Mechanism of Micro Manipulation using Oscillation
Tetsuyou Watanabe

Zhongwei Jiang

Dep. of Mech. Eng.
Yamaguchi University
Ube, 755-8611, Japan
Email: te-watanabe@ieee.org

Dep. of Mech. Eng.
Yamaguchi University
Ube, 755-8611, Japan
Email: jiang@yamaguchi-u.ac.jp

Abstract— In this paper, we analyze the mechanism of thephenomenon between an endeffector, a micro object and asubstrate during a micro manipulation. In a micro range, theattracting forces such as the van der Waals, capillary, andelectrostatic forces dominate and course adhesion between theobject and the endeffector. The adhesion makes the manipulationof an object difficult. Recently, we developed a method to reduce
the attracting/adhesion effect. When bringing an oscillating
endeffector close to a micro object on a substrate, the attracting
force between the object and the endeffector is reduced, attracting
the object to the substrate. Then, it becomes easy to remove
the endeffector from the object. Using this method, a micro
object can be easily manipulated. However, the mechanism of
the phenomenon is still unclear. In this paper, we develop thetheoretical model of the system to analyze the phenomenon,and simulate the dynamical motion of the system. Comparing
the experimental results, we show the validity of our approach.
Using simulation and experiment, we show that the oscillationof the endeffector can reduce the adhesion effect between theendeffector and the object, attracting the object to the substrate.

I. I NTRODUCTION
Recently, there has been a growing interest in a manipulation of a micro/nano sized object. It is the technology required
to assemble or maintain microcomputers, micro electronics
parts, a micro medical equipment, and so on. Different from amanipulation in a macro range, we cannot neglect an adhesion
force between a micro object and an endeffector. In a macro
range, the van der Waals, capillary, and electrostatic forces(proportional to surface area) become more significant than
the inertial and gravitational forces (proportional to volume),
because of a scale effect [1], [2]. These attracting forces (vander Waals, capillary, and electrostatic forces) cause the adhesion between a micro object and an endeffector. Therefore,
even a basic operation such as pick and place becomes very
hard to complete. Especially, a release of an object from an
endeffector is very difficult.
Many researchers have discussed how to release a micro
object [3]–[9]. Arai et. al. [3] proposed an adhesion-type
micro endeffector. There are micro holes on the endeffector.
By controlling the pressure inside the holes by temperature,
we can absorb and release a micro object. But it is hard tocontrol the temperature because the temperature is influenced
by an environment. Also treatable objects depend on the sizeof the holes. Zesch et. al. [4] developed a vacuum gripping
tool consisting of a glass pipette and a computer controlled

vacuum supply. But treatable objects depend on the size of ahole of the pipette. Rollot et. al. [5] proposed a method forpick and place of a micro spherical object when an endeffector
has higher surface energy than a table (substrate). The problem
is the release of the object. The release was done by slopping
the endeffector. But the strategy can be applied to limited
objects. Then, Haliyo et. al. [6], [7] proposed a strategy for the
release, which is to oscillate the endeffector and give the micro
object enough acceleration to remove it from the endeffector.
However, it is hard to control the motion of the object after
the release. Hence, to accurately position the object is very
difficult. Saito et. al. [8] proposed a method for pick andplace of a micro object under an SEM. But, they develop thismethod under the assumption that all the parameters about
environment, object, and endeffector are completely known.
Then, it is not easy to apply the method to practical use.
Also, treatable objects are limited to a sphere. Saito et. al. [9]proposed a way for detachment of an adhering micro particle
from a probe by controlling the electrostatic force. But, it ishard to control the motion of the object after the detachment,
and to accurately position the object.
Recently, we developed a new strategy to cope with theadhesion force [10]. When bringing an oscillating endeffector
close to a micro object on a substrate, the attracting force
between the object and the endeffector is reduced, attracting
the object to the substrate. Then, it becomes easy to remove
the endeffector from the object. Based on this strategy, wedeveloped a sophisticated strategy for pick and place operation
in a micro range, as shown in Fig.1. Using this strategy, a micro manipulation can be done like a macro manipulation. This
strategy can provide an accurate manipulation. However, ”whatphenomenon (actually) happens (between a micro object, an
endeffector, and a substrate)” was not discussed. Therefore, we
do not understand; how does the endeffector move?, how does
the object move?, why the strategy is effective for reducing
the attracting/adhesion effect?, and so on.
In this paper, we develop a theoretical model of thephenomenon between a micro object, an endeffector, and asubstrate during a micro manipulation using the our strategy[10]. We focus on the phenomenon in the case where bringing an oscillating endeffector close to a micro object on asubstrate (see Fig.1 (h)∼ Fig.1 (i) and Fig.2). We derive themotion equations of the endeffector and the object, combining
the vibration analysis for distributed-parameter systems andsupport finger

