This paper proposes the design of a novel 3-DOF monolithic manipulator. This manipulator is capable of performing planar manipulations with three kinematically coupled DOFs, i.e., the translations in the X and Y axes and the rotation about the Z axis. An improved Scott-Russell (ISR) mechanism is utilized to magnify the displacement of the piezoelectric actuator (PEA). Unlike the SR mechanism, a set of leaf parallelograms is incorporated into the drive point of the ISR mechanism as a prismatic joint. As a result, the linearity of motion and stability are improved. With circular flexure hinges being treated as revolute joints, the forward kinematics and inverse kinematics of the 3-DOF manipulator are analytically derived. Computational analyses are performed to validate the established kinematics models. Due to the unwanted compliance of the flexure hinges, the actual displacement amplification ratio of the ISR mechanism is smaller than its theoretical value. This is the main cause of the discrepancies between the analytical and computational results. The reachable workspace and the static/dynamic characteristics of the 3-DOF manipulator are also analyzed.

References

References
1.
Kenton
,
B. J.
, and
Leang
,
K. K.
,
2012
, “
Design and Control of a Three-Axis Serial-Kinematic High-Bandwidth Nanopositioner
,”
IEEE/ASME Trans. Mech.
,
17
(
2
), pp.
356
369
.10.1109/TMECH.2011.2105499
2.
Zubir
,
M. N. M.
,
Shirinzadeh
,
B.
, and
Tian
,
Y.
,
2009
, “
Development of a Novel Flexure-Based Microgripper for High Precision Micro-Object Manipulation
,”
Sens. Actuators, A
,
150
(
2
), pp.
257
266
.10.1016/j.sna.2009.01.016
3.
Kuhnen
,
K.
,
2003
, “
Modelling, Identification and Compensation of Complex Hysteretic Nonlinearities—A Modified Prandtl-Ishlinskii Approach
,”
Eur. J. Control
,
9
(
4
), pp.
407
418
.10.3166/ejc.9.407-418
4.
Qin
,
Y.
,
Tian
,
Y.
,
Zhang
,
D.
,
Shirinzadeh
,
B.
, and
Fatikow
,
S.
,
2013
, “
A Novel Direct Inverse Modeling Approach for Hysteresis Compensation of Piezoelectric Actuator in Feedforward Applications
,”
IEEE/ASME Trans. Mech.
,
18
(
3
), pp.
981
989
.10.1109/TMECH.2012.2194301
5.
Zhong
,
J.
, and
Yao
,
B.
,
2008
, “
Adaptive Robust Precision Motion Control of a Piezoelectric Positioning Stage
,”
IEEE Trans. Control Syst. Technol.
,
16
(
5
), pp.
1039
1046
.10.1109/TCST.2007.916319
6.
Liaw
,
H. C.
, and
Shirinzadeh
,
B.
,
2011
, “
Robust Adaptive Constrained Motion Tracking Control of Piezo-Actuated Flexure-Based Mechanisms for Micro/Nano Manipulation
,”
IEEE Trans. Ind. Electron.
,
58
(
4
), pp.
1406
1415
.10.1109/TIE.2010.2050413
7.
Chen
,
G.
,
Liu
,
X.
, and
Du
,
Y.
,
2011
, “
Elliptical-Arc-Fillet Flexure Hinges: Toward a Generalized Model for Commonly Used Flexure Hinges
,”
ASME J. Mech. Des.
,
133
(
8
), p.
081002
.10.1115/1.4004441
8.
Tian
,
Y.
,
Shirinzadeh
,
B.
, and
Zhang
,
D.
,
2010
, “
Closed-Form Compliance Equations of Filleted V-Shaped Flexure Hinges for Compliant Mechanism Design
,”
Precis. Eng.
,
34
(
3
), pp.
408
418
.10.1016/j.precisioneng.2009.10.002
9.
Lobontiu
,
N.
, and
Garcia
,
E.
,
2005
, “
Circular-Hinge Line Element for Finite Element Analysis of Compliant Mechanisms
,”
ASME J. Mech. Des.
,
127
(
4
), pp.
766
773
.10.1115/1.1825046
10.
