This paper presents an analytical model for calculating the workspace of a flexure-based hexapod nanopositioner previously built by the National Institute of Standards and Technology (NIST). This nanopositioner is capable of producing high-resolution motions in six degrees of freedom by actuating linear actuators on a planar tri-stage. However, the workspace of this positioner is still unknown, which limits its uses in practical applications. In this work, we seek to derive a kinematic model for predicting the workspace of such kinds of flexure based platforms by assuming that their workspace is mainly constrained by the deformation of flexure joints. We first study the maximum deformation including bending and torsion angles of an individual flexure joint. We then derive the inverse kinematics and calculation of bending and torsion angles of each wire flexure in the overall mechanism with given position of the top platform center of the hexapod nanopositioner. At last, we compare results with finite element models of the entire platform. This model is beneficial for workspace analysis and optimization for design of compliant parallel mechanisms.

References

References
1.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley-Interscience
,
New York, NY
.
2.
Awtar
,
S.
,
Slocum
,
A. H.
, and
Sevincer
,
E.
,
2007
, “
Characteristics of Beam-Based Flexure Modules
,”
ASME J. Mech. Des.
,
129
(
6
), pp.
625
639
.10.1115/1.2717231
3.
Yang
,
S. H.
,
Kim
,
Y.-S.
,
Yoo
,
J.-M.
, and
Dagalakis
,
N. G.
,
2012
, “
Microelectromechanical Systems Based Stewart Platform With Sub-Nano Resolution
,”
Appl. Phys. Lett.
,
101
(
6
), p.
061909
.10.1063/1.4739517
4.
Kim
,
Y.-S.
,
Yoo
,
J.-M.
,
Yang
,
S. H.
,
Choi
,
Y.-M.
,
Dagalakis
,
N. G.
, and
Gupta
,
S. K.
,
2012
, “
Design, Fabrication and Testing of a Serial Kinematic MEMS XY Stage for Multifinger Manipulation
,”
J. Micromech. Microeng.
,
22
(
8
), p.
085029
.10.1088/0960-1317/22/8/085029
5.
Kim
,
Y.-S.
,
Dagalakis
,
N. G.
, and
Gupta
,
S. K.
,
2013
, “
Creating Large Out-of-Plane Displacement Electrothermal Motion Stage by Incorporating Beams With Step Features
,”
J. Micromech. Microeng.
,
23
(
5
), p.
055008
.10.1088/0960-1317/23/5/055008
6.
Yong
,
Y. K.
,
Bhikkaji
,
B.
, and
Reza Reza Moheimani
,
S.
,
2013
, “
Design, Modeling, and FPAA-Based Control of a High-Speed Atomic Force Microscope Nanopositioner
,”
IEEE/ASME Trans. Mechatron.
,
18
(
3
), pp.
1060
1071
.10.1109/TMECH.2012.2194161
7.
Fowler
,
A. G.
,
Laskovski
,
A.
,
Hammond
,
A. C.
, and
Moheimani
,
S. O. R.
,
2012
, “
A 2-DOF Electrostatically Actuated MEMS Nanopositioner for On-Chip AFM
,”
J. Microelectromech. Syst.
,
21
(
4
), pp.
771
773
.10.1109/JMEMS.2012.2191940
8.
Yong
,
Y.
, and
Mohemani
,
S.
,
2013
, “
Design of an Inertially Counterbalanced Z-Nanopositioner for High-Speed Atomic Force Microscopy
,”
IEEE Trans. Nanotechnol.
,
12
(
2
), pp.
137
145
.10.1109/TNANO.2012.2233749
9.
Kenton
,
B. J.
, and
Leang
,
K.
,
2012
, “
Design and Control of a Three-Axis Serial-Kinematic High-Bandwidth Nanopositioner
,”
IEEE/ASME Trans. Mechatron.
,
17
(
2
), pp.
356
369
.10.1109/TMECH.2011.2105499
10.
Mohammadi
,
A.
,
Yuce
,
M.
, and
Moheimani
,
S. O. R.
,
2012
, “
A Low-Flicker-Noise MEMS Electrothermal Displacement Sensing Technique
,”
J. Microelectromechan. Syst.
,
21
(
6
), pp.
1279
1281
.10.1109/JMEMS.2012.2219296
11.
Smith
,
S. T.
,
2000
,
Flexure: Element of Elastic Mechanisms
,
CRC Press LLC
,
London, UK
.
12.
Soemers
,
H.
,
2010
,
Design Principles for Precision Mechanisms
,
T-Pointprint
,
Enschede
.
13.
Kang
,
B. H.
,
Wen
,
J. T.
,
Dagalakis
,
N. G.
, and
Gorman
,
J. J.
,
2005
, “
Analysis and Design of Parallel Mechanisms With Flexure Joints
,”
IEEE Trans. Rob
,
21
(
6
), pp.
1179
1185
.10.1109/TRO.2005.855989
14.
Yi
,
B.
,
Na
,
H.
