1 Copyright © 2014 by ASME
DESIGN AND ANALYSIS OF ACTUATED MICRONEEDLES FOR ROBOTIC MANIPULATION
Steven Banerjee Mechanical Engineering University of Canterbury
Christchurch, New Zealand
Wenhui Wang Precision Instruments Tsinghua University
Beijing, China
Stefanie Gutschmidt Mechanical Engineering University of Canterbury
Christchurch, New Zealand
ABSTRACT We present the design of a MEMS based single-unit
actuator consisting of a single microneedle with 3D mobility.
The four-sided single-unit actuator (4SA) microrobot design can
achieve an in-plane actuation (x, y) of 76 μm (±38 μm) at 160 V
and an out-of-plane actuation (z) of more than 6.5 μm at 35 V.
The mechanical stress developed within the operational range is
between 0.08 to 0.5 percent of the yield strength of silicon i.e.
7000 MPa. We discuss both the analytical modeling and finite
element analysis (FEA) simulation of the design based on the
range of dimensions analyzed for the individual actuator
components. Our primary goal is to integrate multiple actuators
into a parallel architecture for independent actuation of multiple
microneedles for targeted micro- and nano-robotic
manipulation tasks, such as single-cell analyses. We have also
successfully fabricated sample 4SA microrobot without the
microneedle as a pre-cursor to experimenting with our future
advanced design of microrobots. We demonstrate successfully
the 3D actuation of the 4SA microrobot of up to 10 μm at 120
V (in-plane) and more than 0.5 μm at 600 V (out-of-plane) with
minimum decoupling.
INTRODUCTION There have been several works done over the past 15 years
to parallelize the microprobe/microneedle architecture in order
to achieve high-throughput results for micro- and nano-robotic
manipulation [1-3]. A recently reported parallel architecture
consists of 4 million static microneedles contained in a 2×2 cm2
chip using manual force as a method of biological delivery [4].
Moreover for biological manipulations such as single-cell
analyses, it is vital to have independent multiple-axes control of
the microneedle for targeted delivery. All such previous robotic
micro-nano manipulation designs are limited in terms of
independent actuation of microneedles across multiple axes.
One of the main reasons for this restricted mobility is the
complexity associated with achieving an out-of-plane actuation.
Additionally, the control of multiple microneedles
independently poses further challenge to automation.
Limitations in fabrication of such a parallel architecture with
mobility across multiple axes pose additional challenges as
well.
One of our major focuses in terms of robotic micro-nano
manipulation is toward single cell analysis and manipulation.
Recent works on single-cell manipulation include development
of several semi-automated or automated systems [5-7]. One
such recent system has demonstrated an automated system for
zebrafish embryo injection which could achieve a high success
rate of injection into single cells at a time [8]. Albeit all such
previous systems are promising, they cannot achieve a high
throughput rate of performing parallel cell manipulation,
critical for disease research and drug discovery.
Toward our goal of achieving a parallel architecture, we
design and analyze the performance of a single-unit actuator
integrated with a micro-stage and a microneedle with 3D
mobility based on MEMS technology. Micro-nano-stages have
been a major area of research for its applications in scanning
probe microscopy, optics, high density data storage etc. From
nanopositioning stages that are actuated thermally [9] to high
aspect ratio MEMS micromirror being driven electrostatically
[10, 11], these structures have been ubiquitous in the semi-
conductor and MEMS industry since the 1990’s. For example,
recent work by Fowler et al [14] on electrostatic actuated
micro-stage can achieve an in-plane actuation of 16 μm at 45 V.
Another group, Kim et al [15] have developed thermally
actuated MEMS stage which can achieve an in-plane
displacement of greater than 50 μm at a driving voltage of 5 V.
Most of these actuators have only a 2D mobility. Some have
achieved 3D mobility [12, 13] but exist mostly as a stand-alone
system rather than being part of a parallel architecture.
In this work, we present the design of the proposed
actuator with 3D mobility. We describe the concept for
analyzing the actuator dimensions by studying the physics of
the component beam behavior for a superior design. Further
Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition IMECE2014
November 14-20, 2014, Montreal, Quebec, Canada
IMECE2014-39308
2 Copyright © 2014 by ASME
these dimensions would enable the integration of a large array
of microneedles into a smaller surface area. We discuss both the
mathematical model based on stiffness matrix approach and
finite element analysis (FEA) simulation of the design based on
the dimensions analyzed above. We investigate the performance
of the design of the 4SA microrobot. Finally, we demonstrate
successful actuation of a fabricated 4SA microrobot excluding
the micro-needle and corroborate it with the analytical and
simulation results. These simulation and experimental results
give us the leverage to efficiently design our future advanced
3SA microrobot (three-sided single-unit actuator) before
fabrication and subsequent robotic manipulation.
