Kinematic Screw Research Articles

ЗАСТОСУВАННЯ ДІАГРАМИ КІНЕМАТИЧНОГО ГВИНТА ПРИ ФОРМУВАННІ КРИВОЛІНІЙНИХ ПОВЕРХОНЬ В ОЗБРОЄННІ ТА ВІЙСЬКОВІЙ ТЕХНІЦІ

The article deals with the formation of surfaces by the movement of auxiliary surfaces (intermediaries), based on a parametric kinematic screw. In modern existing mechanisms operating at high speeds, dynamic loads exceed static loads many times over. To improve accuracy, it is necessary that the process of processing a part with a cutting tool is carried out taking into account the coefficient of uneven rotation in the manufacture of products. The technology of processing complex surfaces by the most productive method of running is closely related to the profiling of conjugated curved surfaces formed by the movement of intermediaries. The mating curved surfaces of kinematic pairs, with different parameters, in turn, require the development of effective kinematic methods of formation and ensuring high accuracy in the processing of products used in mechanisms and processed on automatic lines, allowing to expand the scope of the most advanced methods of processing complex products.. Proposed  1 the kinematic screw has proven itself well for the formation of mating ruled surfaces, so the urgent task arose to investigate the possibility of using a kinematic screw for mating curved surfaces. The study was developed on the basis of the proven theorem of Academician A.N. Podkorytov, about instantaneous envelope axoids, which allows you to form mating curved surfaces, using a parametric kinematic screw, which takes into account the kinematics of metal-cutting machines. When solving the set task, the design time is reduced and the accuracy of manufacturing parts in the mechanisms of weapons and military equipment is increased. Keywords: kinematic method, geometric model, cutting tool, mating surfaces, curved surface, parametric kinematic screw, auxiliary surface (intermediaries), instantaneous axoid envelopes.

Dynamics of a 3-UPS-UPU-S Parallel Mechanism

In this paper, a parallel mechanism with two rotational degrees of freedom is proposed. It could rotate freely and continuously around the two coordinate axes at the fixed origin of the coordinate frame. The structure of the mechanism is a second-order over constraint parallel structure and the moving platform and base platform are connected by five kinematic chains. The motion characteristics of this structure are analyzed by reciprocal screw equation. Then, the kinematics and dynamics modelling are carried out systematically in a unified way. The kinematics of the mechanism is established by means of screws, the displacements and accelerations of each joint and any point on a link could be calculated by the kinematic screw equation directly. The analysis of acceleration and its mathematical expression in screw form are given, and the acceleration matrix could be applied into the dynamic analysis based on the Newton–Euler equation. All the constraint forces and torques could be obtained by a single set of Newton–Euler equations.

КОМПЛЕКСНИЙ СПОСІБ ФОРМУВАННЯ СПРЯЖЕНИХ КРИВОЛІНІЙНИХ ПОВЕРХОНЬ

This article discusses the development of a complex method for processing helical curved surfaces of the cutting tool of a worm cutter for processing the working bodies of hydraulic pumps. Helical curved surfaces with a large angle of elevation of the turns are considered and new methods of profiling are created. A complex geometric method for solving kinematic issues related to determining the characteristics of a curvilinear surface characteristic in conjugated screw elements of hydraulic pumps is presented. The complex solution of such problems is a certain scientific problem, the solution of which is undoubtedly of great importance for the development of a complex screw cutting tool. As a result of traditionally designed screw cutting tools, the effect of chance prevails, and in the process, as a rule, defects occur in the processing of the helical surface of the screws, which reduces their service life. The solution of this problem will reduce the design time for the mating curved surfaces of the propellers and provide the necessary computational and graphical accuracy. When studying a complex method for designing helical conjugated curved surfaces, it was found that the existing methods are not enough in practice in production and have limitations in terms of design requirements. Therefore, for the manufacture of a conjugated curved helical surface of the cutting tool with technological accuracy, parameters are set with given conditions for the manufacture of hydraulic pump screws. The proposed geometric complex method for determining the characteristics of the curved helical surface of the cutting tool, namely the worm cutter, will allow designing and manufacturing automatically with maximum accuracy the conjugated curved surfaces of hydraulic pumps. Keywords: complex method, curved surfaces, kinematic screw, mating surfaces, worm cutter, hydraulic pumps, screws, characteristics, cutting tool.

