Kinematic Pairs Research Articles

Structural Synthesis of Lower-Class Robot Manipulators with General Constraint One

In this research, the structural synthesis of lower-class robot manipulators with general constraint one is investigated. The number of constraints d = 1 and the mobility number λ = 5 for sphere–sphere and sphere–plane combinations of higher kinematic pairs are investigated by using the analytical approach. Structural synthesis of new first- and second-class robot manipulators is investigated by using transformations of higher kinematic pairs to lower kinematic pairs. Therefore, using this approach, we obtain structural groups with general constraint one. Further, kinematic structures and physical models of overconstrained robot manipulators are presented in the research.

ЗАСТОСУВАННЯ МЕХАНІЗМУ ЧЕТВЕРТОГО КЛАСУ ДЛЯ ПРИВОДУ ВУШКОВИХ ГОЛОК ОСНОВОВ’ЯЗАЛЬНОЇ МАШИНИ

Development and research of functionally-adequate target mechanisms of technological machines of light industry with application of applied CAE-programs. Used the apparatus of vector algebra; analytical and numerical methods for determining the position functions of planar mechanisms containing a structural group of the fourth class of the second order, based on the vector transformation of coordinates; random search method for metric synthesis of flat mechanisms; methods of computer visualization and animation of kinematic schemes of flat mechanisms of higher classes. Mathematical models describing the position functions of the mechanism of eyelets of a warp knitting machine containing a structural group of the fourth class of the second order with rotating kinematic pairs in the form of angles of moving links, free vectors constructed on these links and radius vectors of characteristic points of the mechanism as a function of the angle of rotation of the master crank. The geometrical parameters of the flat six-link mechanism of eyelets for the warp knitting machine containing the structural group of the fourth class of the second order with rotating kinematic pairs as a result of metric synthesis of the mechanism by random search in CAE-program are determined; computer circuit modeling of the obtained mechanism is performed; graphs of visualization and animation of the kinematic scheme of the received mechanism are constructed; identification of the kinematic scheme of the obtained mechanism for compliance with the accepted structure; the received graph of function of position of an auricular needle of the mechanism of the fourth class; the functions of the position of the eye needle of the new mechanism and the mechanism of the basic knitting machine OV-7 are compared. The structure of a flat six-link mechanism, containing structural groups of the fourth class of the second order with rotating kinematic pairs, is proposed for use as a drive in a warp knitting machine on the example of the mechanism of oscillating movement of eyelets. The geometric dimensions of the moving parts of the functionally adequate mechanism of the fourth class for the drive of the eye needles of the basic knitting machine are determined. Software blocks for automated computer metric synthesis and calculation of link angles and radius vectors of characteristic points of the mechanism in the CAE program have been created. Practical Value is to use the results for the design and construction of flat mechanisms of the fourth class with rotating kinematic pairs of warp knitting machines, in which the working bodies make stops during the work process.

ДОСЛІДЖЕННЯ КІНЕМАТИЧНИХ ПАРАМЕТРІВ МАШИНИ ДЛЯ ОБРОБКИ ДЕТАЛЕЙ З ДВОМА ЄМКОСТЯМИ, ЩО ВИКОНУЮТЬ СКЛАДНИЙ ПРОСТОРОВИЙ РУХ

Investigation of the main kinematic parameters of a shredding machine with two moving tanks connected by a translational kinematic pair and performing complex spatial motion to be able to further predict the technological result at the design stage of such equipment and the corresponding technological operations of machining parts. Using the SolidWorks-2016 Motion computer-aided design system, 3D modeling was carried out, followed by kinematic analysis, of a machine for processing parts with two movable capacities, which are interconnected by a translational kinematic pair and perform complex spatial motion. The essence of kinematic analysis was to determine the linear velocities and accelerations of points that coincide with the ends of the working tanks of the machine. Based on 3D modeling and kinematic analysis in the SolsdWorks-2016 Motion computer-aided design system, some kinematic parameters of the machine are determined, in particular, the law of the change in the angular velocity of the driven shaft of the machine is obtained in the form of graphical dependencies, the change in the translational speed and translational acceleration of four points, which are conventionally located in the center, is studied the ends of each of the working capacities. The relationship between some kinematic parameters of the developed machine design with two moving capacities that perform complex spatial motion is established. It was found that the kinematic parameters of the two tanks of the machine differ from each other, as a result of which, during the execution of the corresponding technological operations, the intensity of movement of the working array in the two capacities will differ from each other. In addition, the ends of each of the working capacities move with almost the same kinematic parameters, which will facilitate the movement of the working array between the opposite ends of both tanks in opposite directions with the same intensity. The results obtained make it possible to determine the most rational functional purpose of the machine under study.