ACTUATOR DESIGN AND WORKING PRINCIPLE To enable the robotic manipulation of single cells, the
design of the actuator must accommodate design criteria such
as enough actuation capability to cover a broad range of
different cell types with sizes ranging between 2 μm to 50 μm
[16]; independent actuation of microneedles in a parallel
architecture for targeted biomanipulation; decoupled motions
by effectively suppressing motion interference between the
different axes which can otherwise cause problems such as side
instability of comb-drives and limited motion range; and a
minimum out-of-plane actuation of 3-4 μm in order to penetrate
and poke through cells and targeted manipulation inside the
cells.
In the design of the 4SA microrobot, the tethering beams
and the four sets of actuators are placed orthogonal to each
other (Figure 1a). These microrobots are placed in a linear
fashion in the larger parallel architecture structure thus enabling
independent 3D motion capability (Figure 1b).
The micro-stage forms the center of the structure which is
integrated with a micro-needle (2). The tethering beams (1)
connected to the micro-stage provide the necessary actuation
and also act as a spring system. The tethering beam is
connected to a supporting beam (3) which supports the spring
flexure beams (6) and the comb-drive actuators (4). The
moving comb-finger electrodes are connected to the supporting
beam. The different components are electrically isolated from
each other as they all sit on a 1-2 μm thick silicon-dioxide
(SiO2) insulating layer (7). The micro-stage is suspended with a
silicon tower (8) underneath it. The micro-stage and the bottom
tower acts as a parallel plate capacitor which provides the
vertical z-axis actuation due to the capacitive electrostatic force
acting between them. Increasing the lateral stiffness of the
spring flexure beams can reduce the coupling of motion across
the axes. For the 4SA microrobot, the spring flexure beams
provide a significant lateral stiffness of 6.09 × 104 N/m.
Our proposed single-cell analyses and manipulation setup
would involve a separate cell-trapping platform for trapping
single cells. The actuator is mounted using a vertical
macropositioning stage and placed directly on top of the
trapping platform. The inverted microscope captures the images
of the single-cells and the vision software processes these
multiple images to find the targeted zone inside the cell that is
to be manipulated. Once the target zone and its corresponding
(1) Tethering beam (2) Micro-needle (3) Support beam (4) Comb-drive
actuators (5) Metal pads for electrical connections (6) Spring flexure beam (7)
Insulating oxide (8) Si tower
Figure 1. Actuator design (a) a 4SA microrobot with orthogonal arrangement of
the tethering beams (5 mm × 5 mm). (B) a parallel architecture having 10 × 10
4SA microrobots (55 mm × 55 mm).
xy coordinates are identified, this information is fed into the
control software that drives the in-plane motion of the
microneedles on the actuator accordingly. Once the
microneedles have been aligned as per the in-plane coordinates
of the target zone, DC voltage is applied to the parallel plates of
the actuator which pulls the microneedle backward, toward the
silicon tower plate. This retracted position of the actuator is
maintained until the next step. The vertical macropositioning
stage is then driven to bring the actuator in this retracted state
to the proximity of the single cells. The CMOS camera placed
sideways records the vertical motion and verifies whether the
,y v
,x u
,z w
(a)
(b)
(2)
(1)
(3)
(4)
(2)
(7)
(5)
(6)
(8)
3 Copyright © 2014 by ASME
microneedles are in the proximity of the cell. Once this
information is verified, the control software drives the
microneedle out-of-plane (opposite to the previous retracted
position) by decreasing the DC voltage. The voltage-
displacement feedback mechanism in the controller determines
the single cell manipulation at this stage until the microneedle
tip is at the target zone. Once the manipulation is complete, the
vertical macropositioning stage pulls the actuator back and the
next set of manipulation occurs.
DESIGN ANALYSIS FOR ACTUATOR COMPONENTS We investigate the maximum bending and stretching of the
tethering (2) and spring flexure (4) beams due to translational
and axial deflections. We conceptualize the dimensions and
analyze the system for these values. The following criteria have
been considered:
Minimum longitudinal stretching of tethering beam.