ФОРМУВАННЯ КРИВОЛІНІЙНИХ ПОВЕРХОНЬ У СИСТЕМІ MATLAB

This article considers the formation of curved surfaces of the MATLAB system for processing helical curved surfaces in weapons and military equipment. Let us study the general equation of a helical surface, where the generatrix of the helical surface is given by a certain equation. At a given stage, the parameter is determined progressively as the helical surface moves. We study the formation of curved surfaces in the MATLAB system, associated with determining the characteristics of a curved surface, in conjugate kinematic pairs. The solution of such problems is a certain scientific problem, which is of great importance for the development of weapons and military equipment (WME). In traditionally designed spatial kinematic pairs, the effect of chance prevails, and in the process of work, as a rule, defects occur in the surface treatment of products, which reduces their service life. The solution of this problem will make it possible to shorten the period for repair and design of conjugated curved surfaces of weapons and military equipment and to increase the efficiency of the design and production process. When studying the proposed various methods and methods for designing helical mating surfaces, it was found that the existing methods are not enough in practice in production and have limitations in terms of design requirements. Therefore, for the manufacture of a conjugated kinematic screw pair with technological accuracy, we offer graphic-analytical formation of helical surfaces of various profiles in the MATLAB system. Forming a helical curved surface, a semi-ellipse, a semicircle, a hyperbola are proposed, which are often used in the design of kinematic pairs in military equipment and weapons. The formation of such curvilinear surfaces will allow designing and producing automated with maximum accuracy parts and mechanisms in weapons and military equipment using a subroutine in the MATLAB system. Keywords: curved mating surfaces, characteristics, surface formation, kinematic pairs, military equipment and weapons, MATLAB system.

Kinematic screws and dual quaternion based motion controllers

This paper presents a motion control approach with a focus on robotic manipulators based on screw theory and dual quaternions. The stability analysis of a general dual quaternion based controller has been capitalized to design an additional bounded twist controller. This controller is proposed to limit the maximum twist of the end-effector within a desired value, while preserving the accuracy achievable with high-gain feedback controllers. The proposed controllers could be useful for robotic tasks where curved motion is preferred over straight line motion. In that regard, the trajectories taken by the proposed controllers were analyzed for pose-to-pose control and some strategies have been provided for the proposed coupled controller to modify the natural trajectory. These behaviors were verified on a real robot as well as in simulation, comparing the experimental results with conventional decoupled controllers. The proposed controllers achieved smooth coupled motions which can be useful for tasks such as pick and place and assembly operations. Moreover, our coupled controllers based on screw theory need less actuator motion than the conventional decoupled approach for certain situations.

АЛГОРИТМІЧНІ ФОРМУВАННЯ СПРЯЖЕНИХ МОДЕЛЕЙ ДЛЯ ІНФОРМАЦІЙНО-КЕРУЮЧОЇ СИСТЕМИ В РАЗІ ПРОЄКТУВАННЯ КІНЕМАТИЧНИХ ПАР

In modern systems for the automatic design of complex products for military equipment, algorithmic construction of conjugate models of curved surfaces using computer technologies that exclude interference are increasingly being used. This gives a powerful impetus to the development of applied geometry of surfaces and stimulates the search for new ways to improve the technological processes of manufacturing parts, on machines with an information control system. In particular, this applies to technological operations on numerically controlled machines. One of the main directions in modeling kinematic pairs should be considered the study and design of the shapes of surfaces in close connection with the operating conditions of structures in military equipment and weapons in which they are to be used. The shapes of complex curved surfaces affect the reliability and durability of mechanisms in military equipment and weapons and therefore require more careful consideration of external conditions when designing. Much attention is paid to the design of surfaces, taking into account an increasing number of predetermined requirements, conditions for the formation of curved surfaces of kinematic pairs in military equipment. The use of algorithmic constructions of conjugated kinematic pairs for an information control system in the manufacture of real surfaces of military equipment obtained as a result of stamping, the creation of a geometric model of stamping, reflecting a real physical process, is an urgent problem. In recent years, in the manufacture of precision high-quality products of kinematic pairs and cutting tools in military equipment and weapons, complex curved surfaces have been widely used, which require the development of a geometric and mathematical apparatus for their modeling. Algorithmic modeling of curvilinear transformations for the formation of mating surfaces of kinematic pairs in military equipment, based on a parametric kinematic screw, is proposed, which will eliminate interference during their manufacture.

