Abstract

Intrinsic passive compliance of flexible-link parallel mechanisms makes them suitable for situations where compliant manipulation is necessary. In this work, through using elastic rods as limbs, a flexible-link parallel mechanism whose end effector can move translationally with a large workspace is proposed. The middle plate and end effector are connected to the base via two groups of three elastic rods, which are arranged in a cylindrically symmetric way with a phase difference of 60 deg. Concurrently, the middle plate is coupled with the elastic rods connected to the end effector via sliding connection. Besides, a rotating set of coplanar wheels is introduced to provide smooth coupling for the prototype. Three actuation modules are used to drive the end effector, while another three to compensate toward its configuration deviations caused by deformation compatibility. Then, based on principal axes decomposition of compliance matrix, kinetostatics models for inverse and forward kinematics are established. The numerical analysis reveals that the end effector can make quasi 3-degrees-of-freedom (DOF) translation in a large space with extremely small twist. Finally, workspace experiments at four typical slices and pose accuracy evaluation along continuous trajectories are carried out, and the results demonstrate that our design and theoretical model are correct.

References

1.
Merlet
,
J. P.
,
2006
,
Parallel Robots
,
Springer Science & Business Media
,
New York
.
2.
Stewart
,
D.
,
1965
, “
A Platform With Six Degrees of Freedom
,”
Proc. Inst. Mech. Eng.
,
180
(
1
), pp.
371
386
. 10.1243/PIME_PROC_1965_180_029_02
3.
Siciliano
,
B.
,
1999
, “
The Tricept Robot: Inverse Kinematics, Manipulability Analysis and Closed-Loop Direct Kinematics Algorithm
,”
Robotica
,
17
(
4
), pp.
437
445
. 10.1017/S0263574799001678
4.
Nevins
,
J. L.
, and
Whitney
,
D. E.
,
1979
, “
What Is Remote Center Compliance and What It Can Do
,”
Proceedings of 9th International Symposium on Industrial Robots
,
Washington, DC
,
Mar. 13–15
.
5.
FERROBOTICS
, “
Active Compliant Technology
,” https://www.ferrobotics.com/en, Accessed 27 February, 2020.
6.
Wei
,
G.
, and
Dai
,
J. S.
,
2014
, “
Origami-Inspired Integrated Planar-Spherical Overconstrained Mechanisms
,”
ASME J. Mech. Des.
,
136
(
5
), p.
051003
. 10.1115/1.4025821
7.
Chen
,
Y.
,
Sareh
,
P.
,
Yan
,
J.
,
Fallah
,
A. S.
, and
Feng
,
J.
,
2019
, “
An Integrated Geometric-Graph-Theoretic Approach to Representing Origami Structures and Their Corresponding Truss Frameworks
,”
ASME J. Mech. Des.
,
141
(
9
), p.
091402
. 10.1115/1.4042791
8.
Burns
,
R. H.
, and
Crossley
,
F. R.
,
1968
,
Kinetostatic Synthesis of Flexible Link Mechanisms
, (
American Society of Mechanical Engineers (Series)
), Vol.
90
,
ASME
,
New York
, p.
67
. Paper No. 11.
9.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley
,
New York
.
10.
Webster
,
R. J.
, and
Jones
,
B. A.
,
2010
, “
Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review
,”
Int. J. Robot. Res.
,
29
(
13
), pp.
1661
1683
. 10.1177/0278364910368147
11.
Gravagne
,
I. A.
,
Rahn
,
C. D.
, and
Walker
,
I. D.
,
2003
, “
Large Deflection Dynamics and Control for Planar Continuum Robots
,”
IEEE/ASME Trans. Mechatron.
,
8
(
2
), pp.
299
307
. 10.1109/TMECH.2003.812829
12.
Xu
,
K.
, and
Simaan
,
N.
,
2010
, “
Analytic Formulation for Kinematics, Statics, and Shape Restoration of Multibackbone Continuum Robots Via Elliptic Integrals
,”
ASME J. Mech. Robot.
,
2
(
1
), pp.
298
320
. 10.1115/1.4000519
13.
Bajo
,
A.
, and
Simaan
,
N.
,
2012
, “
Kinematics-Based Detection and Localization of Contacts Along Multisegment Continuum Robots
,”
IEEE Trans Rob.
,
28
(
2
), pp.
291
302
. 10.1109/TRO.2011.2175761
14.
Bajo
,
A.
, and
Simaan
,
N.