pushing finger
object (sphere)
substrate

(a)

(b)

(c)

useful information about the object motion, which can not bemeasured in the experiment because of the configuration of
the endeffector and the object (note that the oscillation (of theobject motion) is too high to be caught by the microscope).
This paper is organized as follows. First, we present thetarget system, and develop a model for analyzing the phenomenon between the micro object, the endeffector, and thesubstrate, when bringing an oscillating endeffector close to themicro object on a substrate. Then, we simulate the dynamical
motion of the object and the endeffector, and show the validityof our approach, comparing with some experimental results.
II. TARGET S YSTEM

(d)

(e)

(f)

(g)

(h)

(i)

Fig. 1. Pick and place operation; (a) This is the initial state. (b) Make thesupport finger contact with the object on the substrate from the right side. (c)Make the oscillating pushing finger contact with the object on the substratefrom the left side. The direction of the oscillation is left and right. (d) Pick theobject by moving the pushing and support fingers upward. (e) Place the object
by moving the pushing and support fingers downward. (f) Remove the pushingfinger from the object. (g) Make the oscillating pushing finger contact withthe upper side of the object. The direction of the oscillation is up and down.
(h) Remove the support finger from the object by moving the support finger
upward. (i) Remove the pushing finger from the object by moving the pushingfinger upward. Note that in the procedure (f) and (i), the pushing finger canbe easily removed from the object for the oscillation of the pushing finger,
which reduces the attracting/adhesion effect.

lubrication analysis. Then, we simulate dynamical motions of
the endeffector and the object. Among the attracting forces(van der Waals, capillary, and electrostatic forces), capillary
force is large compared with the other forces. Therefore,
the presented model includes the effect of only meniscus
bridge (capillary force). Using this model, we can analyze
what phenomenon does happen between a micro object, an
endeffector, and a substrate, and obtain useful information forrealizing stable micro manipulation. Especially, we can obtainIn the manipulation shown in Fig.1, the operation is doneby pushing and support fingers. The pushing finger plays arole of pushing the micro object toward the support finger andthe substrate. The support finger plays a role of supporting
the micro object against the pushing forces from the pushing finger. These fingers are beams, and attached on threedimensional manipulators. On the pushing finger, a piezocell isbonded as an actuator for oscillating it. In this paper, we focus
on the case when bringing the oscillating the pushing finger(hereafter, endeffector) close to the object on the substrate,
which corresponds to Fig.1 (h)∼ Fig.1 (i). Fig.2 shows thetarget system. Note that the case shown in Fig.1 (e)∼ Fig.1(f) can be analyzed by the similar way as the target case.
For the simplicity, we assume that; (1) the motion of theendeffector, the object, and the substrate is in a planner space(a gravity force doesn’t work), (2) the object is a sphere, (3)the endeffector and the substrate are made by a same material,(4) among the attracting forces (van der Waals, capillary,and electrostatic forces), only capillary force is considered(because among the attracting forces, capillary force is verylarge compared with the other forces).
The following nomenclatures are used in this paper.
Radius of the sphere (9.7 × 10−5 [m]).
Tip position of the endeffector in y direction.
Position of the center of the object in y direction.
Position of the substrate in y direction (1.5 ×
10−7 [m]+2r0 ).
mo Mass of the object (9.5 × 10−9 [Kg]).
ρ
Density of the endeffector (beam: 8.9 × 103 [Kg/m3 ], PZT:
7.65 × 103 [Kg/m3 ]).
A(x) Cross section area of the endeffector (beam: 9.0 ×
10−7 [m2 ], PZT: 6.0 × 10−7 [m2 ]).
E(x) Young’s modulus of the endeffector (beam: 10.2 ×1010 [N/m2 ], PZT: 6.2 × 1010 [N/m2 ]).
Ee Young’s modulus of the beam (10.2 × 1010 [N/m2 ]).
Eo Young’s modulus of the object (7.5 × 1010 [N/m2 ]).
Es Young’s modulus of the substrate (10.2 × 1010 [N/m2 ]).
I(x) Geometrical moment of inertia of the endeffector (beam:
6.75 × 10−15 [m4 ], PZT: 2.45 × 10−14 [m4 ]).
C
Coefficient of structural damping of the endeffector (1.87×
10−5 [sec]).
Mp Bending moment produced from piezocell.
l1
Length from the root of the beam to piezocell (1[mm]).
l2
Length of piezocell plus l1 (3[mm]).
l
Length of the beam (40[mm]).
lLength from the root of the beam to the contact point withthe object (0.0399[m]).

