Development of a Piezo-actuated Robot for Cell Injection

D. Chakarov, K. Kostadinov, A. Shulev and T. Tiankov

Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 4, 1113, Sofia, Bulgaria

Keywords: Parallel Micromanipulator, Piezo-actuator, Elastic Joint, Preliminary Tension, Cell Injection, Simulations,

Experimental Investigation.

Abstract: In the presented work model and experiments of compliant robots with piezo actuators are carried out. The

robot is designed to perform automatic injection of cells in the range of 10-30 μm. A kinematics model of

serial-parallel structures is presented. Pseudo rigid body approach is used, where the elastic joints are

modelled as revolute joints. Models for tension of parallel structures with elastic joints are developed in

order to eliminate backlashes, to diminish hysteresis, and to improve the performance of the piezo-actuators.

Two design approaches are proposed. First approach ensures preliminary tensioning by assembly translation

along the axes of the driving joints. Second approach ensures preliminary tensioning by assembly

deflections of the basic serial chain elastic joints. The design of new 3-degrees of freedom (DOF) piezo

actuated micro-manipulators with serial-parallel structure including elastic joints capable of performing cell

injection is presented. Numerical experiments are done for tensioning of the manipulator. An estimation of

the manipulator mechanical parameters for different approaches is carried out. Manipulator simulations

with elastic joints are performed using FEA based function of a CAD system. The real manipulator

prototype is experimentally investigated using digital image correlation technique.

1 INTRODUCTION

Micro- and nano- robots have emerged as an

important technological advancement in the last 15

years. The significance of this advancement is

highlighted in many applications where positioning

of components within micrometer or nanometre

accuracy is required. Micro- and nano- robots are

mostly used in biological and microelectronics

researches, cellular technology, chemistry, electro-

chemical impedance technique and investigation of

thin films, in atomic force microscopes and scanning

tunnelling microscopes.

The body of these micromanipulators is

constituted of a high-precision mechanical structure

which is free from backlash, friction and hysteresis

in order to obtain the required sub-micron accuracy

(Kasper, 2004; Pernette, 1997).

As well known, parallel kinematic mechanisms

possess inherent advantages over conventional serial

manipulators, such as high levels of rigidity, load

capacity, velocity, precision, etc. However,

traditional parallel manipulators suffer from errors

due to backlash, hysteresis, and manufacturing

defects in the joints, as for any mechanical systems

composed of conventional joint. Hence, it is a major

challenge to achieve ultrahigh precision with

conventional joints.

On the other hand, compliant mechanisms, i.e.,

flexure-based mechanisms can be utilized into

parallel mechanisms for high precision applications

(Yong, 2008) because the compliant mechanisms

have many advantages in terms of vacuum

compatibility, absence of backlash and non-linear

friction, simple structure and manufacturing

simplicity. Compliant mechanisms generate their

motions through elastic deformation. These

mechanisms use flexure hinges to replace the joints

in a rigid-link mechanisms, thus avoiding the use of

moving and sliding joints.

Many actuation principles have been applied to

drive the compliant mechanism in a micro and nano-

robots. Piezoelectric actuators, electrostatic, electro-

magnetic and shape memory alloy actuators have

been utilised to provide fine motions of the micro-

and nanorobots. Piezoelectric actuators are used

commonly to provide fine resolution of input

displacements in the sub-nanometre range (Chih-

Liang Chu, 2006), since their resolution is dependent

solely on the quality of applied voltage signal. As

Chakarov D., Kostadinov K., Shulev A. and Tiankov T..

Development of a Piezo-actuated Robot for Cell Injection.

DOI: 10.5220/0003984700210030

In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2012), pages 21-30

ISBN: 978-989-8565-22-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

the presence of unwanted transverse loads may

damage some types of motors such as piezoelectric

actuators, the concept of totally decoupling is

accepted to isolate/protect the actuators. To

eliminate the cross-axes coupling errors between the

axes translations in compliant parallel stages, design

of a totally decoupled parallel micro positioning

stages is proposed (

Li Y., 2011).

