Abstract
The paper deals with the elastostatic modeling of a multi-link flexible manipulator based on the two-dimensional (2D) dual-triangle tensegrity mechanism and its nonlinear behavior under external loading. The main attention is paid to the static equilibriums and the manipulator stiffness behavior under the loading for the arbitrary initial configuration. It was proved that there is a quasi-buckling phenomenon for this manipulator while the external loading is increasing. In the neighborhood of these configurations, the manipulator behavior was analyzed using the enhanced virtual joint method (VJM). A relevant simulation study confirmed the obtained theoretical results.
Issue Section:
Research Papers
References
1.
Yang
, Y.
, and Zhang
, W.
, 2015
, “An Elephant-Trunk Manipulator With Twisting Flexional Rods
,” 2015 IEEE International Conference on Robotics and Biomimetics (ROBIO)
, Zhuhai, China
, Dec. 6–9
, pp. 13
–18
.2.
Howell
, L. L.
, 2013
, “Compliant Mechanisms,” 21st Century Kinematics
, Springer London
, London
, pp. 189
–216
.3.
Rolf
, M.
, and Steil
, J. J.
, 2012
, “Constant Curvature Continuum Kinematics as Fast Approximate Model for the Bionic Handling Assistant
,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems
, Vilamoura, Algarve, Portugal
, Oct. 7–12
, pp. 3440
–3446
.4.
Wang
, M. Y.
, and Chen
, S.
, 2009
, “Compliant Mechanism Optimization: Analysis and Design With Intrinsic Characteristic Stiffness
,” Mech. Based Des. Struct. Mach.
, 37
(2
), pp. 183
–200
. 5.
Albu-Schaffer
, A.
, Eiberger
, O.
, Grebenstein
, M.
, Haddadin
, S.
, Ott
, C.
, Wimbock
, T.
, Wolf
, S.
, and Hirzinger
, G.
, 2008
, “Soft Robotics
,” IEEE Robotics & Automation Magazine
, 15
(3
), pp. 20
–30
. 6.
Frecker
, M. I.
, Ananthasuresh
, G. K.
, Nishiwaki
, S.
, Kikuchi
, N.
, and Kota
, S.
, 1997
, “Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimization
,” ASME J. Mech. Des.
, 119
(2
), pp. 238
–245
. 7.
Skelton
, R. E.
, and De Oliveira
, M. C.
, 2009
, Tensegrity Systems
, Springer
, New York
.8.
Moored
, K. W.
, Kemp
, T. H.
, Houle
, N. E.
, and Bart-Smith
, H.
, 2011
, “Analytical Predictions, Optimization, and Design of a Tensegrity-Based Artificial Pectoral fin
,” Int. J. Solids Struct.
, 48
(22
), pp. 3142
–3159
. 9.
Chen
, L.-H.
, Kim
, K.
, Tang
, E.
, Li
, K.
, House
, R.
, Zhu
, E. L.
, Fountain
, K.
, Agogino
, A. M.
, Agogino
, A.
, Sunspiral
, V.
, and Jung
, E.
, 2017
, “Soft Spherical Tensegrity Robot Design Using Rod-Centered Actuation and Control
,” ASME J. Mech. Rob.
, 9
(2
), p. 025001
. 10.
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
. 11.
Zha
, J.
, Wu
, X.
, Kroeger
, J.
, Perez
, N.
, and Mueller
, M. W.
, 2020
, “A Collision-Resilient Aerial Vehicle With Icosahedron Tensegrity Structure
,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
, Vilamoura, Algarve, Portugal
, Oct. 24– Jan. 24
, pp. 1407
–1412
.12.
Kuzdeuov
, A.
, Rubagotti
, M.
, and Varol
, H. A.
, 2020
, “Neural Network Augmented Sensor Fusion for Pose Estimation of Tensegrity Manipulators
,” IEEE Sensors J.
, 20
(7
), pp. 3655
–3666
. 13.
Shintake
, J.
, Zappetti
, D.
, Peter
, T.
, Ikemoto
, Y.
, and Floreano
, D.
, 2020
, “Bio-inspired Tensegrity Fish Robot
,” 2020 IEEE International Conference on Robotics and Automation (ICRA)
, May 31–Aug. 31
, pp. 2887
–2892
.14.
Vasquez
, R. E.
, Crane
, C. D.
, III, and Correa
, J. C.
, 2014
, “Analysis of a Planar Tensegrity Mechanism for Ocean Wave Energy Harvesting
,” ASME J. Mech. Rob.
, 6
(3
), p. 031015
. 15.
Muralidharan
, V.
, and Wenger
, P.
, 2021
, “Optimal Design and Comparative Study of Two Antagonistically Actuated Tensegrity Joints
,” Mech. Mach. Theory
, 159
, p. 104249
. 16.
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
. 17.
Chen
, Y.
, Feng
, J.
, and Wu
, Y.
, 2012
, “Novel Form-Finding of Tensegrity Structures Using Ant Colony Systems
,” ASME J. Mech. Rob.
, 4
(3
), p. 031001
. 18.