r0
yb
yo
ys

l
l2
l1

PZT

LiquidxyFig. 2.

(a)

(b)

(c)

(d)

(e)

(f)

Target system

Fb

Force applied to the beam resulted from the interaction
between the endeffector and the object.
Fo Force applied to the object resulted from the interaction
between the endeffector, the object, and the substrate.
δ(x) Dirac delta function.
δ (x) = ∂δ(x).
∂xP
Normalized pressure of air medium between the object andthe endeffector (= p/pa , p: pressure between the object
and the endeffector, pa : the atmospheric pressure).
plPressure of liquid medium between the object and thesubstrate.
R
Normalized r coordinate (= r/r0 where r0 denotes thecharacteristic length (the radius of the sphere)).
hThickness of the air medium between the endeffector andthe object.
hc Thickness of the air medium at the center of the contact
circle between the object and the endeffector.
H
Normalized thickness of air medium between the endeffector and the object (= h/h0 where h0 denotes thecharacteristic length (= r0 )).
T
Normalized t (time) (= ωt where ω denotes the frequencyof the oscillation).
µViscosity of the liquid (0.001[Pa·sec]).
µair Viscosity of the air (1.86 × 10−5 [Pa·sec]).
σ
Squeeze number (=12µair ωr02 /pa h20 ).
νe Poisson’s ratio of the beam (0.35).
νo Poisson’s ratio of the object (0.17).
νs Poisson’s ratio of the substrate (0.35).
γ
Surface tension (73 × 10−3 [N/m] for water).
hleo Thickness of meniscus bridge between the endeffector andthe object.
hleoc hleo at the center of the object.
hlos Thickness of meniscus bridge between the object and thesubstrate.
hlosc hlos at the center of the object.
hle Thickness of meniscus bridge on the endeffector (3.5[nm]).
hlo Thickness of meniscus bridge on the object (3.5[nm]).
hls Thickness of meniscus bridge on the substrate (3.5[nm]).
θc
Contact angle of meniscus bridge (0[rad]).
Cm Coefficient of damping when the object directly contacts
with the endeffector/substrate.
r2
the wetted radius of meniscus bridge
r1
the meniscus curvature radius.

III. P HENOMENON BETWEEN A MICRO OBJECT, AN
ENDEFFECTOR , AND A SUBSTRATEIn this section, we develop a theoretical model of the phenomenon in the case when bringing an oscillating endeffecter
close to a micro object on a substrate. We derive the motion
equations of the endeffector and the object, combining thevibration analysis for distributed-parameter systems [11] andFig. 3. Six stages of interaction; (a) Flying-contact stage, (b) Flying-diving
stage, (c) Diving-contact stage, (d) Diving-diving stage, (e) Contact-contact
stage, (f) Contact-diving stage

lubrication analysis. The motion equations of the endeffector
and the object, respectively, are given by:∂2∂ ∂ 2 yb
∂ 2 yb+ 2 [E(x)I(x)(1 + C ) 2 ]
2
∂t
∂x
∂t ∂x