The pseudo-rigid-body-model is commonly used

(Zhang, 2002), in order to predict the displacements

of compliant mechanisms with elastic joints. As a

rule, it models an elastic joint as a revolute joint with

a torsion spring attached. The pseudo-rigid-body

method is effective and it simplifies the model of

compliant mechanisms. An analytical model is

created out taking into account compliances of

elastic joints in all axes to estimate the mechanism

stiffness with elastic joints. The analytical model

describes the relationship between input and output

displacements of the mechanism (Pham, 2005).

Different ways exist for the computation of the

stiffness of the elastic joints or of the whole

manipulator. One of them is Finite Element Analysis

(FEA) (Yong, 2008). The FEA method is provided

to be the most accurate and reliable, since the joints

are modelled with their true dimensions and shapes.

Disadvantage of this method is its high

computational expenses.

In recent years, many attempts have been made

to leverage robotic technologies to facilitate the

process of cell injection

(Lu, 2011). Large effort has

been made to integrate robotics technology into

micro-manipulation platform that has substantial

biological relevance (Tang, 2012).

The aim of this work is to create pseudo rigid

body model of closed structures with elastic joints

for micro- and nano- manipulations and to develop

approaches for tension of closed structures with

piezo-actuators. We designed a robot possessing

Figure 1: Kinematics scheme of serial-parallel manipulator

with 3 DOF.

serial-parallel structures capable of automatic cell

injection realization. We performed numeric

experimentation and estimation of the build up

models and approaches as well as experimental

investigation of the prototyped robotic system.

2 PSEUDO-RIGID-BODY MODEL

AND MODEL OF

PRELIMINARY TENSIONING

OF A PARALLEL STRUCTURE

WITH ELASTIC JOINTS

The studied micro-manipulator is a component of a

robot capable of performing automatic cell injection.

The aim of the micro-manipulator is to orientate and

to position the pipette according to the cells, as well

as to perform the necessary motions for cell

injection. The micro manipulator with a serial-

parallel structure is selected as shown in Fig. 1.

Here, pseudo rigid body model is used in order to

describe the compliant micromanipulator (Chakarov,

2009). It models all links as rigid bodies and the

elastic joints as revolute joints. Each 2 DOF elastic

joints are replaced by a 2 DOF universal joint with

torsion stiffness, as shown in Fig. 1.

Base 0, manipulator body 1, actuator А

with

working tool 2 and end- effector M form a serial

chain. The body 1 is linked with the base 0 by means

of 2 DOF universal joints J

. Actuators А

and А

are linked with the base 0 by means of 2 DOF

universal joints J

and J

, thus forming parallel

chains. The actuators are fixed to the body 1 via two

kinematics joints, which are 3 DOF spherical joints

(P3). Actuators А

and А

are modelled as 1 DOF

prismatic joints and the number DOF of the structure

come out to be h=3.

According to this model, generalized parameters

are accepted to be the parameters of the relative

motions in all joints of the structure - elastic and

non-elastic, presented by the vectors:

q = [q

, q

]

(1)

a vector of the generalized coordinates in the joints

of the main serial chain with 3 DOF,

w = [w

, w

]

, (2)

a vector of coordinates in the passive universal joints

, J

of the parallel chains, and

l = [l

, l

]

, (3)

a vector of coordinates in the actuator joints А

,А

and А

ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics

Let the linear coordinates of the end-effector M are

denoted as:

[]

321

X,X,XX =

(4)

The relation between the parameters of the basic

serial chain (1) and the parameters of the end-

effector (4) is known as a direct kinematics problem

for the serial chain

Ψ(q)X =

. This problem on the

level of velocities is presented by the equations:

qJX

(5)

where

[]

qXJ ∂∂=

is the (3 x 3) matrix of Jacoby.

