¹1(22), 2006



Robustness Study of Generic and Non-Generic 3R Positioning Manipulators. S. Caro, Ph. Wenger,  F. Bennis. “Problems of Mechanics”, Tbilisi, 2006, ¹ 1(22), pp. 9-23, (Engl.).

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”, Tbilisi, 2006, ¹ 1(22), pp. 24-40, (Engl.).

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”, Tbilisi, 2006, ¹ 1(22), pp. 41-48, (Engl.).

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 a cone crusher drive. N. Davitashvili. “Problems of Mechanics”, Tbilisi, 2006,
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”, Tbilisi, 2006, ¹ 1(22), pp. 67-72, (Engl.).

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”, Tbilisi, 2006, ¹ 1(22),
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”, Tbilisi, 2006, ¹ 1(22), pp. 78-83, (Engl.).

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”, Tbilisi, 2006, ¹ 1(22), pp. 84-89, (Engl.).

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”, Tbilisi, 2006, ¹ 1(22), pp. 90-94, (Engl.).

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”, Tbilisi, 2006, ¹ 1(22),
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”, Tbilisi, 2006, ¹ 1(22),
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”, Tbilisi, 2006, ¹ 1(22), pp. 109-113, (Engl.).

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”, Tbilisi, 2006, ¹ 1(22), pp. 114-118, (Russ.).

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.


Non-steady flow of a conducting liquid with heat transfer.
V. Tsutskiridze.
“Problems of Mechanics”, Tbilisi, 2006, ¹ 1(22), pp. 119-125, (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 Laplace transformation for the case of a non-steady flow with homogeneous initial and boundary conditions. The energy equation with dissipation terms is simplified by means of Targ’s approximation and is also solved by the operational method. Bibl. 10. Russ.


Definition of the optimum weight of the cylindrical spring. B. Gvasalia, N. Dzhibladze, R. Khurodze. “Problems of Mechanics”, Tbilisi, 2006, ¹ 1(22), pp. 126-131, (Russ.).

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”, Tbilisi, 2006, ¹ 1(22), pp. 132-139, (Russ.).

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.


Non-uniformity of angular rate of rotation the arbor of a transport diesel engine, its cause and consequence. Kh. Mgebrishvili,  A. Muchaidze. “Problems of Mechanics”, Tbilisi, 2006, ¹ 1(22), pp. 140-144, (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 bridge of multiple usage KM-02Ò. E. Medzmariashvili,  N. Tsignadze,  G. Bedukadze. “Problems of Mechanics”, Tbilisi, 2006, ¹ 1(22), pp. 145-150, (Russ.).

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”, Tbilisi, 2006, ¹ 1(22), pp. 151-159, (Russ.).

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”, Tbilisi, 2006, ¹ 1(22), pp. 160-164, (Russ.).

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”, Tbilisi, 2006, ¹ 1(22), pp. 165-170, (Russ.).

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.


Estimation of a technique of definition of the operational charge of fuel on model of movement  of automobiles. I. Chkhetia,  O. Gelashvili.  “Problems of Mechanics”, Tbilisi, 2006, ¹ 1(22), pp. 171-176, (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”, Tbilisi, 2006, ¹ 1(22), pp. 177-181, (Russ.).

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”, Tbilisi, 2006, ¹ 1(22), pp. 182-185, (Russ.).

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”, Tbilisi, 2006, ¹ 1(22), pp. 186-195, (Russ.).

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”, Tbilisi, 2006, ¹ 1(22), pp. 196-199, (Russ.).

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”, Tbilisi, 2006,
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.