(1)
= Mp [δ (x − l1 ) − δ (x − l2 )] + Fb δ(x − l ),2
∂ yo
mo 2 = Fo .
(2)∂t
Air and liquid mediums can exist between the endeffector
and the object. A liquid medium can exist between thesubstrate and the object. Therefore, Fb and Fo vary withrespect to the configuration of the endeffector, the object, andthe substrate. Note that an air medium can exist between thesubstrate and the object. But we do not deal with the situation
where the object is removed from the substrate, because thesituation corresponds to end in failure of manipulation.
Here, to derive Fb and Fo , the six stages are considered,as shown in Fig.3. Flying-contact stage indicates that theendeffector interacts with the object via air medium while
the object directly contacts with the substrate. Flying-diving
stage indicates that the endeffector interacts with the object
via air medium while the object is immersed in the liquidmedium between the object and the substrate. Diving-contact
stage indicates that the endeffector is immersed in the liquidmedium between the object and the endeffector while theobject directly contacts with the substrate. Diving-diving stage
indicates that the endeffector is immersed in the liquid medium
between the object and the endeffector while the object isimmersed in the liquid medium between the object and thesubstrate. Contact-contact stage indicates that the endeffector
directly contacts with the object while the object directly
contacts with the substrate. Contact-diving stage indicates thatthe endeffector directly contacts with the object while theobject is immersed in the liquid medium between the object
and the substrate. In the following, we derive Fb and Fo at
every stage.
ρ(x)A(x)where Qp (D, α) is a Poiseuille flow rate coefficient, Qcon (D)is the coefficient for continuous flow, D is an inverse Knudsen
number, and α is a reflection coefficient. D is expressed by√
D = D0 P H, D0 = pa h0 /(µ 2RT )
(7)

z
φ

meniscusr0hhc

Fig. 4.

rwhere R denotes the gas constant and T denotes the temperature. It is hard to calculate Q̄p . But, a data base of Q̄p isdeveloped for easy calculation [13]. The boundary conditions
with respect to P are as follows; a) P (1, T ) = 1: The pressure(0,T )= 0: The slope
at the periphery is pa at all times. b) ∂P∂R
of the pressure profile at the center is zero at all times.
Solving (5) for P , the force exerted on the endeffector tip
surface at time T is expressed by: 1eFair = 2πpa r02
R(P (R, T ) − 1) dR.
(8)

Air lubrication
z

r0

α

θc
r2
r1

d

r
hl

θc
plane

Fig. 5.

hlc

0Next, we consider the interaction force between the object
and the substrate. Here, We assume that the contact is Hertz’s
contact and structural damping exists. Also, the meniscus(capillary) force is assumed to act.
First, we consider meniscus (capillary) force. In Fig.5, thefollowing relations are obtained:

liquid lubricationM

adhesion/attracting force

Fig. 6.

hlosc = ys − yo − r0 ,2r1 cos(α + θc ) = r0 (1 − cos α) + hlosc ,r2 = r0 cos α + r1 (sin(α + θc ) − 1).

Contact Model(a) Flying-contact stage
First, we consider the interaction force between the endeffector and the object, resulted from the air lubrication.
The length of the endeffector in the longitudinal direction
is very large compared with the size of the object. Therefore,
the surface of the endeffector around the contact/interact pointwith the object is assumed to be oscillated in the verticaldirection to the object surface, as shown in Fig.4. As for the(air) flow, We make the following assumption; (a) The flow
is Newtorian, isothermal, and a compressible perfect gas, (b)The inertia effect of the flow is negligible.
We use cylindrical coordinate. The thickness distribution of
the air medium between the endeffector and the object, h, isgiven by (see Fig.4):
h = hc + r 2 /(2(r0 + hlo )).