In the parallel structure, each closed loop implies

the appearance of a connection between the

generalized parameters (1), (2), (3). These

connections are expressed by 6 scalar functions for

the structure including 2 parallel loops:

,0)l,w,q(

=Ψ

i=1,…,6. The differentiation of the

above equations, gives the matrix of partial

derivations

qwW ∂∂=

and

qlL ∂∂=

with size (4

x 3) and (3 x 3) and the relations between

generalized velocities:

qWw

(6)

qLl

= (7)

As the number of parameters (3) is equal to the DOF

h=3, these parameters can be selected as

independent ones. In equation (7) we have the

inverse relation:

lLq

−

(8)

Equations (5) and (8) allow determining the end-

effector velocities, while equations (6) and (8) - the

velocities of passive joints, as a function of the

velocities of the linear actuator joints

lJLX

−

and (9)

lWLw

1−

. (10)

The displacements of the piezo-actuators are small

as compared to the link lengths. Therefore, the

micro-manipulator is almost configurationally

invariant and its matrix of partial derivations

J, L

and

W are assumed to be constants (Zhang, 2002).

The equations (8), (9), (10) give the relations

between the small displacements of the micro

actuators δl, the joints of the main serial chain

δq,

the end-effector δX and the passive joints δw:

lLq δ=δ

−1

, (11)

lJLX δ=δ

−1

and (12)

lWLw

δ=δ

−

(13)

A preliminary tensioning of the mechanical

micro-manipulation system is necessary in order to

eliminate the backlash of the kinematics joints and

to improve the performance of the piezo-actuators. It

is possible to use deformation in elastic joints to

achieve tension in closed structures resulting in

restoring forces. The following two approaches can

be used for tensioning of the manipulator:

1) Preliminary tensioning by means of assembly

translation along the axes of the linear driving joints,

which leads to deflection in all the system joints and

to tensioning of the actuators with a force

2) Preliminary tensioning by assembly deflections of

the basic serial chain elastic joints, which leads to

deflection only in these joints and to tensioning of

the actuators with a force

2.1 Model of Preliminary Tensioning

by Assembly Translation

along the Axes of the Driving Joints

The assembly displacement along the axes of the

driving joints denoted by the vector Δl

leads to

deflection in all the system joints, appearance of

resistant forces in the elastic joints and tensioning of

the actuators along their axis by force

. The

assembly displacement leads to elastic deformations

in the driving joints denoted by the vector

Δl

The

assembly displacements

Δl

along the axes of the

drives and the working shifts of the drives

Δl

are

combined in the vector:

lll Δ

. (14)

The resultant displacement along the axes of the

driving joints after tensioning is equal to the sum:

lll Δ

−

. (15)

This displacement is defined according to (11)

by means of deflections in the joins of the main

serial chain

. The deflections of the end-effector

according to (12) and the deflections in the

elastic joints of the parallel chains

wδ

according to

(13) are dependent on the resulting displacement

along the axes of the driving joints also (15).

The elastic deformations in the driving joints

Δl

define the resistant forces in them:

DevelopmentofaPiezo-actuatedRobotforCellInjection

lKF

. (16)

The resulting displacements in the driving joints

(15) with the help of (13) define the resistant forces

in the elastic joins of the parallel chains:

wKF

δ=

, (17)

and with the help of (11) define the resistant forces

in the elastic joints of the main chain:

qKF

δ=

. (18)

, K

and K

above, are the matrixes of the axial

stiffness in the driving joints, in the elastic joints of

the parallel chains and in the elastic joints of the

main chain, respectively.

The elastic forces after system tensioning

establish static equilibrium:

+ W

= L

(19)

which according to (18), (17), (11), (13) and (15) is

defined by the equality:

FL]ll[WLKW]ll[LK =Δ−Δ+Δ−Δ

−−

(20)

After considering the inverse form of (16):

FKl

−

=Δ

(21)

and modification of the above equality, the

displacements along the axes of the actuators are

defined as a function of the actuators forces:

F]KL]WKWK[L[l

11 −−

++=Δ , (22)

where:

BKL]WKWK[L =++

−− 11

(23)

is the adduced system compliance to actuator axes.

