Abstract

Continuum mechanisms have drawn wide attention to scholars due to their salient advantages including compliance and dexterity. In this paper, a planar continuum mechanism made of soft panels is proposed. This mechanism has a reduced degree-of-freedom (DOF) compared with some existing continuum mechanisms capable of 3D motion. However, it can meet some application requirements in the field of robot and aerospace due to its characteristics of small stiffness in the motion plane and large stiffness perpendicular to the motion plane. Besides, a combined kinematics and statics modeling approach is presented for this mechanism by using the classical beam theory and a constrained optimization method. In order to ensure the model accuracy, a hybrid approach is proposed to consider gravity depending on the deformation under study. By comparing our results with those from the commonly used constant-curvature method, it is shown that our model is more accurate in predicting the deformation shapes.

References

1.
Burgner-Kahrs
,
J.
,
Rucker
,
D. C.
, and
Choset
,
H.
,
2015
, “
Continuum Robots for Medical Applications: A Survey
,”
IEEE Trans. Rob.
,
31
(
6
), pp.
1261
1280
. 10.1109/TRO.2015.2489500
2.
Walker
,
I. D.
,
Kier
,
W. M.
,
Rahn
,
C. D.
, and
Zhang
,
Q. M.
,
2005
, “
Continuum Robot Arms Inspired by Cephalopods
,”
Proceedings of SPIE—The International Society for Optical Engineering
,
Orlando, FL
,
Oct. 25–28
, Vol.
5804
, pp.
303
314
.
3.
Kier
,
W. M.
, and
Smith
,
K. K.
,
2010
, “
Tongues, Tentacles and Trunks: The Biomechanics of Movement in Muscular-Hydrostats
,”
Zool. J. Linn. Soc.
,
83
(
4
), pp.
307
324
. 10.1111/j.1096-3642.1985.tb01178.x
4.
Robinson
,
G.
, and
Davies
,
J. B. C.
,
1999
, “
Continuum Robots—a State of the Art
,”
Proceedings of IEEE International Conference on Robotics and Automation
,
Detroit, MI
,
May 10–15
, Vol.
2844
, pp.
2849
2854
.
5.
Walker
,
I. D.
,
2013
, “
Continuous Backbone “Continuum” Robot Manipulators
,”
ISRN Rob.
,
2013
(
2013
), pp.
1
19
. 10.5402/2013/726506
6.
Hasanzadeh
,
S.
, and
Janabi-Sharifi
,
F.
,
2014
, “
An Efficient Static Analysis of Continuum Robots
,”
ASME J. Mech. Rob.
,
6
(
3
), p.
031011
. 10.1115/1.4027305
7.
Mahl
,
T.
,
Hildebrandt
,
A.
, and
Sawodny
,
O.
,
2014
, “
A Variable Curvature Continuum Kinematics for Kinematic Control of the Bionic Handling Assistant
,”
IEEE Trans. Rob.
,
30
(
4
), pp.
935
949
. 10.1109/TRO.2014.2314777
8.
Rucker
,
D. C.
,
Jones
,
B. A.
, and
Iii
,
R. J. W.
,
2010
, “
A Geometrically Exact Model for Externally Loaded Concentric-Tube Continuum Robots
,”
IEEE Trans. Rob. A Publication IEEE Rob. Automation Soc.
,
26
(
5
), p.
769
.
9.
Godage
,
I. S.
,
Guglielmino
,
E.
,
Branson
,
D. T.
,
Medrano-Cerda
,
G. A.
, and
Caldwell
,
D. G.
,
2011
, “
Novel Modal Approach for Kinematics of Multisection Continuum Arms
,”
Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems
,
San Francisco, CA
,
Sept. 25–30
, pp.
1093
1098
.
10.
Salvador
,
C. G.
,
David
,
P.
, and
Dragos
,
A.
,
2015
, “
Kinematic Model to Control the end-Effector of a Continuum Robot for Multi-Axis Processing
,”
Robotica
,
35
(
1
), pp.
224
240
.
11.
Lock
,
J.
,
Laing
,
G.
,
Mahvash
,
M.
, and
Dupont
,
P. E.
,
2010
, “
Quasistatic Modeling of Concentric Tube Robots With External Loads
,”
2010 IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Taipei, Taiwan
,
Oct. 18–22
.
12.
Black
,
C. B.
,
Till
,
J.
, and
Rucker
,
D. C.
,
2018
, “
Parallel Continuum Robots: Modeling, Analysis, and Actuation-Based Force Sensing
,”
IEEE Trans. Rob.
,
34
(
1
), pp.
29
47
. 10.1109/TRO.2017.2753829
13.
Till
,
J.
, and
Rucker
,
D. C.
,
2017
, “
Elastic Stability of Cosserat Rods and Parallel Continuum Robots
,”
IEEE Trans. Rob.
,
33
