Deployment of Cylindrical Tensegrity Booms
Publication: Journal of Structural Engineering
Volume 146, Issue 11
Abstract
In this paper, general methods for the analysis of deployment of cylindrical Class-1 and Class-2 tensegrity booms are developed. Investigation of the geometries of cylindrical Class-1 and Class-2 tensegrity booms leads to comprehensive procedures for the deployment of cylindrical tensegrity booms with an arbitrary number () of struts in each stage. For Class-1 tensegrity booms, equilibrium surfaces that show the collection of feasible azimuth and declination angle pairs corresponding to self-equilibrated geometries are obtained numerically. Deployment is achieved by varying the azimuth and declination angle parameters while remaining on this equilibrium surface. For Class-2 tensegrity booms, two deployment strategies, one with constant-length reinforcing cables and another with actively controlled reinforcing cables, are considered, and deployment is achieved by varying the length of certain cables. Deployment is studied in detail for tensegrity booms with four struts in each stage and the results are presented. The developed generalization procedures for analyzing the geometry and deployment of cylindrical tensegrity booms make it possible to address design concerns such as packaging efficiency, stiffness, and stiffness-to-mass ratio.
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Data Availability Statement
All data, models, and codes generated during this study are available from the corresponding author by request.
References
Connelly, R., and M. Terrell. 1995. “Globally rigid symmetric tensegrities.” Struct. Topol. 21: 59–79.
Dalilsafaei, S., A. Eriksson, and G. Tibert. 2012. “Improving bending stiffness of tensegrity booms.” Int. J. Space Struct. 27 (2–3): 117–129. https://doi.org/10.1260/0266-3511.27.2-3.117.
Estrada, G. G. 2007. “Analytical and numerical investigations of form-finding methods for tensegrity structures.” Ph.D. thesis, Dept. of Computer Science and Electrical Engineering, Univ. of Stuttgart.
Furuya, H. 1992. “Concept of deployable tensegrity structures in space application.” Int. J. Space Struct. 7 (2): 143–151. https://doi.org/10.1177/026635119200700207.
Furuya, H., S. Murata, M. Nakahara, D. Jodoi, Y. Terada, and K. Takadama. 2006. “Concept of inflatable tensegrity for large space structures.” In Proc., 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conf. 14th AIAA/ASME/AHS Adaptive Structures Conf. 7th. Reston, VA: American Institute of Aeronautics and Astronautics.
González, A., A. Luo, and D. Shi. 2019. “Reconfiguration method of tensegrity units using infinitesimal mechanisms.” Eng. Comput. 38 (6): 1934–1949. https://doi.org/10.1108/EC-09-2018-0430.
Guest, S. D. 2011. “The stiffness of tensegrity structures.” IMA J. Appl. Math. 76 (1): 57–66. https://doi.org/10.1093/imamat/hxq065.
Hanaor, A. 1993. “Double-layer tensegrity grids as deployable structures.” Int. J. Space Struct. 8 (1–2): 135–143. https://doi.org/10.1177/0266351193008001-214.
Kebiche, K., M. K. Aoual, and R. Motro. 2008. “Continuum models for systems in a selfstress state.” Int. J. Space Struct. 23 (2): 103–115. https://doi.org/10.1260/026635108785260588.
Kebiche, K., M. Kazi-Aoual, and R. Motro. 1999. “Geometrical non-linear analysis of tensegrity systems.” Eng. Struct. 21 (9): 864–876. https://doi.org/10.1016/S0141-0296(98)00014-5.
Liu, M., D. Cao, and D. Zhu. 2019. “Equivalent dynamic model of the space antenna truss with initial stress.” AIAA J. 58 (4): 1851–1863. https://doi.org/10.2514/1.J058647.
Masic, M., and R. Skelton. 2003. “Open-loop shape control of stable unit tensegrity structures.” In Proc., 3rd World Conf. on Structural Control, 439–447. Hoboken, NJ: Wiley.
Masic, M., R. E. Skelton, and P. E. Gill. 2006. “Optimization of tensegrity structures.” Int. J. Solids Struct. 43 (16): 4687–4703. https://doi.org/10.1016/j.ijsolstr.2005.07.046.
Micheletti, A. 2003. “The indeterminacy condition for tensegrity towers: A kinematic approach.” Revue française de génie civil 7 (3): 329–342. https://doi.org/10.1080/12795119.2003.9692498.
Micheletti, A., and W. Williams. 2007. “A marching procedure for form-finding for tensegrity structures.” J. Mech. Mater. Struct. 2 (5): 857–882. https://doi.org/10.2140/jomms.2007.2.857.
