DESIGN OF INCORPORATED MACRO-MICRO ROBOTS

FOR MACRO AND MICRO OPERATIONS

Vladimir Kotev, Kostadin Kostadinov and Penka Genova

Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 4, Sofia, Bulgaria

Keywords: Synthesis of incorporated macro-micro robots with closed kinematic chains, Kinematic geometry.

Abstract: Robots with cooperated regional macro-structures and local micro-structures are implemented in cell

injection systems, production and control of micro-chips as well as other micro and nano technological

operations. A structure for hybrid macro-micro robot with closed kinematic chains with piezo-actuator links

is proposed. An approach for the synthesis of linkage manipulating mechanisms with two DoF is developed

applying the method of Infinitesimally Close Positions. This approach allows for the synthesis of

mechanisms that perform rectilinear trajectory within a specified section. The rectilinear trajectory may be

obtained by controlling the actuators, but in the presence of accelerations which would decrease the

precision of the trajectory.

1 INTRODUCTION

Nowadays, it is hard to enumerate the companies

and types of produced robots. The kinematic chains

(KC) of most universal robots are opened. There are

robots with closed KC or with hybrid open–closed

KC. Generally, robots with closed or hybrid KC are

used in microbiology, clinical laboratories and

surgery (Kobayashi, 1999). On the other hand,

design and development of actuators resulted in the

design of a new generation of manipulators and

robots for extremely precise micro-manipulations.

Robots with cooperated regional macro-structures

and local micro-structures are implemented in cell

injecting, production and control of micro-chips as

well as other micro and nano technological

operations.

The main advantages of the mechanical system

with close kinematic chains are: light constructions

of the mobile links because the motors are taken out

of the frame; minimization of dynamic and inertia

effects; dynamic control is not necessary; improved

positioning precision, which is typical for the

geometry of closed KC; and comparatively smaller

deformation deviations. The main disadvantages are:

the number of kinematic joints (bearing assemblies)

increases; spatial mechanisms with closed kinematic

chains require the use of specialized kinematic joints

of a lower class as compared to the traditional

rotation and translation bearings; in most cases the

inverse kinematic problem is more difficult to solve.

There are known micro–nano robots, wherein the

conventional driving systems or motors are changed

with piezo-actuator modules or elastic-polymer

actuators (Bacher, 2003; Codourey, 2005; Goldfarb,

2002). The various types of actuators allow for

displacement varying from several nanometers to

several mm. The ceramic actuators have wide

application.

This study proposes a five-link mechanism with

closed kinematic chain where actuators or piezo-

ceramic links are incorporated in the links. The

mechanism is linked by a translation module or

kinematic joint along an axis parallel to Оz (Fig.1).

The suggested five-link mechanism is designed for

robots performing extremely precise linear and other

micro displacements. Linear micro displacement is

mainly required in cell injection systems, micro chip

inspection and other micro and nano technological

operations. The most crucial requirement for these

robots is high precision.

Also, an approach for the synthesis of five-link

macro-micro mechanisms with two degrees of

freedom with infinitesimally close positions (ICP)

has been developed. With slight changes the said

approach can be implemented for the synthesis of

mechanisms with open kinematic chains.

273

Kotev V., Kostadinov K. and Genova P..

DESIGN OF INCORPORATED MACRO-MICRO ROBOTS FOR MACRO AND MICRO OPERATIONS.

DOI: 10.5220/0003373402730276

In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2011), pages 273-276

ISBN: 978-989-8425-75-1

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

2 SYNTHESIS OF MECHANISMS

FOR MACRO - MICRO

MECHATRONICS SYSTEMS

APPLYING THE METHODS OF

KINEMATIC GEOMETRY

A mechatronic system (MS) for micro and nano

technological operations based on a five-link

mechanism structure with closed kinematic chain is

synthesized (Fig.1).

Figure 1: A model of hybrid macro-micro manipulation

system for microchip control.

