Abstract

A planar tensegrity manipulator made of two X-mechanisms in series is studied in this paper. Contrary to a classical 2-R linkage, the proposed architecture does not contain elements subject to bending and it can be driven with remote actuation and cables in an antagonistic way. Accordingly, it is an interesting candidate for the design of lightweight manipulators with variable stiffness suitable for safe interactions. On the other hand, its kinematics is more challenging because of a variable instantaneous center of rotation of the X-mechanisms. First, the inverse kinematic problem is solved using an adequate methodology, the singularities are determined, and the workspace shape is analyzed as a function of the design parameters. Then, two actuation schemes are studied and the wrench feasible workspace is analyzed for each of them. The second actuation scheme provides a larger wrench feasible workspace and allows for stiffness control.

References

1.
Buckminster
,
F. R.
,
1962
, “
Tensile-Integrity Structures
,”
Nov.
13
, US Patent No. 3,063,521.
2.
Motro
,
R.
,
1992
, “
Tensegrity Systems: The State of the Art
,”
Int. J. Space Struct.
,
7
(
2
), pp.
75
83
. 10.1177/026635119200700201
3.
Skelton
,
R. E.
, and
de Oliveira
,
M. C.
,
2009
,
Tensegrity Systems
, Vol.
1
,
Springer
,
Boston, MA
.
4.
Levin
,
S. M.
,
2002
, “
The Tensegrity-Truss As a Model for Spine Mechanics: Biotensegrity
,”
J. Mech. Med. Biol.
,
2
(
03n04
), pp.
375
388
. 10.1142/S0219519402000472
5.
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
. 10.1016/j.mechmachtheory.2005.10.014
6.
Crane
,
C. D.
,
Bayat
,
J.
,
Vikas
,
V.
, and
Roberts
,
R.
,
2008
, “Kinematic Analysis of a Planar Tensegrity Mechanism With Pre-Stressed Springs,”
Advances in Robot Kinematics: Analysis and Design
,
J.
Lenarčič
, and
P.
Wenger
, eds.,
Springer
,
Dordrecht, Germany
, pp.
419
427
.
7.
Wenger
,
P.
, and
Chablat
,
D.
,
2017
, “
Kinetostatic Analysis and Solution Classification of a Planar Tensegrity Mechanism
,”
Proceedings of the 7th International Workshop on Computational Kinematics
,
May 22–24
,
Poitiers, France
,
S.
Zeghloul
,
L.
Romdhane
, and
M.
Laribi
, eds.,
Springer
,
New York
, pp.
422
431
.
8.
Rieffel
,
J.
, and
Mouret
,
J.-B.
,
2018
, “
Adaptive and Resilient Soft Tensegrity Robots
,”
Soft Rob.
,
5
(
3
), pp.
318
329
. 10.1089/soro.2017.0066
9.
Böhm
,
V.
,
Kaufhold
,
T.
,
Schale
,
F.
, and
Zimmermann
,
K.
,
2016
, “
Spherical Mobile Robot Based on a Tensegrity Structure With Curved Compressed Members
,”
2016 IEEE International Conference on Advanced Intelligent Mechatronics (AIM)
,
July 12–15
,
Banff, AB, Canada
,
IEEE
,
New York
, pp.
1509
1514
.
10.
Vespignani
,
M.
,
Friesen
,
J. M.
,
SunSpiral
,
V.
, and
Bruce
,
J.
,
2018
, “
Design of Superball V2, A Compliant Tensegrity Robot for Absorbing Large Impacts
,”
2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
,
Oct. 1–5
,
Madrid, Spain
,
IEEE
,
New York
, pp.
2865
2871
.
11.
Bakker
,
D. L.
,
Matsuura
,
D.
,
Takeda
,
Y.
, and
Herder
,
J. L.
,
2015
, “
Design of An Environmentally Interactive Continuum Manipulator
,”
Proceedings of 14th IFToMM World Congress in Mechanism and Machine Science
,
Oct. 25–30
,
Taipei, Taiwan
, pp.