Substantial stretching can lead to increasing stiffness of the
tethering beam which affects its fatigue life under cyclic
loading thus inducing plastic behavior and a permanent
elongation of the beam. This affects the accuracy of motion
performance.
Maximum bending of tethering beams for 3D motion range
with decoupled motion across the axes.
Relationship between bending of spring flexure beams
with bending of tethering beams.
Three thicknesses 10 μm, 20 μm and 25 μm are used to
study the beam behaviors as limiting parameters. Increasing the
thickness further can significantly limit the critical out-of-plane
motion performance. The interference in deflection of the
tethering and spring flexure beams for both in-plane and out-of-
plane actuation needs to be taken into account. Thus, we have
mapped out and analyzed six such scenarios to conceptualize
the beam dimensions for a superior design. We have shown just
three such scenarios in Figure 2. The deflection behaviors have
been investigated for,
Cross-section area (w×h),
Aspect ratio (w/h), and
Length (l) of the beam,
due to their significance in the motion of the actuator. The
longitudinal stretching of the tethering beam is computed by
[17],
eF lL
EA
t (1)
where Fe is the electrostatic force applied to the end of the
tethering beam to compute the stretching, lt is the length of the
tethering beam, E is the Young’s modulus of silicon, 129.5 GPa
and A is the cross-section area of the beam.
The bending of the tethering beam is computed by,
3
max3
e t
t
F l
EIw (2)
where It is the second moment of inertia of the tethering beam.
The bending of the spring flexure beam is computed by,
3
max192
e s
s
F lW
EI (3)
where ls is the length of spring flexure beam and Is is the second
moment of inertia of the spring flexure beam.
Referring to Figure 2c, the longitudinal stretching in
tethering beam ranges from four to five orders of magnitude
lower than the corresponding bending at a particular cross-
section area and aspect ratio. Thus, we neglect the effect of
stretching toward the motion of the actuator. To find the range
of dimensions for further analyses, the aspect ratio is a better
metric compared to cross-sectional area since it represents the
true dimensions of the beams. For example, we observe that
with respect to aspect ratio, the out-of-plane bending for both
tethering and spring flexure beams decreases by 2.3-2.5 times
as the thickness increases from 10 µm to 25 µm. On the
contrary with respect to area, the bending increases by the same
Figure 2. Beam behavior profiles under the application of force. (a) In-plane
and out-of-plane tethering beam bending with area. (b) In-plane and out-of-plane spring flexure beam bending with aspect ratio. (c) Stretching and bending
of tethering and spring flexure beams with length.
0 50 100 150 200 250 300 350 400 450 500
101
102
103
104
105
Area
Ben
din
g (
µm
)
in-plane tethering bending 10µm
in-plane tethering bending 20µm
in-plane tethering bending 25µm
out-of-plane tethering bending 10µm
out-of-plane tethering bending 20µm
out-of-plane tethering bending 25µm
Area of Interest
Intersection points become
further apart as the thickness
increases
0 0.5 1 1.5 2 2.5 3 3.5 4
10-2
10-1
100
101
102
103
Aspect Ratio (w/h)
Ben
din
g (
µm
)
in-plane spring bending 10µm
in-plane spring bending 20µm
in-plane spring bending 25µm
out-of-plane spring bending 10µm
out-of-plane spring bending 20µm
out-of-plane spring bending 25µm
Area of Interest
0 200 400 600 800 1000 1200 1400 1600 1800 2000
10-5
100
105
Length (µm)
Str
etc
hin
g/b
en
din
g (
µm
)
in-plane tethering stretching
in-plane tethering bending
out-of-plane tethering bending
in-plane spring bending
out-of-plane spring bending
Area of Interest for
spring flexure beamArea of Interest for
tethering beam
(a)
(b)
(c)
4 Copyright © 2014 by ASME
TABLE I. DESIGN PARAMETERS OF THE SINGLE-UNIT ACTUATOR
magnitude for the increase in thickness from 10 µm to 25 µm.
Similar trends can be observed for in-plane bending of both
types of beams.
