The 14th IFToMM World Congress, Taipei, Taiwan, October 25-30, 2015
DOI Number: 10.6567/IFToMM.14TH.WC.OS3.034
Design and Analysis of a New XYZ Parallel Flexure Stage
Xiaozhi Zhang* and Qingsong Xu
University of Macau
Macau, P.R. China
Abstract: In this paper, the design of a new compliant
XYZ totally decoupled parallel-kinematic nanopositioning
stage based on flexure mechanism is presented, which is
driven by PZT actuators. The output of the flexure stage is
enlarged by a compound amplifier of three order based on
bridge principle with the amplification ratio of As3 which
is larger than the ratio of As for one simple amplifier. The
three-dimensional amplifier can overcome the shortage of
the displacement limitation of the actuator. The flexure
stage with three actuators can obtain the motion along X,
Y and Z axes with cross-axis errors less than 1% and the
natural frequency larger than 100 Hz. In order to verify
the dimension of the objective stage simulation GA
method is conducted. FEA simulation results demonstrate
the performance of the designed multi-axis nanopositioning stage.
Keywords: Bridge amplifier of three orders, Decouple, Crossaxis error, FEA, GA method
I. Introduction
Nowadays, micro/nano-positioning stage is widely
used in modern high technology. It enables a significant
advance especially in atomic force microscopy [1],
micro/nano-assembly and manipulation [2, 3], X-ray
lithography [4], bio-medicine and bio-micro-surgery [5, 6],
and micro scanning [7].
In order to implement nanometer-level positioning
with high resolution and smooth motion, the stick–slip
phenomenon of the traditional kinematic pairs should be
avoided. To solve this problem, flexure-based
mechanisms are generally utilized to guide the motion of
the platform. Flexure hinges have a number of advantages
including no friction, no backlash [10], free of lubrication
[11], no noise [12], sub-nanometric precision, vacuum
compatibility, and easy manufacturing [13]. As one of the
key devices, flexure stage enables the micro/nano
positioning to be a common methodology applied to
various domains. As is known, the performance of the
static and dynamic characteristics of the micro/nano
positioning mechanisms is mainly dependent on the
structure of the mechanism and the dynamics of the
employed actuators [8]. Among the available types of
actuators, piezoelectric actuator is one of the best choices
for the micro/nano-positioning mechanisms due to its
infinite resolution, high stiffness, and large bandwidth.
Recent research efforts have been directed towards the
mechanical design optimization of flexure-based
mechanisms, which can be divided into two categories,
namely, serial-kinematic mechanisms and parallelkinematic mechanisms. The motion of each axis can be
*
†
mb35516@ umac.mo
Corresponding author. [email protected]
†
independently measured and controlled in a serialkinematic mechanism. Thus, it is easier to construct and
implement. However, the assembly error and different
dynamic performance in different motion axes are the
shortcomings of such kind of mechanisms. On the
contrary, the parallel-kinematic mechanism has a number
of advantages including structural compactness and high
stiffness. But the cross coupling motion, complex
kinematic equation and small workspace are the
bottleneck, which blocks practical applications of this
kind of mechanisms. Thus, it is necessary to develop
decoupled flexure-based mechanisms for micro/nanopositioning technology [9]. The objective of this work is
to devise a new decoupled XYZ compliant parallel stage.
Piezoelectric actuator (PZT) produces large force with
linear motion and high stiffness, while its output
displacement is relatively small. The stage usually needs
displacement amplifiers to enlarge the output
displacement of the actuator. The popular amplifiers can
be classified into bridge, level and hydromantic types by
principle. The level amplifier in [14] seems have the
distortion while the enlarge ratio is over 5.0 or more.
Frequency response of the hydrometric amplifier is lower
than the others. Hence, in this work, the bridge amplifier
is used owing to the advantage of high enlargement ratio
and without distortion. Specifically, a three-order bridge
amplifier is introduced to yield a large amplification ratio.
If the loss of the amplifier ratio by serial connection can
be reduced by 10%, the total enlargement ratio can be
increased more than 30%, which shows the advantage of
the three-order amplifier.
Additionally, in majority of recent research, PZTactuated flexure stage can provide one to three degree-offreedom movement. The limited DOF is inconvenient and
insufficient during complex manipulation. Recently, the
demand of more DOFs is increased in order to perform
more dexterous operation. For example, a 5-DOF flexure
stage with the module of 2×T-R, 1×T and the interface of
3×T-R-RT is proposed in [15], where a new modular
concept is introduced with a double-stage, flexure-based
pivot which allows to significantly reduce the time-tomarket. However, as compared with existing design, the
weakness of this compact structure is apparent. So
redesign of the stage as a complex combination of
movement and rotation is greatly in need.
