MSMechanical SciencesMSMech. Sci.2191-916XCopernicus PublicationsGöttingen, Germany10.5194/ms-8-117-2017Design and analysis of a 3-DOF planar micromanipulation stage with large rotational displacement for micromanipulation systemDingBingxiaoLiYangminyangmin.li@polyu.edu.hkhttps://orcid.org/0000-0002-4448-3310XiaoXiaoTangYiruiLiBinDepartment of Electromechanical Engineering, University of Macau, Taipa, Macao SAR, ChinaDepartment of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong SAR, ChinaTianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, Tianjin University
of Technology, Tianjin, ChinaYangmin Li (yangmin.li@polyu.edu.hk)23May20178111712628October201620March201721March2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://ms.copernicus.org/articles/8/117/2017/ms-8-117-2017.htmlThe full text article is available as a PDF file from https://ms.copernicus.org/articles/8/117/2017/ms-8-117-2017.pdf
Flexure-based mechanisms have been widely used for scanning tunneling
microscopy, nanoimprint lithography, fast servo tool system and micro/nano
manipulation. In this paper, a novel planar micromanipulation stage with
large rotational displacement is proposed. The designed monolithic
manipulator has three degrees of freedom (DOF), i.e. two translations along
the X and Y axes and one rotation around Z axis. In order to get a
large workspace, the lever mechanism is adopted to magnify the stroke of the
piezoelectric actuators and also the leaf beam flexure is utilized due to its
large rotational scope. Different from conventional pre-tightening mechanism,
a modified pre-tightening mechanism, which is less harmful to the stacked
actuators, is proposed in this paper. Taking the circular flexure hinges and
leaf beam flexures hinges as revolute joints, the forward kinematics and
inverse kinematics models of this stage are derived. The workspace of the
micromanipulator is finally obtained, which is based on the derived kinematic
models.
Introduction
Recently, flexure based mechanism with ultrahigh precision plays an
increasing important role in many kinds of fields where high resolution and
high repeatability accuracy are demanded, such as optical fiber alignment
, bioengineering , scanning tunnel microscopy (STM)
. In precision applications such as following issues have
attracted much attention: (1) resolution; (2) number of degrees of
freedom(DOF); (3) workspace. The resolution refers to the capability of the
system that can distinguish and detect the smallest change of the variable,
in micromanipulation system this variable refers to the displacement of the
end-effector other than the actuator, because of the amplification mechanism
will degrade the system resolution . For planar mechanism, the
maximum number of the DOF is three, i.e. translations along X/Y axis and
rotation around Z axis, it can meet most of planar applications. The
workspace of a manipulator is often defined as the set of points that can be
reached by its end-effector, namely, it is the space in which the manipulator
can work in either a 3-D space or a 2-D surface. The motion range of the micro
manipulation stage is typically within several microns, for the reason of
limited rotational scope of flexure hinges and limited stroke of
piezoelectric actuators which are widely utilized in all kinds of
flexure-based stages . For the purpose of getting better
performance of the micromanipulation stage, more and more optimized flexure
hinges with outstanding characteristics, such as more accurate in position
and large motion scope, are designed by researchers
(; ; ; ).
The stage should meet the design requirements when it is used in this
specific application, this paper proposes a compliant parallel manipulator
which adopts lever amplification mechanism to magnify the displacement of the
piezoelectric actuators. Based on the structure of the flexure-based stage
and the distribution of the actuators, manipulators can also be classified
into two categories, i.e. serial structure and parallel structure. The serial
structure of the stage enables a simple control strategy, however it endows
with high inertia, low natural frequency and cumulative errors. To overcome
such drawbacks, parallel kinematic structure is designed because it can
provide high load capacity, low inertia, high accuracy and high stiffness.
However, the disadvantages are limited workspace and complicated control
strategies. Although the compliant parallel mechanism possesses such
drawbacks, it has attracted much attention and become an hot issue.
