Abstract

We propose a method to design a tensegrity joint, making its elastic deformation an accurate joint-like motion, such as a rotation around the designed rotational center. The tensegrity joint can be a revolute, universal, and ball joint through this method. Axis drift is presented as a design criterion to describe the rotational center’s deviation degree with respect to the compliance center since the rotational center is not fixed to one point for different positions of the tensegrity joint. The axis drift is designed to be in a prescribed range so that the tensegrity joint is approximately equivalent to a rigid joint. In other words, the tensegrity joint’s elastic response under external torque and force becomes precise rigid joint-like kinematics and can replace rigid joints to transfer motion, force, and energy. A large-size tensegrity rotational joint is developed to verify the joint equivalence experimentally. The experimental results show that the tensegrity joint achieved maximum dimensionless axis drift of less than 2%, which indicates an excellent joint equivalence. The tensegrity joints’ ability to replace rigid joints as modular joints to construct a hyper redundant serial structure is demonstrated using a tensegrity robotic arm. The proposed compliant tensegrity joint has notable benefits of tensegrity structure, such as high mechanical efficiency, modularity, and scalability. It can be extended to many robotic applications, such as large-size serial robotic arms and snake-like robots.

References

1.
Skelton
,
R.
, and
de Oliveira
,
M.
,
2009
,
Tensegrity Systems
,
Springer
,
New York
.
2.
Sultan
,
C.
,
2009
, “Tensegrity: 60 Years of Art, Science, and Engineering,”
Advances in Applied Mechanics
,
Elsevier
, Vol. 43, pp.
69
145
.
3.
Motro
,
R.
,
2003
,
Tensegrity: Structural Systems for the Future
,
Kogan Page Science
,
London
.
4.
Ingber
,
D.
,
2003
, “
Tensegrity I. Cell Structure and Hierarchical Systems Biology
,”
J. Cell Sci.
,
116
(
7
), pp.
1157
1173
.
5.
Rhode-Barbarigos
,
L.
,
Ali
,
N. B. H.
,
Motro
,
R.
, and
Smith
,
I.
,
2010
, “
Designing Tensegrity Modules for Pedestrian Bridges
,”
Eng. Struct.
,
32
(
4
), pp.
1158
1167
.
6.
Pellegrino
,
S.
,
1992
, “
A Class of Tensegrity Domes
,”
Int. J. Space Struct.
,
7
(
2
), pp.
127
142
.
7.
Scarr
,
G.
,
2010
, “
Simple Geometry in Complex Organisms
,”
J. Bodyw. Mov. Ther.
,
14
(
4
), pp.
424
444
.
8.
Snelson
,
K.
,
2012
, “
The Art of Tensegrity
,”
Int. J. Space Struct.
,
27
(
2–3
), pp.
71
80
.
9.
Paul
,
C.
,
Valero-Cuevas
,
F. J.
, and
Lipson
,
H.
,
2006
, “
Design and Control of Tensegrity Robots for Locomotion
,”
IEEE Trans. Robot.
,
22
(
5
), pp.
944
957
.
10.
Sun
,
J.
,
Song
,
G.
,
Chu
,
J.
, and
Ren
,
L.
,
2019
, “
An Adaptive Bioinspired Foot Mechanism Based on Tensegrity Structures
,”
Soft Robot.
,
6
(
6
), p.
soro.2018.0168
.
11.
Orki
,
O.
,
Ayali
,
A.
,
Shai
,
O.
, and
Ben-Hanan
,
U.
,
2012
, “
Modeling of Caterpillar Crawl Using Novel Tensegrity Structures
,”
Bioinspir. Biomim.
,
7
(
4
), p.
046006
.
12.
Koizumi
,
Y.
,
Shibata
,
M.
, and
Hirai
,
S.
,
2012
, “
Rolling Tensegrity Driven by Pneumatic Soft Actuators
,”
IEEE International Conference on Robotics and Automation
,
Saint Paul, MN
,
May 14–18
, pp.
1988
1993
.
13.
Sabelhaus
,
A. P.
,
Bruce
,
J.
,
Caluwaerts
,
K.
,
Manovi
,
P.
