Scholar

  • [16] Pellegrino S., “Analysis of Prestressed Mechanisms,” International Journal of Solids and Structures, Vol. 26, No. 12, 1990, pp. 1329–1350. doi:https://doi.org/10.1016/0020-7683(90)90082-7 IJSOAD 0020-7683 CrossrefGoogle Scholar

  • [17] Williamson D., Skelton R. E. and Han J., “Equilibrium Conditions of a Tensegrity Structure,” International Journal of Solids and Structures, Vol. 40, No. 23, 2003, pp. 6347–6367. doi:https://doi.org/10.1016/S0020-7683(03)00400-1 IJSOAD 0020-7683 CrossrefGoogle Scholar

  • [18] de Jager B. and Skelton R. E., “Stiffness of Planar Tensegrity Truss Topologies,” International Journal of Solids and Structures, Vol. 43, No. 5, 2006, pp. 1308–1330. doi:https://doi.org/10.1016/j.ijsolstr.2005.06.049 IJSOAD 0020-7683 CrossrefGoogle Scholar

  • [19] Guest S., “The Stiffness of Prestressed Frameworks: A Unifying Approach,” International Journal of Solids and Structures, Vol. 43, Nos. 3–4, 2006, pp. 842–854.doi:https://doi.org/10.1016/j.ijsolstr.2005.03.008 IJSOAD 0020-7683 CrossrefGoogle Scholar

  • [20] Zhang J. Y. and Ohsaki M., “Stability Conditions for Tensegrity Structures,” International Journal of Solids and Structures, Vol. 44, Nos. 11–12, 2007, pp. 3875–3886. doi:https://doi.org/10.1016/j.ijsolstr.2006.10.027 IJSOAD 0020-7683 CrossrefGoogle Scholar

  • [21] Motro R., “Forms and Forces in Tensegrity Systems,” Proceedings of the Third International Conference on Space Structures, Elsevier, Amsterdam, 1984, pp. 180–185. Google Scholar

  • [22] Pellegrino S., “Mechanics of Kinematically Indeterminate Structures,” Ph.D. Thesis, Univ. of Cambridge, Cambridge, England, U.K., 1986. Google Scholar

  • [23] Vassart N. and Motro R., “Multiparametered Formfinding Method: Application to Tensegrity Systems,” International Journal of Space Structures, Vol. 14, No. 2, 1999, pp. 147–154. doi:https://doi.org/10.1260/0266351991494768 ISSTER CrossrefGoogle Scholar

  • [24] Masic M., Skelton R. E. and Gill P. E., “Algebraic Tensegrity Form-Finding,” International Journal of Solids and Structures, Vol. 42, Nos. 16–17, Aug. 2005, pp. 4833–4858. doi:https://doi.org/10.1016/j.ijsolstr.2005.01.014 IJSOAD 0020-7683 CrossrefGoogle Scholar

  • [25] Tran H. C. and Lee J., “Advanced Form-Finding of Tensegrity Structures,” Computers & Structures, Vol. 88, Nos. 3–4, 2010, pp. 237–246. CrossrefGoogle Scholar

  • [26] Motro R., Najari S. and Jouanna P., “Static and Dynamic Analysis of Tensegrity Systems,” Shell and Spatial Structures: Computational Aspects, Vol. 26, Springer-Verlag Berlin, Heidelberg, Germany, 1987, pp. 270–279. CrossrefGoogle Scholar

  • [27] Murakami H., “Static and Dynamic Analyses of Tensegrity Structures, Part 1. Nonlinear Equations of Motion,” International Journal of Solids and Structures, Vol. 38, No. 20, 2001, pp. 3599–3613. IJSOAD 0020-7683 CrossrefGoogle Scholar

  • [28] Kanchanasaratool N. and Williamson D., “Modelling and Control of Class NSP Tensegrity Structures,” International Journal of Control, Vol. 75, No. 2, 2002, pp. 123–139. doi:https://doi.org/10.1080/00207170110070563 IJCOAZ 0020-7179 CrossrefGoogle Scholar

