Tensegrity systems have been used in several disciplines such as architecture, biology, aerospace, mechanics, and robotics during the last 50 years. However, just a few references in literature have stated the possibility of using such systems in ocean or energy-related applications. This work addresses the kinematic and dynamic analyses of a planar tensegrity mechanism for ocean wave energy harvesting. Ocean wave mechanics and the most important concepts related to fluid–structure interaction are presented. Then, a planar 3 degrees of freedom (3-dof) tensegrity mechanism, based on a morphology defined by Kenneth Snelson in 1960 which is known as “X-frame,” is proposed as connecting linkage to transmit wave-generated forces. A geometric approach is used to solve the forward and reverse displacement problems. The theory of screws is used to perform the forward and reverse velocity analyses of the device. The Lagrangian approach is used to deduce the equations of motion considering the interaction between the mechanism and ocean waves. The tensegrity-based mechanism is analyzed using a linear model of ocean waves and its energy harvesting capabilities are compared to a purely heaving device. Results show that the proposed tensegrity configuration allows to harvest 10% more energy than the traditional heaving mechanism used in several wave energy harvesting applications. Therefore, tensegrity systems could play an important role in the expansion of clean energy technologies that help the world's sustainable development.

References

References
1.
Redondo-Gil
,
C.
,
Esquibel
,
L.
,
Alonso Sanchez
,
A.
, and
Zapico
,
P.
,
2009
, “
European Strategic Energy Technology Plan
,”
International Conference on Renewable Energy and Power Quality (ICREPQ'09), Valencia, Spain, April 15–17.
2.
Scruggs
,
J.
, and
Jacob
,
P.
,
2009
, “
Engineering: Harvesting Ocean Wave Energy
,”
Science
,
323
(
5918
), pp.
1176
1178
.10.1126/science.1168245
3.
AEA Energy & Environment,
2006
, “
Review and Analysis of Ocean Energy Systems, Development and Supporting Policies
,” Sustainable Energy Ireland for the IEA's Implementing Agreement on Ocean Energy Systems, Dublin, Ireland.
4.
Cornett
,
A.
, and
Tabotton
,
M.
,
2006
, “
Inventory of Canadian Marine Renewable Energy Resources
,” Canadian Hydraulics Centre, National Research Council Canada and Triton Consultants Ltd., Ottawa, Canada, Technical Report No. CHC-TR-041.
5.
Bedard
,
R.
,
Previsic
,
M.
,
Hagerman
,
G.
,
Polagye
,
B.
,
Musial
,
W.
,
Klure
,
J.
,
von Jouanne
,
A.
,
Mathur
,
U.
,
Partin
,
J.
,
Collar
,
C.
,
Hopper
,
C.
, and
Amsden
,
S.
,
2007
, “North American Ocean Energy Status—March 2007,” 7th European Wave and Tidal Energy Conference (EWTEC), Porto, Portugal, September 11–13.
6.
Khan
,
J.
, and
Bhuyan
,
G.
,
2009
, “
Ocean Energy: Global Technology Development Status
,” Ocean Energy Systems Implementing Agreement, International Energy Agency (IEA-OES), Paris, Technical Report No. T0104.
7.
Pontes
,
M.
,
Aguiar
,
R.
, and
Oliveira Pires
,
H.
,
2005
, “
A Nearshore Wave Energy Atlas for Portugal
,”
ASME J. Offshore Mech. Arct. Eng.
,
127
(
3
), pp.
249
255
.10.1115/1.1951779
8.
Henfridsson
,
U.
,
Neimane
,
V.
,
Strand
,
K.
,
Kapper
,
R.
,
Bernhoff
,
H.
,
Danielsson
,
O.
,
Leijon
,
M.
,
Sundberg
,
J.
,
Thorburn
,
K.
,
Ericsson
,
E.
, and
Bergman
,
K.
,
2007
, “
Wave Energy Potential in the Baltic Sea and the Danish Part of the North Sea, With Reflections on the Skagerrak
,”
Renewable Energy
,
32
(
12
), pp.
2069
2084
.10.1016/j.renene.2006.10.006
9.
Defne
,
Z.
,
Haas
,
K.
, and
Fritz
,
H.
,
2009
, “
Wave Power Potential Along the Atlantic Coast of the Southeastern USA
,”
Renewable Energy
,
34
(
10
), pp.
2197
2205
.10.1016/j.renene.2009.02.019
10.
Florez
,
D. A.
,
Correa
,
J. C.
,
Posada
,
N. L.
,
Valencia
,
R. A.
, and
Zuluaga
,
C. A.
,
2010
, “
Marine Energy Devices for Colombian Seas
,”
ASME
Paper No. IMECE2010-38546.10.1115/IMECE2010-38546
11.