In this paper, a novel XYZ flexure parallel stage is
designed and analyzed in detail. In the subsequent section,
the mechanism design of the flexure stage is described and
its working principle is addressed in detail. Then, finiteelement analysis (FEA) simulation is performed to testify
the performance of the reported decoupled XYZ flexure
stage.
Figure 2. Bridge type of amplifier.
Figure 1. CAD model of the total flexure stage.
II. Mechanism Design
In this section, the flexure stage, which is totally
decoupled, is realized by using two-dimensional flexure
hinges, which are assembled compactly so as to meet the
limited space and get high natural frequency. Moreover, a
decoupled stage will also benefit the controller design
process, since single-input-single-output (SISO) control
schemes are sufficient [10].
The objective of the XYZ stage with decoupled output
motion is to eliminate the cross-axis coupling errors
between the directional translations of the X, Y, and Z
axes. The most important part of this design is to ensure
that the stage moves along the correlative axis without
transverse displacements along the remaining two axes.
PZT is selected for actuation due to its large output force
and stiffness.
A. Implementation of the XYZ Parallel Stage
For the actuator, if it is installed in the middle of the
displacement, the output can be either pull or push force
by sacrificing the half exportation. To make full use of the
output, one side of the output stage in blue (see Fig. 1),
which is located in the center, needs to be fixed first of all.
The CAD model in Fig. 1 illustrates the details about the
fixed base of the flexure stage.
Concerning the displacement of the work plane, in
order to meet the need of the large displacement in X, Y
and Z axes, the three-order bridge amplifier is employed.
The PZT actuator is placed in the center of the amplifier to
get the displacement and force in both positive and
negative directions. The first stage of amplifier is shown
in Fig. 2. If the PZT actuator placed in the center of the
first-order stage in green (see Fig. 3) gives the push force,
the second-order stage in orange (see Fig. 3) will get the
pull force along the Z axis and transfer it to be the push
force for the third-order stage, and finally be turned into a
negative displacement along the X axis for the work plane.
On the other hand, a positive displacement will be
obtained by the pull force of the actuator.
B. Calculation of Amplification Ratio
t
The total enlarge ratio As of this three-order series
amplifier of bridge principle can be inferred by the
equation below.
Figure 3. Three-order amplifier.
As = k1 L1 / L2
(1)
where L1 and L2 are the parameters as shown in Fig. 2, k1
is the constant coefficient which can be obtained from the
literature [11].
Defining the coefficient k2 to be the loss of the
magnifying ratio as the series connection of this threeorder amplifying mechanical structure. Then,
Ast = (k2 As )
3
(2)
Hence, the total enlarge ratio is obtained as
Ast = ( k1k2 L1 / L2 )3
(3)
The three-order amplifying mechanical structure is
connected by two pairs of two-dimensional flexure hinges
to decouple the cross axis displacement, so as to enable a
SISO control.
The above mentioned design realizes the stable large
displacement by combining this three-order bridge
principle amplifier with the PZT actuator. In order to
overcome the cross axis interference, the flexure
mechanical structure as shown in Fig. 4 is employed. The
flexure hinges used in this structure is located
symmetrically to keep the balance of the displacement.
And the combination of the series and parallel orthogonal
circular flexure hinges get good performance by a suitable
design of the flexure parameters. It is notable that other
types of flexure hinges can also be employed [16]. This
three-order amplifier can decouple the interference by the
flexure hinges between each order, which ensures the
input to be the linear displacement. As a consequence, the
control system also will be simplified.
Figure 4. The connection flexure.
Figure 6. Modal analysis result of the first resonant mode.
Figure 5. Simulation result of the flexure stage along Y axis.
TABLE I. The design parameters of XYZ flexure stage
Symbol
t
ρ
E
wf
lf
σ
γ
Parameter
Material thickness
Density
Young’s modulus of AL6061
Width of flexure
Length of flexure
Yield strength
Poisson’s ratio
Value
3.0 mm
2700 kg/m3
69 GPa
0.3 mm
8 mm
276 MPa
0.33
Figure 7. The cross axis error of Y-X
As the flexure stage is totally central symmetry for the
directions of X, Y and Z axes of the mechanical structure,
the amplifier ratio is almost the same value for the motion
in the other two axes.
III. Simulation Study
In this section, the performance of the designed XYZ
stage is examined by carrying finite-element analysis
simulation using ANSYS software package.
A. Simulation Study of the Displacement in X, Y and
Z axes
As an example, an XYZ stage is designed by using the
parameters as shown in Table I. The performance of the
devised stage is evaluated through FEA simulations as
follow.
