Abstract

In this paper, we derive a model based on the principle of virtual work to describe the deformations of cylindrical pressure-driven soft actuators with four types of fiber reinforcement and with externally applied forces. Such cylindrical actuators are often used as the basis for multi-chamber soft robotic systems, for example, bending actuators. In the virtual work model, each type of reinforcement leads to particular geometric constraints; the energy of the stretched material is determined by the Yeoh material model. Finally, the stretch of the actuator is solved numerically by a minimization problem. The virtual work model yielded only little deviations of the predicted stretch relative to finite element simulations in abaqus. The key contribution of the virtual work model is improved parameter identification for the modeling of cylindrical soft actuators, as it illustrates the possibility to distinguish between material-dependent behavior and geometry-dependent behavior of these actuators. Also, the virtual work model is applicable in the design process of the investigated actuators. We demonstrate that an optimization of the actuator’s inner and outer radii and of its fiber angle, respectively, is possible and we derive design rules including criteria for the choice of fiber reinforcement.

References

1.
Boyraz
,
P.
,
Runge
,
G.
, and
Raatz
,
A.
,
2018
, “
An Overview of Novel Actuators for Soft Robotics
,”
Actuators
,
7
(
3
), p.
48
.
2.
Calisti
,
M.
,
Picardi
,
G.
, and
Laschi
,
C.
,
2017
, “
Fundamentals of Soft Robot Locomotion
,”
J. R. Soc. Interface
,
14
, pp. 1–16.
3.
Cianchetti
,
M.
,
Ranzani
,
T.
,
Gerboni
,
G.
,
De Falco
,
I.
,
Laschi
,
C.
, and
Menciassi
,
A.
,
2013
, “
Stiff-Flop Surgical Manipulator: Mechanical Design and Experimental Characterization of the Single Module
,”
2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
,
Tokyo, Japan
,
Nov. 3–7
, pp.
3576
3581
.
4.
Trivedi
,
D.
,
Rahn
,
C. D.
,
Kier
,
W. M.
, and
Walker
,
I. D.
,
2008
, “
Soft Robotics: Biological Inspiration, State of the Art, and Future Research
,”
Appl. Bionics Biomech.
,
5
(
3
), pp.
99
117
.
5.
Wall
,
V.
,
Zöller
,
G.
, and
Brock
,
O.
,
2017
, “
A Method for Sensorizing Soft Actuators and Its Application to the RBO Hand 2
,”
2017 IEEE International Conference on Robotics and Automation (ICRA)
,
Singapore
,
May 29–June 3
, pp.
4965
4970
.
6.
Suzumori
,
K.
,
Endo
,
S.
,
Kanda
,
T.
,
Kato
,
N.
, and
Suzuki
,
H.
,
2007
, “
A Bending Pneumatic Rubber Actuator Realizing Soft-Bodied Manta Swimming Robot
,”
2007 IEEE International Conference on Robotics and Automation (ICRA)
,
Roma, Italy
,
Apr. 10–14
, IEEE, pp.
4975
4980
.
7.
Polygerinos
,
P.
,
Lyne
,
S.
,
Wang
,
Z.
,
Nicolini
,
L. F.
,
Mosadegh
,
B.
,
Whitesides
,
G. M.
, and
Walsh
,
C. J.
,
2013
, “
Towards a Soft Pneumatic Glove for Hand Rehabilitation
,”
2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
,
Tokyo, Japan
,
Nov. 3–7
, pp.
1512
1517
.
8.
Song
,
Y. S.
,
Sun
,
Y.
,
Van Den Brand
,
R.
,
Von Zitzewitz
,
J.
,
Micera
,
S.
,
Courtine
,
G.
, and
Paik
,
J.
,
2013
, “
Soft Robot for Gait Rehabilitation of Spinalized Rodents
,”
2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
,
Tokyo, Japan
,
Nov. 3–7
, pp.
971
976
.