KINEMATIC PAIRS: NOVEL KINDS AND SCIENTIFIC CLASSIFICATION

This paper deals with kinematic pairs in the most general sense, and, in particular, with those used in gear design. The paper begins with a brief overview of the earlier performed research in the field. Different kinds of kinematic pairs are distinguished, namely, point-contact kinematic pairs, line-contact kinematic pairs, and surface-to-surface-contact kinematic pairs. Contact geometry of functional surfaces in kinematic pairs is involved into the analysis aiming more in detail analysis of design, and the development of a scientific classification of kinematic pairs. A scientific classification of all possible kinds of kinematic pairs is developed. All known designs of kinematic pairs are covered by the classification. Moreover, kinematic pairs of all notknown yet designs are also covered by the classification. This means that the proposed classification of kinematic pairs possesses predictive properties.

Replacement in a Plane Geared Linkage of High Kinematic Pairs with Lower Pairs

The analysis of constraints in plane mechanisms is an urgent problem in the theory of machines and mechanisms. Although kinematic pairs’ classification has been known for a long time, the issue of the conjugation of links, being at the heart of the analysis and synthesis of mechanisms and machines, is of considerable theoretical and practical interest and continues to attract scientists. One of the tasks that are solved in the process of analysis and synthesis of the structures of mechanisms is the re-placement of higher kinematic pairs by lower ones. As a rule, such a replacement is made to identify kinematic chains of zero mobility, Assur's structural groups, in a mechanism. The replacement may also aim at obtaining the necessary kinematic relations. That is because specific computational difficulties hamper the kinematic analysis of chains with higher kinematic pairs due to the relative sliding and shape irregularity of mating surfaces. Yet, the use of replacements to obtain kinematic and transmission functions is difficult due to nonisomorphism of the equivalent mechanism. Simultaneously, for mixed-type mechanisms, which include geared linkages, the equivalent replacement will allow unifying the kinematic analysis methods. The paper suggests the technology of replacing higher kinematic pairs with links with lower pairs as applied to a plane geared linkage. The technology is based on the properties of the involute of a circumference. The paper proved the structural and kinematic equivalence of such a replacement. The isomorphism of the equivalent linkage will enhance the kinematic analysis, make it possible using kinematic functions, and applying methods based on the instantaneous relative rotations of links, in particular, the Aronhold-Kennedy theorem. Another application of the replacement method presented in the paper will be the expansion of opportunities for identifying idle constraints in the mechanism.

The Specifics of Calculating the Efficiency of the Continuously Variable Mechanical Transmission with Oscillatory Movement of Internal Links and Force Function Control

The paper discusses the energy flow in the continuously variable mechanical transmission with oscillatory movement of internal links and force function control. It is proposed to treat the potential energy of the twisted torsion bars, which is transferred back to the drive shaft, as useful. The formula for calculating the transmission efficiency, taking into account the return of energy flow back to the motor, hysteresis losses, and energy dissipation in the mechanical rectifier while taking up the free play, is given. When calculating the efficiency of the continuously variable mechanical transmission, it is suggested to take into consideration the clearances in the rectifier and kinematic pairs using ‘kinematic efficiency’. The examples of measured and calculated transmission efficiency in the ‘stop’ mode are given.