Further for the same thickness, with respect to cross-
section area and aspect ratio alike, the in-plane and out-of-plane
bending in tethering beams is almost 37.5 times higher than the
bending in the spring flexure beams. There is almost a common
95% drop in in-plane and out-of-plane bending for the two
types of beams up to cross-section area range of 50 µm2 - 60
µm2 and aspect ratio range of 0.5-0.6. We define this region as
Area of Interest. Beyond these points, the percentage drop in
bending becomes comparatively lower as the cross-section area
or the aspect ratio increases. Thus, while increasing the
thickness can offer better in-plane bending, the out-of-plane
bending is significantly compromised. Accounting for the effect
of length, both types of bending drops down significantly from
87% to 42% respectively between length range of 200 µm –
400 µm and 1000 µm - 1200 µm. While having short beams
can increase the stiffness significantly and reduce the 3D
motion, too long beams with slender structure can make the
actuator very fragile and increase its size. Thus for further
analyses, we choose the range of dimensions of the different
beams as summarized in Table I.
Additionally, we have investigated the motion performance
of the 4SA microrobot design using FEA simulations discussed
later for three different types of spring flexure beams -
clamped-clamped, crab leg and single folded as shown in
Figure 3. The clamped-clamped spring flexure beam has a
significant stiff nonlinear spring constant due to extensional
axial stress in the rectangular beams. When the thigh section is
added to the clamped flexure beam, it forms the crab leg spring
flexure beam which reduces stiffness in the undesired direction
Figure 3. Different spring flexure beam types used for analysis (a) clamped-
clamped (b) crab leg (c) single folded (d) In-plane and out-of-plane
displacements for three different spring flexure beam types for different applied DC voltages for 3SA microrobot. The tethering beam length is 800 μm and the
suspended structure thickness = 10 μm.
and extensional axial stress in the flexure. The single folded
flexure beam also reduces axial stress components in the beams
by adding a truss to the parallel arrangement of beams and they
are anchored near the center.This truss allows the end of the
flexure to expand or contract in all directions [18].
For both in-plane and out-of-plane (Figure 3d) motion, the
performance of the actuator with single-folded flexure beam is
40% higher than the other two spring flexure beam types.
Nonetheless with a folded flexure beam, during out-of-plane
motion, the comb-drive actuators get disoriented out-of-plane
by as much as 35-40% of the total motion of the central
microstage-microneedle structure. This can significantly affect
the overall stability of the actuator during 3D motion. Therefore
we choose the clamped-clamped beam as the best possible
option for the design of our 4SA microrobotic actuator.
ANALYTICAL MODELING OF THE MICROROBOTIC ACTUATOR The electromechanical behavior of the 4SA microrobotic
actuator is investigated by analytically deriving the effective
stiffness of the actuator [19-20] on the basis of the following
assumptions:
0 10 20 30 40 50 60 70 80 900
2
4
6
8
10
12
Voltage (V)
Dis
pla
cem
ent (µ
m)
In-plane (x,y) Clamped
In-plane (x,y) Crab leg
In-plane (x,y) Folded
Out-of-plane (z) Clamped
Out-of-plane (z) Crab leg
Out-of-plane (z) Folded
Mechanical properties of silicon
Young’s modulus 129.5 GPa
Poisson’s ratio 0.28
Desired actuation parameters
In-plane actuation At least 35 µm
Out-of-plane actuation At least 5 µm
Resonant frequency 10 – 40 KHz
Structural parameters
Area of Interest Cross-section area = 50 µm2
Aspect ratio = 0.5
Spring flexure beams sw 5 – 10 µm, sh 10 – 25
µm, sw 400 – 600 µm
Tethering beams tw 4 – 10 µm,
th 10 – 25 µm,
tw 800 – 1200 µm
Diameter of micro-stage 300 µm
Height of Silicon tower 385 – 425 µm
Micro-needle Height = 50 µm, Tip diameter = 30
– 50 nm
Comb-drive actuator i = 800-1000,f
t 2 – 5 µm ,
fgs 2 – 5 µm , h =10 – 25 µm
(d)
(a)
(b)
(c)
(d)
5 Copyright © 2014 by ASME
Longitudinal stretching of the tethering beams is
negligible.
Small torsional rotation about the x and y axes and bending
rotation about the z axis are considered during out-of-plane
motion.
Stiffness in one direction is not significantly affected by
the structural deformations along other directions.