,
2015
, “
Hybrid Motion/Force Control of Multi-Backbone Continuum Robots
,”
Int. J. Robot. Res.
,
35
(
4
), pp.
422
434
. 10.1177/0278364915584806
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.
Abadi
,
B. N. R.
,
Shekarforoush
,
S. M. M.
,
Mahzoon
,
M.
, and
Farid
,
M.
,
2014
, “
Kinematic, Stiffness, and Dynamic Analyses of a Compliant Tensegrity Mechanism
,”
ASME J. Mech. Robot
,
6
(
4
), p.
041001
. 10.1115/1.4027699
17.
Carricato
,
M.
, and
Parenti-Castelli
,
V.
,
2003
, “
A Family of 3-dof Translational Parallel Manipulators
,”
ASME J. Mech. Des.
,
125
(
2
), pp.
302
307
. 10.1115/1.1563635
18.
Clavel
,
R.
,
1988
, “
Delta, a Fast Robot With Parallel Geometry
,”
Proceeding International Symposium on Industrial Robots
,
Sydney, Australia
,
Apr. 26–28
, pp.
91
100
.
19.
Gregorio
,
R. D.
, and
Parenti-Castelli
,
V.
,
2002
, “
Mobility Analysis of the 3-upu Parallel Mechanism Assembled for a Pure Translational Motion
,”
ASME J. Mech. Des.
,
124
(
2
), pp.
259
264
. 10.1115/1.1471530
20.
Gosselin
,
C. M.
,
Kong
,
X.
,
Foucault
,
S.
, and
Bonev
,
I. A.
,
2004
, “A Fully Decoupled 3-dof Translational Parallel Mechanism,”
Parallel Kinematic Machines in Research and Practice
,
Verlag Wissenschaftliche Scripten
,
Germany
, pp.
595
610
,
4th Chemnitz Parallel Kinematics Seminar
.
21.
Chablat
,
D.
, and
Wenger
,
P.
,
2007
, “
Architecture Optimization of a 3-dof Translational Parallel Mechanism for Machining Applications, the Orthoglide
,”
IEEE Trans Rob. Auto.
,
19
(
3
), pp.
403
410
. 10.1109/TRA.2003.810242
22.
Masters
,
N. D.
, and
Howell
,
L. L.
,
2003
, “
A Self-retracting Fully Compliant Bistable Micromechanism
,”
ASME J. Microelectromech. Syst.
,
12
(
3
), pp.
273
280
. 10.1109/JMEMS.2003.811751
23.
Han
,
J. S.
,
Muller
,
C.
,
Wallrabe
,
U.
, and
Korvink
,
J. G.
,
2007
, “
Design, Simulation, and Fabrication of a Quadstable Monolithic Mechanism With X- and Y-directional Bistable Curved Beams
,”
ASME J. Mech. Des.
,
129
(
11
), pp.
1198
1203
. 10.1115/1.2771577
24.
Oh
,
Y. S.
, and
Kota
,
S.
,
2009
, “
Synthesis of Multi-Stable Equilibrium Compliant Mechanisms Using Combinations of Bi-Stable Mechanisms
,”
ASME J. Mech. Des.
,
131
(
2
), p.
021002
. 10.1115/1.3013316
25.
Chen
,
G.
,
Aten
,
Q. T.
,
Zirbel
,
S.
,
Jensen
,
B. D.
, and
Howell
,
L. L.
,
2010
, “
A Tristable Mechanism Configuration Employing Orthogonal Compliant Mechanisms
,”
ASME J. Mech. Des.
,
2
(
1
), p.
014501
. 10.1115/1.4000529
26.
Chen
,
G.
,
Gou
,
Y.
, and
Zhang
,
A.
,
2011
, “
Synthesis of Compliant Multistable Mechanisms Through Use of a Single Bistable Mechanism
,”
ASME J. Mech. Des.
,
133
(
8
), p.
081007
. 10.1115/1.4004543
27.
Chen
,
G.
, and
Ma
,
F.
,
2015
, “
Kinetostatic Modeling of Fully Compliant Bistable Mechanisms Using Timoshenko Beam Constraint Model
,”
ASME J. Mech. Des.
,
137
(
2
), p.
022301
. 10.1115/1.4029024
28.
Chen
,
G.
,
Han
,
Q.
, and
Jin
,
K.
,
2020
, “
A Fully Compliant Tristable Mechanism Employing Both Tensural and Compresural Segments
,”
ASME J. Mech. Des.
,
12
(
1
), p.