During the literature review, the current research about flexure-based
micromanipulation stages for planar application can be classified into 1-DOF,
2-DOF and 3-DOF manipulation stage. Although 1-DOF micromanipulator possesses
the advantages of easy to control and no parasitic motion, it has limited
applications. So the 2-DOF parallel symmetric micromanipulation stages with
decoupled motion are proposed for many planar applications. However, to fully
describe the movement of an object needs two translations and one rotation in
planar applications, this paper presents a 3-DOF flexure-based parallel
micromanipulation stage with large rotational scope for micromanipulation
system. In micromanipulation application field, the operator often needs to
adjust the position and orientation of biological objects under microscope to
do cutting and filtering operation. As shown in Fig. 1, the stage is placed
under the microscope, the operator can adjust the position of the object with
the 3-DOF micro stage, it can make the manipulation more dexterous by
operators.
During the literature review, a myriad of 3-DOF flexure-based compliant
parallel mechanism has been fabricated by previous researchers. Generally
speaking, the flexure-based micromanipulation stage has limited workspace, to
overcome this drawback, many different kinds of amplification mechanisms are
adopted to amplify the stroke of piezoelectric actuators. Lu et al.
designed compliant parallel micro motion stage with two translations (along
X and Y direction) and one rotation (around Z axis), also adopted
piezoelectric actuators, but without amplification mechanism, the drawback of
this design is the very small workspace ; Bhagat et al. also designed a planar 3-DOF micromanipulator, this
mechanism adopted three piezoelectric actuators to achieve required
displacements in X, Y and θ and utilized lever amplifier to
enhance the displacement of the mechanism ; Hao fabricated a
flexure-based spatial 3-DOF compliant parallel mechanism with three
translational motions along X, Y and Z axis, respectively, moreover
this monolithic CPM can be used as positioning stage, acceleration sensor and
energy harvesting device ; Wang and Zhang proposed a
3-DOF nanopositioning stage with two-level lever amplifier with over two
hundreds of microns translational displacement along x/y, however the
rotational scope and natural frequency are relatively small in
. In addition, other researchers have also designed many kinds
of 3-DOF compliant parallel stages with different characteristics
(; ).
The proposed flexure-based positioning stage is featured with two kinds of
flexure hinges, right circular hinge and leaf beam flexure hinge in different
places and an optimized lever amplification mechanism is adopted to
compensate the limited stroke of piezoelectric actuators. The remainder of
this paper is organized as follows: The flexure-based parallel positioning
stage with optimized structure is proposed in Sect. 2, and also the
rotational stiffness is compared between right circular hinge and leaf spring
beam flexure hinge; In Sect. 3, the flexure-based mechanism is modeled
based on PRB method and the pivot drifting analysis is also conducted; The
kinematic analysis of this manipulation stage and the numerical simulation is
conducted in Sects. 4 and 5 respectively; The dynamic characteristics and
performance of this stage are evaluated in Sect. 6; Finally, the whole
works of this research are concluded in Sect. 7 with future works
indicated.
Three-DOF micromanipulation-stage design
For a planar 3-DOF parallel kinematic micromanipulation stage, the
end-effector can translate along X/Y axis and rotate around Z axis.
During the literature review, there are many kinds of 3-DOF planar mechanism
configurations . Several typical planar parallel 3-DOF stages are
shown in Fig. 2. For the (a) mechanism structural configuration, each chain
has only revolute joint; the mechanisms (b) and (c) have prismatic joints and
revolute joints. In this study, the (a) structure configuration is adopted to
design the micromanipulation stage due to its easy to design and fabricate.
When designing a flexure based micromanipulation stage, the structure,
flexure hinges and actuators are needed to take into consideration,
particularly, the goal of this study is to design a micromanipulation stage
with large workspace and high resolution. Compared with shape memory alloy
(SMA) and giant magnetostrictive actuator (GMA), the piezoelectric actuator
is much cheaper and easily obtained, moreover the PEAs can achieve sub-nano
level resolution and has fast response characteristics . Although
the voice coil motor(VCM) and electromagnetic actuator (EMA) possess the
advantages of large output stroke and driven force, the disadvantages are low
resolution and slowly response. Considering all aspects, this design adopts
PEA to drive the stage integrated with amplification mechanism to amplify the
stroke of the PEAs.
The typical planar parallel 3-DOF kinematic stages.