The links 2 and 5 are set to motion by universal

motors, mounted on the fixed link 1 and perform

macro motion. Actuators or micro-motors are

incorporated in the linkage of this KC, whereby their

lengths can be changed within a specified range. A

serious problem in this solution is to maintain high

precision in micro operation. We suggest a

resolution by redundancy of MS for micro motions.

We study the working zone of the five-link macro-

micro MS at different positions and with switched

on actuators. Different trajectories of the end-

effector are obtained depending on the operating

actuators and motors. The transmition ratio (TRs) of

the MS actuators is determined analytically, as well

as strategies of control of hybrid MS are developed.

Also, the direct and inverse problems of kinematics

for such macro–micro MS are solved (Tiankov,

2009, Genova, 2010, Kotev, 2010).

2.1 Methods of Finding the Kinematic

Invariants

Micro operations are performed with small range

motions. In this respect the synthesis of

manipulation mechanisms (ММ) by means of the

methods of infinitesimally close positions (ICP) is

particularly appropriate. With the mechanisms with

two DoF two principally different problems can be

formulated of the synthesis with ICP: a direct

problem and an inverse problem, the direct problem

being for a given mechanism configuration and a

given transfer ratio of the velocities at the two inputs

in order to find the point of Boll. Those Boll points

are used which are known to have rectilinear

trajectories for a limited motion interval, and which

do not require any special control to be

implemented.

Formulation of the Problem

The purpose is to elaborate an approach for the

synthesis of MM with two DoF with open or closed

kinematic chains for precise rectilinear finishing

operations. To solve the direct problem of synthesis,

all kinematic invariants (KI) should be found, which

are necessary for the synthesis of the output link

(OL), as well as a characteristic point, which in a

certain position will coincide with the point of Boll.

The necessary KI are: the instantaneous centers of

rotation (ICR), axes of co-linearization (AC), polar

tangent and normal, inflection circle (IC), constants

of the circle-point curve (CPC) and centring point

curve (CenPC), polar coordinates of Boll points. As

a final result the rectilinear section of OL trajectory

must be defined. For the inverse problem KI are also

necessary, but the sequence of solution is different.

By using said synthesized MS, not only the

position accuracy is improved, but also the

complexity of algorithms for control is greatly

reduced, since the trajectory is achieved only by the

motion of the mechanical system.

2.2 Methods of Finding the Kinematic

Invariants

The five-link closed kinematic chain with two DoF

appears to be a more general case compared to the

open one with two DoF, since it may be viewed as

composed of two open KCs (ОАВ and DСВ –

Fig.2). The base point is a kinematic joint В.

ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

274

Figure 2: Five-link closed kinematic chain – ICR.

2.2.1 The Instantaneous Centers of

Rotation – ICR

ICR of all links of a given KC are found using the

Aranhold-Kennedy theorem. For KC with two DoF

the theorem may be applied only if at least one of

the five ICR which have to be found is defined.

Thus, for example, with the direct problem of

kinematics (DPK) the transmission ration is

specified, i.e. ICR-25, and with the inverse problem

of kinematics (IPK) the trajectory of point В is

determined (Fig.2). On the normal to the trajectory

of the end-effector lie two of the searched centres of

rotation (ICR-13 and ICR-14). As these points also

lie on the straight lines ОА (12-23) and СD (45-15),

they are the points of intersection of said lines with

the normal. Fig.2 shows all ten ICR for the five-link

KC. Kinematic invariants of the rocker links 3 and 4,

respectively, are found by means of the general

theorems of kinematic geometry or modifications

thereof.

2.2.2 Axis of Co-linearization

The line AC is the straight line which connects the

points of intersection of the normals to the

trajectories of two points of a body moving in a

plane and it is also the line which connects the two

points and their centers of curvature (CC). On Fig.2

it is seen that two points, namely А and В are given

on link 3 moving in a plane and only one point of

CC, i.e. centre О of point А. The centre ОВ of point

В must be found. It is known that the radius of

curvature, and coordinates of CC, respectively,

depend on the second derivatives of the coordinates

of point В. According to the definition, co-

linearization is the straight line passing through ICR

Н≡13 and Р (Fig.3), which is marked with „к-к” and

an axis line is drawn.