The desired tensioning force

defines according to

(22) and (14) the necessary assembly displacement

along the axes of the driving joints

Δl

= Δl, when

the actuators are not

active (Δl

=0). The actuators

driving shifts Δl

after system tensioning with

displacement

Δl

lead to a force variation of the

actuators

with the value of F

defined by (22):

]FF[Bll

lll 2020

Δ+Δ

. (24)

The end-effector varies after manipulator tensioning

according to equalities (12), (15) and (14):

]lll[JLX

120

Δ−Δ+Δ=δ

−

, (25)

where

]FF[Kl

lll 20

+=Δ

−

. (26)

2.2 Model of Preliminary Tensioning

by Assembly Deflections of the

Basic Serial Chain Elastic Joints

The assembly displacement along the axes of the

elastic joints of the basic serial chain denoted by the

vector

Δq

leads to a deflection

in all the system

joints, appearance of resisting forces in the elastic

joints and tensioning of the actuators along their

axes with a force

. The raising elastic deformations

in the driving joints are denoted as in the previous

case with

Δl

, the working shifts of the actuators -

with Δl

and then the resultant displacements along

the axes of the driving joints are equal to the sum:

lll Δ−

. (27)

These displacements lead to additional deformations

in the joints of the base chain according to (11).The

resultant joint displacements of the base chain after

their tensioning by the deformations

Δq

are:

qqq δ+

. (28)

The resistant torques which arise in the elastic joints

of the basic chain are defined by their stiffness

and deformations according to (28), (11) and (27):

]]ll[Lq[KF

qq 12

Δ−Δ+Δ=

−

. (29)

The resistant forces in the elastic joints of the

parallel chains are derived in the same way as in the

previous case according to equality (17) where the

equalities (13) and (27) are also valid. The static

system equilibrium (19) established after taking into

account (29) and (17) is defined by the value:

FL]ll[WLKW

]]ll[Lq[K

=Δ−Δ

+Δ−Δ+Δ

−

(30)

The upper equality allows definition of the pre-

tensioning in the basic joints, after taking into

account the dependence of the deformations in the

driving joints on the value of the driving forces (21):

]FKl[L

]FL]FKl[WLKW[K

llw

−−

−−−

−Δ−

−−Δ−

=Δ

(31)

The desired tensioning force of the actuators F

when they are not active (Δl

=0), defines according

to (31) the necessary assembly displacement along

the axes of the elastic joints of the basic serial chain

Δq

The working actuator shifts Δl

after system

ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics

tensioning lead to force variation of the actuators

which according to (31) is defined by the equality:

]lL]WKWK[qK[

]LKL]WKWK[[F

111

Δ++Δ∗

++=

−

−−−

(32)

The end-effector position varies at manipulator

tensioning and at performing of the work shift

according to the equalities (12), (27):

]ll[JLX

Δ−Δ=δ

−

. (33)

The raising elastic deformations in the driving joints

above are defined according to (21) and (32).

3 DESIGN AND NUMERICAL

EXPERIMENTATION OF THE

MICRO-MANIPULATOR

3.1 Design of a Robot System for Cell

Injection

A robot has been designed to perform automatic cell

injection (Kostadinov, 2009). The robot system

includes a macro-manipulator and a local micro-

manipulator. The macro-manipulator is scheduled to

insert the micro-manipulator with the injection

pipette in hand in the working zone. Here, the

biological cells on the range of 10-30 [μm] are

preliminary positioned in a matrix feeder. The aim

of the micro-manipulator is to orientate and to

position the pipette according to the cells, as well as

to perform the injection motions. The micro-

manipulator is designed as it is shown in the

simulation in Fig. 2. The manipulator body 1 is

linked to the base body 0 by means of an elastic joint

forming a serial chain. Actuators А

and А

are

located perpendicularly to the body 1 and they are

linked to the base 0 by means of elastic joints J

and

, thus forming parallel chains. The actuators are

fixed to the body 1 via spherical joints. Parallel

structure comprising actuators А

and А

performs

orientation motions, while the actuator А

performs

injection through the pipette 2 attached to it.

Piezoelectric stack actuators are chosen, hereafter

called piezo-actuators, for their smooth motion, high

accuracy, and fast response.

The joints J

, J

and J

are recognized as double

notched elastic beam joints. These joints allow by

means of a preliminary deformation to achieve pre-

tension of the piezo-actuators. The joint geometry

shown in Fig. 3 is accomplished with the help of

electro-discharge machining. This geometry allows

the desired low stiffness to be achieved in two

transverse mutually perpendicular directions of

bending and high stiffness in the rest non-motional

direction.