We only discuss the analytical model of the 4SA
microrobot due to the similarity of analytical treatment for both
types of actuator. To compute the in-plane displacement of the
node 9 (from D to D’) because of electrostatic force Fe, due to
an electric field when voltage V is applied to the comb-drive
actuators at node C, we form an equivalent elastic stiffness
matrix of the tethering and spring flexure beams. We apply
similar mathematical treatment to compute the out-of-place
displacement of the node 9, because of the electrostatic force
Fz, due to an electric field when voltage V is applied to the
parallel-plate actuator arrangement of a long standing silicon
tower beneath the microstage. The schematic of the actuator is
divided into nine nodes, 1 to 9 and eight elements E1 to E8,
each corresponding to a beam structure, as shown in Figure 4.
Every spring represents two pairs of spring flexure beams
which have been condensed into a single element. Dividing the
model into larger number of nodes and elements can lead to
greater precision of the results while compromising the
simplicity of the current approach. For out-of-plane motion
(Figure 4b) the degrees of freedom and nodal forces at each
node respectively are a vertical deflection vector zi and a
transverse force vector fiz about the z axis, a torsional rotation
vector Φix and a torsional moment vector mix about the x axis
and a bending rotation vector Φiy and a bending moment vector
miy about the y axis. The element stiffness matrix of individual
elements which are not in local coordinates are transformed
into global coordinates. These individual element matrices are
then added into their corresponding locations in the 21 × 21
and 27 × 27 global stiffness matrix [K] for computing in-plane
and out-of-plane displacement respectively. Detailed
mathematical treatment for both in-plane and out-of-plane
motion can be found in [21]. Thus the equivalent global
stiffness matrix for computing the in-plane displacement is,
2 2
2 2
2 2 2
2 2
3
3 4 5 6 73
8eq
s
Spring
c cs c csEhw cs s cs s
K k k k k k kc cs c cslcs s cs s
2 2
2 2
2 2
2 2
3
12
t
Tethering
s cs s csEI cs c cs c
s cs s cslcs c cs c
(4)
where c = cos θ and s = sin θ.
Thus, the final in-plane and out-of-plane displacement
(Annex A) of node 7 is,
1
eqU K F
(5)
Figure 4 Schematic of the 4SA microrobot for analyzing the (a) in-plane motion using elastic stiffness matrix model. (b) out-of-plane motion using grid stiffness
matrix model.
where [F] represents Fe or Fz which in turn are [22],
21
2
f
f
e
i tF V
gs
(6)
2
2
1
2z
VF A
d (7)
Where i = number of actuation comb-finger pairs, ε =
permittivity of air, 8.85×10-12
C2N
-1m
-2, tf = thickness of comb
finger, V = actuation voltage, gsf = the gap spacing between the
(a)
(b)
6 Copyright © 2014 by ASME
adjacent comb fingers, A = microstage area and d = distance
between the silicon tower and microstage.
FINITE ELEMENT ANALYSIS OF THE MICROROBOTIC ACTUATOR We have performed a series of FEA simulations in ANSYS
v13.0/14.5 in order to further validate the electrostatic and
structural behavior of the design in addition to the analytical
model discussed in the preceeding section. The simulations are
same for both types of actuators. Nonetheless, we focus on the
results of the 4SA microrobot in this paper as it is our primary
design focus. We first perform electrostatic simulations on the
comb-drive actuators; and the parallel-plate actuator to compute
the in-plane and out-of-plane electrostatic forces respectively.
We then apply these forces as structural forces on the grid to
find the displacements. We have made a few assumptions such
as - replacing the microneedle by adding an equivalent mass
and density to the microstage, and replacing the comb-drive
actuators by rectangular beams of equivalent mass and density.
We have performed convergense tests for both electrostatic
and structural simulations in order to optimize the number of
nodes and elements for meshing. The comb-drive actuators are
meshed with approximately 1.5 million SOLID123 (3D 10-
node) elements. The parallel-plate actuators are meshed with
approximately 2 million PLANE121 (2D 8-node) elements for
the plates (silicon tower and microstage) and SOLID122 (3D
20-node) elements for the air-gap volume. The suspended
actuator grid structure is meshed with approximately 5 million
SOLID187 (3D 10-node) elements. Types of elements used for
meshing along with finer mesh density can lead to a closer
conformity between the analytical and simulation results,
shown in Figure 6a.