,
Firoozi
,
R. F.
,
Dobi
,
S.
,
Agogino
,
A. M.
, and
SunSpiral
,
V.
,
2015
, “
System Design and Locomotion of Superball, an Untethered Tensegrity Robot
,”
IEEE International Conference on Robotics and Automation
,
Seattle, WA
,
May 26–30
, pp.
2867
2873
.
14.
Friesen
,
J.
,
Pogue
,
A.
,
Bewley
,
T.
,
de Oliveira
,
M.
, and
Sunspiral
,
V.
,
2014
, “
Ductt: A Tensegrity Robot for Exploring Duct Systems
,”
IEEE International Conference on Robotics and Automation
,
Hong Kong, China
,
31 May-June 7
.
15.
Bliss
,
T.
,
Iwasaki
,
T.
, and
Bart-Smith
,
H.
,
2012
, “
Central Pattern Generator Control of a Tensegrity Swimmer
,”
IEEE-ASME Trans. Mechatron.
,
18
(
2
), pp.
586
597
.
16.
Chen
,
B.
, and
Jiang
,
H.
,
2019
, “
Swimming Performance of a Tensegrity Robotic Fish
,”
Soft Robot.
,
6
(
4
), p.
soro.2018.0079
.
17.
Flemons
,
T.
,
2012
, “
The Bones of Tensegrity
,” http://intensiondesigns.ca/bones-of-tensegrity/, Accessed November, 2019.
18.
Levin
,
S. M.
,
1997
, “
Putting the Shoulder to the Wheel: A New Biomechanical Model for the Shoulder Girdle
,”
J. Biomed. Sci. Instrum.
,
33
, pp.
412
417
.
19.
Levin
,
S. M.
,
2002
, “
The Tensegrity-Truss as a Model for Spine Mechanics: Biotensegrity
,”
J. Mech. Med. Biol.
,
2
(
03n04
), pp.
375
388
.
20.
Scarr
,
G.
, and
Harrison
,
H.
,
2017
, “
Examining the Temporo-Mandibular Joint From a Biotensegrity Perspective: A Change in Thinking
,”
J. Appl. Biomed.
,
15
(
1
), pp.
55
62
.
21.
Lessard
,
S.
,
Castro
,
D.
,
Asper
,
W.
,
Chopra
,
S. D.
,
Baltaxe-Admony
,
L. B.
,
Teodorescu
,
M.
,
SunSpiral
,
V.
, and
Agogino
,
A.
,
2016
, “
A Bio-Inspired Tensegrity Manipulator With Multi-dof, Structurally Compliant Joints
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
,
Daejeon, South Korea
,
Oct. 9–14
, pp.
5515
5520
.
22.
Lessard
,
S.
,
Bruce
,
J.
,
Jung
,
E.
,
Teodorescu
,
M.
,
SunSpiral
,
V.
, and
Agogino
,
A.
,
2016
, “
A Lightweight, Multi-Axis Compliant Tensegrity Joint
,”
IEEE International Conference on Robotics and Automation
,
Stockholm, Sweden
,
May 16–21
, pp.
630
635
.
23.
Friesen
,
J. M.
,
Dean
,
J. L.
,
Bewley
,
T.
, and
Sunspiral
,
V.
,
2018
, “
A Tensegrity-Inspired Compliant 3-dof Compliant Joint
,”
IEEE International Conference on Robotics and Automation
,
Brisbane, QLD, Australia
,
May 21–25
, pp.
3301
3306
.
24.
Jung
,
E.
,
Ly
,
V.
,
Cessna
,
N.
,
Ngo
,
M. L.
,
Castro
,
D.
,
SunSpiral
,
V.
, and
Teodorescu
,
M.
,
2018
, “
Bio-Inspired Tensegrity Flexural Joints
,”
IEEE International Conference on Robotics and Automation
,
Brisbane, QLD, Australia
,
May 21–25
, pp.
5561
5566
.
25.
Howell
,
L. L.
,
2013
,
Compliant Mechanisms
,
Springer
,
London
.
26.
Machekposhti
,
D. F.
,
Tolou
,
N.