(3)Note that hlosc < 0. On the other hand, r1 and r2 are relatedwith the following Kelvin equation [15]):(

Vγ cos θc,
RT log(p/p0 )sFmen ∼= π(r22 − r0 |hlosc |)γ/r1 .
r1 ∼
=−

(4)

The air flow is characterized by Knudsen number Kn (Kn =λ/h where λ denotes the molecular mean free path. λ =0.064[µm] at the atmosphere). Here, we use the generalized
Reynolds equation [12]. It can be used even when the Knudsen
number is large. Considering the symmetry of the system, theReynolds equation, governing the system, is given by:∂P∂(P H)
1 ∂{P H 3 RQ̄p
}=σ
.
R ∂R
∂R
∂T

(5)

where
Q̄p = Qp (D, α)/Qcon (D),Qcon (D) = D/6

1Vγ cos θc1+ )−1 = −r1
r2
RT log(p/p0 )

(6)

(12)

where V denotes mole volume of the liquid (water) and p/p0
denotes relative vapor pressure (humidity). In this stage, theobject directly contacts with the substrate. The radius of thecontact area is given by r0 |hlosc |. Meniscus (capillary) force
is assumed to act at only the area where the object contacts
with the substrate via the liquid (water). Then, the meniscus(capillary) force is expressed by:
s
1
1
(13)
Fmen = π(r22 − r0 |hlosc |)γ( − ).
r1
r2
In this stage, r1  r2 . Therefore, (12) and (13) become:Using hle , hlo , yb , yo , and r0 , hc is given by:
hc = yo − yb − r0 − hle − hlo .

(9)
(10)
(11)

(14)
(15)

On the other hand, the Hertz force and damping force areexpressed by (see Fig.6);
s



1/2

FHe = −4/3Eos r0 (yo + r0 − ys )3/2 ,(16)

Fdam = −Cm ẏo ,

(17)

s



1/Eos = (1 − νo2 )/Eo + (1 − νs2 )/Es ,Cm = Cos |ẏoimp |,(18)

where Cos is a constant, and ẏoimp denotes ẏo at the instantwhen the collision occurs between the object and the substrate.

It is well known that the coefficient of restitution decreases
with the increase of the velocity immediately before thecollision. Therefore, we use (18). Note that these forces are
represented as the forces applied to the object.
ee
On the endeffector, Fair is exerted. On the object, Fair ,sss
Fmen , FHe , and Fdam are exerted. Hence, from (8), (15),(16), and (17), Fb and Fo are given by:e

Fb = −Fair ,
s

(19)
s

s

e

Fo = FHe + Fdam + Fmen + Fair .

(20)(b) Flying-diving stage
We consider the interaction force between the object andsubstrate, resulted from liquid lubrication. We consider themodel as shown in Fig.5. Liquid lubrication is governed by
the following Reynolds equation;
h3los

∂hlos
1 ∂
∂pl
{
}=
.
r
r ∂r 12µl ∂r∂te

Fb = −Fair ,

(21)

(22)
(23)

(28)

s

e

Fo = −Fliq + Fair .

hleoc = yo − ro − yb .
Using hleoc , meniscus force is given by:
6πµr02 ḣleocer22

hleoc(hleoc + 2r0

r 4 r 2 hl
1
1
( 22 + 2 eoc )−πr22 γ( − ).
4r
r
r
r
2
0
1
2
0
)
(30)

e

s

s

e

Fb = −Fliq

(31)

s

s

s

e

Fo = FHe + Fdam + Fmen + Fliq .

(32)(d) Diving-diving stagee
On the endeffector, Fliq (30) is exerted. On the object,esFliq (30) and Fliq (27) are exerted. Therefore, Fb and Fo are
given by:eFb = −Fliq ,

(33)

s

hlos has the following relation with r:
hlos = hlosc +

r2
.
2r0

(24)

It is assumed that both the object and the substrates are
sufficiently rigid so that the deformations of both the object
and the substrates due to the interaction force are negligible.
Then, the following relation is obtained:ḣlos = ḣlosc .