The main dimensions of the studied manipulator

according to Fig.1 are a

=0.066[m],

=0.007[m], b

=0.030[m], b

=0.180[m]. The

travel of the piezo-actuators used is as follow:

actuator A

:60 10

-6

[m]; actuators A

, A

: 30 10

-6

[m].

The actuators possess axial stiffness 27 10

[N/m]

and pushing force capacity 1000 [N]. The torque

limits of the actuators are 0.35 [N/m].

Forces

in the driving joints which tension

axially the actuators А

and А

are defined by the

stiffness of the elastic joints J

and J

, J

and by the

preliminary deflections according to the mentioned

above approaches.

Figure 2: Micro-manipulator: a) general view; b) cross

section. (0-base; 1 – coupling body; 2: glass pipette; A

-A

– piezo actuators; J

, J

– elastic joints).

Figure 3: Joints J

and J

performed as double notched

elastic beam joints.

The joint geometry presented in Fig. 3 allows the

desired angular stiffness to be achieved by means of

the width Δ variation of the most bending loaded

area. An assessment of the realized stiffness is

performed using FEA-based technique, applied to

the entire elastic system.

DevelopmentofaPiezo-actuatedRobotforCellInjection

The selected material of the elastic joint is

stainless steel (X2CrNi18-9) with Young’s modulus

E = 190 [GPa] and Yield strength σ=0.465 [GPa].

Joints J

, J

are selected with Δ

= Δ

= 0.0012 [m]

and joint J

with Δ

= 0.0020 [m] in developing

manipulator.

In result of the assessment, the value of join

angular stiffness is 91.3 [Nm/rad] for joints J

, J

and

340.3 [Nm/rad] for joint J

. The angular stiffness

matrices are defined as:

0][Nm/rad] 340.3; .3;340diagK

; (34)

[Nm/rad] 91.3] 91.3; 91.3; diag[91.3;K

(35)

The linear stiffness matrix of actuators is defined as:

[N/m] 10 0] 27; diag[27;K

(36)

3.2 Numeric Experimentation

The matrix of partial derivations J, L and W, with

size (3x3), (3x3) and (4x3) are assumed to be

constant according the pseudo-rigid-body-model of

serial-parallel structures build up as presented in

chapter 2. A software application based on the

matrix equalities (11), (12), (13) and (19) is

developed to carry out numerical experiments.

Experiments are conducted of the preliminary joint

deflections for manipulator tensioning according to

the presented in chapter 2 approaches.

3.2.1 Mechanical Micro-manipulation

System Preliminary tensed According

to Approach 1

The value of forces in the driving joints is selected

to be 10% from the push force capacity of the

actuators used or 100 [N]. The vector of desired

actuator forces is defined as:

[N]0100100F

];;[ −−=

(37)

Experiments are carried out when tension forces are

presented by vector (37), the stiffness of the elastic

joint J

is presented by matrix (34), the stiffness of

the elastic joints J

, J

by matrix (35) and the

stiffness of piezo-actuators A

, A

- by matrix (36).

Desired assembly deflection

in the driving joints,

which leads to deflection in all the system joints and

to tension of the actuators with a force 100

[N]

according to (22) is:

][];.;.[ m100707256704256l

−

−−=Δ

(38)

Deformations

Δl

in the driving joints as a result

of the piezo-actuators’ compliance, shown by the

matrix (36), is defined by the equality (21):

][];.;.[ m10070337033l

−

−−=Δ

(39)

Equation (15) allows determination of the

effective motion

in the driving joints, shown below:

][];.;.[ m100001253001253l

6T −

−−=δ

(40)

According to (12) and giving an account of (40),

the deflections of the end-effector are:

];.;.[

−

−−=Δ 000615180061518X

-6

[m]. (41)

For the effective motion

in the driving joints (40)

and selected angular stiffness, the torques of the

elastic joints J

and J

, J

according (11), (18) and

(13), (17) possess values:

086928692F ];.;.[−=

[Nm], (42)

0316003160F ];.;;.[ −= [Nm]. (43)

Torques (43) of the elastic joints J

, J

lead to

undesirable bending loading of the linear piezo-

actuators, but they are close to the torque limit of the

actuators 0.35 [N/m].