327
336
.
12.
Snelson
,
K. D.
,
1965
, “
Continuous Tension, Discontinuous Compression Structures
,”
Feb.
16
, US Patent No. 3,169,611.
13.
Zweers
,
G.
,
Bout
,
R.
, and
Heidweiller
,
J.
,
1994
, “Motor Organization of the Avian Head-Neck System,”
Perception and Motor Control in Birds : An Ecological Approach
,
M. N. O.
Davies
and
P. R.
Green
, eds.,
Springer
,
Dordrecht, Germany
, pp.
201
221
.
14.
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
. 10.1115/1.4029809
15.
Van Riesen
,
A.
,
Furet
,
M.
,
Chevallereau
,
C.
, and
Wenger
,
P.
,
2018
, “
Dynamic Analysis and Control of An Antagonistically Actuated Tensegrity Mechanism
,”
Proceedings of the 22nd CISM IFToMM Symposium on Robot Design, Dynamics and Control (ROMANSY)
,
June 25–28
,
Rennes, France
,
Springer
, pp.
481
490
.
16.
Aldrich
,
J.
, and
Skelton
,
R.
,
2005
, “
Time-Energy Optimal Control of Hyper-Actuated Mechanical Systems With Geometric Path Constraints
,”
Proceedings of the 44th IEEE Conference on Decision and Control
,
Dec. 15
,
Seville, Spain
,
IEEE
,
New York
, pp.
8246
8253
.
17.
Arsenault
,
M.
, and
Gosselin
,
C. M.
,
2006
, “
Kinematic and Static Analysis of A Planar Modular 2-DoF Tensegrity Mechanism
,”
Proceedings of the 2006 IEEE International Conference on Robotics and Automation (ICRA)
,
May 15–19
,
Orlando, FL, USA
,
IEEE
,
New York
, pp.
4193
4198
.
18.
Chen
,
S.
, and
Arsenault
,
M.
,
2012
, “
Analytical Computation of the Actuator and Cartesian Workspace Boundaries for a Planar 2-Degree-of-Freedom Translational Tensegrity Mechanism
,”
ASME J. Mech. Rob.
,
4
(
1
), p.
011010
. 10.1115/1.4005335
19.
Furet
,
M.
,
Van Riesen
,
A.
,
Chevallereau
,
C.
, and
Wenger
,
P.
,
2018
, “
Optimal Design of Tensegrity Mechanisms Used in a Bird Neck Model
,”
Proceedings of the 7th European Conference on Mechanism Science (EuCoMeS)
,
Sept. 4–6
,
Aachen, Germany
,
Springer
, pp.
365
375
.
20.
Furet
,
M.
,
Lettl
,
M.
, and
Wenger
,
P.
,
2018
, “
Kinematic Analysis of Planar Tensegrity 2-X Manipulators
,”
Proceedings of the 16th International Symposium on Advances in Robot Kinematics (ARK)
,
July 1–5
,
Bologna, Italia
,
Springer
,
New York
, pp.
153
160
.
21.
Furet
,
M.
, and
Wenger
,
P.
,
2018
, “
Workspace and Cuspidality Analysis of a 2-X Planar Manipulator
,”
Proceedings of the 4th IFToMM Symposium on Mechanism Design for Robotics (MEDER)
,
Sept. 11–13
,
Udine, Italy
,
Springer
,
New York
, pp.
110
117
.
22.
Jha
,
R.
,
Chablat
,
D.
,
Baron
,
L.
,
Rouillier
,
F.
, and
Moroz
,
G.
,
2018
, “
Workspace, Joint Space and Singularities of a Family of Delta-Like Robot
,”
Mech. Mach. Theory
,
127
(
1
), pp.
73
95
. 10.1016/j.mechmachtheory.2018.05.004
23.
Manubens
,
M.
,
Moroz
,
G.
,
Chablat
,
D.
,
Wenger
,
P.
, and
Rouillier
,
F.