Flexure hinges
Flexure hinges are basically designing elements in the flexure-based
micromanipulation stages, which have been widely used in these applications
where ultrahigh precision motion is needed such as aerospace field, high
precision machine and bioengineering field. Furthermore, micromanipulation
technology has become an important technology along with the appearance of
using flexures. Compared with conventional joints, flexure hinges possess the
advantages of no needing for lubrication, no hysteresis, no clearance and no
wear. Therefore, flexure-based micromanipulation stages are capable of
achieving highly precise positioning accuracy. The goal of this study is to
design a compliant parallel micromanipulation stage with large workspace.
Taking fabrication process and motion precision into consideration, this
design chooses two types of flexures: leaf spring flexure and right circular
cut flexure. The rotational stiffness of each type of flexure hinge can be
calculated by the following equations, respectively :
KθzMz=EI2axKθzMz=2Ebt5/29πax1/2
Here, E represents the Young's modulus of aluminum alloy material, I
denotes the second moment of area about the neutral axis and b is depth of
the flexure hinge. What's more, the relationship between rotational stiffness
of different notch types of flexure hinges and t, ax are illustrated in
Fig. 3a, b respectively, here E=71.7 GPa, b=8 mm. As Fig. 3 depicted,
the leaf spring flexure has lower stiffness than right circular cut flexure
with the same t and ax, therefore the leaf spring flexure hinge has a
larger rotation than right circular cut flexure with the same driven force.
Different types of single DOF flexure hinge and its rotational
stiffness with t and ax. (a) leaf spring flexure and its rotational
stiffness; (b) right circular cut flexure and its rotational stiffness.
The lever amplification mechanism with different geometric forms.
Lever amplification mechanism
The lever amplification mechanism is adopted to compensate the stoke of
piezoelectric actuators for its advantage of simple mechanism and easy
fabrication comparing with Scott-Russell (SR) Mechanism and Bridge Type
Mechanism (BTM). As shown in Fig. 4, three types of lever amplification with
different geometric forms have the same amplification ratio and the black dot
line denotes the centroid of lever amplification mechanism. Moreover, the
geometric form of the lever amplification mechanism will affect the
acceleration of the end-effector. The inertia moment of each amplifier
mechanism can be calculated by the following equation:
Jz=∑miri2
where the mi denotes mass distribution and ri denotes the distance
between each mass and rotational axis. So the following equation can be
derived:
J1=mr12J2=mr22J3=mr32
For the reason of r1<r3<r2, the following relationship can be obtained:
J1<J3<J2
With the same driving force F, inducing the same moment τ, the
acceleration of the end-effector with different geometries can be written as:
αi=τJi
where i=1, 2, 3. From above analysis, inducing α1>α3>α2, it means that Fig. 4a is the reasonable geometry of lever
amplification mechanism, (b) and (c) will degrade the response time of the
manipulation stage.
Preload mechanism
It is well known that the piezoelectric actuator possesses the advantages of
high resolution and fast response, however, it can not bear the lateral force
since the lateral force or moment may cause the damage to the piezoelectric
actuators, so shear stress and tensile stress must be avoided during the
actuation. Also during the positioning process, the piezoelectric actuator
needs to maintain a continuous connection state with the mobile platform.
During the literature review, the typical pre-tightening mechanism uses the
bolt to generate the thrust force and the bolt contact with piezoelectric
directly, as shown in Fig. 5a, however the lateral force and moment can
not be avoided and pre-load force can not be measured. A new pre-tightening
mechanism is proposed in this study, as shown in Fig. 5b, the
piezoelectric actuator and mobile platform maintain a line-face contact. The
interaction of the semi-cylinder and the adjustable pre-load force block
preclude the generation of the lateral force and bending moment.
Pre-tightening mechanism. (a) traditional pre-tightening mechanism;
(b) proposed pre-tightening mechanism; 1, mobile platform; 2, fixed platform;
3, piezoelectric actuator; 4, bolt; 5, adjustable pre-load force block.
Structural configuration
For a 3-RRR (R refers to revolute joint) parallel mechanism, it has two
interesting configurations of the structure. As depicted in Fig. 6a and
b, the same symbol denotes the same meaning, it means that the two
schematic diagrams have the same geometric architecture configuration. The
3-RRR diagram (a) and (b) represent the structure with minimal rotation and
maximal rotation, respectively. With the equal actuation force, the torque
can be calculated by following equation:
M1=F1⋅(DB1+C1O)+F2⋅(DB2+C2O)+F3⋅(DB3+C3O)M2=F1⋅DB1+F2⋅DB2+F3⋅DB3
Obviously, M1>M2, it means that with the equal driving force, the (b)
will generate a large rotational angle. So the structural configuration (b)
is adopted to design the 3-DOF micromanipulation stage for a large rotational
scope.