(25)

From (21), (24), (25), and the boundary conditions, thefollowing relation can be obtained:
3µr0 ḣlosc
2r(hlosc + 2r
)20+

3µr0 ḣlosc(hlosc11− γ( − ). (26)
r22 2
r1
r2
+
)
2r0

Then, the force resulted from liquid lubrication is given by:
 r2
spl r drFliq = 2π0

6πµr02 ḣlosc

r22

hlosc (hlosc + 2r0e

Fo = −Fliq + Fliq .

d = r0 (1 − cos α).

=−sOn the object, Fliq (30), Fmen (13), FHe (16), and Fdam (17)are exerted. Therefore, Fb and Fo are given by:where

pl = −(29)(c) Diving-contact stage
First, Fb is derived by the similar way as the derivation ofs
Fliq in (27). The thickness of meniscus bridge at the centerof the object, hleoc , is given by:

Fliq = −hlosc is given by (10). The boundary conditions are given by:a) ∂pl (r = 0)/∂r = 0: The slope of the pressure profile at thecenter is zero at all times. b) pl (r = r2 ) = −γ( r11 − r12 ): The
pressure at the boundary of the menuscus bridge is Laplacepressure [14], [15]. r1 and r2 are given by (10), (11), and (12).
When r1  r2 , r1 and r2 are given by (10), (11), and (14).
When α ∼= 0, r1 and r2 are given by (12) andd + hlosc,
r1 =2 cos θc
r2 = 2r0 d,Here, the first term represents the damping force by a squeeze
effect, and the second term represents the meniscus force.
From (8) and (27), Fb and Fo are given by:

r22 hlosc
r24
1
1+) − πr22 γ( − ).
2
r0
r1
r2
)2 4r0
(

(27)

(34)

(e) Contact-contact stage
First, the interaction force between the endeffector and theobject is derived by the similar way as the derivation of Fmen ,FHe , and Fdam in (13), (16), and (17). Fb is given by:eee

Fb = FHe + Fdam + Fmen ,e11
Fmen = π(r22 − r0 |hleoc |)γ( − ).
r1
r2
e

FHe = −4/3Eeo ro1/2 (yb − yo + r0 )3/2 ,(37)

Fdam = −Cm (ẏb − ẏo ),

(38)

e

e

(35)
(36)



1/Eeo = (1 − νe2 )/Ee + (1 − νo2 )/Eo ,e

Cm = Ceo |ẏbimp − ẏoimp |,(39)

where Ceo is a constant, and ẏbimp − ẏoimp denotes ẏb − ẏo at
the instant when the collision occurs between the object andthe endeffector.
sssNext, on the object, Fmen (13), FHe (16), Fdam (17),eeeFmen (36), FHe (37), and Fdam (38) are exerted. Therefore, Fo
is given by:
s

s

s

e

e

e

Fo = FHe + Fdam + Fmen − FHe − Fdam − Fmen .
(f) Contact-diving stage(40)

Select the stage

Endeffector

Calculate the interaction
forceszx
Substrate

Laser displacement meter

Calculate the equationsof motiont =t +∆t
Fig. 7.

(a) Photo of the experimental set up

Flow cart for numerical solution procedure
Endeffector

e

e

e

On the endeffector, Fmen (36), FHe (37), and Fdam (38) areseeexerted. On the object, Fliq (27), Fmen (36), FHe (37), ande
Fdam (38) are exerted. Therefore, Fb and Fo are given by:eee

Fb = FHe + Fdam + Fmen .
see

Lazer displacement meter

y

(41)
e

Fo = −Fliq − FHe − Fdam − Fmen .

Objectx

Substrate(42)(b) The overview of the experimental set up

Based on this analysis, we consider to simulate the dynamical motion of the endeffector and the object. Fig.7 shows
the flow chart for the numerical solution procedure. First,
according to hleoc , hlosc , and r2 , we deicide which stage
the system is belonging to, at t (note that r2 is used when
judging whether the endeffector/object is at flying or diving
stage. when r2 becomes zero, the endeffector/object is judged
to come into flying stage). Next, we calculate Fb and Fo .
Third, substituting the calculated Fb and Fo into (1) and (2),we calculate the dynamical motion of the endeffector and theobject. Forth, we go next time step (t = t + ∆t). Iterating
the above steps, we can calculate the dynamical motion of theendeffector and the object.
IV. R ESULTS FOR SIMULATION AND EXPERIMENT
To show the validity of our approach, we show somesimulation results and some experimental results.
First, the simulation setting is described.
• The parameter values for the simulation are listed in theabove nomenclatures.
• Practically, pizocell is driven by voltage. The relationshipbetween the bending moment produced from pizocell, Mp ,and the input voltage to the pizocell, Vin , is given by:
Mp = kmv Vin .

