Abstract
Most studies regarding models of tensegrity systems miss the possibility of large static deformations or provide elaborate and lengthy solutions to determine the system dynamics. Contrarily, this work presents a straightforward methodology to find the dynamic characteristics of a guyed tensegrity beam structure, allowing the application of vibration control strategies in conditions of large deformations. The methodology is based on a low-order, adaptive, nonlinear finite element model with pre-stressed components. The method is applied to numerical and experimental models of a class 2 tensegrity structure with a high length-to-width aspect ratio. Image processing and accelerometer data are combined to extract the experimental natural frequencies of the structure, which are compared to numerical results. Prony’s method is applied to estimate damping, and a numerical control strategy is employed using the dynamical model of the structure.
Issue Section:
Special Issue: Mechanisms, Transmissions, and Applications
References
1.
Fuller
, R. B.
, and Applewhite
, E. J.
, 1975
, Synergetics: Explorations in the Geometry of Thinking
, Macmillan
, Sebastopol, CA
.2.
Zhang
, J. Y.
, and Ohsaki
, M.
, 2015
, Tensegrity Structures—Form, Stability and Symmetry
, Springer
, New York
.3.
Motro
, R.
, 1992
, “Tensegrity Systems: The State of the Art
,” Int. J. Space Struct.
, 7
(2
), pp. 75
–83
. 4.
Estrada
, G. G.
, Bungartz
, H. -J.
, and Mohrdieck
, C.
, 2006
, “Numerical Form-Finding of Tensegrity Structures
,” Int. J. Solids Struct.
, 43
(22
), pp. 6855
–6868
. 5.
Kan
, Z.
, Peng
, H.
, Chen
, B.
, Xie
, X.
, and Sun
, L.
, 2019
, “Investigation of Strut Collision in Tensegrity Statics and Dynamics
,” Int. J. Solids Struct.
, 167
, pp. 202
–219
. 6.
Kan
, Z.
, Song
, N.
, Peng
, H.
, Chen
, B.
, and Song
, X.
, 2021
, “A Comprehensive Framework for Multibody System Analysis With Clustered Cables: Examples of Tensegrity Structures
,” Int. J. Solids Struct.
, 210
, pp. 289
–309
. 7.
Ashwear
, N.
, and Eriksson
, A.
, 2014
, “Natural Frequencies Describe the Pre-stress in Tensegrity Structures
,” Comput. Struct.
, 136
, pp. 162
–171
. 8.
Zhang
, J.
, and Ohsaki
, M.
, 2006
, “Adaptive Force Density Method for Form-Finding Problem of Tensegrity Structures
,” Int. J. Solids Struct.
, 43
(18
), pp. 5658
–5673
. 9.
Paul
, C.
, Valero-Cuevas
, F. J.
, and Lipson
, H.
, 2006
, “Design and Control of Tensegrity Robots for Locomotion
,” IEEE Trans. Rob.
, 22
(5
), pp. 944
–957
. 10.
Goyal
, R.
, Skelton
, R. E.
, and Peraza Hernandez
, E. A.
, 2020
, “Efficient Design of Lightweight Reinforced Tensegrities Under Local and Global Failure Constraints
,” ASME J. Appl. Mech.
, 87
(11
), p. 111005
. 11.
Ali
, N. B. H.
, and Smith
, I.
, 2010
, “Dynamic Behavior and Vibration Control of a Tensegrity Structure
,” Int. J. Solids Struct.
, 47
(9
), pp. 1285
–1296
.12.
Yang
, S.
, and Sultan
, C.
, 2019
, “Deployment of Foldable Tensegrity-Membrane Systems Via Transition Between Tensegrity Configurations and Tensegrity-Membrane Configurations
,” Int. J. Solids Struct.
, 160
, pp. 103
–119
. 13.
Zhu
, D.
, and Deng
, H.
, 2020
, “Deployment of Tensegrities Subjected to Load-Carrying Stiffness Constraints
,” Int. J. Solids Struct.
, 206
, pp. 224
–235
. 14.