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.

Рухомий і нерухомий аксоїди тригранника френе напрямної кривої на прикладі циліндричної лінії

If the solid body makes a spatial motion, then at any point in time this motion can be decomposed into rotational at angular velocity and translational at linear velocity. The direction of the axis of rotation and the magnitude of the angular velocity, that is the vector of rotational motion at a given time does not change regardless of the point of the solid body (pole), relative to which the decomposition of velocities. For linear velocity translational motion is the opposite: the magnitude and direction of the vector depend on the choice of the pole. In a solid body, you can find a point, that is, a pole with respect to which both vectors of rotational and translational motions have the same direction. The common line given by these two vectors is called the instantaneous axis of rotation and sliding, or the kinematic screw. It is characterized by the direction and parameter - the ratio of linear and angular velocity. If the linear velocity is zero and the angular velocity is not, then at this point in time the body performs only rotational motion. If it is the other way around, then the body moves in translational manner without rotating motion. The accompanying trihedral moves along the directing curve, it makes a spatial motion, that is, at any given time it is possible to find the position of the axis of the kinematic screw. Its location in the trihedral, as in a solid body, is well defined and depends entirely on the differential characteristics of the curve at the point of location of the trihedral – its curvature and torsion. Since, in the general case, the curvature and torsion change as the trihedral moves along the curve, then the position of the axis of the kinematic screw will also change. Multitude of these positions form a linear surface - an axoid. At the same time distinguish the fixed axoid relative to the fixed coordinate system, and the moving - which is formed in the system of the trihedral and moves with it. The shape of the moving and fixed axoids depends on the curve. The curve itself can be reproduced by rolling a moving axoid over a fixed one, while sliding along a common touch line at a linear velocity, which is also determined by the curvature and torsion of the curve at a particular point. For flat curves, there is no sliding, that is, the movable axoid is rolling over a stationary one without sliding. There is a set of curves for which the angular velocity of the rotation of the trihedral is constant. These include the helical line too. The article deals with axoids of cylindrical lines and some of them are constructed.

ВИКОРИСТАННЯ СТРУКТУРНО-ПАРАМЕТРИЧНОГО МОДЕЛЮВАННЯ ПРИ ВИМІРЮВАННІ ВЕЛИЧИНИ КУТІВ, ПОВ’ЯЗАНИХ З КОЛОМ

The article considers the possible cases of the position of the magnitude of the angles relative to the circle and formulates the basics and principles of the method of structural - parametric modeling in measuring the magnitude of the angles associated with the circle. The method of structural-parametric modeling allows at the first stage, which is the location of the vertex of the angle, to determine its value on the basis of generalized principles of dependences, which is determined by the previously published theorem on measuring the magnitude of angles associated with a circle. The cases of the position of the vertex of the angles relative to the circle were reduced to the following three possible placements, namely: - in the circle: - on the circle and outside it. Separately, there were cases of position of the vertex of the angle in the center of the circle (central angle) and outside the circle, provided that the vertex of the angle goes to infinity (secant vertices of the angle - parallel to each other). This method should be used when constructing geometric dependences on the scheme of the modified kinematic screw, because to construct conjugate surfaces it is necessary to accurately determine the geometric parameters of the magnitude of the angles in the circle. This approach is also important when constructing angles on the wheel, which is of great importance in kinematics. By determining the structural-parametric dependences, based on the considered cases, it is convenient to model a set of complex geometrically conjugate helical surfaces with similar characteristics, changing only the corresponding analytical values. Accordingly, the cases described above allow us to solve certain problems of geometric modeling, and due to the variability of the value of the angle (from zero to 180 °) at its apex make it true for all possible cases. Therefore, for further modeling of complex geometric surfaces it is expedient to use these structural-parametric dependences in a circle (wheel). Keywords: a magnitude of angles, circle, a wheel, modeling, difficult geometrical surfaces, a central angle, an inscribed angle, a tangent, secant.