,
2012
, “
Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators
,”
ASME J. Mech. Rob.
,
4
(
4
), p.
041003
. 10.1115/1.4006921
24.
Moroz
,
G.
,
Rouiller
,
F.
,
Chablat
,
D.
, and
Wenger
,
P.
,
2010
, “
On the Determination of Cusp Points of 3-RPR Parallel Manipulators
,”
Mech. Mach. Theory
,
45
(
11
), pp.
1555
1567
. 10.1016/j.mechmachtheory.2010.06.016
25.
Borrel
,
P.
, and
Liégeois
,
A.
,
1986
, “
A Study of Multiple Manipulator Inverse Kinematic Solutions with Applications to Trajectory Planning and Workspace Determination
,”
Proceedings of 1986 IEEE International Conference on Robotics and Automation (ICRA)
,
Apr. 7–10
,
San Francisco, CA
, Vol.
3
,
IEEE
,
New York
, pp.
1180
1185
.
26.
El Omri
,
J.
, and
Wenger
,
P.
,
1995
, “
How to Recognize Simply a Non-Singular Posture Changing 3-DoF Manipulator
,”
Proceedings of the 7th International Conference on Advanced Robotics (ICAR)
,
Sept. 20–22
,
Sant Feliu de Guixois, Spain
, pp.
215
222
.
27.
Wenger
,
P.
,
2007
, “
Cuspidal and Noncuspidal Robot Manipulators
,”
Robotica
,
25
(
6
), pp.
677
689
. 10.1017/S0263574707003761
28.
Furet
,
M.
, and
Wenger
,
P.
,
2018
, Derivation of a polynomial equation for the boundaries of 2-X manipulators, Technical report.
29.
Thomas
,
F.
, and
Wenger
,
P.
,
2011
, “
On the Topological Characterization of Robot Singularity Loci. A Catastrophe-Theoretic Approach
,”
Proceedings of 2011 IEEE International Conference on Robotics and Automation (ICRA)
,
May 9–13
,
Shanghai, China
,
IEEE
,
New York
, pp.
3940
3945
.
30.
Wenger
,
P.
,
Chablat
,
D.
, and
Baili
,
M.
,
2005
, “
A DH-Parameter Based Condition for 3R Orthogonal Manipulators to Have Four Distinct Inverse Kinematic Solutions
,”
ASME J. Mech. Des.
,
127
(
1
), pp.
150
155
. 10.1115/1.1828460
31.
Moored
,
K.
,
Kemp
,
T.
,
Houle
,
N.
, and
Bart-Smith
,
H.
,
2011
, “
Analytical Predictions, Optimization, and Design of a Tensegrity-Based Artificial Pectoral Fin
,”
Int. J. Solids. Struct.
,
48
(
22–23
), pp.
3142
3159
. 10.1016/j.ijsolstr.2011.07.008
32.
Quennouelle
,
C.
, and
Gosselin
,
C.
,
2008
, “Stiffness Matrix of Compliant Parallel Mechanisms,”
Advances in Robot Kinematics: Analysis and Design
,
J.
Lenarčič
and
P.
Wenger
, eds., pp.
331
341
.
33.
Ebert-Uphoff
,
I.
, and
Voglewede
,
P. A.
,
2004
, “
On the Connections Between Cable-Driven Robots, Parallel Manipulators and Grasping
,”
Proceedings of 2004 IEEE International Conference on Robotics and Automation (ICRA)
,
April 26–May 1
,
New Orleans, LA
, Vol.
5
,
IEEE
,
New York
, pp.
4521
4526
.
34.
Fasquelle
,
B.
,
Furet
,
M.
,
Chevallereau
,
C.
, and
Wenger
,
P.
,
2019
, “
Dynamic Modeling and Control of a Tensegrity Manipulator Mimicking a Bird Neck
,”
Proceedings of the 15th IFToMM World Congress on Mechanism and Machine Science
,
June 30–July 4
,
Krakow, Poland
,
Springer
,
New York
, pp.
2087
2097
.
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