Tibert
, A. G.
, and Pellegrino
, S.
, 2003
, “Deployable Tensegrity Masts
,” 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
, Norfolk, VA
, Apr. 7–10
, p. 1978
.15.
Sultan
, C.
, and Skelton
, R.
, 2003
, “Deployment of Tensegrity Structures
,” Int. J. Solids Struct.
, 40
(18
), pp. 4637
–4657
. 16.
Feng
, X.
, Miah
, M. S.
, and Ou
, Y.
, 2018
, “Dynamic Behavior and Vibration Mitigation of a Spatial Tensegrity Beam
,” Eng. Struct.
, 171
, pp. 1007
–1016
. 17.
Schorr
, P.
, Chavez
, J.
, Zentner
, L.
, and Böhm
, V.
, 2021
, “Reconfiguration of Planar Quadrilateral Linkages Utilizing the Tensegrity Principle
,” Mech. Mach. Theory
, 156
, p. 104172
. 18.
Begey
, J.
, Vedrines
, M.
, Andreff
, N.
, and Renaud
, P.
, 2020
, “Selection of Actuation Mode for Tensegrity Mechanisms: The Case Study of the Actuated Snelson Cross
,” Mech. Mach. Theory
, 152
, p. 103881
. 19.
Muralidharan
, V.
, and Wenger
, P.
, 2021
, “Optimal Design and Comparative Study of Two Antagonistically Actuated Tensegrity Joints
,” Mech. Mach. Theory
, 159
, p. 104249
. 20.
Chen
, L.-H.
, Kim
, K.
, Tang
, E.
, Li
, K.
, House
, R.
, Zhu
, E. L.
, Fountain
, K.
, Agogino
, A. M.
, Agogino
, A.
, and Sunspiral
, V.
, 2017
, “Soft Spherical Tensegrity Robot Design Using Rod-Centered Actuation and Control
,” ASME J. Mech. Rob.
, 9
(2
), p. 025001
. 21.
Fazli
, N.
, and Abedian
, A.
, 2011
, “Design of Tensegrity Structures for Supporting Deployable Mesh Antennas
,” Sci. Iranica
, 18
(5
), pp. 1078
–1087
. 22.
Scoccia
, C.
, Carbonari
, L.
, Palmieri
, G.
, Callegari
, M.
, Rossi
, M.
, Munafó
, P.
, Marchione
, F.
, and Chiappini
, G.
, 2022
, “Design of a Tensegrity Servo-actuated Structure for Civil Applications
,” ASME J. Mech. Des.
, 144
(4
), p. 043302
. 23.
Bansod
, Y. D.
, Matsumoto
, T.
, Nagayama
, K.
, and Bursa
, J.
, 2018
, “A Finite Element Bendo-tensegrity Model of Eukaryotic Cell
,” ASME J. Biomech. Eng.
, 140
(10
), p. 101001
. 24.
Raafat
, M.
, and Baz
, A.
, 2022
, “Damping and Bandgap Characteristics of a Viscoelastic Tensegrity Damper
,” ASME J. Vib. Acoust.
, 144
(1
), p. 011001
. 25.
Pham
, N. K.
, and Peraza Hernandez
, E. A.
, 2021
, “Modeling and Design Exploration of a Tensegrity-Based Twisting Wing
,” ASME J. Mech. Rob.
, 13
(3
), p. 031019
. 26.
Vasquez
, R. E.
, Crane III
, C. D.
, and Correa
, J. C.
, 2014
, “Analysis of a Planar Tensegrity Mechanism for Ocean Wave Energy Harvesting
,” ASME J. Mech. Rob.
, 6
(3
), p. 031015
. 27.
Dong
, W.
, Stafford
, P. J.
, and Ruiz-Teran
, A. M.
, 2019
, “Inverse Form-Finding for Tensegrity Structures
,” Comput. Struct.
, 215
, pp. 27
–42
. 28.
Yuan
, S.
, and Yang
, B.
, 2019
, “The Fixed Nodal Position Method for Form Finding of High-Precision Lightweight Truss Structures
,” Int. J. Solids Struct.