, and
Herder
,
J. L.
,
2015
, “
A Review on Compliant Joints and Rigid-Body Constant Velocity Universal Joints Toward the Design of Compliant Homokinetic Couplings
,”
ASME J. Mech. Des.
,
137
(
3
), p.
032301
.
27.
Yong
,
Y.
,
Lu
,
T.
, and
Handley
,
D. C.
,
2008
, “
Review of Circular Flexure Hinge Design Equations and Derivation of Empirical Formulations
,”
Precis. Eng.-J. Int. Soc. Precis. Eng. Nanotechnol.
,
32
(
2
), pp.
63
70
.
28.
Thomas
,
T. L.
,
Kalpathy Venkiteswaran
,
V.
,
Ananthasuresh
,
G. K.
, and
Misra
,
S.
,
2021
, “
Surgical Applications of Compliant Mechanisms: A Review
,”
ASME J. Mech. Robot.
,
13
(
2
), p.
020801
.
29.
Mirletz
,
B. T.
,
Bhandal
,
P.
,
Adams
,
R. D.
,
Agogino
,
A. K.
,
Quinn
,
R. D.
, and
SunSpiral
,
V.
,
2015
, “
Goal-directed CPG-Based Control for Tensegrity Spines With Many Degrees of Freedom Traversing Irregular Terrain
,”
Soft Rob.
,
2
(
4
), pp.
165
176
.
30.
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)
,
Banff, AB, Canada
,
July 12–15
, pp.
1509
1514
.
31.
Dasgupta
,
B.
, and
Mruthyunjaya
,
T.
,
2000
, “
The Stewart Platform Manipulator: A Review
,”
Mech. Mach. Theory
,
35
(
1
), pp.
15
40
.
32.
Azadi
,
M.
,
Behzadipour
,
S.
, and
Faulkner
,
G.
,
2009
, “
Antagonistic Variable Stiffness Elements
,”
Mech. Mach. Theory
,
44
(
9
), pp.
1746
1758
.
33.
Jiang
,
H.
,
He
,
J.
, and
Tong
,
Z.
,
2010
, “
Characteristics Analysis of Joint Space Inverse Mass Matrix for the Optimal Design of a 6-dof Parallel Manipulator
,”
Mech. Mach. Theory
,
45
(
5
), pp.
722
739
.
34.
Angeles
,
J.
,
2006
, “
Is There a Characteristic Length of a Rigid-Body Displacement?
,”
Mech. Mach. Theory
,
41
(
8
), pp.
884
896
.
35.
Juan
,
S. H.
, and
Tur
,
J. M. M.
,
2008
, “
Tensegrity Frameworks: Static Analysis Review
,”
Mech. Mach. Theory
,
43
(
7
), pp.
859
881
.
36.
Tur
,
J. M. M.
, and
Juan
,
S. H.
,
2009
, “
Tensegrity Frameworks: Dynamic Analysis Review and Open Problems
,”
Mech. Mach. Theory.
,
44
(
1
), pp.
1
18
.
37.
Arsenault
,
M.
, and
Gosselin
,
C.
,
2006
, “
Kinematic and Static Analysis of a Planar Modular 2-dof Tensegrity Mechanism
,”
Proceedings 2006 IEEE International Conference on Robotics and Automation
,
Orlando, FL
,
May 15–19
, pp.
4193
4198
.
38.
Muralidharan
,
V.
, and
Wenger
,
P.
,
2019
, “
Kinetostatic Analysis and Actuation Strategy of a Planar Tensegrity 2-x Manipulator
,”
ASME J. Mech. Robot.
,
11
(
6
), p.
060904
.
39.
Moored
,
K. W.
,
Kemp
,
T.
,
Houle
,
N.
, and
Bart-Smith
,
H.
,
2011
, “
Analytical Predictions, Optimization, and Design of a Tensegrity-Based Artificial Pectoral Fin
,”
Int. J. Space Struct.
,
48
(
22–23
), pp.
3142
3159
.
40.
Muralidharan
,
V.
, and
Wenger
,
P.
,
2021
, “
Optimal Design and Comparative Study of Two Antagonistically Actuated Tensegrity Joints
,”
Mech. Mach. Theory
,
159
, p.
104249
.
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