Graphical Abstract Figure
Graphical Abstract Figure
Close modal

Abstract

In this paper, a spherical parallel continuum manipulator (SPCM) which is the flexible version of the 3-RRR“Agile Eye” mechanism is proposed and analyzed. The SPCM consists of three parallel flexible limbs, each limb is formed by compliant truncated cone elements, and the moving platform connects each limb with a passive revolute joint. Three servo motors are used to control the manipulator actively, and the spherical motion is realized by the coupled large deflections of the flexible links. An equivalent compliance analysis method of the element is developed based on finite element analysis and principal axis decomposition. By combining all three limbs, the kinetostatics model of the whole manipulator is derived, and a gradient iteration algorithm is developed to solve the forward and inverse kinetostatics. Finally, a prototype of the manipulator is constructed using 3D-printing technology, and the accuracy for element equivalence and end-effector characteristics is validated by experiments. The results show that the derived kinetostatics model can accurately describe the force–deflection behavior of the SPCM.

References

1.
Bryson
,
C. E.
, and
Rucker
,
D. C.
,
2014
, “
Toward Parallel Continuum Manipulators
,”
2014 IEEE International Conference on Robotics and Automation (ICRA)
,
Hong Kong, China
,
May 31–June 7
,
IEEE, pp. 778–785
.
2.
Black
,
C. B.
,
Till
,
J.
, and
Rucker
,
D. C.
,
2018
, “
Parallel Continuum Robots: Modeling, Analysis, and Actuation-Based Force Sensing
,”
IEEE Trans. Robot.
,
34
(
1
), pp.
29
47
.
3.
Chen
,
G.
,
Zhang
,
Z.
, and
Wang
,
H.
,
2018
, “
A General Approach to the Large Deflection Problems of Spatial Flexible Rods Using Principal Axes Decomposition of Compliance Matrices
,”
ASME J. Mech. Rob.
,
10
(
3
), p.
031012
.
4.
Altuzarra
,
O.
,
Caballero
,
D.
,
Campa
,
F. J.
, and
Pinto
,
C.
,
2018
, “
Forward and Inverse Kinematics in 2-DOF Planar Parallel Continuum Manipulators
,”
EuCoMeS 2018: Proceedings of the 7th European Conference on Mechanism Science
,
Aachen, Germany
,
Sept. 4–6
, pp.
231
238
.
5.
Young
,
E. M.
, and
Kuchenbecker
,
K. J.
,
2019
, “
Implementation of a 6-DOF Parallel Continuum Manipulator for Delivering Fingertip Tactile Cues
,”
IEEE Trans. Haptics
,
12
(
3
), pp.
295
306
.
6.
Chen
,
G.
,
Zhang
,
Z.
,
Kong
,
L.
, and
Wang
,
H.
,
2020
, “
Analysis and Validation of a Flexible Planar Two Degrees-of-Freedom Parallel Manipulator With Structural Passive Compliance
,”
ASME J. Mech. Rob.
,
12
(
1
), p.
011011
.
7.
Boettcher
,
G.
,
Lilge
,
S.
, and
Burgner-Kahrs
,
J.
,
2021
, “
Design of a Reconfigurable Parallel Continuum Robot With Tendon-Actuated Kinematic Chains
,”
IEEE Robot. Autom. Lett.
,
6
(
2
), pp.
1272
1279
.
8.
Chen
,
G.
,
Tang
,
S.
,
Duan
,
X.
, and
Wang
,
H.
,
2024
, “
Design, Modeling, and Evaluation of Parallel Continuum Robots: A Survey
,”
Sci. China Technol. Sci
,
67
(
3
), pp.
673
695
.
9.
Van Ham
,
R.
,
Sugar
,
T. G.
,
Vanderborght
,
B.
,
Hollander
,
K. W.
, and
Lefeber
,
D.
,
2009
, “
Compliant Actuator Designs
,”
IEEE Robot. Autom. Mag.
,
16
(
3
), pp.
81
94
.
10.
Yu
,
H.
,
Huang
,
S.
,
Chen
,
G.
, and
Thakor
,
N.
,
2013
, “
Control Design of a Novel Compliant Actuator for Rehabilitation Robots
,”
Mechatronics
,
23
(
8
), pp.
1072
1083
.
11.
Trease
,
B. P.
,
Moon
,
Y. -M.
, and
Kota
,
S.
,
2005
, “
Design of Large-Displacement Compliant Joints
,”
ASME J. Mech. Des.
,
127
(
4
), pp.