Ehara
, S.
, and Kanno
, Y.
, 2010
, “Topology Design of Tensegrity Structures via Mixed Integer Programming
,” Int. J. Solids Struct.
, 47
(5
), pp. 571
–579
. 19.
Koohestani
, K.
, 2012
, “Form-Finding of Tensegrity Structures via Genetic Algorithm
,” Int. J. Solids Struct.
, 49
(5
), pp. 739
–747
. 20.
Wang
, Y.
, Xu
, X.
, and Luo
, Y.
, 2021
, “Form-Finding of Tensegrity Structures via Rank Minimization of Force Density Matrix
,” Eng. Struct.
, 227
, p. 111419
. 21.
Zhang
, L.-Y.
, Zhu
, S.-X.
, Li
, S.-X.
, and Xu
, G.-K.
, 2018
, “Analytical Form-Finding of Tensegrities Using Determinant of Force-Density Matrix
,” Compos. Struct.
, 189
, pp. 87
–98
. 22.
Chen
, Y.
, Sun
, Q.
, and Feng
, J.
, 2018
, “Improved Form-Finding of Tensegrity Structures Using Blocks of Symmetry-Adapted Force Density Matrix
,” J. Struct. Eng.
, 144
(10
), p. 04018174
. 23.
Nouri Rahmat Abadi
, B.
, Mehdi Shekarforoush
, S. M.
, Mahzoon
, M.
, and Farid
, M.
, 2014
, “Kinematic, Stiffness, and Dynamic Analyses of a Compliant Tensegrity Mechanism
,” ASME J. Mech. Rob.
, 6
(4
), p. 041001
. 24.
Wang
, R.
, Goyal
, R.
, Chakravorty
, S.
, and Skelton
, R. E.
, 2020
, “Model and Data Based Approaches to the Control of Tensegrity Robots
,” IEEE Robot. Autom. Lett.
, 5
(3
), pp. 3846
–3853
. 25.
Zhang
, M.
, Geng
, X.
, Bruce
, J.
, Caluwaerts
, K.
, Vespignani
, M.
, SunSpiral
, V.
, Abbeel
, P.
, and Levine
, S.
, 2017
, “Deep Reinforcement Learning for Tensegrity Robot Locomotion
,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA)
, Singapore
, May 29–June 3
, pp. 634
–641
.26.
Luo
, J.
, Edmunds
, R.
, Rice
, F.
, and Agogino
, A. M.
, 2018
, “Tensegrity Robot Locomotion Under Limited Sensory Inputs via Deep Reinforcement Learning
,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA)
, Brisbane, Australia
, May 21–25
, pp. 6260
–6267
.27.
Cera
, B.
, and Agogino
, A. M.
, 2018
, “Multi-Cable Rolling Locomotion With Spherical Tensegrities Using Model Predictive Control and Deep Learning
,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
, Madrid, Spain
, Oct. 1–5
, pp. 1
–9
.28.
Savin
, S.
, Balakhnov
, O.
, and Klimchik
, A.
, 2020
, “Convex Optimization-Based Stiffness Control for Tensegrity Robotic Structures
,” Proceedings of the 28th Mediterranean Conference on Control and Automation (MED)
, Saint-Raphaël, France
, Sept. 15–18
, pp. 990
–995
.29.
Zhakatayev
, A.
, Abdikadirova
, B.
, Sarmonov
, S.
, and Varol
, H. A.
, 2020
, “Dynamics of Tensegrity Robots With Negative Stiffness Elements
,” IEEE Access
, 8
, pp. 187114
–187125
. 30.
Schorr
, P.
, Zentner
, L.
, Zimmermann
, K.
, and Böhm
, V.
, 2021
, “Jumping Locomotion System Based on a Multistable Tensegrity Structure
,” Mech. Syst. Signal Process
, 152
, p. 107384
. 31.
Melancon
, D.
, Gorissen
, B.
, García-Mora
, C. J.
, Hoberman
, C.
, and Bertoldi
, K.
, 2021
, “Multistable Inflatable Origami Structures at the Metre Scale
,” Nature
, 592
(7855
), pp. 545
–550
. 32.
Sareh
, P.
, Chermprayong
, P.
, Emmanuelli
, M.
, Nadeem
, H.
, and Kovac
, M.
, 2018
, “Rotorigami: A Rotary Origami Protective System for Robotic Rotorcraft
,” Sci. Rob.
, 3
(22
), p. eaah5228
. 33.
Dureisseix
, D.
, 2012
, “An Overview of Mechanisms and Patterns With Origami
,” Int. J. Space Struct.
, 27
(1
), pp. 1
–14
. 34.
Rohmer
, J. L.
, Peraza Hernandez
, E. A.
, Skelton
, R. E.
, Hartl
, D. J.
, and Lagoudas
, D. C.
, 2015
, “An Experimental and Numerical Study of Shape Memory Alloy-Based Tensegrity/Origami Structures
,” Proceedings of the ASME 2015 International Mechanical Engineering Congress and Exposition, Volume 9: Mechanics of Solids, Structures and Fluids
, Houston, TX
, Nov. 13–19
, p. V009T12A064
.35.