Technological systems investigation machines tools with parallel structure kinematics

In the article examines the structure of technological systems with a parallel kinematic structure. The path location optimization problem consists of three sets, namely a set of design variables, a set of objective functions, and a set of design constraints. Accordingly, the optimization task is aimed at identifying design variables, such as hexapod, tripod, triglide, and others, that characterize the surface fabrication path in order to minimize or maximize objective functions subject to design constraints. The Hexapod mathematical model includes inverse and direct kinematic problems. The solution of the inverse kinematic problem for hexapods is tied to calculating the length of the racks and the location of the hinges at a given position of the movable platform. The spectral characteristics and qualitative and quantitative indicators of the processed samples were measured. Calculations were also performed on the ratio of initial parameters, cutting modes, and obtaining quality characteristics of Ra and T for each of the 25 samples. Kinematic pairs by class are reviewed and their functional and structural characteristics are determined , which makes it possible to estimate the degree of freedom for mechanisms with parallel structure kinematics. For Structural Simplification and reduction of time and complexity when choosing a PSKM scheme, they are shown in the graphical form of kinematic structures. To assess the quality of the system, as well as its ability to perform the functions assigned to it in the basic state, a table of output data was compiled, as well as a sample from which a data matrix was compiled to cover the entire possible range of output parameters, which significantly affects the result. The graphs show the spectral characteristics of technological systems with PSKV for the sections of the treated surfaces of samples No. 1, No. 2 and No. 3.

Development of the active spatial rolling contact pair to generate the specified trajectory

Linkage mechanisms with 1 DOF composed of only lower pairs cannot generate the specified motion completely because of severe kinematic limitation of lower pairs. In order to relax the kinematic limitation and to generate the specified spatial trajectory completely, the authors have proposed the spatial rolling contact pair (SRCP), where two links in contact at a line roll relatively with generating the specified relative spatial trajectory completely, as a novel kinematic pair used for a spatial-path generator with 1 DOF. However, since it is a passive kinematic pair, it must be used in a closed-loop mechanism. Thus, the spatial-path generator with the SRCP cannot be simplified enough. In this paper, the ”active” spatial rolling contact pair (ASRCP), which is driven by several active elastic elements such as flexible linear actuators, is developed to achieve a simple spatial-path generator. Firstly, a design method to optimally arrange active elastic elements between two links of the SRCP based on a transmission index is proposed. Here, a method to use more than the minimum number of active elastic elements which are required to constitute force-closure state is described to design the ASRCP in order to achieve sufficient motion range. Besides, a control method of the ASRCP to generate the ideal rolling motion is proposed, where actuation forces of active elastic elements to get high stability between the links are calculated with the use of the actuation redundancy. As examples, the ASRCP driven with reeled-wires and the ASRCP driven with fluid-driven artificial muscles are designed and prototyped. Then, they are controlled with the proposed method, and their performances are investigated through motion capture experiments.

Force analysis of the two-satellite planetary mechanism with elliptical gears

Abstract Non-circular gears can be used in modern machines and mechanisms for the implementation of various types of motion and have high strength and compactness compared to linkage mechanisms. This article presents the force analysis of non-circular gear on the example of the planetary mechanism with elliptical gears, providing the rotationally reciprocating motion of the impeller of the stirred tank. Based on the calculation schemes of the links, kinetostatic balance equations for each link of the mechanism are compiled and solved. Reaction forces in kinematic pairs and balancing moment on the input shaft of the mechanism are found. The results can be used in the synthesis and analysis of various machines with the proposed kinematic scheme of the mechanism.

МОДЕЛЮВАННЯ СПРЯЖЕНИХ КРИВОЛІНІЙНИХ ПОВЕРХОНЬ НА БАЗІ КІНЕМАТИЧНОГО ГВИНТА

Modeling of mating curved surfaces for practical use in the design of mechanical engineering products based on a parametric kinematic screw. In mechanical engineering, when modeling conjugate curved surfaces of kinematic pairs, trochoid graphs and electronic modeling installations were used, they had low accuracy and productivity. It is proposed to optimize the process of creating universal graphic tools, where there is, in fact, a graphic representation of the parameters of kinematic conjugate curved surfaces, a change in one of which leads to a change in others, opens up the possibility of obtaining the shapes of parts with predetermined parameters. It should include wishes to expand the capabilities of the propeller diagram [1], taking into account the real picture of the kinematics in the design, which, when the distance between the axes of the propellers changes, would give a real idea of the change in the geometry of the contact surface at each point of the instantaneous movement of the wheels. The kinematic screw has proven itself well for the formation of conjugate ruled surfaces [3], therefore, geometric 3d-modeling of the kinematic parametric screw diagram for the formation of conjugate curved surfaces has become an urgent problem. The technique of 3d-modeling of the kinematic screw diagram is based on the theorems of Professor A.M. Podkorytova [4]. Modeling of mating curved surfaces on the basis of a parametric kinematic screw means that from graphic constructions at any stage of design, you can easily go to the calculation by an analytical method, if you need to check or accurately determine the parameters. It will allow you to visually represent the process of obtaining conjugate curvilinear kinematic pairs, to analyze the influence of each parameter on the profile and its structural dimensions, you can identify errors in the profiling of conjugate curved surfaces where to avoid them, which is what this article is about.