011003
. 10.1115/1.4044736
29.
Simaan
,
N.
, and
Taylor
,
R.
,
2004
, “
A Dexterous System for Laryngeal Surgery Multi-Backbone Bending Snakelike Slaves for Teleoperated Dexterous Surgical Tool Manipulation
,”
2004 IEEE International Conference on Robotics and Automation (ICRA)
,
New Orleans, LA
,
Apr. 26–May 1
, Vol.
1
,
IEEE
, pp.
351
357
.
30.
Orekhov
,
A. L.
,
Aloi
,
A. V.
, and
Rucker
,
D. C.
,
2017
, “
Modeling Parallel Continuum Robots With General Intermediate Constraints
,”
2017 IEEE International Conference on Robotics and Automation (ICRA)
,
Singapore
,
May 29–June 3
, Vol.
1
,
IEEE
, pp.
6142
6149
.
31.
Xu
,
K.
,
Zhao
,
J.
, and
Fu
,
M.
,
2014
, “
Development of the Sjtu Unfoldable Robotic System (surs) for Single Port Laparoscopy
,”
IEEE/ASME Trans. Mechatronics
,
20
(
5
), pp.
2133
2145
. 10.1109/TMECH.2014.2364625
32.
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 5
,
IEEE
, pp.
778
785
.
33.
Orekhov
,
A. L.
,
Black
,
B. C.
,
Till
,
J.
,
Chung
,
S.
, and
Rucker
,
D. C.
,
2016
, “
Analysis and Validation of a Teleoperated Surgical Parallel Continuum Manipulator
,”
IEEE Trans Rob.
,
1
(
2
), pp.
828
835
. 10.1109/lra.2016.2525720
34.
Black
,
B. C.
,
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
35.
Young
,
E. M.
, and
Kuchenbecker
,
K. J.
,
2017
, “
Design of a Parallel Continuum Manipulator for 6-dof Fingertip Haptic Display
,”
2017 IEEE World Haptics Conference (WHC)
,
Munich, Germany
,
June 5–9
, IEEE, pp.
599
604
.
36.
Altuzarra
,
O.
,
Caballero
,
D.
,
Campa
,
F. J.
, and
Pinto
,
C.
,
2019
, “
Position Analysis in Planar Parallel Continuum Mechanisms
,”
Mech. Mach. Theory
,
132
, pp.
13
29
. 10.1016/j.mechmachtheory.2018.10.014
37.
FESTO
,
2011
, “
Brosch tripod 3
,” https://www.festo.com/net, Accessed 27 February, 2020.
38.
Wu
,
G.
, and
Shi
,
G.
,
2019
, “
Experimental Statics Calibration of a Multi-Constraint Parallel Continuum Robot
,”
Mech. Mach. Theory
,
136
, pp.
72
85
. 10.1016/j.mechmachtheory.2019.02.013
39.
Chen
,
G.
,
Wang
,
H.
,
Lin
,
Z.
, and
Lai
,
X.
,
2015
, “
The Principal Axes Decomposition of Spatial Stiffness Matrices
,”
IEEE Trans Rob.
,
31
(
1
), pp.
191
207
. 10.1109/TRO.2015.2389415
40.
Zhang
,
Z.
,
Chen
,
G.
,
Kong
,
L.
, and
Wang
,
H.
,
2018
, “
Design and Analysis of a Cross Trapezoid Spatial Compliant Device With Variable Stiffness
,”
42nd Mechanisms and Robotics Conference of International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Quebec City, Canada
,
Aug. 26–29
, Vol.
5A
, p.
V05AT07A037
.
41.
Du
,
C.
,
Chen
,
G.
,
Zhang
,
Z.
,
Tang
,
L.
, and
Wang
,
H.
,
2019
, “Design and Experimental Analysis of a Planar Compliant Parallel Manipulator,”
Intelligent Robotics and Applications
,
Springer
,
New York
, pp.
637
647
.
42.
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. Robot
,
12
(
1
), pp.
191
207
. 10.1115/1.4045036
43.
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. Robot
,
10
(
3
), p.
031012
. 10.1115/1.4039223
44.
Wei
,
G.
,
Chen
,
Y.
, and
Dai
,
J. S.
,
2014
, “
Synthesis, Mobility, and Multifurcation of Deployable Polyhedral Mechanisms With Radially Reciprocating Motion
,”
ASME J. Mech. Des.
,
136
(
9
), p.
091003
. 10.1115/1.4027638
45.
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
.
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