**¹1(22), 2006**

**SUMMARIES**

Robustness Study of
Generic and Non-Generic 3R Positioning Manipulators. **S. ****Caro, Ph.
Wenger, F. Bennis. **“Problems of Mechanics”,

This
paper presents a robustness study of 3R manipulators and aims at answering the
following question: are generic manipulators more robust than their non-generic
manipulators? We exploit several properties specific to 3R manipulators such as
singularities, cuspidality, homotopy classes, and path feasibility, in order to
find some correlations between genericity and robustness concepts. It turns out that the farther a
manipulator is from non-generic ones, the more robust it is with respect to
homotopy class and number of cusps. Besides, we state that the proximity of a
manipulator to non-generic frontiers may severely affect its robustness with
respect to path-feasibility. Finally, we notice that the dexterity and
the accuracy of 3R manipulators do not depend on genericity. 27 ill. Bibl. 17.
Engl.; summ. in Russ.

Performance Indices For
Kinematically Redundant Parallel Planar Manipulators. **O.A. Gómez, Ph. Wenger,
A. Pámanes. **“Problems of Mechanics”,

This paper investigates the
problem of defining a consistent kinetostatic performance index for the optimal
kinematic inversion of a class of planar 3-DOF parallel manipulators. The
condition number of the Jacobian matrix is known to be an interesting index.
But since the Jacobian matrix is dimensionally inhomogeneous, a normalizing
length must be used. This paper proposes two distinct kinetostatic indices. The
first one is defined as the reciprocal of the condition number of the Jacobian
matrix normalized with a convenient characteristic length. The second index is
defined by a geometric interpretation of the “distance” to singularity. The two
indices are compared and applied to the kinematic inversion in the presence of
redundancy. 23 ill. Bibl. 23. Engl.; summ. in Russ.

A spinor method of solution of manipulators’
inverse kinematics problem. **A. Milnikov, H. Onal, C. Erguven, I. Rodonaia. **“Problems of Mechanics”,

A new method and algorithm of solution of multijoints
spherical manipulators inverse kinematic problem was created. The method is
based on the principally new approach spinor representation of the spatial
generalized rotations. One of the advantages of the method is that it allows
elaborating formulation of technological tasks for manipulators in terms of
Cartesian coordinates instead of traditional angles’ terms. Besides the method
allows using only one (absolute) coordinate system and it does not require a
set of different (relative) coordinate systems. It provides easy, reliable and
efficient way of solution of inverse kinematics problem of multijoints
spherical manipulators. 2 ill. Bibl. 4. Engl.; summ. in
Russ.

Dynamic analysis of the
spherical four-link mechanism of **N. Davitashvili. **“Problems of Mechanics”,

¹ 1(22), pp. 49-66, (Engl.).

In this paper, the dynamic investigation of the
spherical four-link slider-crank mechanism used as a cone crusher drive is
given. The case is considered with taking into account the elasticity of links.
It is determined: the elastic deformation of a link with distributed masses
without setting differential equations in partial derivatives and the reduced
coefficient of rigidity, which is a nonlinear function of generalized
coordinate and a variable value. The second order differential equations of
motion of an electric engine and spherical four-link mechanism are received.
The results, obtained by dynamic investigation of spherical slider-crank
mechanism, can be used in its synthesis and construction of cone crusher drive.
9 ill. Bibl. 15. Engl.; summ. in Russ.

Kinematic analysis of
spherical linkages with sliding kinematic pairs. **Özgür Kilit. **“Problems of Mechanics”,

In this paper, kinematic equations of spherical linkages with sliding kinematic pairs are derived. In the first instance, two basic types of sliding kinematic pairs are considered and their application to spherical linkages is discussed. Second, kinematic equations for one and two degree-of-freedom spherical serial chains with and without sliding kinematic pairs are derived. Finally, a numerical example is given about forward and reverse kinematic problems of spherical five-bar linkage with one sliding pair. In addition, the three-dimensional graphical representations of different kinds of spherical chains are illustrated. The description of spherical chains with sliding pair provided here has great significance for adaptable robots with adjustable link-length. 4 ill. Bibl. 15. Engl.; summ. in Russ.

A dynamic model with
clearances in hinged connections for Hooke’s joint of a cardan-reduction gear
of an undercar generator. **G. Sharashenidze**. “Problems of Mechanics”,

pp. 73-77, (Engl.).

In this paper, the problem of formulation of a dynamic
model with clearances in hinged connections for Hooke’s joint of a
cardan-reduction gear of a passenger rail car’s undercar generator is
considered. The analytical expressions for generalized spherical coordinates of
position, velocity and acceleration are received. Certain kinds of
complementary motions of Hooke’s joint are determined and analytical** **expressions for passage from one kind
of complementary motion to another are given. The developed dynamic model can
be used in formulation of differential equations of motion of Hooke’s joint and
for investigation of dynamic loads. 2 ill. Bibl. 9. Engl.; summ. in
Russ.

