Design and Analysis of Actuated Microneedles for Robotic ...

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


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)


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



out-of-plane tethering bending 10µm



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



out-of-plane spring bending 10µm



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)


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)


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)


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)


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


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)


REFERENCES

[1] Ivanova, Y.S.K. et al., 2008, "Scanning proximal probes for parallel imaging and lithography," Journal of Vacuum Science & Technology B, 26, pp. 2367-2373.

[2] Favre, M. et al., 2011, "Parallel AFM imaging and force spectroscopy using two-dimensional probe arrays for applications in cell biology," Journal of Molecular Recognition, 24, pp. 446-452.

[3] King, W.P. et al., 2002, "Design of Atomic Force Microscope cantilevers for combined thermomechanical writing and thermal reading in array operation," Journal of Microelectromechanical Systems, 11, pp. 765-774.

[4] Teichert, G.H., Burnett, S., and Jensen, B.D., 2013, "A microneedle array able to inject tens of thousands of cells simultaneously," Journal of Micromechanics and Microengineering, 23, pp. 1-10.

[5] Zappe, S., Fish, M., Scott, M.P., and Solgaard, O., 2006, "Automated MEMS-based Drosophila embryo injection system for high-throughput RNAi screens," Lab Chip, 6, pp. 1012-1019.

[6] Anis, Y.H., Holl, M.R., and Meldrum, D.R., 2008, "Automated vision-based selection and placement of single cells in microwell array formats," Proc. 4th IEEE Conf Aut Sci Engg, Washington DC, pp. 315-320.

[7] Zhang, Y., Chen, B.K., Liu, X.Y., and Sun, Y., 2010, "Autonomous Robotic Pick-and-Place of Microobjects," IEEE Trans Robotics, 26(1), pp. 200-207.

[8] Wang, W.H., Liu, X. Y. and Sun, Y., 2009, “High-Throughput Automated Injection of Individual Biological Cells,” IEEE Trans Aut Sci Engg, 6(2), pp. 209-219.

[9] Hubbard, N.B., and Howell, L.L., 2005, "Design and characterization of a dual-stage, thermally actuated nanopositioner," J Micromech Microen., 15, pp. 1482–1493.

[10] Joudrey, K., Adams, G.G. and McGruer, N.E., 2006, "Design, modeling, fabrication and testing of a high aspect ratio electrostatic torsional MEMS micromirror," J Micromech Microeng, 16, pp. 2147–2156.

[11] Kim, J., and Lin, L., 2005, "Electrostatic scanning micromirrors using localized plastic deformation of silicon", J Micromech Microeng, 15, pp. 1777–1785.

[12] Ferreira, P.M., Dong, J., and Mukhopadhyay, D., 2012, "High precision Silicon-on-insulator MEMS parallel kinematic stages," U.S. Patent 8,310,128 B2.

[13] Lee, DJ. et al., 2005, "Development of 3-axis nano stage for precision positioning in lithography system," Proc IEEE Intl Conf Mechatron Aut, Canada, pp. 1598-1603.

[14] Fowler, A.G., Laskovski, A. N., Hammond, A.C., and Moheimani, S.O.R., 2012, "A 2-DOF electrostatically actuated MEMS nanopositioner for on-chip AFM," Journal of Microelectromechanical Systems, 21(4), pp. 771-773.

[15] Kim, YS. et al., 2012, "Design, fabrication and testing of a serial kinematic MEMS XY stage for multifinger manipulation," Journal of Micromechanics and Microengineering, 22, pp. 1-10.

[16] Alberts, B., 2009, Essential cell biology, Garland Science, 3rd ed.

[17] Hibbeler, R.C., 2010, Mechanics of materials, Prentice Hall, 8th ed.

[18] Fedder, G.K., 1994, Simulation of Microelectromechanical Systems, Ph.D. thesis, University of California, Berkeley, USA.

[19] Logan, D.L., 2007, A First Course in the Finite Element Method, Cengage Learning, 4th ed., pp. 214-304.

[20] Zhu, Y., Corigliano, A., and Espinosa, H.D., 2006, "A thermal actuator for nanoscale in situ microscopy testing: design and characterization", Journal of Micromechanics and Microengineering, 16, pp. 242-253.

[21] Banerjee, S., 2014, "A 3D microrobotic actuator for micro and nano manipulation," Ph.D. thesis, University of Canterbury, Christchurch, NZ.

[22] Popovic, Z., and Popovic, B.D., 2000, Introductory electromagnetics, Prentice Hall, New Jersey, USA.

[23] Murray, L.M., 2012, Influence of substrate topography and materials on behaviour of biological cells, Ph.D. thesis, University of Canterbury, Christchurch, NZ.


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

Design and Analysis of Actuated Microneedles for Robotic ...

Documents

Transcript of Design and Analysis of Actuated Microneedles for Robotic ...