The tensioning force (37) varies at the working

shifts of the actuators in a manipulator tension state

according to (24). When maximal actuator shifts are

presented by the vector:

][];;[ m1003030l

−

−−=Δ

(44)

Following (38) and (14), the actuator deflections are:

][];.;.[ m100704286704286l

6T −

−−=Δ

. (45)

The already changed tensioning force at maximal

actuator shifts according (24) is defined by the

vector:

][];.;.[ N0686111686111FF

2l0l

−−=+

. (46)

The effective shifts in the driving joints according to

(26) and (15) and the effective shift of the end-

effector according to (25) are:

][];.;.[ m100568282568282l

6T −

−−=δ

(47)

040816954081695X ];.;.[ −−=δ

-6

[m]. (48)

The difference

between displacements (41) and

(48) forms the working range of the micro-

manipulator:

ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics

][];.;.[ m1060402177402177

6T −

=χ . (49)

3.2.2 Mechanical Micro-manipulation

System Preliminary tensed According

to Approach 2

Like the above case, experiments are carried out

when tension forces are presented by vector (37), the

stiffness of the elastic joint J

is presented by matrix

(34), the stiffness of the elastic joints J

, J

by matrix

(35) and the stiffness of piezo-actuators A

, A

matrix (36).

The preliminary displacements in the joints of

the basic chain, for actuator tensioning when they

are at starting position (Δl

=0), are defined by (31):

094489448q ];.;.[−=Δ

-3

[rad]. (50)

In the tensioned actuators elastic deformations arise

according as (21), which following (27) are equal to:

070337033l ];.;.[=δ

-6

[m]; (51)

and according as (12) define the deflections of the

end effector after tensioning of the actuators:

];.;.[

−

=δ 02182221822X

-6

[m]. (52)

The resistance torque in the elastic joint of the basic

chain after the system tensioning defined by (29) is:

000230023F ];.;.[−= [Nm]. (53)

When manipulator in a tensioned state performs the

maximal shifts of the actuator (44), the driving

forces change according to (32) and they are:

][];.;.[ N0686111686111F

−−=

. (54)

Elastic deformations of the actuators according to

(21) and (54) are:

][];.;.[ m10013641364l

−

=Δ

. (55)

The resultant displacement along the axes of the

drives according to (27) is:

];.;.[l 08642586425 −−=δ

-6

[m] (56)

and the end-effector position according (12) is:

T−

−−=δ ]0;184.155;184.155[X

-6

[m]. (57)

The difference

between positions (52) and (57)

forms the working range of the micro-manipulator:

][];.;.[ m1060402177402177

6T −

=χ

(58)

The performed experiments show that after

system tensioning deflections arise from the starting

position of the end-effector and at the first approach

these deflections are considerable (41), while at the

second one they are smaller (52). The end-effector

effective displacements at the same shifts of the

actuators in both approaches are equal (49 and 58).

3.3 FEA Simulations

An additional experiment of the static load by

actuator tensioning was carried out using FEA

modelling as a function of a CAD system.

Simulations were conducted when tension forces are

attached at the end of motor loop A

, J

and A

, J

respectively. Each motor loop is restricted at the end

as linear joints. All the system bodies are simulated

by means of the presented above material -

X2CrNi18-9, and the stack piezo-actuators are

modelled as an elastic joint possessing an axial

stiffness 27 10

[N/m]. The screen with the carried

out simulations is shown in Fig. 4.

Figure 4: Screen with effective displacements in X

direction.

3.3.1 Mechanical Micro-manipulation

System Preliminary tensed According

to Approach 1

The first experiment is carried out when the tension

forces have the values

=-100 [N] and F

=-100

[N]. Effective displacements at the end point of the

end-effector δx and δy

were reported by the CAD

system, respectively

in X and Y direction as it is

shown in Table 1.