Two different 3-RRR structural configurations.
Based on the above analysis, the designed monolithic 3-DOF compliant parallel
mechanism integrated with lever amplification mechanism is presented in
Fig. 7. The proposed compliant parallel mechanism is designed to be used as a
high precision planar positioning stage to manipulate objects under the
microscopy and the dimension scale of this stage is approximately
120×120×8 mm3. In order to validate the correction of the
designed mechanism, the Workbench software is adopted to simulate this
parallel mechanism. As shown in Fig. 8, it does not exist any physical
interferences under the condition of maximum input displacement, which
indicates that the structural design is reasonable. The main design criteria
of this compliant mechanism is to get a large workspace of the end-effector,
to achieve this goal the beam flexures are exploited to connect the motion
platform and lever amplification mechanism, meanwhile right circular hinges
are adopted as revolute joints. The exact architectural parameters of flexure
hinges are presented in Table 1.
The whole assembled diagram of this three-DOF microstage:
(1) The base platform; (2) The pre-tightening
mechanism; (3) The lever amplifier; (4) The grounding
bolt; (5) The central motion platform.
The motion simulation of manipulation stage with the condition of maximum input displacement.
Compliant mechanisms involving with nonlinearity characteristics make the
analysis and modeling very difficult. To facilitate the analysis of the
manipulation stage, the pseudo-rigid-body (PRB) model is adopted in this
study. With the identified mechanism topology and each flexure hinge replaced
by a revolute joint and a torsional spring, the PRB model of the proposed
flexure-based mechanism is developed as shown in Fig. 9. The stage is actuated
by three stacked PZT actuators, where P1, P2, P3 represents each actuator
location and input driving force direction. The mobile platform C1C2C3
is an equilateral triangle, which is connected by three identical linkages,
namely, A1B1=A2B2=A3B3, B1C1=B2C2=B3C3. The global frame
XOY is grounded at the center of triangle A1A2A3 and the local frame
is attached at the center of platform C1C2C3.
The PRB model of the designed compliant parallel stage.
Pivot drifting analysis
The workspace of the manipulation stage depends on the actual input
displacement of the piezoelectric actuator and the actual amplification ratio
of the lever mechanism, not the theoretical amplification ratio. From the
experience, the lever mechanism will produce bending deformation and pivot
drifting when a loading is applied, the bending deformation can be ignored in
this research for the geometric form of the lever amplifier mechanism. As
shown in Fig. 10a, the theoretical magnification ratio of the mechanism is
A1B1/A1p, and the output displacement is B1B3′. However, the
actual output displacement of the lever amplifier mechanism is B1B2′,
when considering the displacement loss caused by the pivot drifting.
Obviously, the actual amplification ratio Aamp=dout/da is smaller
than the theoretical ratio due to the displacement loss of the lever
mechanism. The displacement loss needs to be taken into consideration in
order to get a more accurate relationship between the input stroke and output
displacement of the mobile platform.
Lever amplifier mechanism. (a) Bending schematic diagram; (b) analysis model.
As shown in Fig. 10b, when the driving force Fp is applied on the
mechanism, a pivot drift displacement δAy will be produced along
the y direction of the circular flexure hinge for its compliance in y
axis. And δAy can be solved by the following equation:
δAy=FpKAy
where KAy is the stiffness of the circular hinge along the Y axis,
and it can be calculated by the following equation: :
KAy=Ew/2(2r/t+1)4r/t+1arctan4r/t+1-π2Fp=Kpy⋅da
where Kpy=Kpc+Kpb denotes the total stiffness of the position
p along the driven direction, Kpc=KAy is the stiffness of the
circular hinge along the y axis and Kpb=Eb3w4l3
represents the stiffness of the beam flexure hinge; da is the actual
output displacement of the piezoelectric actuator; and the output
displacement is dout=(da-δAy)(1+l2l3)+δAy. So the relationship between the input displacement and the
output displacement of the lever mechanism Aamp can be derived as
follows:
doutda=1+l2l3⋅b3⋅2(2r/t+1)4r/t+1arctan4r/t+1-π24l3
Here, E denotes the Young's modulus of the aluminum alloy material, and the
parameters w, t, r and l are illustrated in Fig. 8. The amplification
ratio is 3.2780 when taking the pivot drift into consideration, it exists
about 8.16 % deviation compared with nominal amplification ratio (3.5455);
and exists about 3.68 % deviation error compared with simulation result
(3.1573).