9.
Faudzi
,
A. A. M.
,
Razif
,
M.
,
Nordin
,
I. N. A. M.
,
Suzumori
,
K.
,
Wakimoto
,
S.
,
Hirooka
,
D.
, and
Ruzydi
,
M-
,
2012
, “
Development of Bending Soft Actuator With Different Braided Angles
,”
2012 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)
,
Kaohsiung, Taiwan
,
July 11–14
.
10.
Trivedi
,
D.
,
Lotfi
,
A.
, and
Rahn
,
C. D.
,
2007
, “
Geometrically Exact Dynamic Models for Soft Robotic Manipulators
,”
2007 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
,
San Diego, CA
,
Oct. 29–Nov. 2
, pp.
1497
1502
.
11.
Suzumori
,
K.
,
Iikura
,
S.
, and
Tanaka
,
H.
,
1991
, “
Development of Flexible Microactuator and Its Applications to Robotic Mechanisms
,”
1991 IEEE International Conference on Robotics and Automation (ICRA)
,
Sacramento, CA
,
Apr.
, pp.
1622
1627
.
12.
Bishop-Moser
,
J.
,
Krishnan
,
G.
,
Kim
,
C.
, and
Kota
,
S.
,
2012
, “
Design of Soft Robotic Actuators Using Fluid-Filled Fiber-Reinforced Elastomeric Enclosures in Parallel Combinations
,”
2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
,
Vilamoura, Algarve, Portugal
,
Oct. 7–12
, pp.
4264
4269
.
13.
Mustaza
,
S. M.
,
Elsayed
,
Y.
,
Lekakou
,
C.
,
Saaj
,
C.
, and
Fras
,
J.
,
2019
, “
Dynamic Modeling of Fiber-Reinforced Soft Manipulator: A Visco-Hyperelastic Material-Based Continuum Mechanics Approach
,”
Soft Rob.
,
6
(
3
), pp.
305
317
.
14.
Liu
,
W.
, and
Rahn
,
C. R.
,
2003
, “
Fiber-Reinforced Membrane Models of McKibben Actuators
,”
ASME J. Appl. Mech.
,
70
(
6
), pp.
853
859
.
15.
Kothera
,
C. S.
,
Jangid
,
M.
,
Sirohi
,
J.
, and
Wereley
,
N. M.
,
2009
, “
Experimental Characterization and Static Modeling of McKibben Actuators
,”
ASME J. Mech. Des.
,
131
(
9
), p.
091010
.
16.
Tu
,
Q.
,
Wang
,
Y.
,
Yue
,
D.
, and
Dwomoh
,
F. A.
,
2020
, “
Analysis on the Impact Factors for the Pulling Force of the McKibben Pneumatic Artificial Muscle by a FEM Model
,”
J. Rob.
,
2020
, pp.
1
11
.
17.
Krishnan
,
G.
,
Bishop-Moser
,
J.
,
Kim
,
C.
, and
Kota
,
S.
,
2015
, “
Kinematics of a Generalized Class of Pneumatic Artificial Muscles
,”
ASME J. Mech. Rob.
,
7
(
4
), p.
041014
.
18.
Singh
,
G.
, and
Krishnan
,
G.
,
2015
, “
An Isoperimetric Formulation to Predict Deformation Behavior of Pneumatic Fiber Reinforced Elastomeric Actuators
,”
2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
,
Hamburg, Germany
,
Sept. 28–Oct. 2
, pp.
1738
1743
.
19.
Bishop-Moser
,
J.
, and
Kota
,
S.
,
2015
, “
Design and Modeling of Generalized Fiber-Reinforced Pneumatic Soft Actuators
,”
IEEE Trans. Rob.
,
31
(
3
), pp.
536
545
.
20.
Sedal
,
A.
,
Bruder
,
D.
,
Bishop-Moser
,
J.
,
Vasudevan
,
R.
, and
Kota
,
S.