,
Chung
,
G. B.
,
Kim
,
W. K.
, and
Suh
,
I. H.
,
2002
, “
Design and Experiment of a 3 DOF Parallel Micro-Mechanism Utilizing Flexure Hinges
,”
IEEE International Conference on Robotics and Automation, Proceedings. ICRA ’02
, Vol.
2
, IEEE, pp.
1167
1172
.
15.
Wu
,
T.
,
Chen
,
J.
, and
Chang
,
S.
,
2008
, “
A Six-DOF Prismatic-Spherical-Spherical Parallel Compliant Nanopositioner
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
,
55
(
12
), pp.
2544
2551
.10.1109/TUFFC.2008.970
16.
Liang
,
Q.
,
Zhang
,
D.
,
Song
,
Q.
, and
Ge
,
Y.
,
2010
, “
Micromanipulator With Integrated Force Sensor Based on Compliant Parallel Mechanism
,”
2010 IEEE International Conference on Robotics and Biomimetics (ROBIO), IEEE
, pp.
709
714
.
17.
Su
,
H.-J.
,
Shi
,
H.
, and
Yu
,
J.
,
2011
, “
Analytical Compliance Analysis and Synthesis of Flexure Mechanisms
,”
Proceedings of ASME IDETC/CIE
.
Washington, DC
, Aug. 29–31.
18.
Merlet
,
J.
,
2006
,
Parallel Robots
,
2nd ed.
Springer
,
New York
.
19.
Chen
,
J.-S.
, and
Hsu
,
W.-Y.
,
2004
, “
Design and Analysis of a Tripod Machine Tool With an Integrated Cartesian Guiding and Metrology Mechanism
,”
Precis. Eng.
,
28
(
1
), pp.
46
57
.10.1016/S0141-6359(03)00073-4
20.
Shi
,
H.
, and
Su
,
H.-J.
,
2012
, “
Workspace of a Flexure Hexapod Nanopositioner
,”
Proceedings of ASME IDETC/CIE, Chicago
,
Illinois
, Aug. 12–15.
21.
Chen
,
S.-C.
, and
Culpepper
,
M. L.
,
2006
, “
Design of a Six-Axis Micro-Scale Nanopositioner-HexFlex
,”
Precis. Eng.
,
30
(
3
), pp.
314
324
.10.1016/j.precisioneng.2005.11.002
22.
Su
,
H.-J.
,
Shi
,
H.
, and
Yu
,
J.
,
2012
, “
A Symbolic Formulation for Analytical Compliance Analysis and Synthesis of Flexure Mechanisms
,”
ASME J. Mech. Des.
,
134
(
5
), p.
051009
.10.1115/1.4006441
23.
Chao
,
D.
,
Zong
,
G.
,
Liu
,
R.
, and
Yu
,
J.
,
2006
, “
A Novel Kinematic Calibration Method for a 3DOF Flexure-based Parallel Mechanism
,”
2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, IEEE
, pp.
4660
4665
.
24.
Brouwer
,
D.
,
de Jong
,
B.
, and
Soemers
,
H.
,
2010
, “
Design and Modeling of a Six DOFs MEMS-Based Precision Manipulator
,”
Precis. Eng.
,
34
(
2
), pp.
307
319
.10.1016/j.precisioneng.2009.08.001
25.
Shi
,
H.
,
Su
,
H.-J.
,
Dagalakis
,
N.
, and
Kramar
,
J. A.
,
2013
, “
Kinematic Modeling and Calibration of a Flexure Based Hexapod Nanopositioner
,”
Precis. Eng.
,
37
(
1
), pp.
117
128
.10.1016/j.precisioneng.2012.07.006
26.
Lobontiu
,
N.
, and
Paine
,
J. S. N.
,
2002
, “
Design of Circular Cross-Section Corner-Filleted Flexure Hinges for Three-Dimensional Compliant Mechanisms
,”
ASME J. Mech. Des.
,
124
(
3
), pp.
479
484
.10.1115/1.1480022
27.
Chen
,
G.
,
Shao
,
X.
, and
Huang
,
X.
,
2008
, “
A New Generalized Model for Elliptical Arc Flexure Hinges
,”
Rev. Sci. Instrum.
,
79
(
9
), p.
095103
.10.1063/1.2976756
28.
Zhang
,
S.
, and
Fasse
,
E. D.
,
2001
, “
A Finite-Element-Based Method to Determine the Spatial Stiffness Properties of a Notch Hinge
,”
J. Mech. Des
,
123
(
1
), pp.
141
147
.10.1115/1.1342157
29.
Li
,
Q. X.
, and
Yangmin
,
2006
, “
Kinematic Analysis and Optimization of a New Compliant Parallel Micromanipulator
,”
Int. J. Adv. Rob. Syst.
,
3
(
4
), pp.
351–358
.
30.
Speich
,
J.
, and
Goldfarb
,
M.
,
2000
, “
A Compliant-Mechanism-Based Three Degree-of-Freedom Manipulator for Small-Scale Manipulation
,”
Robotica
,
18
(
1
), pp.
95
104
.10.1017/S0263574799001903
You do not currently have access to this content.