The kinematic schematic of 3-PRR planar mechanism.
Kinematic analysis
The kinematic diagram of the designed mechanism is presented in Fig. 11,
qi, (i=1,2,3) denotes the output displacement of the lever mechanism,
it means that qi=dout. The workspace of mobile platform is
defined by a vector μ=(x,y,θ)T, which represents the position and orientation of the
reference point. And the input stroke of each stacked actuator can be denoted
by di, (i=1,2,3); the Jacobian matrix which connects
the input stroke and output displacement of end-effector is denoted by J,
so we can get the following equation:
xyθ=Jd1d2d3
Here, we use l0, l1 to denote the length of CiO and BiCi,
(i=1,2,3), respectively, homogeneous transformation matrix from the global
frame XOY to the coordinates XOiY can be described by this equation:
OTi=ci-sil0sici-l1001
where ci=cosαi, si=sinαi, α1=0, α2=2π3, α3=4π3, i=1,2,3.Also, the motion of the mobile platform can be described in the global frame XOY.
oTO=c-sxscy001
where, c=cosθ,s=sinθ. Here, we adopt oTi to represent
the homogeneous transformation matrix from the mobile platform to each
coordinate XOiY. Combining the Eqs. (13) and (14) together, we can
get the following equation:
oTi=ci-sil0sici-l1001c-sxscy001
Here, we define the s=θ, c=1, because the rotational angle of the
platform is very tiny. After a further processing of Eq. (15), we can
obtain the relatively simple oTi as follows:
oTi=ci-siθ-ciθ-sixci-ysi+l0si+Ciθci-siθxsi+yci-l1001
In the frame of XOY, the coordinates value of Ci, (i=1,2,3) can be
expressed as oC1=(-l0,0), oC2=l02,3l02, oC3=l02,-3l02.
iCix=(ci-siθ)oCix-(ciθ+s)oCiy+xci-ysi+l0iCiy=(si+ciθ)oCix-(siθcsi)oCiy+xsi-yci-l1
where i=1,2,3.
For the length of BiCi is constant constraint, we can obtain the following equation:
(qi+iCiy)2+iCix2=l12
So the qi can be calculated by the following equation:
qi=l11-ixl12-iCiy
The above Eq. (19) is a nonlinear equation, after further analysis, we
can get iCix/l1≈0, subsequently, we can get the following
linearized equation:
qi=l1-iCiy
We can obtain the following equations after substituting (17) into (20).
q1=l0θ+yq2=l0θ-32x-12yq3=l0θ+32x-12y
So the relationship between input stroke of piezoelectric actuators and the
position and orientation of the central platform can be written as follows:
xyθ=Aamp0-33-3323-13-1313l013l013l0d1d2d3
where the Aamp is the actual amplification ratio of the lever amplifier.
Workspace analysis
The workspace of the 3-DOF manipulator can be calculated by the above
aforementioned kinematic analysis. Actually, the reachable workspace of the
manipulator not only depends on the above Eq. (22), but also has the
relationship with material property. The following list is the constraint
condition of the 3-DOF micromanipulator:
0≤di≤dmax,i=1,2,3σ<σm
where di denotes the output displacement of the piezoelectric actuators; and σ is the stress of the material.
Length parameters of microstage.
parametersvalues(mm)A1B139B1C116C1C212A1P111
Reachable workspace of the stage. (a) 3-D workspace; (b) maximum projection on XY plane.
Here, the piezoelectric actuators P-820.20 are adopted to drive the stage,
so the first constraint condition is the input stroke of each piezoelectric
actuator:
0≤di≤20
where i=1,2,3.