Monad Theory of Structural Synthesis of Mechanisms

Structural synthesis creates a structural scheme according to the given structural characteristics - the degree of abnormality of the structure S and the degree of its irrationality s. Structural scheme is created at the first stage of synthesis, containing only rotational kinematic pairs and corresponds to a given degree of abnormality, which is ensured by the ratio of structural units – plus monads, minus monads and null monads. At the second stage, the independence of structural characteristics makes it possible to bring the obtained scheme to a given degree of irrationality by downgrading the class of kinematic pairs. The proposed algorithm makes it possible to synthesize structural schemes of both normal structure and adaptive (with redundant motions), as well as indifferent (with redundant links). Monadic approach to structure research allows to formalize the structural features of the circuit and to create a knowledge base for automated design of structural circuits with given structural properties.

Six-Legged Walking Robot (Hexabot), Kinematics, Dynamics and Motion Optimization

The movement of a walking six – legged robot hexabot (a "spider" robot) with the possibility of implementing various movements is considered. The equations of kinematics and dynamics of a separate robot leg with three degrees of freedom are written out, and the question of optimizing the robot movement is considered based on the study of dynamic equations. At the first stage for solving this problem, one leg is considered separately, as a kinematic system with open kinematics and with three degrees of freedom. The kinematics equations were presented in matrix form using the principle of rotation of the coordinate system. The dynamics equations are based on Lagrange equations of the second kind. The mass of the legs, reduced to the center of gravity, moments of inertia, moments developed by engines were taken into account, and ets. The conclusions were made about the optimal movement of the leg based on the obtained equation of kinetic energy of the robot’s leg based on the obtained equation of the kinetic energy of the robot leg. This paper doesn’t consider the movement of the entire platform (the spider’s “body”), nor does it consider the influence of the friction force that occurs in kinematic pairs and when the robot’s legs touch the surface during movement.

ИССЛЕДОВАНИЕ ВЛИЯНИЯ РАЗБРОСА ДЕЙСТВИТЕЛЬНЫХ РАЗМЕРОВ ЗВЕНЬЕВ НА ПЕРЕДАТОЧНУЮ ФУНКЦИЮ МЕХАНИЗМА СКАЛОЧНОЙ ПОЛУАВТОМАТИКИ

In this work, the analysis of real deviations from the nominal dimensions links, and their cumulative effect on the final movement of the chain linkage element rolling semiautomatic mechanism. The considered mechanism was converted to an equivalent one, consisting of lower translational and rotational kinematic pairs. In the course of the structural analysis, the mechanism was divided into Assur groups in order to simplify further kinematic calculations. The calculation was carried out sequentially for each of the structural groups separately. Based on this, a mathematical model of the kinematics of a rolling semiautomatic mechanism was developed, taking into account the real size of the links, that is, possible deviations of the links size from the nominal values for any combination of them. Using a specific example with the given installation dimensions of the mechanism, the transfer function of the output link (wedge) is built, and the range of its possible change is determined according to the specified dimensional tolerances. Combinations of link sizes for the boundaries of the range of change of the transfer function have been determined It is shown that with the tolerances indicated in accordance with the Unified system of tolerances and fits, the deviation of the position of the output link at the extreme position of the input link (pusher) can reach ±10 of that calculated by the nominal dimensions. This model can be used to solve the problems of optimal selection of tolerances and reduce the cost of manufacturing a product, based on the kinematic restrictions imposed on the functionality of the mechanism. The proposed approach to the construction and analysis of analytical mathematical models can be relevant for a wide variety of industries: machine tool building, engine building, weapons industry and aircraft building, especially where mechanisms are used that form long kinematic chains.