Simulation studies on the designed 4SA microrobot show
that the displacement of the central microstage is almost
independent of the length of the tethering beams as it increases
from 800 µm to 1200 µm. A total in-plane displacement of 76
µm (±38 µm) can be achieved in a pull-pull mode at 160 V
when either one or two sides is/are actuated (Figure 6a). For
out-of-plane motion, more displacement can be achieved at
lesser voltage as length of tethering beam increases. An out-of-
plane displacement of more than 6.5 µm can be achieved at 35
V with a tethering beam length of 800 µm (Figure 6a)
Figure 5. Structural simulation of the structure (a) In-plane motion (b) Out-of-
plane motion
Figure 6. Static displacement response from applied DC voltage. (a) In-plane
actuation and out-of-plane actuation of the designed 4SA microrobot. (b) Simulation surface plot of the in-plane motion of the fabricated 4SA microrobot
when compared to Figure 8.
compared to the same achievable displacement at 17 V with a
tethering beam length of 1200 µm. The simulated surface plot
of the zone of actuation of the fabricated microrobot is shown
in Figure 6b which shows a close conformity with the
experimental results in Figure 8, thus showing the accuracy of
our simulation model.
The maximum von Mises stress developed in the structure
is around 800 MPa at 160 V which is between 5-10% of the
yield strength of silicon, 7000 MPa. We have also simulated the
downward sagging of the device under its own weight of the
suspended structures, to be less than 0.005 nm, which is
0 20 40 60 80 100 120 140 160 180 2000
10
20
30
40
50
60
Voltage (V)D
ispla
cem
ent (µ
m)
In-plane (x,y) Simulation 1 side
In-plane (x,y) Analytical 1 side
In-plane (x,y) Simulation 2 sides
Out-of-plane (z) Simulation
Out-of-plane (z) Analytical
Distance between the micro-stage and bottom metal
plate of the parallel plate actuator is 15 µm, which
limits the out-of-plane actuation
-15 -10 -5 0 5 10 15-15
-10
-5
0
5
10
15
x Displacement (µm)
y D
ispla
cem
ent (µ
m)
190V
170V
150V
100V
70V
35V
(b)
Spring flexure xy bending
Tethering xy bending
Spring flexure z bending
Tethering z bending
(a)
(a)
(b)
7 Copyright © 2014 by ASME
insignificant compared to the overall dimensions of the
actuator. Albeit, the current behavior of the actuator is purely
static, knowing the natural frequencies of the microrobot would
be useful for widening the application of the arrayed
architecture in the near future. Such applications involve single
molecule force spectroscopy, cell mechanical measurements,
local functionalization of polymeric layers and molecular
electronics such as depositing conductive polymers onto
nanoelectrodes. A high designed natural frequency would allow
the actuator to respond quickly and accurately to the rapid
changes in the command signal. For the vertical out-of-plane
motion of the microstage the first in-plane mode of vibration at
12 KHz is pure translational. The second mode of vibration at
27 KHz is out-of-plane translational plus rotation. The last three
modes of vibration at 29 KHz involve parasitic rotation of the
comb-finger electrodes. The last three eigen-frequencies are
almost 2.5 times higher than the desired translational mode of
the microstage. Since these modes are located far from the first
dominant mode, it indicates a significantly high stiffness to
excite these parasitic motions.
CHARACTERIZATION OF 4SA MICROROBOT The motion performance of the fabricated 4SA microrobot
(Figure 7) has been experimentally characterized for maximum
displacement in a 3D workspace, positioning repeatibility and
decoupling in motion. These preliminary results are a precursor
to designing the 3SA microrobot and its subsequent fabrication.
The actuator is controlled via a PC running the LabVIEW
program written to automate the actuation and direct the
microstage to any position within the 3D workspace that
follows a square path for in-plane motion. The out-of-plane
motion is set at a single level with a particular voltage value.