2.2.3 Polar Tangent and Normal

In accordance with the theorem of Bobilier, the

angle γ measured from AC to one of the normals

crossing in Н is equal to the angle µ measured in the

opposite direction from the tangent to the other

normal. Hence, the polar tangent t is found and the

normal n, respectively.

2.2.4 Inflection Circle

The Euler-Savary equation can be applied. The point

Т is on IC. In this case RC of the trajectory of point

А is АО = 12. The point of Boll is the point of

intersection of IC and CPC. To find this point it is

necessary to find the constants of the polar equations

of CPC and CenPC. According to the theory of KG,

the problem is reduced to finding the Boll point of

IV or V series. When the Boll point is of the IV

series, it is a point of intersection of the circle of

inflexions and the circle point curve (Chung 1989,

Genova 1995, 2009, 2010).

Figure 3: Kinematic invariants and point of Boll.

2.3 The Inverse Problem of the

Synthesis is Formulated Applying

the KG Methods of ICP

The inverse problem of KG, as we formulated it,

consists of either defining the characteristic point,

for example that of Boll, or some of the main

dimensions to synthesize the configuration, or both,

depending on which will satisfy the given problem.

The synthesis is solved with a given point of

Boll. In the selected coordinate system, the directrix

of the tangent of the trajectory of Boll point is also

given (actually, in the synthesis of ICP, this directrix

coincides with the trajectory itself up to the third

series), and the conditional position of the initial link

is given. These input data are enough to determine

DESIGN OF INCORPORATED MACRO-MICRO ROBOTS FOR MACRO AND MICRO OPERATIONS

275

the kinematic invariants, including the CPC and

CenPC for the relatively movable link, for which we

already know the kinematic joint connecting it to the

input link as well as the Boll point. If we synthesize

a five-link mechanism, then the choice of the closed

kinematic pair can be subjected to the convenient

ratio of the two input velocities for the realization of

the transfer function of the third series.

Theoretically, the solutions are numerous, i.e.

numerous four-link CKC can be synthesized

(Genova 2010). Also, some special cases are studied

where the first transfer function is a constant, i.e. its

derivatives are zero, as well as solutions are

examined for a rectilinear section of maximum

length around the Boll point.

Further problems of the synthesis of hybrid

macro-micro mechatronic systems (MS):

- Synthesis of MS with three DoF and given

orientation of the trajectory of output link.

- Synthesis of MS with given points of

Burmester.

- Synthesis of MS combined with micro motions

by means of the methods of kinematic geometry of

infinitesimally close positions.

3 CONCLUSIONS

A design approach for the synthesis of five-link

mechanisms with two DoF with infinitesimally close

positions has been developed. With slight changes

this approach can also be implemented for the

synthesis of mechanisms with open kinematic

chains. The obtained results clearly demonstrate that

with the methods of kinematic geometry rectilinear

micro motions can be achieved with very high

precision and they can be successfully combined

with the motion of macro mechatronic systems

(MS). Such macro-micro MS are useful in the

performance of operations such as precise delivery

of probes in microelectronics and optics, pipetting,

cell injection and other microbiological operations.

Of course, the rectilinear trajectory may be obtained

by controlling the actuators, but inertial forces may

appear which will decrease the precision of the

trajectory.

With the two DoF mechanisms two principally

different problems can be formulated of the

synthesis with ICP: a direct problem and an inverse

problem. The direct problem is solved for a given

mechanism configuration and a given transfer ratio

of the velocities at the two inputs in order to find the

point of Boll. Furthermore, the results of these

examples show that optimal solutions can be sought

depending on the technological operation.

ACKNOWLEDGEMENTS

This work was funded by Bulgarian National

Science Fund through the project SpeSi-MINT Nr.

DO 0171/2008.

Dr. Kotev also acknowledges the support of the

ESF grant through the project BG051PO001-

3.3.0/40.

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