АНАЛІТИЧНЕ ЗНАХОДЖЕННЯ РУХОМОГО І НЕРУХОМОГО АКСОЇДІВ ТРИГРАННИКА ФРЕНЕ НАПРЯМНОЇ КРИВОЇ

The accompanying Frenet trihedral of a directing curve at movement on it carries out some spatial movement. In theoretical mechanics, the spatial motion of a solid body is described analytically, and at each instant it is considered as the sum of rotational and translational motions. If the accompanying trihedral is regarded as a solid body, its motion is entirely due to the differential characteristics of the directing curve, viz the curvature and torsion at the point of location of the trihedral.  The spatial motion of a solid body at any given time can be decomposed into many variants of rotational and translational displacement, each of which depends on the choice of the point of the solid body , that is, the pole with respect to which the motion is decomposed. For the points of the body acting as a pole, the vector and the magnitude of the rotational motion are unchanged and for the translational motion they are variable. In a solid at a particular point in time, you can find the pole for which the vectors of rotational and translational motions will coincide in the direction. This direction is the axis of the kinematic screw. Around this axis, at a specific point in time, the body rotates at a certain angular velocity and slides along it at a certain linear velocity. The relation between these velocities is a parameter of the kinematic screw. When moving the body, the axis of the kinematic screw changes its direction and position in the body, that is, it forms а ruled surface. Multitude of the positions of the axes of the kinematic screw can be considered with respect to the fixed coordinate system and with respect to the movable one (in our case, in the Frenet trihedral system). In the first case we get a fixed axoid, and in the second - a moving axoid. When moving a solid body, the moving axoid rolls over a fixed one and simultaneously slides along a common directing line of contact. The article shows the position of the axis of the kinematic screw in the accompanying Frenet trihedral, the set of which forms a moving axoid, and also, through the directing cosines, the position in a fixed system is found, that is, a fixed axoid is found. According to the developed algorithm, it is possible to construct fixed and moving axoids with a common axis of the kinematic screw for any point of the directing curve. Parametric equations of moving and fixed axoids are given. Keywords: moving and fixed axoids, kinematic screw, Frene trihedral, directing curve, curvature, torsion.

МОДЕЛЮВАННЯ ВЗАЄМНООГИНАЮЧИХ СПРЯЖЕНИХ ПОВЕРХОНЬ

Geometric modeling of mating surfaces for practical use in the design of products having a spatially complex surface that is closely associated with the formation of mutually bending mating surfaces. At the present stage of rapid development of complex designs of machines and apparatuses with the complex interaction of their parts, descriptive geometry methods are widely used in solving various complex technical problems. One of the common methods for the formation of geometric objects is geometric modeling, which allows the desired geometry of the product, determination of the contact characteristics of the conjugated kinematic pairs of systems of complex movements and during many other tasks during the creative creation of the structure, even at the design stage. Since the surface is conjugated, each of these surfaces can be represented as bypassed with respect to the second movable surface. The paper proposes to optimize the process of creating universal graphic tools, where there is essentially a graphic image of the parameters of kinematic mating surfaces, changing one of which leads to a change in the other, opens up the possibility of obtaining the shapes of parts with predetermined parameters. You should include suggestions in expanding the capabilities of the screw diagram [1], taking into account the real picture of kinematics during design, which, if the distance between the axes of the screws 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 theory of envelope surfaces was further developed in the design of conjugate kinematic surfaces. Concerning the design of a cutting tool based on a kinematic screw, profiling consists in the fact that from graphical constructions at any stage of design, it is easy to go over to the calculation using the analytical method, if necessary, checking or accurately determining the parameters. Graphic methods allow you to visualize the process of obtaining the profile of the part, to analyze the influence of each parameter on the profile and its design dimensions, where effortlessly you can identify the profiling errors of conjugate kinematic surfaces. For accurate design, it is necessary to carry out quite a number of geometric constructions, where it is accompanied by the introduction of completely objective errors that can be avoided, and also requires substantial creative preparation, which this article is devoted to.

Identification and viewing of singularities for a new type of 6SS parallel mechanism

This paper presents a method for determining the singular configurations of a 6RSS parallel mechanism based on its kinematic model. The parallel mechanism consists of a fixed plate and a mobile platform connected through six independent kinematic chains. Each of the six kinematic chains has an actuating rotational joint and two spherical joints. The kinematic analysis is based on the kinematic screw method. The resultant motion can thus be represented by composing the kinematic screws of the component motions. Starting from the two Jacobian matrices of the kinematic model, the two types of singularities encountered in parallel mechanisms are identified. Singular configurations are determined by an algorithm which is further used to produce three-dimensional representations of the two matrices determinants. Also, with the same program, it is possible to accurately establish the existence or inexistence of a mechanism for a given position and orientation.