, 161
, pp. 82
–95
. 29.
Koohestani
, K.
, 2020
, “Innovative Numerical Form-Finding of Tensegrity Structures
,” Int. J. Solids Struct.
, 206
, pp. 304
–313
. 30.
Wang
, Y.
, and Senatore
, G.
, 2020
, “Extended Integrated Force Method for the Analysis of Prestress-Stable Statically and Kinematically Indeterminate Structures
,” Int. J. Solids Struct.
, 202
, pp. 798
–815
. 31.
Wang
, Y.
, Xu
, X.
, and Luo
, Y.
, 2020
, “Topology Design of General Tensegrity With Rigid Bodies
,” Int. J. Solids Struct.
, 202
, pp. 278
–298
. 32.
Su
, Y.
, Zhang
, J.
, Ohsaki
, M.
, and Wu
, Y.
, 2020
, “Topology Optimization and Shape Design Method for Large-Span Tensegrity Structures With Reciprocal Struts
,” Int. J. Solids Struct.
, 206
, pp. 9
–22
. 33.
Wang
, Y.
, Xu
, X.
, and Luo
, Y.
, 2021
, “A Unifying Framework for Form-Finding and Topology-Finding of Tensegrity Structures
,” Comput. Struct.
, 247
, p. 106486
. 34.
Fernández-Ruiz
, M. A.
, Hernández-Montes
, E.
, Carbonell-Márquez
, J. F.
, and Gil-Martín
, L. M.
, 2019
, “Octahedron Family: The Double-Expanded Octahedron Tensegrity
,” Int. J. Solids Struct.
, 165
, pp. 1
–13
. 35.
Fernández-Ruiz
, M. A.
, Hernandez-Montes
, E.
, and Gil-Martin
, L. M.
, 2021
, “The Octahedron Family as a Source of Tensegrity Families: The X-Octahedron Family
,” Int. J. Solids Struct.
, 208–209
, pp. 1
–12
. 36.
Liu
, S.
, Li
, Q.
, Wang
, P.
, and Guo
, F.
, 2020
, “Kinematic and Static Analysis of a Novel Tensegrity Robot
,” Mech. Mach. Theory
, 149
, p. 103788
. 37.
Zhu
, D.
, Deng
, H.
, and Wu
, X.
, 2020
, “Selecting Active Members to Drive the Mechanism Displacement of Tensegrities
,” Int. J. Solids Struct.
, 191–192
, pp. 278
–292
. 38.
Kebiche
, K.
, Kazi-Aoual
, M.
, and Motro
, R.
, 1999
, “Geometrical Non-linear Analysis of Tensegrity Systems
,” Eng. Struct.
, 21
(9
), pp. 864
–876
. 39.
Kan
, Z.
, Peng
, H.
, and Chen
, B.
, 2018
, “Complementarity Framework for Nonlinear Analysis of Tensegrity Structures With Slack Cables
,” AIAA J.
, 56
(12
), pp. 5013
–5027
. 40.
Shi
, C.
, Guo
, H.
, Cheng
, Y.
, Liu
, R.
, and Deng
, Z.
, 2020
, “Design and Multi-objective Comprehensive Optimization of Cable-Strut Tensioned Antenna Mechanism
,” Acta Astronaut.
, 1
(178
), pp. 406
–422
.41.
Tran
, H. C.
, and Lee
, J.
, 2011
, “Geometric and Material Nonlinear Analysis of Tensegrity Structures
,” Acta Mech. Sin.
, 27
(6
), pp. 938
–949
. 42.
Zhang
, L.-Y.
, Li
, Y.
, Cao
, Y.-P.
, Feng
, X.-Q.
, and Gao
, H.
, 2013
, “A Numerical Method for Simulating Nonlinear Mechanical Responses of Tensegrity Structures Under Large Deformations
,” J. Appl. Mech.
, 80
(6
), p. 061018
. 43.
Furet
, M.
, and Wenger
, P.