Based on above analysis, the workspace of the micromanipulator can be
obtained by calculating the outputs of the reference point. The 3-D workspace
is graphically illustrated in Fig. 12a. From the simulation results, the
reachable workspace of the end-effector is a hexahedron, and the projection
area on XY plane is varying with the θ value. The maximum projection
on the XY plane is shown in Fig. 12b. From the simulation results, the
reachable workspace along X/Y axis and around Z is [-42.31,42.31]µm, [-48.56,48.56]µm, [0,10.28]mrad, respectively.
Dynamic characteristics
The dynamic response has to be modeled in order to fully describe the free
vibrations of the 3-DOF micro manipulation stage and ensure the flexure-based
mechanism operate properly in the dynamic range. Referring to the PRB method,
the flexure hinges generated rotational motion around Z axis are treated as
an ideal revolute joint with torsional spring. The output variables of the
end-effector are defined as O→=[xo,yo,θo]T.
During the simulation analysis, the motion type of the lever AiBi(i=1,2,3) is mainly rotational motion, and beam links BiCi(i=1,2,3) will
be generated bending deformation when the input is applied. So the total
kinematic energy of the manipulation stage is composed by the translational
kinematic energy Tt of the end-effector and rotational kinematic energy
Tr of the lever AiBi(i=1,2,3) and the end-effector.
Tr=12∑i=13JAiBiωAiBi2+12Joθ˙o2Tt=12mox˙o2+y˙o2
where JAiBi denotes the moment of inertia of each lever;
ωAiBi represents the angular velocity of each lever. As
illustrated in Fig. 8, the potential energy mainly concentrates on beam type
flexure hinges at position Pi(i=1,2,3) and beam links BiCi(i=1,2,3)
when input force is applied. So the total potential energy V of the
manipulation stage can be calculated by the following equation:
V=12Kxxo2+12Kyyo2+12Kθθo2+32KpbdoutAamp2
where the Kx, Ky, Kθ denotes the equivalent stiffness of the
micro manipulation stage along X/Y axis and around Z axis, respectively.
The numerical solution of Kx,Ky, and Kθ can be obtained by some
experimental techniques. Substituting the potential energy and kinematic
energy into the Lagrange's equation can yield to the following equation:
M[x¨oy¨oθ¨o]T+K[xoyoθo]T=[F1F2F3]T
where Fi(i=1,2,3) is the ith input force generated by piezoelectric
actuator. Then the following mass-stiffness matrix characteristic equation
can be obtained:
|K-Mλi2|=0
So the natural frequencies can be calculated by fi=λi/2π.
In this section, the dynamic characteristics of the manipulation stage are
obtained through the modal analysis by Workbench. The first four modal shapes
of the micromanipulation stage without piezoelectric actuator assembled are
represented in Fig. 13. The first four natural frequencies are 1280.3,
1308.4, 1618.6 and 1918.2 Hz. It should be noticed that dynamic
performance of micro-manipulation stage will be mainly determined by some
experimental procedures, which are planned in our future work and the
aforementioned analysis and simulation results will be validated.
The lever amplification mechanism with different geometric forms.
Conclusions
A flexure-based monolithic micro manipulation stage with large workspace is
designed and analyzed in this paper. The piezoelectric actuators are adopted
to drive the manipulation stage because they can provide with the fast
response and large output driven force. The optimized lever amplifier is
integrated into the mechanism in order to compensate the stroke of the
piezoelectric actuators. For the purpose of getting larger workspace,
different kinds of flexure hinges, different structural configurations and
lever amplifiers with different geometric forms are compared in this paper.
To validate the design, the kinematics model and reachable workspace of the
manipulation stage are analytically obtained. The working range of the
manipulation stage along each axis is ±42.31µm, ±48.56µm,
0–10.28 mrad, respectively. Then the dynamic characteristics and performance
evaluation of the designed mechanism are conducted via the Workbench
software. The prototype fabrication and experimental validations, and control
of the micro manipulation stage will be performed in our future work.
All the data used in this manuscript can be obtained by requesting from the corresponding author.
The authors declare that they have no conflict of
interest.
Acknowledgements
This work is partially supported by National Natural Science Foundation of
China (51575544,51275353), Macao Science and Technology Development
Fund (110/2013/A3,108/2012/A3), Research Committee of University of Macau
(MYRG2015-00194-FST, MYRG203(Y1-L4)-FST11-LYM).