Solution of the Rodriguez Equation in Modeling Volumetric Geometric Accuracy of Multi-Coordinate Systems

The article describes the solution to the Rodrigues equation for determining the volumetric accuracy of multi-axis CNC-controlled systems. An algorithm for calculating the position of the axis of a rotary kinematic pair in problems of volumetric accuracy of mechanical motion of a portal-type system with an additional pair of rotation. The algorithm is based on the analytical solution of the Rodrigues equation in the inverse problem of finding the vector of the final rotation of the known modulus from the known initial and final values of the characteristic vector of the rotated rigid body. In contrast to the well-known direct problem, where based on a finite rotation vector known in direction and magnitude, and the initial value of the characteristic vector of a body, its final value is found, the inverse problem of the Rodrigues equation is not that common due to the nonlinearity and need to solve a nonlinear coupled system of second order equations. The results of this work make it possible to expand the dimension of the space of generalized coordinates of the system analyzed for the volumetric accuracy from three to four. This is expected contribute to the development of ultra-precise systems of controlled mechanical movement. The analytical results of this study were verified by comparing with numerical solutions of the inverse problem in Maple.

НОРМИРОВАНИЕ ДОПУСКАЕМОЙ ПОГРЕШНОСТИ И ВЫБОР СРЕДСТВ ИЗМЕРЕНИЯ ПРИ КОНТРОЛЕ ОТКЛОНЕНИЯ ФОРМЫ И РАСПОЛОЖЕНИЯ ПОВЕРХНОСТЕЙ

The reliability of repaired engines is determined by many factors, among which the accuracy of the geometric parameters of engine parts plays an important role. Errors in the shape and location of the surfaces of parts cause additional acceleration of moving parts and reduce the accuracy of kinematic pairs. Violation of the movement kinematics of parts leads to a deterioration in the technical performance of the engine. In this regard, increasing the level of metrological control of shape deviation and surface location is one of the ways to improve the quality of engine repairs. Analysis of the measurement tools recommended in the reference literature has shown that they were chosen irrespective of the controlled values and without taking into account the type of measurement. The purpose of this study is to develop recommendations for improving metrological control of deviations in the shape and location of surfaces of parts during engine repairs. The paper provides theoretical grounds for choosing the criteria for selecting measuring instruments to control deviations in the shape and location of the surfaces of parts, taking into account the relevant formula. The result of indirect measurement and the measurement error (deviation of the shape and location of the surfaces of parts) are considered random values functionally related to the measured values (diameters of a part). The limits of permissible measurement errors and measurement tool errors are determined to control the deviation of the shape and location of the surfaces of new engine parts and parts subject to troubleshooting. The authors have carried out a comparative analysis of the obtained values with the error values of measuring instruments recommended in the reference literature. It has been established that most of the recommended measuring instruments have an error greater than the allowed measurement error. To reduce the risk of accepting parts that exceed the deviation norms relating to the shape and location of surfaces, it has been suggested using special criteria when selecting measuring instruments.

Analysis and Experimental Validation of the Tribological and Dynamic Characteristics of Journal Bearings

Sliding bearings are the main kinematic pair of a Stirling engine, and one of the main sources of friction power loss and excitation force. There is a coupling effect between the lubrication state and the excitation force. In this paper, the dynamic model of a Sapphire bearing fatigue test bed, which includes thermo-elasto-hydrodynamic (EHD) property, is established and the accuracy of the model is verified by the experimental data. Based on the model, the effects of the load, the oil supply temperature, the oil supply pressure, the bearing clearance on the tribological and dynamic characteristics are studied. With an increase in the load, the orbital path of the journal moves downward, the lubrication state changes from the full hydrodynamic lubrication to the boundary lubrication, the friction power loss increases, and the bearing excitation frequency increases. Due to the decrease of the oil viscosity, the hydraulic friction power loss decreases, but the friction power loss derived from the asperity contact increase, so does the total friction power loss. With the increase of the radial clearance, the shape of the orbital path and the minimum oil film thickness remain unchanged. The increase of the bearing clearance results in the collisions between the journal and bearing bush, thus the amplitude of the frequency multiplication component in the bearing load increases, and the asperity and the total friction power loss increase.