(
3
), pp.
718
733
. 10.1109/TRO.2017.2664879
14.
Xu
,
K.
, and
Simaan
,
N.
,
2010
, “
Analytic Formulation for Kinematics, Statics, and Shape Restoration of Multibackbone Continuum Robots Via Elliptic Integrals
,”
ASME J. Mech. Rob.
,
2
(
1
), p.
011006
. 10.1115/1.4000519
15.
Kang
,
B.
,
Kojcev
,
R.
, and
Sinibaldi
,
E.
,
2016
, “
The First Interlaced Continuum Robot, Devised to Intrinsically Follow the Leader
,”
PLoS One
,
11
(
2
), p.
e0150278
. 10.1371/journal.pone.0150278
16.
Rone
,
W. S.
, and
Ben-Tzvi
,
P.
,
2014
, “
Mechanics Modeling of Multisegment Rod-Driven Continuum Robots
,”
ASME J. Mech. Rob.
,
6
(
4
), p.
041006
. 10.1115/1.4027235
17.
Wang
,
L.
,
Giudice
,
G. D.
, and
Simaan
,
N.
,
2019
, “
Simplified Kinematics of Continuum Robot Equilibrium Modulation Via Moment Coupling Effects and Model Calibration
,”
ASME J. Mech. Rob.
,
11
(
5
), p.
1
. 10.1115/1.4044162
18.
Webster
,
R. J.
, and
Jones
,
B. A.
,
2010
, “
Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review
,”
Int. J. Rob. Res.
,
29
(
13
), pp.
1661
1683
. 10.1177/0278364910368147
19.
Tian
,
Y.
,
Luan
,
M.
,
Gao
,
X.
,
Wang
,
W.
, and
Li
,
L.
,
2016
, “
Kinematic Analysis of Continuum Robot Consisted of Driven Flexible Rods
,”
Math. Probl. Eng.
,
2016
(
2016
), pp.
1
7
.
20.
Howell
,
L. L.
,
2001
, “Compliant Mechanisms,”
21st Century Kinematics
, Vol.
1
,
Springer
,
London
, pp.
457
463
.
21.
Kimball
,
C.
, and
Tsai
,
L.-W.
,
2002
, “
Modeling of Flexural Beams Subjected to Arbitrary End Loads
,”
ASME J. Mech. Des.
,
124
(
2
), pp.
223
235
. 10.1115/1.1455031
22.
Jin
,
M.
,
Yang
,
Z.
,
Ynchausti
,
C.
,
Zhu
,
B.
,
Zhang
,
X.
, and
Howell
,
L. L.
,
2020
, “
Large Deflection Analysis of General Beams in Contact-Aided Compliant Mechanisms Using Chained Pseudo-Rigid-Body Model
,”
ASME J. Mech. Rob.
,
12
(
3
), pp.
1
14
.
23.
Ma
,
F.
, and
Chen
,
G.
,
2016
, “
Modeling Large Planar Deflections of Flexible Beams in Compliant Mechanisms Using Chained Beam-Constraint-Model
,”
ASME J. Mech. Rob.
,
8
(
2
), p.
021018
. 10.1115/1.4031028
24.
Zhu
,
S.-K.
, and
Yu
,
Y.-Q.
,
2017
, “
Pseudo-Rigid-Body Model for the Flexural Beam With an Inflection Point in Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
9
(
3
), p.
031005
. 10.1115/1.4035986
25.
Li
,
N.
,
Su
,
H.
, and
Zhang
,
X.
,
2017
, “
Accuracy Assessment of Pseudo-Rigid-Body Model for Dynamic Analysis of Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
9
(
5
), p.
054503
. 10.1115/1.4037186
26.
Jr
,
R. P. C.
,
Todd
,
R. H.
,
Howell
,
L. L.
, and
Magleby
,
S. P.
,
2011
, “
A 3-D Chain Algorithm With Pseudo-Rigid-Body Model Elements
,”
Mech. Based Des. Struct. Mach.
,
39
(
1
), pp.
142
156
. 10.1080/15397734.2011.541783
27.
Zhang
,
A.
, and
Chen
,
G.
,
2013
, “
A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Thin Beams in Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
5
(
2
), p.
021006
. 10.1115/1.4023558
28.
Altuzarra
,
O.
,
Diez
,
M.
,
Corral
,
J.
,
Teoli
,
G.
, and
Ceccarelli
,
M.
,
2017
, “Kinematic Analysis of a Continuum Parallel Robot,”
New Trends in Mechanism and Machine Science
, Vol.
1
,
Springer
,
Cham
, pp.
173
180
.
29.
Li
,
L.
,
Zhao
,
Y.
,
Tian
,
Y.
,
Wang
,
W.
,
Chen
,
W.
,
Gao
,
Z.
,
Lu
,
Y.
, and
Xi
,
F.
, “
Shape Modeling of a Parallel Soft Panel Continuum Robot
,”
Proceedings of 2018 IEEE International Conference on Robotics and Biomimetics (ROBIO)
,
Kuala Lumpur, Malaysia
,
Dec. 12–15
, pp.
367
372
.
30.
Banerjee
,
A.
,
Bhattacharya
,
B.
, and
Mallik
,
A. K.
,
2008
, “
Large Deflection of Cantilever Beams With Geometric Non-Linearity: Analytical and Numerical Approaches
,”
Int. J. Non-Linear Mech.
,
43
(
5
), pp.
366
376
. 10.1016/j.ijnonlinmec.2007.12.020
You do not currently have access to this content.