, 2019
, “Kinetostatic Analysis and Actuation Strategy of a Planar Tensegrity 2-X Manipulator
,” J. Mech. Rob.
, 11
(6
), p. 060904
. 44.
Kurka
, P.
, Izuka
, J.
, Gonzalez
, P.
, Burdick
, J.
, and Elfes
, A.
, 2014
, “Vibration of a Long, Tip Pulled Deflected Beam
,” AIAA J.
, 52
(7
), pp. 1559
–1563
. 45.
Kurka
, P.
, Izuka
, J.
, Gonzalez
, P.
, and Teixeira
, L.
, 2016
, “Large Deflections and Vibrations of a Tip Pulled Beam With Variable Transversal Section
,” Mech. Syst. Signal Process.
, 79
, pp. 271
–288
. 46.
Ramos
, P.
, Izuka
, J.
, and Kurka
, P.
, 2016
, “Experimental Robust Control of Vibration of a Long Elastic Guyed Beam Arm With Large Deformation and Variable Transversal Section
,” Proceedings of ISMA2016 Including USD2016
, Leuven, Belgium
, Sept. 19–21
, pp. 155
–170
.47.
Lai
, G.
, Plummer
, A.
, and Cleaver
, D.
, 2020
, “Distributed Actuation and Control of a Morphing Tensegrity Structure
,” ASME J. Dyn. Syst. Meas. Control
, 142
(7
), p. 071006
. 48.
Skelton
, R. E.
, and de Oliveira
, M.
, 2009
, Tensegrity Systems
, Springer US
, New York
, pp. 45
–72
.49.
Nelson
, C. A.
, 2015
, “A Software Tool for Analyzing Motions and Loading in Spatial Tensegrity Structures
,” International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Boston, MA
, Aug. 2–5
.50.
Crisfield
, M. A.
, 1991
, Non-linear Finite Element Analysis of Solids and Structures
, John Wiley & Sons
, Chichester, UK
.51.
Bathe
, K. J.
, and Cimento
, A. P.
, 1980
, “Some Practical Procedures for the Solution of Nonlinear Finite Element Equations
,” Comput. Methods Appl. Mech. Eng.
, 22
(1
), pp. 59
–85
. 52.
Boehler
, Q.
, Charpentier
, I.
, Vedrines
, M. S.
, and Renaud
, P.
, 2015
, “Definition and Computation of Tensegrity Mechanism Workspace
,” ASME J. Mech. Rob.
, 7
(4
), p. 044502
. 53.
Sultan
, C.
, 2009
, “Designing Structures for Dynamical Properties Via Natural Frequencies Separation: Application to Tensegrity Structures Design
,” Mech. Syst. Signal Process.
, 23
(4
), pp. 1112
–1122
. 54.
Sultan
, C.
, 2010
, “Proportional Damping Approximation Using the Energy Gain and Simultaneous Perturbation Stochastic Approximation
,” Mech. Syst. Signal Process.
, 24
(7
), pp. 2210
–2224
. 55.
Kurka
, P. R. G.
, 2015
, Vibrações de sistemas dinâmicos – anâlise e síntese
, LTC
, Barueri
.56.
Holland
, D. B.
, Virgin
, L. N.
, and Plaut
, R. H.
, 2008
, “Large Deflections and Vibration of a Tapered Cantilever Pulled at Its Tip by a Cable
,” J. Sound Vib.
, 310
(1–2
), pp. 433
–441
. 57.
Zhao
, W.
, Pashkevich
, A.
, Klimchik
, A.
, and Chablat
, D.
, 2022
, “Elastostatic Modeling of Multi-link Flexible Manipulator Based on Two-Dimensional Dual-Triangle Tensegrity Mechanism
,” ASME J. Mech. Rob.
, 14
(2
), p. 021002
. 58.
Arsenault
, M.
, 2011
, “Stiffness Analysis of a 2DOF Planar Tensegrity Mechanism
,” ASME J. Mech. Rob.
, 3
(2
), p. 021011
. Copyright © 2024 by ASME
You do not currently have access to this content.