,
2018
, “
A Continuum Model for Fiber-Reinforced Soft Robot Actuators
,”
ASME J. Mech. Rob.
,
10
(
2
), p.
024501
.
21.
Singh
,
G.
, and
Krishnan
,
G.
,
2017
, “
A Constrained Maximization Formulation to Analyze Deformation of Fiber Reinforced Elastomeric Actuators
,”
Smart Mater. Struct.
,
26
(
6
), p.
065024
.
22.
Polygerinos
,
P.
,
Wang
,
Z.
,
Overvelde
,
J. T. B.
,
Galloway
,
K. C.
,
Wood
,
R. J.
,
Bertoldi
,
K.
, and
Walsh
,
C. J.
,
2015
, “
Modeling of Soft Fiber-Reinforced Bending Actuators
,”
IEEE Trans. Rob.
,
31
(
3
), pp.
778
789
.
23.
Majidi
,
C.
,
Shepherd
,
R. F.
,
Kramer
,
R. K.
,
Whitesides
,
G. M.
, and
Wood
,
R. J.
,
2013
, “
Influence of Surface Traction on Soft Robot Undulation
,”
Int. J. Rob. Res.
,
32
(
13
), pp.
1577
1584
.
24.
Connolly
,
F.
,
Walsh
,
C. J.
, and
Bertoldi
,
K.
,
2016
, “
Automatic Design of Fiber-Reinforced Soft Actuators for Trajectory Matching
,”
Proc. Natl. Acad. Sci. U.S.A.
,
114
(
1
), pp.
51
56
.
25.
Connolly
,
F.
,
Polygerinos
,
P.
,
Walsh
,
C. J.
, and
Bertoldi
,
K.
,
2015
, “
Mechanical Programming of Soft Actuators by Varying Fiber Angle
,”
Soft Rob.
,
2
(
1
), pp.
26
32
.
26.
Chou
,
C.-P.
, and
Hannaford
,
B.
,
1996
, “
Measurement and Modeling of McKibben Pneumatic Artificial Muscles
,”
IEEE Trans. Rob. Autom.
,
12
(
1
), pp.
90
102
.
27.
Yeoh
,
O. H.
,
1993
, “
Some Forms of the Strain Energy Function for Rubber
,”
Rubber Chem. Technol.
,
66
(
5
), pp.
754
771
.
28.
Ogden
,
R.
,
1976
, “
Volume Changes Associated With the Deformation of Rubber-Like Solids
,”
J. Mech. Phys. Solids
,
24
(
6
), pp.
323
338
.
29.
Pamplona
,
D.
, and
Mota
,
D.
,
2012
, “
Numerical and Experimental Analysis of Inflating a Circular Hyperelastic Membrane Over a Rigid and Elastic Foundation
,”
Int. J. Mech. Sci.
,
65
(
1
), pp.
18
23
.
30.
Needleman
,
A.
,
1977
, “
Inflation of Spherical Rubber Balloons
,”
Int. J. Solids Struct.
,
13
(
5
), pp.
409
421
.
31.
Zhang
,
H.
,
Wang
,
M. Y.
,
Chen
,
F.
,
Wang
,
Y.
,
Kumar
,
A. S.
, and
Fuh
,
J. Y. H.
,
2017
, “
Design and Development of a Soft Gripper With Topology Optimization
,” 2017
IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
,
IEEE
.
32.
Ortmaier
,
T. J.
,
Raatz
,
A.
, and
Wallaschek
,
J.
,
2020
, “
Smart—Soft Material Robotics Toolbox
,”
November
, Online, www.spp2100.de/project?tx˙news_pi1%5Baction%5D=detail&tx˙news˙pi1%5Bco%ntroller%5D=News&tx˙news_pi1%5Bnews%5D=12&cHash=66628cae687f767773561b87dfb4%0bd0, Accessed December 17, 2020.
You do not currently have access to this content.