The 3D motion is visualized under an inverted fluorescence
microscope (Leica DM IRM for in-plane motion) and an optical
microscope (Olympus BH for out-of-plane motion), fitted with a
digital camera (Spot insight, 2.0 megapixel resolutions). The in-
plane images are post-processed in MATLAB using an image
processing algorithm [21] by measuring the resultant motion of
the comb-drive actuators, at the edge of the fingers and
microstage, at the edge of the stage. The measured out-of-plane
motion values are computed using a calibration technique on
the microscope [21]. The in-plane motion plotted as a surface
plot has been compared with the size of a typical mammalian
cell of 15 μm in diameter, to visualize the zone of actuation for
a typical biomanipulation task, shown in Figure 8. The actuator
has a total in-plane motion range of up to 10 μm (> ±4.5 μm) at
a driving voltage of 120 V satisfactorily covering almost 60%
surface area of the cell. The out-of-plane motion is plotted as a
line graph where the microstage can move more than 0.5 μm at
around 600 V, shown in Figure 9. The close conformity
between the experimental, simulation and analytical results has
been illustrated in Figures 8 and 9, thus proving the accuracy of
our model. The preliminary out-of-plane motion performance is
significantly lower compared to what it has been designed for
the 4SA microrobot, owing to the limitations in fabrication
infrastructure. For example, the in-plane stiffness of the
fabricated 4SA microrobot is 91.75 μN/μm, which is 316 times
greater than that of the designed 4SA microrobot i.e. 0.29
μN/μm. Similarly, the out-of-plane stiffness of the fabricated
4SA microrobot is 124.78 μN/μm, which is 524 times greater
than that of the designed 4SA microrobot i.e. 0.23 μN/μm.
Nonetheless, our hypothesis of a parallel-plate actuator
using an arrangement of a long standing silicon tower
underneath a microstage is proven by this vertical motion.
Further, the in-plane motion is linear to the square of the
actuation voltage with minimal coupling effects. The
displacements of the comb-drives have almost similar values to
the micro-stage for in-plane motion verifying the predicted
negligible stretching from our design optimization simulation.
The standard deviations of the maximum 3D actuation during
Figure 7. Scanning electron micrographs of (a) fabricated 4SA microrobot (without the microneedle) (b) Zoomed-in views of the parallel-plate actuator (c) Comb-drive
actuators
30 μm
30 μm
(a)
(b)
(c)
200 μm
8 Copyright © 2014 by ASME
Figure 8. (a) Surface plot of the in-plane actuation zone of the 4SA microrobot (dotted lines represent the experimental values and the solid lines represent the
analytical values). (b) Confocal microscopy images of ISHI cells growing on glass. F-actin stained with Texas Red phalloidin (red); nucleus stained with Hoechst 33342
(green/blue) [22]
Figure 9. Line experimental plot of the out-of-plane (z) actuation testing.
the repeatability trials have been found to be 268 nm, 329 nm
and 21 nm well within the elastic limit of the tethering and
spring flexure beams
SUMMARY In this paper, we present the design and development of a
single unit microrobotic actuator, that will become a part of the
parallel architecture technology for multiple micro-nano-
manipulation tasks. We mainly focus on the design of a 4SA
microrobot for biomanipulation tasks such as single-cell
analysis conceptualizing on the range of dimensions and
analyzing the mechanical performance and integrity of the
actuator for these dimensions. The design conceptualization
reveals that the cross-section area of the beams must not be
greater than 50 μm2 and the aspect ratio not greater than 0.5 for
optimal tradeoff between bending and integration of multiple
actuators in a parallel architecture. The analytical modeling in
based on calculating the displacement using stiffness matrix
equations for the structure under loading.
The finite element analysis of the actuator is based on a
coupled electrical and mechanical investigation of the structure.
The simulations are performed for different dimensions of the
microrobotic actuator and for different configurations of spring
flexure beams. The 3D motion capability of the 4SA microrobot
can achieve an in-plane motion of upto 76 µm (±38 µm) at 160
V in a pull-pull mode and an out-of-plane motion of more than
6.5 µm at 35 V. Albeit using a single-folded spring flexure
beam can achieve 40% higher 3D actuation capability
compared to clamped-clamped or crab leg beam, during out-of-
plane motion, this results in a vertical disorientation of the
comb-drive actuators by as much as 35-40% of the total motion
of the central microstage-microneedle structure. Thus clamped-
clamped spring flexure beam offers the best option in terms of
design.
We have fabricated sample 4SA microrobots (without the
microneedle) and performed electrical tests on them as a
precursor to the design and fabrication of our advanced
microrobot design. Owing to limitations in fabrication
infrastructure, the preliminary motion is limited but
successfully demonstrates our hypothesis of achieving vertical
motion using a parallel-plate actuator of long standing silicon
tower under the microstage. The 4SA microrobot can achieve
up to 10 μm in-plane actuation at 120 V in a pull-pull mode and
and an out-of-plane actuation of more than 0.5 μm at 600 V
with good performance in terms of achieving decoupled motion
and positioning repeatability.