Elastic-plastic
stretching of a plate with a hole of arbitrary outline. **V. Tarkhnishvili, G.
Kipiani, M. Bekirishvili. **“Problems of Mechanics”,

The problem of the elastic-plastic stretching of plates
with openings of arbitrary outline is solved. In particular, it is received an
equation of the line of boundary between elastic and plastic domains. For this
purpose it is used the method of functions of complex variables. Solution of
the problem is reduced to numerical results. 3 ill. Bibl. 7. Engl.;
summ. in Russ.

The effect of the fuel temperature on the variation
in the course of the pressure for the speed below idle run. **K.F. Abramek. **“Problems of Mechanics”,

The paper presents the
results of the examinations of the pressure course at the injector inlet and
injector needle valve lift for rpm values of 60, 150 and 200, at various
temperatures of the diesel oil (253, 273, 293 K) thus at various fuel viscosity
values. 11 ill. Bibl 3. Engl.; summ. in Russ.

The experimental
definition of the position of the centre of gravity of air core having the
heterogeneous density with modeling method. **A. Ugulava, K. Mgaloblishvili, T. Tskipurishvili. **“Problems of Mechanics”,

The method of experimental definition of the position of air baloon centre of gravity having heterogeneous density is presented. The experimental plate is made by theoretical calculations and accounts, that presents itself the reduced model of the plate, received by vertical-diametrical section of the air baloon. The position of its centre of gravity is defined with experimental rule relative to its geometrical centre as well as relative to the surface of the earth. 2 ill. Bibl. 4. Engl.; summ. in Russ.

Reduction to the
one-layer plate with one cut and the method of solution. **N. Chorkhauli. **“Problems of Mechanics”,

pp. 95-101, (Engl.).

The method of solution of a differential equation for critical state and determination of a critical load, based on solution of corresponding static problem, are offered. Since in static problem due to introduction of discontinuous functions we receive series with rather fast convergence in all points of a surface, then the process of consecutive approximation for determination of critical load converges also rather fast. 1 ill. Bibl. 4. Engl.; summ. in Russ.

Kinematics of spatial rotations and Euler’s angles. C**. Erguven,
A. Milnikov, H. Onal, I. Rodonaia. ** “Problems of Mechanics”,

pp. 102-108, (Engl.).

The expressions of Euler angles
obtained earlier on the basis of the developed spinor model of rotations of
three-dimensional space are presented as function of time. This completely
determines the kinematics of rotation process and serves a starting point for
synthesis of optimum control of this process. Results of the offered theory
allow reducing the three-dimensional problem of spatial movement control to be
reduced to the one-dimensional one. 1 ill.
Bibl. 3. Engl.; summ. in Russ.

Generalized uncertainty
principle, gravitation error due to curvatre and extra dimensions. **B. Midodashvili, P. Midodashvili,
L. Midodashvili. ** “Problems of Mechanics”,

In the article we consider derivation of generalized uncertainty principle (GUP) by the method of using gravitational error due to spacetime curvature. We explicitly show that this method can work only in 4- dimensional spacetime. In the case of spacetimes with extra dimensions gravitational error due to curvature is small as compared with the inevitable error of order of the size of clock used in measurement. We also show that correctly derived fluctuations of spacetime satisfy the holographic principle in any spacetime with extra dimensions. In this context the ADD braneworld model is also considered. Bibl. 5. Engl.; summ. in Russ.

On one nonlinear analogue to the characteristic Goursat problem for a
equation of nonlinear oscillation. **R.
Bitsadze. ** “Problems of Mechanics”,

Nonlinear analogue to the charañteristic Goursat problem for a quasilinear equation of nonlinear oscillation is given in the paper. The sufficient conditions for global solvability of the characteristic problem are istablished. The regular solutions with its domains of definition are found. Bibl 1. Russ.

The steady flow of a viscous, incompressible,
electricity conducting fluid between
parallel plane surfaces in the presence of a magnetic field has been
studied by Hartmann. The present paper contains a new solution of this problem
using the

Definition of the
optimum weight of the cylindrical spring. **B. Gvasalia, N. Dzhibladze, R. Khurodze.
**“Problems
of Mechanics”,

The problem of definition of the optimum weight of the cylindrical spring is considered in the work, by selection of diameter of the wires and mean diameter of the spring. The methods of randomization and the centres of gravity are used at definition of the global minimum of criterion functions. The developed computer programs provide the solution of difficult extreme tasks with accuracy acceptable in engineering practice. 1 ill. Bibl. 4. Russ.

Two-dimensional wave
process in a thin cylindrical shell of finite length. **T. Gegelashvili, L.
Verulashvili, G. Kipiani. **“Problems of Mechanics”,

An initial-boundary problem for elastic cylindrical shell under non-axis-symmetrical compressive-twisting impact on a face plane is considered. For considered shells it is proved that the maximal cross deflections are formed in the later stage of the process of non-stationary deformation. 3 ill. Bibl. 3. Russ.