To generate a linear displacement in Y direction, the
actuator placed along Y axis is assigned a displacement of
7.5 um, which is the half of the maximum value of the
PZT actuator. The FEA result is shown in Fig. 5, which
indicates that the output displacement is about 22.31 um
t
along the Y direction. Hence, the amplifier ratio As is
about 3.0 and the loss of the series connection of the three
order bridge amplifier can be deduced by equation (3).
B. Modal Analysis of the XYZ Stage
In addition, modal FEA simulation is conducted to
evaluate the dynamic performance of the developed stage.
The result of the simulation is shown in Fig. 6, which
indicates that the first natural frequency is 106.13 Hz
along the working direction.
C. Cross-Axis Error Analysis of the XYZ Stage
Moreover, the cross-axis error analysis of each
working axis has been conducted. For instance, in order to
generate the displacement in Y direction, the pull and
push displacements of the actuators in pair are set as 7.5
um, which is the maximum value of the closed-loop travel
of the PZT, and the results are shown in Fig. 7.
The absolute percentage error of the cross-axis in the
Y direction is 0.38%, as shown in Fig. 7. The absolute
percentage error in the direction of Z axis is 0.59%, which
can be observed from Fig. 8. These results reveal that the
displacement of Y axis is totally decoupled with respect to
the other two working axes.
modal analysis demonstrates that the XYZ stage has a
relatively reasonable resonant frequency of 106.3 Hz.
The major disadvantage of the proposed structure
arises from the serial connection of the three-order
compact amplifier, which can be overcome by an
optimization of the parameters of the amplifier.
Specifically, as the parameter L1 varies, the output motion
of the stage is obtained by FEA simulations.
The simulation results in Table II show that when the
width of the weakest part of the flexure hinge is 0.16 mm,
the maximum output is obtained. In addition, the
optimization of L1 and L2 by genetic algorithm (GA) will
be conducted in the further work.
Figure 8. The cross axis error of Y-Z
Figure 9. The maximum principal stress analysis
TABLE II. The results of FEA simulation with different parameters
t
L1
Output
0.10 mm
0.15 mm
0.16 mm
0.18 mm
0.20 mm
0.30 mm
1.90 mm
1.85 mm
1.84 mm
1.82 mm
1.80 mm
1.70 mm
19.0 um
21.9 um
22.3 um
21.4 um
20.1 um
15.2 um
D. Stress Analysis of the XYZ Stage
The yield strength of the Al-6061 is [σ] =276 MPa. As
can be seen from the Figure 9, the induced maximum
stress is 112.16 MPa which is less than the limited value
of 276 MPa. It obtains a safety factor of 4.48 for the
material, which shows the good performance in bearing
stress.
IV. Optimization of the Flexure Stage
The forgoing FEA simulations reveal the performances
of the designed XYZ stage. In static structural FEA, with
an input displacement 7.5 um applied on the input ends of
the first-order amplifier, the total deformations of the
stage are depicted in Fig. 5. It is obtained that the axial
output displacement of the stage is 22.32 um. The
optimized stage has an amplification ratio of 3.00. The
V. Conclusions
This paper presents the design and analysis of a
parallel-kinematic XYZ flexure stage. In order to achieve
a large displacement, a compound bridge amplifier of
three orders is proposed, which is driven by PZT actuator.
The aim of the flexure mechanical structure is to decouple
the cross axis error produced by the parallel structure.
With one side of the amplifier fixed, it turns out to be
more efficient in making full use of the output of the
actuator in both sides. It is notable that the value of the
natural resonant frequency over 100 Hz is reasonable in
the field of flexure stage designing [11]. And the enlarge
ratio of 3.0 is also acceptable in the present work. The
percentage cross axis error is suppressed to be less than
1%, which is a negligible level.
Further improvement of the research can be made from
the aspects given below.
1) Conduct the optimization of the parameters of the
bridge amplifier and flexure hinges by GA method to
obtain a high amplification ratio;
2) Perform analytical analysis of the flexure stage and
compare the result with FEA simulation result;
3) The improvement of the stage will be conducted to
yield more degrees of freedom by adding rotational
motion;
4) A prototype of the optimized XYZ stage will be
developed and experiments will be conducted for
performance demonstration;
5) The control of this mechanical structure will be
carried out in the future;
6) The current configuration seems to be too large
three-dimensionally as the length of PZT actuator is over
72 mm. So, more work need to be done in the size
reduction of the actuator and flexures.
Acknowledgment
This work was supported by the Macao Science and
Technology
Development
Fund
under
Grants
052/2014/A1 and the Research Committee of the
University of Macau under Grants MYRG083(Y1-L2)FST12-XQS and MYRG078(Y1-L2)-FST13-XQS.
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