The pointed out results are

averaged values from several simulations.

Effective

displacement δz in Z direction are very small (in

submicron range) and they are not object of the

present stuffy. Second experiment is carried out

when the tension forces have the values

DevelopmentofaPiezo-actuatedRobotforCellInjection

111.686 [N] and F

=-111.686 [N].

The difference χ

between end-effector

displacements in the two shown above cases define

the working range of the micromanipulator in X and

Y direction χ

=184.10

-6

[m] and χ

=181.10

-6

[m]. In

the third experiment tension forces have the values

=-100 [N] and F

=-111.686[N]. Comparing the

last result with CAD results obtained one give

difference between end-effector displacements in X

and Y direction χ

=6.10

-6

[m] and χ

=175.10

-6

[m] as

it is shown in Table 1. The derived results show very

close parameter values to those calculated in chapter

3.2.1. We can conclude that because of axis

coupling, each of the actuators A

, A

influences the

displacements of both axes (X and Y). For example,

the displacement of X and Y direction in the second

experiment have a difference in the range of 3 μm

and displacement of Y direction and effective

displacement of X direction in the third experiment,

has a disturbance in a range of 6 μm.

Table 1: Effective displacements at the end-effector (1).

=-100[N

]

=-100 [N

]

=-111.686[N]

=-111.686 [N]

χ [m]

δx

[m]

-1517.10

-6

-1701.10

-6

184.10

-6

δy

[m]

-1518.10

-6

-1699.10

-6

181.10

-6

=-100

=-111

δx

[m]

-1517.10

-6

-1523 10

-6

6.10

-6

δy

[m]

-1518.10

-6

-1693 10

-6

175.10

-6

3.3.2 Mechanical Micro-manipulation

System Preliminary tensed According

to Approach 2

In this case the preliminary tensioning in the elastic

joints of the basic chain is presented with torques

(53) attached to the body 1 of the basic chain near to

the joint J

. Actuator loads are presented with forces

attached at the end of motor loop A

, J

and A

, J

respectively, similar to the experiments carried out

in the previous section, as shown in Fig. 4.

Simulations were conducted at values of the actuator

forces -100[N] or -111.686[N], similar to the

previous experiments. Effective displacements at

the end point of the end-effector δx and δy

in X and

Y direction and difference χ

between displacements

are shown in Table 2. The derived results show very

close parameter values with those calculated in

chapter 3.2.2. In this case, as well as in the previous

one, the simulations consider influence of each

actuator on the displacements along both axes (X

and Y), but this influence is smaller as the

deflections reach 2-3 μm.

Table 2: Effective displacements at the end-effector (2).

=-100

[N]

=-111.686

[N]

χ [m]

δx[m] 23.2 10

-6

-155.1 10

-6

178.3 10

-6

δy[m] 25.0 10

-6

-155.7 10

-6

180.7 10

-6

=-100

=-111

δx[m] 23.2 10

-6

25.4 10

-6

2.2 10

-6

δy[m] 25.0 10

-6

-154.7 10

-6

179.7 10

-6

4 EXPERIMENTAL SET-UP

& RESULTS

Some experiments proving the functionality of the

prototyped micromanipulator (Fig.5.) are performed.

An experimental set-up, consisting of an optical

system and a translational stage with 3 DOF, has

been built up (Fig. 6), to investigate the micro-

manipulator. The translational stage is used for

precise alignment of the micro-manipulator with

respect to the optical system and the image space

calibration. It contains 3 orthogonal translational

modules (M1÷M3) with integrated linear positioning

sensors possessing resolution of 0.1 µm. The micro-

manipulator is fixed to the translational stage

allowing precise positioning of its end-effector in the

image space of the optical system.

This optical system consists of a zoom imaging

lens with magnification of 2.5x - 10x at a constant

working distance of 35 mm. The camera sensor is

CMOS with 2592×1944 pixels and the pixel

dimensions are 2.2×2.2 µm

. The frame rate at full

resolution is 3 frames per second (fps) and at VGA –

30 fps. It defines how many times per second we can

inspect the system. This parameter together with the

computational power and the algorithm effectiveness

define the vision control speed (

Liu, 2006). If we

have efficient numerical algorithms and fast

computer system, the vision control is limited only

by the camera frame rate (Jin, 2005). The used

digital image correlation technique shows that the

minimal displacement resolution obtained

experimentally is 50 nm (Shulev, 2011).