Yong
,
Y. K.
, and
Lu
,
T.-F.
,
2009
, “
Kinetostatic Modeling of 3-RRR Compliant Micro-Motion Stages with Flexure Hinges
,”
Mech. Mach. Theory
,
44
(
6
), pp.
1156
1175
.10.1016/j.mechmachtheory.2008.09.005
11.
Tian
,
Y.
,
Shirinzadeh
,
B.
, and
Zhang
,
D.
,
2009
, “
A Flexure-Based Five-Bar Mechanism for Micro/Nano Manipulation
,”
Sens. Actuators, A
,
153
(
1
), pp.
96
104
.10.1016/j.sna.2009.04.022
12.
Choi
,
S. B.
,
Han
,
S. S.
,
Han
,
Y. M.
, and
Thompson
,
B. S.
,
2007
, “
A Magnification Device for Precision Mechanisms Featuring Piezoactuators and Flexure Hinges: Design and Experimental Validation
,”
Mech. Mach. Theory
,
42
(
9
), pp.
1184
1198
.10.1016/j.mechmachtheory.2006.08.009
13.
Tian
,
Y.
,
Shirinzadeh
,
B.
,
Zhang
,
D.
, and
Alici
,
G.
,
2009
, “
Development and Dynamic Modelling of a Flexure-Based Scott-Russell Mechanism for Nano-Manipulation
,”
Mech. Syst. Signal Process.
,
23
(
3
), pp.
957
978
.10.1016/j.ymssp.2008.06.007
14.
Ha
,
J.-L.
,
Kung
,
Y.-S.
,
Hu
,
S.-C.
, and
Fung
,
R.-F.
,
2006
, “
Optimal Design of a Micro-Positioning Scott-Russell Mechanism by Taguchi Method
,”
Sens. Actuators A
,
125
(
2
), pp.
565
572
.10.1016/j.sna.2005.06.025
15.
Chang
,
S. H.
, and
Du
,
B. C.
,
1998
, “
A Precision Piezodriven Micropositioner Mechanism with Large Travel Range
,”
Rev. Sci. Instrum.
,
69
(
4
), pp.
1785
1791
.10.1063/1.1148842
16.
Hwang
,
D.
,
Byun
,
J.
,
Jeong
,
J.
, and
Lee
,
M. G.
,
2011
, “
Robust Design and Performance Verification of an in-Plane XYθ Micropositioning Stage
,”
IEEE Trans. Nanotechnol.
,
10
(
6
), pp.
1412
1423
.10.1109/TNANO.2011.2159015
17.
Wu
,
Y.
, and
Zhou
,
Z.
,
2004
, “
An XYθ Mechanism Actuated by One Actuator
,”
Mech. Mach. Theory
,
39
(
10
), pp.
1101
1110
.10.1016/j.mechmachtheory.2003.09.001
18.
Lobontiu
,
N.
, and
Garcia
,
E.
,
2003
, “
Analytical Model of Displacement Amplification and Stiffness Optimization for a Class of Flexure-Based Compliant Mechanisms
,”
Comput. Struct.
,
81
(
32
), pp.
2797
2810
.10.1016/j.compstruc.2003.07.003
19.
Xu
,
Q.
, and
Li
,
Y.
,
2011
, “
Analytical Modeling, Optimization and Testing of a Compound Bridge-Type Compliance Displacement Amplifier
,”
Mech. Mach. Theory
,
46
(
2
), pp.
183
200
.10.1016/j.mechmachtheory.2010.09.007
20.
Secord
,
T.
, and
Asada
,
H. H.
,
2010
, “
A Variable Stiffness PZT Actuator Having Tunable Resonant Frequencies
,”
IEEE Trans. Rob.
,
26
(
6
), pp.
993
1005
.10.1109/TRO.2010.2076850
21.
Liaw
,
H. C.
,
Shirinzadeh
,
B.
, and
Smith
,
J.
,
2008
, “
Robust Motion Tracking Control of Piezo-Driven Flexure-Based Four-Bar Mechanism for Micro/Nano Manipulation
,”
Mechatronics
,
18
(
2
), pp.