788
798
.
12.
Cestari
,
M.
,
Sanz-Merodio
,
D.
,
Arevalo
,
J. C.
, and
Garcia
,
E.
,
2015
, “
An Adjustable Compliant Joint for Lower-Limb Exoskeletons
,”
IEEE/ASME Trans. Mechatron.
,
20
(
2
), pp.
889
898
.
13.
She
,
Y.
,
Meng
,
D.
,
Cui
,
J.
, and
Su
,
H.-J.
,
2017
, “
On the Impact Force of Human-Robot Interaction: Joint Compliance Versus Link Compliance
,”
2017 IEEE International Conference on Robotics and Automation (ICRA)
,
Marina Bay, Singapore
,
May 29–June 3
,
IEEE, pp. 6718–6723
.
14.
Campa
,
F. J.
,
Diez
,
M.
,
Diaz-Caneja
,
D.
, and
Altuzarra
,
O.
,
2019
, “
A 2 Dof Continuum Parallel Robot for Pick & Place Collaborative Tasks
,”
Proceedings of the 15th IFToMM World Congress on Mechanism and Machine Science
,
Krakow, Poland
,
June 30–July 4
, pp.
1979
1988
.
15.
Mauze
,
B.
,
Dahmouche
,
R.
,
Laurent
,
G. J.
,
Andre
,
A. N.
,
Rougeot
,
P.
,
Sandoz
,
P.
, and
Clevy
,
C.
,
2020
, “
Nanometer Precision With a Planar Parallel Continuum Robot
,”
IEEE Robot. Autom. Lett.
,
5
(
3
), pp.
3806
3813
.
16.
Lilge
,
S.
,
Nuelle
,
K.
,
Boettcher
,
G.
,
Spindeldreier
,
S.
, and
Burgner-Kahrs
,
J.
,
2020
, “
Tendon Actuated Continuous Structures in Planar Parallel Robots: A Kinematic Analysis
,”
ASME J. Mech. Rob.
,
13
(
1
), p.
011025
.
17.
Nuelle
,
K.
,
Sterneck
,
T.
,
Lilge
,
S.
,
Xiong
,
D.
,
Burgner-Kahrs
,
J.
, and
Ortmaier
,
T.
,
2020
, “
Modeling, Calibration, and Evaluation of a Tendon-Actuated Planar Parallel Continuum Robot
,”
IEEE Robot. Autom. Lett.
,
5
(
4
), pp.
5811
5818
.
18.
Duan
,
X.
,
Yan
,
W.
,
Chen
,
G.
, and
Wang
,
H.
,
2022
, “
Analysis and Validation of a Planar Parallel Continuum Manipulator With Variable Cartesian Stiffness
,”
Mech. Mach. Theory
,
177
, p.
105030
.
19.
Festo
,
2011
, “Bionic Tripod 3.0: A Highly Dynamic Flexible Tripod,”.
20.
Till
,
J.
,
Bryson
,
C. E.
,
Chung
,
S.
,
Orekhov
,
A.
, and
Rucker
,
D. C.
,
2015
, “
Efficient Computation of Multiple Coupled Cosserat Rod Models for Real-Time Simulation and Control of Parallel Continuum Manipulators
,”
2015 IEEE International Conference on Robotics and Automation (ICRA)
,
Seattle, WA
,
May 25–30
,
IEEE, pp. 5067–5074
.
21.
Orekhov
,
A. L.
,
Bryson
,
C. E.
,
Till
,
J.
,
Chung
,
S.
, and
Rucker
,
D. C.
,
2015
, “
A Surgical Parallel Continuum Manipulator With a Cable-Driven Grasper
,”
2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)
,
Milan, Italy
,
Aug. 25–29
, pp.
5264
5267
.
22.
Orekhov
,
A. L.
,
Black
,
C. B.
,
Till
,
J.
,
Chung
,
S.
, and
Rucker
,
D. C.
,
2016
, “
Analysis and Validation of a Teleoperated Surgical Parallel Continuum Manipulator
,”
IEEE Robot. Autom. Lett.
,
1
(
2
), pp.
828
835
.
23.
Till
,
J.
, and
Rucker
,
D. C.
,
2017
, “
Elastic Stability of Cosserat Rods and Parallel Continuum Robots
,”
IEEE Trans. Robot.
,
33
(
3
), pp.
718
733
.
24.
Aloi
,
V.
,
Black
,
C.
, and
Rucker
,
C.