The first approach for manipulator tensioning is

experimented. Each piezo-actuated axis of the

micromanipulator was tested separately, thus

investigating the working space of the manipulator.

The obtained result for axis X actuated by piezo-

actuators A1 is presented in Fig. 7. Results show the

motion range along the axes X and Y, i.e.: χ

= χ

226 μm. The result is determined by the used glass

pipette length. To measure repeatability, the piezo-

ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics

Figure 5: Prototype of micromanipulator with 3 DOF.

Figure 6: Scheme of the experimental set-up.

actuators with open loop control have been set at a

given position 200 times and the end-effector

position was measured. Experiments are conducted

separately for manipulator tensed according

approach 1 and approach 2 and without hysteresis

compensation. The obtained results for both

approaches are shown in Fig. 8 a) and b). The

working shifts of the actuators A1 and A2 are given

equal to 1

μm. It was found that end-effector

maximal positioning error is in a range of (3-5)

μm

for approach 1 and (0-1)

μm for approach 2.

5 CONCLUSIONS

In this paper a model and experiments of compliant

robots with piezo-actuators for micro- and nano-

manipulations are presented. A kinematics model of

serial-parallel structures is presented. Pseudo rigid

body approach is used, where the elastic joints are

modelled as revolute joints.

Methods for tension of serial-parallel structures

with elastic joints are developed in order to

eliminate backlashes, to diminish hysteresis, and to

improve the performance of the piezo-actuators.

Two design approaches are proposed. First

approach ensures preliminary tensioning by

assembly translation along the axes of the driving

joints. Second approach ensures preliminary

tensioning by assembly deflections of the basic

serial chain elastic joints.

The new 3 DOF piezo-actuated micro-

manipulator designed to perform cell injection is

presented. Numerical experiments are done for the

manipulator tensioning.

0 5 10 15 20 25 30

100

150

200

250

A1 [um]

[

]

0 5 10 15 20 25 30

100

150

200

250

A2 [um]

Y [um]

Figure 7: Experimental results of the range of motion for

axes: a) X actuated by actuator A1; b) Y actuated by A2.

0 2 4 6 8 10

[

]

[

]

0 2 4 6 8 10

X [um]

Y [um]

Figure 8: End-effector repeatability measurement:

a) approach 1; b) approach 2.

An estimation of the manipulator mechanical

parameters for different approaches is carried out.

The performed experiments show that after system

tensioning deflections arise from the starting

position of the end-effector. At the first approach,

these deflections are considerable, and at the second

one they are smaller. At both approaches, the end-

effector effective displacements at the same shifts of

the actuators are equal.

Simulations of the manipulator with elastic joints

are carried out using FEA based function of a CAD

system. The simulations performed show that the

motion of one axis interferes with the other axis and

this influence is bigger at the first approach for pre-

tensioning and smaller at the second one.

The proposed approaches for manipulator

tensioning are experimented on the real manipulator

prototype. Experimental investigation of the

prototyped robotic system is realized by a digital

image correlation technique. Obtained results of

experiments testing of the prototyped micro-

manipulator on the range of motion along the axes X

and Y is χ

= χ

= 226 μm. The repeatability of the

end-effector position is obtained for the case with

open loop control system and without compensation

of hysteresis. It was found for this case that maximal

positioning error for the first approach is (3-5)

μm

and for the second one - (0-1)

μm.

Further investigations and experiments are under

DevelopmentofaPiezo-actuatedRobotforCellInjection

consideration for closed loop control of the X and Y

axes including hysteresis compensation method for

piezo-actuators based on the discrete Preisach model

(Marinov, 2009), as well as for injector pipette in Z-

axis in order to realize the successful cell injection.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the support for

this work through the project SpeSy-MiNT funded

by the Bulgarian National Science Foundation under

the Contract Nr. DO 0171/16.12.2008.

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