Iglesias
,
G.
, and
Carballo
,
R.
,
2010
, “
Wave Energy Resource in the Estaca de Bares Area (Spain)
,”
Renewable Energy
,
35
(
7
), pp.
1574
1584
.10.1016/j.renene.2009.10.019
12.
Ortega
,
S.
,
Osorio
,
A. F.
, and
Agudelo
,
P.
,
2013
, “
Estimation of the Wave Power Resource in the Caribbean Sea in Areas With Scarce Instrumentation. Case Study: Isla Fuerte, Colombia
,”
Renewable Energy
,
57
, pp.
240
248
.10.1016/j.renene.2012.11.038
13.
Falcão
,
A.
,
2010
, “
Wave Energy Utilization: A Review of the Technologies
,”
Renewable Sustainable Energy Rev.
,
14
(
3
), pp.
899
918
.10.1016/j.rser.2009.11.003
14.
U.S. Department of Energy, “
Marine and Hydrokinetic Technology Database
,” http://en.openei.org/wiki/Marine_and_Hydrokinetic_Technology_Database
15.
Falnes
,
J.
,
2007
, “
A Review of Wave-Energy Extraction
,”
Mar. Struct.
,
20
(
4
), pp.
185
201
.10.1016/j.marstruc.2007.09.001
16.
Budal
,
K.
, and
Falnes
,
J.
,
1975
, “
A Resonant Point Absorber of Ocean-Wave Power
,”
Nature
,
256
(5517), pp.
478
479
.10.1038/256478a0
17.
Mei
,
C.
,
1976
, “
Power Extraction From Water Waves
,”
J. Ship Res.
,
20
(2), pp.
63
66
.
18.
Evans
,
D.
,
1976
, “
A Theory for Wave-Power Absorption by Oscillating Bodies
,”
J. Fluid Mech.
,
77
(
01
), pp.
1
25
.10.1017/S0022112076001109
19.
Newman
,
J.
,
1979
, “
Absorption of Wave Energy by Elongated Bodies
,”
Appl. Ocean Res.
,
1
(
4
), pp.
189
196
.10.1016/0141-1187(79)90026-9
20.
Baker
,
N. J.
, and
Mueller
,
M. A.
,
2001
, “
Direct Drive Wave Energy Converters
,”
Rev. Energ. Ren.: Power Engineering
, pp.
1
7
.
21.
Mueller
,
M.
,
2002
, “
Electrical Generators for Direct Drive Wave Energy Converters
,”
IEEE Proc.
,
149
(
4
), pp.
446
456
.10.1049/ip-gtd:20020394
22.
Leijon
,
M.
,
Danielsson
,
O.
,
Eriksson
,
M.
,
Thorburn
,
K.
,
Bernhoff
,
H.
,
Isberg
,
J.
,
Sundberg
,
J.
,
Ivanova
, I
.
,
Sjöstedt
,
E.
,
Agren
,
O.
,
Karlsson
,
K.
, and
Wolfbrandt
,
A.
,
2006
, “
An Electrical Approach to Wave Energy Conversion
,”
Renewable Energy
,
31
(
9
), pp.
1309
1319
.10.1016/j.renene.2005.07.009
23.
Rhinefrank
,
K.
,
Agamloh
,
E.
,
von Jouanne
,
A.
,
Wallace
,
A.
,
Prudell
,
J.
,
Kimble
,
K.
,
Aills
,
J.
,
Schmidt
,
E.
,
Chan
,
P.
,
Sweeny
,
B.
, and
Schacher
,
A.
,
2006
, “
Novel Ocean Energy Permanent Magnet Linear Generator Buoy
,”
Renewable Energy
,
31
(
9
), pp.
1279
1298
.10.1016/j.renene.2005.07.005
24.
Trapanese
,
M.
,
2008
, “
Optimization of a Sea Wave Energy Harvesting Electromagnetic Device
,”
IEEE Trans. Magn.
,
44
(
11
), pp.
4365
4368
.10.1109/TMAG.2008.2002192
25.
Füller
,
R.
,
1962
, “
Tensile-Integrity Structures
,” U.S. Patent No. 3,063,521, November 13.
26.
Emmerich
,
D.
,
1964
, “Construction de Réseaux Autotendants, French Patent No. 1,377,290, September 28.
27.
Snelson
,
K.
,
1965
, “
Continuous Tension, Discontinuous Compression Structures
,” U.S. Patent No. 3,169,611, February 16.