Classification of schemes of volumetric hydraulic machines according to the types of plain kinematic chains limiting their working chambers

A classification of volumetric hydraulic machines is proposed, which is based on the structure of a plain kinematic chain that closes the working chamber. The class of the hydraulic machine determines the number of bodies included in this chain; the series determines composition of the kinematic pairs of this chain. The classification covers all volumetric hydraulic machines used in modern technology. Keywords: volumetric hydraulic machine, classification, working chamber, kinematic chain, mechanism structure. vlkv48@mail.ru

Folded surface elements coupled with planar scissor linkages: A novel hybrid type of deployable structures

AbstractOrigami folding structures can find significant applications in the general area of building design, as they can be lightweight and deployable. An inherent property of folded surfaces, which is related to the degrees of freedom of each origami crease pattern, is form flexibility. Therefore, when building-scale applications are considered, in many instances, the folded surfaces, in order to become stiff and load-bearing, need to be constrained. A study of different types of deployable structures has led to the observation that in planar scissor linkages, hinges and pivots follow the same deployment path in space, as sets of vertices in certain origami structures. Due to the similarities in their kinematic behavior, selected origami patterns and scissor linkages can function as effective kinematic pairs, leading to structures able to transform in a controlled manner through a wide range of possible spatial configurations. A few examples of combining these two types of structures already exist [1–3]. In this paper a systematic approach for coupling origami crease patterns characterized by biaxial and rotational symmetry, with translational, polar and angulated scissor linkages, towards the development of novel forms of deployable structures, has been attempted. For the design and evaluation of the kinematic performance of the developed new structures, existing geometric modeling and calculation methods, parametric and simulation processes, as well as testing with physical models have been used. It is anticipated that research in this direction will lead to promising novel hybrid types of deployable structures.

COMPUTER MODELING IN MSC ADAMS/VIEW AS PART OF A MODERN APPROACH TO THE DESIGN OF MECHANICAL SYSTEMS OF ROBOTS

The presented paper deals with the use of computer simulation in the design of a robot model with 4 degrees of freedom of movement. The MSC Adams program is used in the computer simulation, and the use of the Matlab program is also shown. The robot's mechanism is an open kinematic chain. During kinematic analysis, attention is paid to solving the direct problem of kinematics in MSC Adams and in Matlab. The result of the solution is the calculated trajectory of the movement of the selected point of the end effector. The trajectory is shown in graphical form. In Matlab, the magnitude of the position vector of the effector point is calculated as a function of time at the selected course of angular deflection in individual kinematic pairs at constant angular velocities in individual joints of the robot.

ANALYSIS OF THE REVERSING MECHANISM OF LIGHT INDUSTRY EQUIPMENT

To create reliable and highly efficient, en- ergy-saving machines for light industry, it is necessary to study the dynamic processes of movement of the links of the mechanisms of which they are composed. Especially such studies should be given attention for machines, the mechanisms of which have a cyclic nature of action. During the execution of a technological operation in light industry machines with a periodic cyclic movement of the working bodies, an uneven movement of the main shaft occurs. This is caused by the movement of the links of the mechanism with certain accelerations and taking into account the periodic nature of the action of technological loads, which vary in magnitude and direction. The uneven nature of the movement leads to the appearance of additional loads in the kinematic pairs of mechanisms, mechanical vibrations in the mechanical trans- mission systems of motion, leads to the appearance of vibrations and violations in the positioning of the working bodies, affects the techno- logical process of the equipment. Uniform and stable tension of the threads is the key to a high-quality performance of the loop formation process in knitwear. Additional dynamic loads affect the technological tension of textile threads during equipment operation. These loads are caused by the accelerated movement of the links of the mechanism, which is especially important for technological equipment with the pres- ence of a reverse working stroke of its links. In such mechanisms, the values of the angular acceleration of the links and the linear accelera- tion of their individual points can acquire critically permissible values. It is possible to ensure the movement of the working bodies of the machine according to the law for which the tension of the threads will be optimally necessary. To do this, you need to choose the right type of mechanism that sets them in motion. The aim of the work is to conduct a structural-kinematic research of the mechanism of the reversible movement of the needle drum of a knitting machine, which will justify the selection of the required type of mechanism for such equipment. The confirmation of the improvement of the conditions for the formation of loops when knitting on a knitting machine with a reversible needle drum movement, made on the basis of a rocker mechanism, has been obtained.