Edited by: G. Hao
Reviewed by: two anonymous referees
References
Acer, M. and Sabanovic, A.: Micro position control of a designed 3-PRR
compliant mechanism using experimental models, 9th Asian Control
Conference, 1–6, 2013.
Bhagat, U., Shirinzadeh, B., Clark, L., Chea, P., Qin, Y. D., Tian, Y. L.,
and Zhang, D. W.: Design and analysis of a novel flexure-based 3-DOF
mechanism, Mech. Mach. Theory, 7, 173–187, 2014.
Culpepper, M. L. and Anderson, G.: Design of a low-cost nano-manipulator
which utilizes a monolithic, spatial compliant mechanism, Precision
Engineering, 28, 469–482, 2004.
Dong, Y., Gao, F., and Yue, Y.: Modeling and experimental study of a novel
3-RPR parallel micro-manipulator, Robotics and
Computer-IntegratedManufacturing, 37, 115–124, 2016.
Gao, F., Li, W. M., Zhao, X. C., Jin, Z. L., and Zhao, H.: New kinematic
structures for 2-, 3-, 4-, and 5-DOF parallel manipulator designs, Mech.
Mach. Theory, 37, 1395–1411, 2002.Hao, G.: Towards the design of monolithic decoupled XYZ compliant parallel
mechanisms for multi-function applications, Mech. Sci., 4, 291–302,
10.5194/ms-4-291-2013, 2013.Hao, G. B. and Li, H. Y.: Design of 3-legged XYZ compliant parallel
manipulators with minimised parasitic rotations, Robotica, 33, 787–806,
2014.
Hubbard, N. B., Culpepper, M. L., and Howell, L. L.: Actuators for
micropositioners and nanopositioners, Appl. Mech. Rev., 59, 324–334, 2006.
Ku, S. S., Pinsopon, U., Cetinkunt, S., and Nakajima, S. I.: Design,
fabrication, and real-time neural network control of a
three-degrees-of-freedom nanopositioer, IEEE/ASME Transactions on
Mechatronics, 5, 273–280, 2000.
Li, Y. M. and Xu, Q. S.: A novel design and analysis of a 2-DOF compliant
parallel micromanipulator for nanomanipulation, IEEE Transactions on
Automation Science and Engineering, 3, 248–254, 2006.
Lu, T. F., Handley, D. C., Yong, Y. K., and Eales, C.: A three-DOF compliant
micromotion stage with flexure hinges, Industrial Robot: An International
Journal, 31, 355–361, 2004.
Polit, S. and Dong, J.: Development of a high-bandwidth XY nanopositioning
stage for high-rate micro-/nanomanufacturing, IEEE/ASME Transactions on
Mechatronics, 16, 724–733, 2011.
Qin, Y. D., Shirinzadeh, B., Zhang, D. W., and Tian, Y. L.: Design and
kinematics modeling of a novel 3-dof monolithic manipulator featuring
improved Scott-Russell mechanisms, Journal of Mechanical Design, 135, 1–9,
2013.
Schitter, G., Thurner, P. J., and Hansma, P. K.: Design and input-shaping
control of a novel scanner for high-speed atomic force microscopy,
Mechatronics, 18, 282–288, 2008.
Smith, S. T.: Flexures: elements of elastic mechanisms, CRC Press, 2000.
Tian, Y. L. and Shirinzadeh, B.: Development of a flexure-based 3-RRR
parallel mechanism for nano-manipulation, IEEE/ASME International Conference
on Advanced Intelligent Mechatronics, 1324–1329, 2009.
Wang, R. Z. and Zhang, X. M.: A planar 3-DOF nanopositioning platform with
large magnification, Precision Engineering, 46, 221–231, 2016.
Wu, Y. F. and Zhou, Z. Y.: Design of flexure hinges, Eng. Mech., 19,
136–140, 2002.
Yi, B., Chung, G., Na, H., Kim, W., and Suh, I.: Design and experiment of a
3-DOF parallel micromechanism utilizing flexure hinges, IEEE Transactions on
Robotics and Automation, 19, 604–612, 2003.