,
2018
, “
Stiffness Control of Parallel Continuum Robots
,”
ASME 2018 Dynamic Systems and Control Conference
,
Atlanta, GA
,
Sept. 30–Oct. 3
,
p. V001T04A012
.
25.
Pan
,
H.
,
Chen
,
G.
,
Kang
,
Y.
, and
Wang
,
H.
,
2020
, “
‘Design and Kinematic Analysis of a Flexible-Link Parallel Mechanism With a Spatially Quasi-translational End Effector’
,”
ASME J. Mech. Rob.
,
13
(
1
), p.
011022
.
26.
Yang
,
Z.
,
Zhu
,
X.
, and
Xu
,
K.
,
2018
, “
Continuum Delta Robot: A Novel Translational Parallel Robot With Continuum Joints
,”
2018 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)
,
Auckland, New Zealand
,
July 9–12
,
IEEE, pp. 748–755
.
27.
Bouri
,
M.
, and
Clavel
,
R.
,
2010
, “
The Linear Delta: Developments and Applications
,”
ISR 2010 (41st International Symposium on Robotics) and ROBOTIK 2010 (6th German Conference on Robotics)
,
Munich, Germany
,
June 7–9
, pp.
1
8
.
28.
Gosselin
,
C. M.
, and
Hamel
,
J. -F.
,
1994
, “
The Agile Eye: A High-Performance Three-Degree-of-Freedom Camera-Orienting Device
,”
Proceedings of the 1994 IEEE International Conference on Robotics and Automation
,
San Diego, CA
,
May 8–13
,
IEEE, pp. 781–786
.
29.
Arredondo-Soto
,
M.
,
Cuan-Urquizo
,
E.
,
Gómez-Espinosa
,
A.
,
Roman-Flores
,
A.
,
Coronado
,
P. D. U.
, and
Jimenez-Martinez
,
M.
,
2023
, “
The Compliant Version of the 3-RRR Spherical Parallel Mechanism Known as “Agile-Eye”: Kinetostatic Analysis and Parasitic Displacement Evaluation
,”
Mech. Mach. Theory
,
180
, p.
105160
.
30.
Rubbert
,
L.
,
Renaud
,
P.
, and
Gangloff
,
J.
,
2012
, “
Design and Optimization for a Cardiac Active Stabilizer Based on Planar Parallel Compliant Mechanisms
,”
ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis, Volume 3: Advanced Composite Materials and Processing; Robotics; Information Management and PLM; Design Engineering
,
Nantes, France
,
July 2–4
, pp.
235
244
.
31.
Rommers
,
J.
,
van der Wijk
,
V.
, and
Herder
,
J. L.
,
2021
, “
A New Type of Spherical Flexure Joint Based on Tetrahedron Elements
,”
Precis. Eng.
,
71
, pp.
130
140
.
32.
Chen
,
G.
,
Wang
,
H.
,
Lin
,
Z.
, and
Lai
,
X.
,
2015
, “
The Principal Axes Decomposition of Spatial Stiffness Matrices
,”
IEEE Trans. Robot.
,
31
(
1
), pp.
191
207
.
33.
Klimchik
,
A.
,
Pashkevich
,
A.
, and
Chablat
,
D.
,
2013
, “
CAD-Based Approach for Identification of Elasto-Static Parameters of Robotic Manipulators
,”
Finite Elem. Anal. Des.
,
75
, pp.
19
30
.
34.
Lynch
,
K. M.
, and
Park
,
F. C.
,
2017
,
Modern Robotics
,
Cambridge University Press
,
Cambridge, UK
.
35.
Selig
,
J. M.
,
2004
,
Geometric Fundamentals of Robotics
,
Springer Science & Business Media
,
New York
.
36.
Chen
,
G.
,
Kang
,
Y.
,
Liang
,
Z.
,
Zhang
,
Z.
, and
Wang
,
H.
,
2021
, “
Kinetostatics Modeling and Analysis of Parallel Continuum Manipulators
,”
Mech. Mach. Theory
,
163
, p.
104380
.
37.
Chen
,
C.
, and
Jackson
,
D.
,
2011
, “
Parameterization and Evaluation of Robotic Orientation Workspace: A Geometric Treatment
,”
IEEE Trans. Robot.
,
27
(
4
), pp.
656
663
.
38.
Chen
,
X.
,
Chen
,
C.
, and
Liu
,
X.-J.
,
2015
, “
Evaluation of Force/torque Transmission Quality for Parallel Manipulators
,”
ASME J. Mech. Rob.
,
7
(
4
), p.
041013
.
You do not currently have access to this content.