Influencing periodic component of a torque on uniformity of a fast-track mode of a diesel motor is parsed, when the availability of a centrifugal governor can promote originating of continuous forced vibrations and resonance of angular rate of the working arbor. In this case separate the composing harmonicses of vibratory process, receiving strengthening, can break stability of an operational mode. Is rotined, that the resonance oscillations of angular rate can show simultaneously on two composing harmonicses mainly in an idling of a diesel engine small shaft speeds. Bibl. 2. Russ.

Fast eractable inventory transportable **E. Medzmariashvili, N. Tsignadze,
G. Bedukadze.** “Problems of Mechanics”,

The
design of collapsible metal
bridge’s set with falcated modules KM-02T and it’s working drawings were worked up. It’s modular elements for short bridge crossing
were made in manufacture conditions, and factory tested on the proving ground and in field environments.
Bridge’s assembling method for different local
conditions is also developed. 6 ill. Bibl. 3. Russ.

Analytical solution of
the problem on non-stationary deformation of a semi-infinite cylindrical shell.
**T. Gegelashvili,
D. Kipiani. ** “Problems of Mechanics”,

The wave process of propagation of deformation along the axis of a closed semi-infinite cylindrical shell of homogeneous composition and constant thickness is investigated in linear approximation. In image space it is received an exact solution of the initial-boundary problem. By the received expressions it is constructed a solution for the problem of Mellin improper integrals. Numerical calculations are given. Bibl. 5. Russ.

Research of manure
hashihg process in biogas installation and substantiation of mixer parameters. **A.
Agasaryan, V. Mheryan. **“Problems of Mechanics”,

In the work are carried out the account of durability and rigidity of a design of a vertical blade mixer for mixing liquid manure in biogas installation, where before submission of substratum into metantank it is previously prepared in manure receiver. Are determined the thickness and width of the blade and is strengthened its cross section in closing up through edges of rigidity. 2 ill. Bibl. 2. Russ.

Expediency, problem and path of usage of gaseous fuel on motor transport. **G. Tsipuria, T. Apkhazava, O. Gelashvili, T. Natriashvili, N. Dvalishvili. **“Problems of Mechanics”,

In activity the expediency of
application of gaseous fuel on motor transport with fuel - economical and
ecological points of view is justified. The perspective pathes of transferof
diesel engines of gasdiesel process are
rotined. Bibl. 19. Russ.

The estimation of the technique, developed by us, of account of the operational charge of fuel on model of movement of automobiles is carried out and the theoretical analysis of the operational dynamic and fuel characteristics for each phase is given. On the basis of the analysis of results of trial runs of diesel automobiles the estimation of accuracy of forecasting of the linear charge of automobile fuel is given. 1 ill. Bibl. 3. Russ.

On aerodynamic stability of guy bridge pier. **Yu. Melashvili, B.
Maisuradze. **“Problems of Mechanics”,

A new method of calculation of aerodynamic stability of a guy bridge flexible single-support pier is presented at wind load action. A formula is obtained for determination of critical fore of wind when there arises the possibility of a aerodynamic stability loss of a guy bridge pier. The proposed method provides an accurate solution of the problems of the given class. 1 ill. Bibl. 6. Russ.

Dynamics of process of winding of the flexible
string on the packing. **A. Tvalchrelidze, N.
Saginadze, E. Bakuradze. **“Problems of Mechanics”,

The mathematical model of dynamics of process of winding of a flexible string on the packing is described. On the basis of model the problem of dynamic balance of the extreme coil which is reeled up at the string driver reverser has been numerically investigated, some results are resulted. 3 ill. Bibl. 5. Russ.

Method ifs for
fractal of compression of the images. **G. Murjikneli, V. Steperman. **“Problems of Mechanics”,

In given article one more approach to the decision of problems of compression of the digital images, namely - fractal methods of compression of the images is considered. One of the ways of generation of the fractal images is IFS (Iterated Function System) systems - in this case the image is generated with the use of a set of affine transformations resulting in scaling of the initial image. The major of this method is a mathematical basis and as a result the examples, are given attractors of the constructed fractals. 7 ill. Bibl. 5. Russ.

The algorithm for monitoring and control on aircraft movement during
approach. **S.
Khoshtaria, J. Ebanoidze, C. Khoshtaria, T. Maziashvili, K. Balakhadze. **“Problems of Mechanics”,

It is proposed the algorithm for processing and reflection of approach information, providing reflection of aircraft movement and its horizontal and vertical attitude about runway. Hereby it is possible visual monitoring and active control on aircraft movement. 2 ill. Bibl. 4. Russ.

Model of basis knowledge for automatical system differential
teaching. **L****. Khutsishvili.
**“Problems
of Mechanics”,

¹
1(22), pp. 200-205, (Russ.).

Article
relates to the necessity of advancement to differential studies, where important
impact is played by automated teaching lessons. The basis of computer lessons
is to be formed differential groups that differs as in volume as with its
difficulty coefficient article discusses module of knowledge basis with its
proper schemes. 5 ill. Bibl. 2. Russ.