Klimchik
, A.
, Pashkevich
, A.
, and Chablat
, D.
, 2019
, “Fundamentals of Manipulator Stiffness Modeling Using Matrix Structural Analysis
,” Mech. Mach. Theory
, 133
, pp. 365
–394
. 36.
Deblaise
, D.
, Hernot
, X.
, and Maurine
, P.
, 2006
, “A Systematic Analytical Method for PKM Stiffness Matrix Calculation
,” IEEE International Conference on Robotics and Automation (ICRA 2006)
, Orlando, FL
, May 15–19
, IEEE
, pp. 4213
–4219
.37.
Klimchik
, A.
, Chablat
, D.
, and Pashkevich
, A.
, 2014
, “Stiffness Modeling for Perfect and Non-Perfect Parallel Manipulators Under Internal and External Loadings
,” Mech. Mach. Theory
, 79
, pp. 1
–28
. 38.
Pashkevich
, A.
, Klimchik
, A.
, and Chablat
, D.
, 2011
, “Enhanced Stiffness Modeling of Manipulators With Passive Joints
,” Mech. Mach. Theory
, 46
(5
), pp. 662
–679
. 39.
Quennouelle
, C.
, and Gosselin
, C. M.
, 2008
, “Stiffness Matrix of Compliant Parallel Mechanisms,” Advances in Robot Kinematics: Analysis and Design
, Springer
, pp. 331
–341
.40.
Liu
, H.
, Huang
, T.
, Chetwynd
, D. G.
, and Kecskeméthy
, A.
, 2017
, “Stiffness Modeling of Parallel Mechanisms at Limb and Joint/Link Levels
,” IEEE Trans. Rob.
, 33
(3
), pp. 734
–741
. 41.
Klimchik
, A.
, Chablat
, D.
, and Pashkevich
, A.
, 2015
, “Static Stability of Manipulator Configuration: Influence of the External Loading
,” Eur. J. Mech. A. Solids
, 51
, pp. 193
–203
. 42.
Carricato
, M.
, and Merlet
, J.
, 2013
, “Stability Analysis of Underconstrained Cable-Driven Parallel Robots
,” IEEE Trans. Rob.
, 29
(1
), pp. 288
–296
. 43.
Arsenault
, M.
, and Gosselin
, C. M.
, 2006
, “Kinematic, Static and Dynamic Analysis of a Planar 2-DOF Tensegrity Mechanism
,” Mech. Mach. Theory
, 41
(9
), pp. 1072
–1089
. 44.
Furet
, M.
, Lettl
, M.
, and Wenger
, P.
, 2018
, “Kinematic Analysis of Planar Tensegrity 2-X Manipulators
,” International Symposium on Advances in Robot Kinematics
, Ljubljana, Slovenia
, Dec. 6–10
, Springer
, pp. 153
–160
.45.
Wenger
, P.
, and Chablat
, D.
, 2019
, “Kinetostatic Analysis and Solution Classification of a Class of Planar Tensegrity Mechanisms
,” Robotica
, 37
(7
), pp. 1214
–1224
. 46.
Moon
, Y.
, Crane
, C. D.
, III, and Roberts
, R. G.
, 2012
, “Position and Force Analysis of a Planar Tensegrity-Based Compliant Mechanism
,” ASME J. Mech. Rob.
, 4
(1
), p. 011004
. 47.
Ilewicz
, G.
, and Harlecki
, A.
, 2020
, “Multi-Objective Optimization and Linear Buckling of Serial Chain of a Medical Robot Tool for Soft Tissue Surgery
,” Int. J. Rob. Autom.
, 9
(1
), p. 17
. 48.
Wang
, H.
, and Yamamoto
, A.
, 2017
, “Analyses and Solutions for the Buckling of Thin and Flexible Electrostatic Inchworm Climbing Robots
,” IEEE Trans. Rob.
, 33
(4
), pp. 889
–900
. 49.
Yamada
, A.
, Mameda
, H.
, Mochiyama
, H.
, and Fujimoto
, H.
, 2010
, “A Compact Jumping Robot Utilizing Snap-Through Buckling With Bend and Twist
,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems
, Oct. 18–22
, pp. 389
–394
.50.
Zhao
, W.
, Pashkevich
, A.
, Klimchik
, A.
, and Chablat
, D.
, 2020
, “Stiffness Analysis of a New Tensegrity Mechanism Based on Planar Dual-Triangles
,” Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics
, Vol. 1
, pp. 402
–411
.51.
Zhao
, W.
, Pashkevich
, A.
, Klimchik
, A.
, and Chablat
, D.
, 2020
, “The Stability and Stiffness Analysis of a Dual-Triangle Planar Rotation Mechanism
,” ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Volume 10: 44th Mechanisms and Robotics Conference (MR)
, p. V010T10A064
.52.
Chen
, S.-F.
, and Kao
, I.
, 2000
, “Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotic Hands and Fingers
,” Int. J. Rob. Res.
, 19
(9
), pp. 835
–847
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