  • [29] Sultan C., Corless M. and Skelton R. E., “Linear Dynamics of Tensegrity Structures,” Engineering Structures, Vol. 24, No. 6, 2002, pp. 671–685. doi:https://doi.org/10.1016/S0141-0296(01)00130-4 ENSTDF 0141-0296 CrossrefGoogle Scholar

  • [30] Skelton R., “Dynamics and Control of Tensegrity Systems,” IUTAM Symposium on Vibration Control of Nonlinear Mechanisms and Structures: Solid Mechanics and Its Applications, Vol. 130, Springer Academic Publishers, Dordrecht, The Netherlands, 2005, pp. 309–318. Google Scholar

  • [31] Motro R., Tensegrity: Structural Systems for the Future, Kogan Page Science, London, 2003, pp. 1–32. CrossrefGoogle Scholar

  • [32] Skelton R. E. and de Oliveira M. C., Tensegrity Systems, Springer, New York, 2009, pp. 1–72, 157–178. Google Scholar

  • [33] Tibert A. G. and Pellegrino S., “Review of Form-Finding Methods for Tensegrity Structures,” International Journal of Space Structures, Vol. 18, No. 4, 2003, pp. 209–223. ISSTER CrossrefGoogle Scholar

  • [34] Juan S. H. and Mirats-Tur J. M., “Tensegrity Frameworks: Static Analysis Review,” Mechanism and Machine Theory, Vol. 43, No. 7, 2008, pp. 859–881. doi:https://doi.org/10.1016/j.mechmachtheory.2007.06.010 MHMTAS 0094-114X CrossrefGoogle Scholar

  • [35] Mirats-Tur J. M. and Juan S. H., “Tensegrity Frameworks: Dynamic Analysis Review and Open Problems,” Mechanism and Machine Theory, Vol. 44, No. 1, 2009, pp. 1–18. doi:https://doi.org/10.1016/j.mechmachtheory.2008.06.008 MHMTAS 0094-114X CrossrefGoogle Scholar

  • [36] Yoshimura Y., “On the Mechanism of Buckling of a Circular Cylindrical Shell Under Axial Compression,” NACA TM-1390, 1955. Google Scholar

  • [37] Hoff N. J., Madsen W. A. and Mayers J., “Postbuckling Equilibrium of Axially Compressed Circular Cylindrical Shells,” AIAA Journal, Vol. 4, No. 1, 1966, pp. 126–133. doi:https://doi.org/10.2514/3.3395 AIAJAH 0001-1452 LinkGoogle Scholar

  • [38] Miura K. and Furuya H., “Adaptive Structure Concept for Future Space Applications,” AIAA Journal, Vol. 26, No. 8, 1988, pp. 995–1002. doi:https://doi.org/10.2514/3.10002 AIAJAH 0001-1452 LinkGoogle Scholar

  • [39] Schek H. J., “The Force Density Method for Form Finding and Computation of General Networks,” Computer Methods in Applied Mechanics and Engineering, Vol. 3, No. 1, 1974, pp. 115–134. doi:https://doi.org/10.1016/0045-7825(74)90045-0 CMMECC 0045-7825 CrossrefGoogle Scholar

  • [40] Masic M., Skelton R. E. and Gill P. E., “Optimization of Tensegrity Structures,” International Journal of Solids and Structures, Vol. 43, No. 16, Aug. 2006, pp. 4687–4703. doi:https://doi.org/10.1016/j.ijsolstr.2005.07.046 IJSOAD 0020-7683 CrossrefGoogle Scholar

  • [41] Nagase K. and Skelton R. E., “Minimal Mass Tensegrity Structures,” Journal of the International Association for Shell and Spatial Structures, Vol. 55, No. 1, 2014, pp. 37–48. Google Scholar

Previous article
Next article