ACKNOWLEDGMENTS This material is based upon work supported by the
University of Canterbury (UC) Mechanical Engineering
Premier PhD Scholarship, Innovation Stimulator Grant from
the UC Research & Innovation Office, Maurice & Phyllis
Paykel Trust Travel Grant and UC College of Engineering
Research Travel Grant Award. The fabrication of the 4SA
microrobotic actuator has been jointly undertaken at the
Canadian Microelectronics Corporation in Quebec, Canada and
UC Nanofabrication Laboratory. Wenhui Wang is supported by
NSFC (No. 61376120), National Instrumentation Program (NIP,
No. 2013YQ19046701), and One-Thousand Young Talent
Program of China. The authors would like to thank Xinyu Liu
of Mechanical Engineering department at McGill University
and Maan Alkaisi of Electrical and Computer Engineering
department of UC for their support with the fabrication process.
100 150 200 250 300 350 400 450 500 550 6000
100
200
300
400
500
Voltage (V)
Dis
pla
cem
ent (n
m)
Experiment
Simulation
(a)
(b)
9 Copyright © 2014 by ASME
REFERENCES
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10 Copyright © 2014 by ASME
ANNEX A
GRID STIFFNESS MATRIX MODEL FOR COMPUTING OUT-OF-PLANE MOTION OF ACTUATOR
The local stiffness matrix equation for a grid element
joining nodes i and j [19] is,
3 2 3 2
2 2
3 2 3 2
2 2
12 6 12 60 0
0 0 0 0
6 4 6 20 0
12 6 12 60 0
0 0 0 0
6 2 6 40 0
iz
ix
iy
jz
jx
jy
t t t t
t t
t t t t
t t t t
t t
t t t t
EI EI EI EI
l l l l
GJ GJ
f l lm EI EI EI EIm l l l lf EI EI EI EI
m l l l lm GJ GJ
l l
EI EI EI EI
l l l l
iz
ix
iy
jz
jx
jy
u
u
A1
where [k]m for a grid element represents the local stiffness
matrix where m is the number of the grid element, G is the
shear modulus of rigidity and J is the torsional constant for the
rectangular cross-section of the tethering beam.
Equation (A1) can be rewritten as,
6 6
m m m
m m
m m
m mij
m m
ii iji i
j jji jj
iy iy
ix ixii
iz iz
jy jy
ji jjjx jx
jz jz
f k u
k kf u
f uk k
f u
m k k
m
f u
k km
m
A2
where i, j denotes the node number in the 4SA microrobot
design.
The global stiffness matrix for a grid element arbitrarily
oriented in the x-y plane is,
T
G GmK T k T
A3
where [TG] is the transformation matrix relating local to global
degrees of freedom for a grid.
Combining all the grid element stiffness matrix equations
obtained in Equation A3 into the corresponding locations of the
global stiffness matrix equation, the final connectivity matrix
becomes,
i ii iF k U A4
, ,, 1 , 2
1 1, 1, 1 1, 2 1,
22, 2, 1 2, 1
.... .... .... .... ....
.... .... .... .... ....
.... .... .... ........
....
....
....
....
m m m mi i i ji i i i i
m m m mi i i i i i i i j
m m mii i i i i i
j
k k k kF
F k k k k
Fk k k
F
2,
, ,
....
.... .... .... .... .... .... .... .... ....
.... .... .... .... .... .... .... .... ....
.... .... .... .... .... .... .... .... ....
.... .... .... .... .... .... .... .... ....
.... .... .... .... .... .... .... .... ....
mi j
mj i j i
k
k k
1
2
,1 , 2 27 27
....
....
....
....
....
.... .... .... .... ....
i
i
i
m m mjj jj i
U
U
U
Uk k
A5
Thus, the final connectivity stiffness matrix equation is,
27 27
27 2727 27
.... ....[ ]
iz iz
ix ix
iy iy
jz jz
jx jx
jy jy
F UMM
KF U
M
M
A6
Equation (A6) can be further decomposed depending on the
nodes that are fixed and have zero displacement. Since only the
vertical out-of-plane displacement of the microneedle node is
considered, the other nodes will have zero vertical
displacement, torsional and bending moments. Thus, the
vertical out-of-plane displacement is,
1
27 27z zU K F
A7