111
120
.10.1016/j.mechatronics.2007.09.002
22.
Ouyang
,
P. R.
,
Zhang
,
W. J.
, and
Gupta
,
M. M.
,
2008
, “
A New Compliant Mechanical Amplifier Based on a Symmetric Five-Bar Topology
,”
ASME J. Mech. Des.
,
130
(
10
),
p. 104501
.10.1115/1.2965600
23.
Li
,
Y.
, and
Xu
,
Q.
,
2010
, “
Development and Assessment of a Novel Decoupled XY Parallel Micropositioning Platform
,”
IEEE/ASME Trans. Mech.
,
15
(
1
), pp.
125
135
.10.1109/TMECH.2009.2026473
24.
Qin
,
Y.
,
Shirinzadeh
,
B.
,
Tian
,
Y.
, and
Zhang
,
D.
,
2013
, “
Design Issues in a Decoupled XY Stage: Static and Dynamics Modeling, Hysteresis Compensation, and Tracking Control
,”
Sens. Actuators
,
194
, pp.
95
105
.10.1016/j.sna.2013.02.003
25.
Polit
,
S.
, and
Dong
,
J.
,
2011
, “
Development of a High-Bandwidth XY Nanopositioning Stage for High-Rate Micro-/Nanomanufacturing
,”
IEEE/ASME Trans. Mech.
,
16
(
4
), pp.
724
733
.10.1109/TMECH.2010.2052107
26.
Yao
,
Q.
,
Dong
,
J.
, and
Ferreira
,
P. M.
,
2007
, “
Design, Analysis, Fabrication and Testing of a Parallel-Kinematic Micropositioning Xy Stage
,”
Int. J. Mach. Tools Manuf.
,
47
(
6
), pp.
946
961
.10.1016/j.ijmachtools.2006.07.007
27.
Qin
,
Y.
,
Shirinzadeh
,
B.
,
Tian
,
Y.
,
Zhang
,
D.
, and
Bhagat
,
U.
, “
Design and Computational Optimization of a Decoupled 2-DOF Monolithic Mechanism
,”
IEEE/ASME Trans. Mech.
, (in press).10.1109/TMECH.2013.2262801
28.
Tian
,
Y.
,
Shirinzadeh
,
B.
, and
Zhang
,
D.
,
2010
, “
Design and Dynamics of a 3-DOF Flexure-Based Parallel Mechanism for Micro/Nano Manipulation
,”
Microelectron. Eng.
,
87
(
2
), pp.
230
241
.10.1016/j.mee.2009.08.001
29.
Dong
,
J.
,
Yao
,
Q.
, and
Ferreira
,
P. M.
,
2008
, “
A Novel Parallel-Kinematics Mechanism for Integrated, Multi-Axis Nanopositioning—Part 2: Dynamics, Control and Performance Analysis
,”
Precis. Eng.
,
32
(
1
), pp.
20
33
.10.1016/j.precisioneng.2007.03.002
30.
Paros
,
J. M.
, and
Weisbord
,
L.
,
1965
, “
How to Design Flexure Hinges
,”
Mach. Des.
,
37
(
27
), pp.
151
156
.
31.
Wu
,
Y.
, and
Zhou
,
Z.
,
2002
, “
Design Calculations for Flexure Hinges
,”
Rev. Sci. Instrum.
,
73
(
8
), pp.
3101
3106
.10.1063/1.1494855
32.
Qin
,
Y.
,
Shirinzadeh
,
B.
,
Zhang
,
D.
, and
Tian
,
Y.
,
2013
, “
Compliance Modeling and Analysis of the Statically Indeterminate Symmetric Flexure Structure
,”
Precis. Eng.
,
37
(
2
), pp.
415
424
.10.1016/j.precisioneng.2012.11.004
33.
Fung
,
R.-F.
,
Weng
,
M.-H.
, and
Kung
,
Y.-S.
,
2009
, “
FPGA-Based Adaptive Backstepping Fuzzy Control for a Micro-Positioning Scott-Russell Mechanism
,”
Mech. Syst. Signal Process.
,
23
(
8
), pp.
2671
2686
.10.1016/j.ymssp.2009.01.005
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