28.
Motro
,
R.
,
1992
, “
Tensegrity Systems: The State of the Art
,”
Int. J. Space Struct.
,
7
(
2
), pp.
75
83
.
29.
Skelton
,
R.
, and
de Oliveira
,
M. C.
,
2009
,
Tensegrity Systems
,
Springer
, New York.
30.
Motro
,
R.
,
2003
,
Tensegrity: Structural Systems for the Future
,
Kogan Page Science
,
Guildford, UK
.
31.
Rhode-Barbarigos
,
L.
,
Bel Hadj Ali
,
N.
,
Motro
,
R.
, and
Smith
,
I. F.
,
2010
, “
Designing Tensegrity Modules for Pedestrian Bridges
,”
Eng. Struct.
,
32
(
4
), pp.
1158
1167
.10.1016/j.engstruct.2009.12.042
32.
Duffy
,
J.
,
Rooney
,
J.
,
Knight
,
B.
, and
Crane
,
C. D.
, III
,
2000
, “
A Review of a Family of Self-Deploying Tensegrity Structures With Elastic Ties
,”
Shock Vib. Dig.
,
32
(
2
), pp.
100
106
.10.1177/058310240003200202
33.
Tibert
,
G.
,
2002
, “
Deployable Tensegrity Structures for Space Applications
,” Ph.D. thesis, Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden.
34.
Sultan
,
C.
, and
Skelton
,
R.
,
2003
, “
Deployment of Tensegrity Structures
,”
Int. J. Solids Struct.
,
40
(
18
), pp.
4637
4657
.10.1016/S0020-7683(03)00267-1
35.
Ingber
,
D. E.
,
1998
, “
The Architecture of Life
,”
Sci. Am.
,
278
(1), pp.
48
57
.10.1038/scientificamerican0198-48
36.
Cretu
,
S.
,
2009
, “
Tensegrity as a Structural Framework in Life Sciences and Bioengineering
,”
Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems
,
Springer
, Houten,
Netherlands
, pp.
301
311
.
37.
Sultan
,
C.
,
Corless
,
M.
, and
Skelton
,
R.
,
2000
, “
Tensegrity Flight Simulator
,”
J. Guid. Control Dyn.
,
23
(
6
), pp.
1055
1064
.10.2514/2.4647
38.
Sultan
,
C.
, and
Skelton
,
R.
,
2004
, “
A Force and Torque Tensegrity Sensor
,”
Sens. Actuators, A
,
112
(
2–3
), pp.
220
231
.10.1016/j.sna.2004.01.039
39.
Arsenault
,
M.
, and
Gosselin
,
C.
,
2005
, “
Kinematic, Static, and Dynamic Analysis of a Planar One-Degree-of-Freedom Tensegrity Mechanism
,”
ASME J. Mech. Des.
,
127
(
6
), pp.
1152
1160
.10.1115/1.1913705
40.
Arsenault
,
M.
, and
Gosselin
,
C.
,
2006
, “
Kinematic, Static, and Dynamic Analysis of a Spatial Three-Degree-of-Freedom Tensegrity Mechanism
,”
ASME J. Mech. Des.
,
128
(
5
), pp.
1061
1069
.10.1115/1.2218881
41.
Arsenault
,
M.
, and
Gosselin
,
C.
,
2006
, “
Kinematic, Static and Dynamic Analysis of a Planar 2-DOF Tensegrity Mechanism
,”
Mech. Mach. Theory
,
41
(
9
), pp.
1072
1089
.10.1016/j.mechmachtheory.2005.10.014
42.
Vasquez
,
R.
, and
Correa
,
J.
,
2007
, “
Kinematics, Dynamics and Control of a Planar 3-DOF Tensegrity Robot Manipulator
,”
ASME
Paper No. DETC2007-34975.10.1115/DETC2007-34975
43.
Sunny
,
M. R.
,
Sultan
,
C.
, and
Kapania
,
R. K.
,
2013
, “
Optimal Energy Harvesting From a Membrane Attached to a Tensegrity Structure
,” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Boston, MA, April 8–11,
AIAA
Paper No. 2013-1607.10.2514/6.2013-1607
44.
McCarthy
,
J. M.
,
2011
, “
21st Century Kinematics: Synthesis, Compliance, and Tensegrity
,”
ASME J. Mech. Rob.
,
3
(
2
), p.
020201
.10.1115/1.4003181
45.
Scruggs
,
J.
, and
Skelton
,
R.
,
2006
, “
Regenerative Tensegrity Structures for Energy Harvesting Applications
,”
45th IEEE Conference on Decision & Control
, San Diego, CA, December 13–15, pp.