(43)where kmv is a constant value derived based on the theory ofelasticity [11]. We set Vin as follows:
Vin = Vamp sin(ωt).

(44)

where Vamp is the amplitude of the input voltage. ω is
set to 22607[rad/sec], which corresponds to the forth mode
frequency of the endeffector. The value of ω is theoreticallyFig. 8.

Experimental set up for investigating the endeffector motion

calculated. The initial value of yb is set to 0[m], and the initialvalue of yo is set to ys − r0 . We simulated in the case where
Vamp is 5, 10, and 20[V].
• Eq. (1) can be solved by introducing the discrete variable
method and applying Duhamel integral [11].
• In the calculation of P produced from (5), we employed thefinite difference method based on the divergence formulation
method, direct simulation of the flow conservation, and the
Newton-Raphson linearization method. The nodal points forthe calculation are set to 50, equally spaced along the rcoordinate.
• The Poiseuille flow rate coefficient, Qp (D, α), are calculated, using the database produced by Fukui and Kaneko [13].
• We simulated the following case: First, we oscillate theendeffector freely. Then, at t = 0.0121, we approach theendeffector to the object on the substrate.
• The sampling time is set to 0.5[µsec]. Considering hysteresis, Ceo in (39) is set to 1 for ẏbimp − ẏoimp > 0 and 10
for ẏbimp − ẏoimp < 0. Similarly, Cos in (18) is set to 1 forẏoimp > 0 and 10 for ẏoimp < 0.
Fig.8 shows the experimental set up. This system consists of the manipulation system, the image-capturing system,
the finger-oscillating system, and the displacement measuringsystem. The manipulation system consists of the endeffector(pushing finger), the substrate, and the object. The endeffector
is a copper cut in size of 40×3×0.3mm. On the endeffector, the piezocell (FUJI CERAMICS C6) of 4×3×0.3mm
is bonded as an actuator for oscillating it. The endeffector
is attached on the XYZ stage (PMZG413 SURUGASEIKI)

0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0

0.005

0.01
Time[sec]

0.015

1

25

0.8

Motion of the object[nm]Motion of the endeffector[µm]Motion of the endeffector[µm]

0.4

0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8

0.02

−1
0

0.005

0.01
Time[sec]

0.015

0.02

20

15

10

5

0

−5
0

0.005

0.01

0.015

0.02

0.015

0.02

Time[sec](a) Vamp = 5 V

0
−1
−2
−3
−4
−5
0

0.005

0.01
Time[sec]

0.015

0.02

(a) Vamp = 5 V

4
80

3

Motion of the object[nm]1

Motion of the endeffector[µm]Motion of the endeffector[µm](a) Vamp = 5 V

2
1
0
−1
−2
−3
−4
0

0.005

0.01
Time[sec]

0.015

0.02

70
60
50
40
30
20
10
0
−10
0

0.005

0.01

Time[sec](b) Vamp = 10 V

0
−2
−4
−6
−8
−10
−12
−14
0

0.005

0.01
Time[sec]

0.015

0.02

(b) Vamp = 10 V

10
160

8

Motion of the object[nm]2

Motion of the endeffector[µm]Motion of the endeffector[µm](b) Vamp = 10 V

6
4
2
0
−2
−4
−6
−8
−10
0

0.005

0.01
Time[sec]

0.015

140
120
100
80
60
40
20
0

0.02
−20
0

0.005

0.01

0.015

0.02

Time[sec](c) Vamp = 20 V
Fig. 9.
results)