Motro, R. 2003. Tensegrity: Structural systems for the future. Amsterdam, Netherlands: Elsevier.
Murakami, H. 2001. “Static and dynamic analyses of tensegrity structures. Part II: Quasi-static analysis.” Int. J. Solids Struct. 38 (20): 3615–3629. https://doi.org/10.1016/S0020-7683(00)00233-X.
Murakami, H., and Y. Nishimura. 2001. “Initial shape finding and modal analyses of cyclic right-cylindrical tensegrity modules.” Comput. Struct. 79 (9): 891–917. https://doi.org/10.1016/S0045-7949(00)00196-6.
Nishimura, Y. 2000. “Static and dynamic analyses of tensegrity structures.” Ph.D. thesis, Dept. of Engineering Sciences, Univ. of California at San Diego.
Pinaud, J.-P., S. Solari, and R. E. Skelton. 2004. “Deployment of a class 2 tensegrity boom.” In Vol. 5390 of Proc., Smart Structures and Materials 2004: Smart Structures and Integrated Systems, 155–163. Bellingham, WA: International Society for Optics and Photonics.
Pugh, A. 1976. An introduction to tensegrity. Berkeley, CA: University of California Press.
Rhode-Barbarigos, L., N. B. H. Ali, R. Motro, and I. F. Smith. 2010. “Designing tensegrity modules for pedestrian bridges.” Eng. Struct. 32 (4): 1158–1167. https://doi.org/10.1016/j.engstruct.2009.12.042.
Rhode-Barbarigos, L., C. Schulin, N. B. H. Ali, R. Motro, and I. F. Smith. 2012. “Mechanism-based approach for the deployment of a tensegrity-ring module.” J. Struct. Eng. 138 (4): 539–548. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000491.
Russell, C., and G. Tibert. 2008. “Deployment simulations of inflatable tensegrity structures.” Int. J. Space Struct. 23 (2): 63–77. https://doi.org/10.1260/026635108785260597.
Skelton, R. E., and M. C. de Oliveira. 2009. Vol. 1 of Tensegrity systems. New York: Springer.
Sultan, C. 2014. “Tensegrity deployment using infinitesimal mechanisms.” Int. J. Solids Struct. 51 (21–22): 3653–3668. https://doi.org/10.1016/j.ijsolstr.2014.06.025.
Sultan, C., and R. Skelton. 2003. “Deployment of tensegrity structures.” Int. J. Solids Struct. 40 (18): 4637–4657. https://doi.org/10.1016/S0020-7683(03)00267-1.
Sultan, C., and R. T. Skelton. 1998. “Tendon control deployment of tensegrity structures.” In Vol. 3323 of Proc., Smart Structures and Materials 1998: Mathematics and Control in Smart Structures, 455–467. Bellingham, WA: International Society for Optics and Photonics.
Sychterz, A. C., and I. F. Smith. 2017. “Joint friction during deployment of a near-full-scale tensegrity footbridge.” J. Struct. Eng. 143 (9): 04017081. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001817.
Tibert, G., and S. Pellegrino. 2003. “Deployable tensegrity masts.” In Proc., 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conf. Reston, VA: American Institute of Aeronautics and Astronautics. https://arc.aiaa.org/doi/abs/10.2514/6.2003-1978.
Tran, H. C., and J. Lee. 2010. “Initial self-stress design of tensegrity grid structures.” Comput. Struct. 88 (9–10): 558–566. https://doi.org/10.1016/j.compstruc.2010.01.011.
Vu, K., J. R. Liew, and K. Anandasivam. 2006. “Deployable tension-strut structures: From concept to implementation.” J. Constr. Steel Res. 62 (3): 195–209. https://doi.org/10.1016/j.jcsr.2005.07.007.
Yıldız, K. 2018. “Cable actuated tensegrity structures for deployable space booms with enhanced stiffness.” Ph.D. thesis, Dept. of Aerospace Engineering, Pennsylvania State Univ.
Yıldız, K., and G. A. Lesieutre. 2019. “Effective beam stiffness properties of cylindrical tensegrity towers.” AIAA J. 57 (5): 2185–2194. https://doi.org/10.2514/1.J057774.
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Published In
Journal of Structural Engineering
Volume 146 • Issue 11 • November 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Sep 25, 2019
Accepted: May 27, 2020
Published online: Aug 24, 2020
Published in print: Nov 1, 2020
Discussion open until: Jan 24, 2021
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