2282
2287
.10.1109/CDC.2006.377503
46.
Jensen
,
O.
,
Wroldsen
,
A.
,
Lader
,
P.
,
Fredheim
,
A.
, and
Heide
,
M.
,
2007
, “
Finite Element Analysis of Tensegrity Structures in Offshore Aquaculture Installations
,”
Aquacult. Eng.
,
36
(
3
), pp.
272
284
.10.1016/j.aquaeng.2007.01.001
47.
Wroldsen
,
A. S.
,
Rustad
,
A. M.
,
Perez
,
T.
,
Sørensen
,
A. J.
,
Johansen
,
V.
,
Lader
,
P. F.
,
Fredheim
,
A.
, and
Heide
,
M. A.
,
2006
, “
Tensegrity Marine Structure
,” U.S. Patent No. 2006/102088 A1, May 18.
48.
Craik
,
A. D.
,
2004
, “
The Origins of Water Wave Theory
,”
Annu. Rev. Fluid Mech.
,
36
(
1
), pp.
1
28
.10.1146/annurev.fluid.36.050802.122118
49.
McCormick
,
M.
,
2009
,
Ocean Engineering Mechanics With Applications
,
Cambridge University Press
, New York.
50.
Falnes
,
J.
,
2002
,
Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction
,
Cambridge University Press
, New York.
51.
Kristiansen
,
E.
, and
Egeland
,
O.
,
2003
, “
Frequency Dependent Added Mass in Models for Controller Design for Wave Motion Ship Damping
,”
6th IFAC Conference on Manoeuvring and Control of Marine Craft (MCMC'03)
, Girona, Spain, September 17–19.
52.
Taghipour
,
R.
,
Perez
,
T.
, and
Moan
,
T.
,
2008
, “
Hybrid Frequency–Time Domain Models for Dynamic Response Analysis of Marine Structures
,”
Ocean Eng.
,
35
(
7
), pp.
685
705
.10.1016/j.oceaneng.2007.11.002
53.
McCormick
,
M.
,
2007
,
Ocean Wave Energy Conversion
,
Dover Publications
, Mineola, NY.
54.
Vasquez
,
R. E.
,
2011
, “
Analysis of a Tensegrity System for Ocean Wave Energy Harvesting
,” Ph.D. thesis, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL.
55.
Salter
,
S.
,
Taylor
,
J.
, and
Caldwell
,
N.
,
2002
, “
Power Conversion Mechanisms for Wave Energy
,”
Proc. Inst. Mech. Eng., Part M
,
216
(
1
), pp.
1
27
.10.1243/09576500260251129
56.
Vasquez
,
R.
,
Crane
,
C. D.
, III
, and
Correa
,
J. C.
,
2012
, “
Kinematic Analysis of a Planar Tensegrity Mechanism for Wave Energy Harvesting
,”
Latest Advances in Robot Kinematics
,
Springer
, New York, pp.
107
114
.
57.
Crane
,
C. D.
, III
,
Rico
,
J. M.
, and
Duffy
,
J.
,
2009
, “
Screw Theory and Its Application to Spatial Robot Manipulators
,” Center for Intelligent Machines and Robotics, University of Florida, Gainesville, FL, Technical Report.
58.
Rico
,
J. M.
,
Gallardo
,
J.
, and
Duffy
,
J.
,
1999
, “
Screw Theory and Higher Order Kinematic Analysis of Open Serial and Closed Chains
,”
Mech. Mach. Theory
,
34
(
4
), pp.
559
586
.10.1016/S0094-114X(98)00029-9
59.
Ball
,
S. R. S.
,
1900
,
A Treatise on the Theory of Screws
,
Cambridge University Press
, New York.
60.
Doughty
,
S.
,
1988
,
Mechanics of Machines
,
John Wiley & Sons
,
New York
.
61.
Ortega
,
S.
,
2010
, “
Estudio de Aprovechamiento de la Energía del Oleaje en Isla Fuerte (Caribe colombiano)
,” Master's thesis, School of Geosciences and Environment, National University of Colombia, Medellin, Colombia.
62.
Ortega
,
S.
,
Osorio
,
A. F.
,
Agudelo-Restrepo
,
P.
, and
Velez
,
J.
,
2011
, “
Methodology for Estimating Wave Power Potential in Places With Scarce Instrumentation in the Caribbean Sea
,”
Oceans 2011 IEEE—Spain
, Santander, Spain, June 6–9.10.1109/Oceans-Spain.2011.6003653
You do not currently have access to this content.