The endeffector motion (simulation(c) Vamp = 20 V
Fig. 10. The endeffector motion (experimental
results)

which can be controlled by PC. The substrate is also a
copper cut. The endeffector and the substrate are grounded
for preventing an extra charge. The object is a glass sphere(UNION, unibeads) with a radius of 97[µm]. The imagecapturing system is for recording the movie of the motionof the endeffector and the object. The motion is captured by
the CCD camera (IAI, CV-S3200) through the microscope(MORITEX, ML-Z07545). The captured data is send to PC
through the capture board (V-STREAM, VS-TV2800R). The
oscillation of the endeffector is generated by oscillating thepiezocell by the function generator (YOKOGAWA, FG120)
through the power amplifier (NF, 4010). The displacement of
the endeffector is measured by the laser displacement meter(SONY, VL10). Note that the laser displacement meter canmeasure only a relative displacement. The frequency is set to3.136 [kHz] which corresponds to 3rd mode frequency of theendeffector. The input signal is a sine curve. We measured in(c) Vamp = 20 V
Fig. 11. The object motion (simulation results)

the case where the amplitude of the input voltage is 5, 10, and20 [V].
Fig.9 and Fig.11 respectively show the calculated motionsof the endeffector and the objects in the simulation.
Fig.10 shows the measured displacement of the endeffector.
At every case, the endeffector contacts with the object. Notethat when the endeffector freely vibrates, the amplitude isabout 0.2[µm] at 5[V] of Vamp , about 0.4[µm] at 10[V] of
Vamp , and about 0.8[µm] at 20[V] of Vamp .
Comparing with Fig.9 and Fig.10, we can see that thecalculated wave form resembles the measured wave form.
The amplitude of the calculated wave form is almost sameas the amplitude of the measured wave form. The period of
the calculated wave form is also almost same as the period of
the measured wave form. Then, we can show the validity ofour theoretical model and the simulation.
From Fig.9 and Fig.10, we can see that; (1) Comparing withthe case where the endeffector freely vibrates, the amplitude
becomes very large in the case where the endeffector interacts
with the object. (2) In the case where the endeffector interacts
with the object, the oscillation is disturbed by the collision,and the lower order mode oscillation is excited. Therefore, theaverage period changes. (3) The amplitude of the oscillation
increases with the increase of the input voltage. It is because
the velocity magnitude at the collision increases with theincrease of the input voltage.
From Fig.11, we can see that the object is not removed
from the substrate when the oscillating endeffector approaches
to the object on the substrate. Namely, the oscillation of theendeffector can reduce the adhesion effect between the endeffector and the object, attracting the object to the substrate.
One of the reason why the object is not removed is considered
to be for the damping force resulted from the liquid lubricant(refer to (27) ). When the object tries to be removed from thesubstrate, not only the meniscus force but also the damping
force attract the object to the substrate. We can also see that theobject is compressed on the substrate. Especially, the object isdeeply compressed around when the collision occurs between
the endeffector and the object. Note that in the experiment, we
can not measure the object motion because of the configurationof the endeffector, the object, and the substrate (and the laser
displacement meter). Using the simulation, we can estimate
the object motion.
V. C ONCLUSION
In this paper, we have analyzed the mechanism of thephenomenon between an endeffector, a micro object, and asubstrate, when the oscillating endeffector approaches to themicro object on the substrate. In a micro range, the attracting
forces such as the van der Waals, capillary, and electrostaticforces dominate. Therefore, the adhesion occurs between theendeffector and the object during the micro manipulation.
Then, it is hard to complete the micro manipulation. Recently,
we proposed the method to reduce the adhesion effect [10].
When bringing an oscillating endeffecter close to a micro
object on a substrate, the attracting force between the object
and the endeffector is reduced, attracting the object to thesubstrate. Then, it becomes easy to remove the endeffector
from the object. However, the mechanism was unclear. In thispaper, we have derived a theoretical model of the phenomenon,and simulate the dynamical motion of the endeffector and theobject. Comparing the simulation results and the experimental
results, we show the validity of our approach. From thesimulation results and the experimental results, we show thatthe oscillation of the endeffector can reduce the adhesion effectbetween the endeffector and the object, attracting the object
to the substrate.
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