Разработка плоского механизма параллельной структуры с одной степенью свободы для возбуждения колебаний по любому кинематическому винту

Разработка плоского механизма параллельной структуры с одной степенью свободы для возбуждения колебаний по любому кинематическому винту

Screw based kinematic calibration method for robot manipulators with joint compliance using circular point analysis

Abstract In this paper, a new kinematic calibration method that takes into consideration the effect of joint compliance in robot manipulators is proposed. A modified product-of-exponential (POE) kinematic model is formulated in such a way that it accommodates static joint deflection by gravitational force. A novel nonlinear cost function is constructed by combining the modified POE kinematic model and the end point measurements of the deflected circular trajectory, so that the kinematic screw and joint compliance are simultaneously identified after minimizing the cost function. An in-depth discussion of how to select a good reference configuration for better parameter identification is also given. Simulation and experimental results are provided to demonstrate the effectiveness of the proposed kinematic calibration method for an industrial 6-DOF (degree-of-freedom) robot manipulator and a custom 9-DOF robot manipulator.

A Class of Symmetrical 3T, 3T-1R, and 3R Mechanisms With Parallel Linear Motion Elements

A kind of kinematic chain with parallel linear motion elements (PLMEs) is proposed and studied in this paper. Based on screw theory, the kinematic screw equations of these linkages are established. The two special categories of PLMEs, with pure translational motion and with pure rotational motion respectively, are identified. The mobilities and the singularities of these kinematic chains are also investigated. By the utilization of these PLMEs, three types of the compound limbs are invented and analyzed. Through assembling these compound limbs in different ways, a class of lower mobility symmetrical 3T, 3T-1R, and 3R mechanisms is synthesized and presented for the first time. The simplified kinematic equations for this class of mechanisms driven by the linear actuators are derived. And the workspaces, singularities, and kinematic performance are addressed. Finally, three typical prototypes with regard to 3T, 3T-1R, and 3R mechanisms are manufactured and experimented to validate the mobility and motion feasibility of these mechanisms.

МОДЕЛЮВАННЯ СПРЯЖЕННИХ ГВИНТОВИХ ПОВЕРХОНЬ, ЩО ВИКЛЮЧАЄ ІНТЕРФЕРЕНЦІЮ

Research is the need to create effective methods for perfect processing of products on flexible automated production facilities, on processing modules, on machines with numerical programmed control, cannot be achieved without computer-oriented technologies that allow efficient geometric design of cutting tools. One of the main problems of modeling mating surfaces is the phenomenon of interference. The constant growth of requirements for the quality of products, the development of computer technology and the creation of new production equipment are objective factors that stimulate the improvement of methods for eliminating interference of the interfaced surfaces of products [2]. One of the most obvious ways to detect interference is an automated graph analytical method for constructing a parametric kinematic screw, which in turn will improve productivity, relative to the cutting edge of the worm milling machine, which will be able to process a complex screw surface of the product and a quick changeover of the machine. Professor A.N. Podkorytov proposed a screw diagram and applied it to form complex curvilinear conjugate surfaces [1]. In recent years, complex screw surfaces have become widely used in aircraft manufacturing, mechanical engineering, and shipbuilding. Modern technologies for processing products in flexible automated production facilities on processing modules, in turn, require the development of effective methods for geometrical and mathematical modeling of coupled helical surfaces eliminating interference at the design stage.

Development of structural schemes of parallel structure manipulators using screw calculus

The paper considers the approach to the structural analysis and synthesis of parallel structure robots based on the mathematical apparatus of groups of screws and on a concept of reciprocity of screws. The results are depicted of synthesis of parallel structure robots with different numbers of degrees of freedom, corresponding to the different groups of screws. Power screws are applied with this aim, based on the principle of static-kinematic analogy; the power screws are similar to the orts of axes of not driven kinematic pairs of a corresponding connecting chain. Accordingly, kinematic screws of the outlet chain of a robot are simultaneously determined which are reciprocal to power screws of kinematic sub-chains. Solution of certain synthesis problems is illustrated with practical applications. Closed groups of screws can have eight types. The three-membered groups of screws are of greatest significance, as well as four-membered screw groups [1] and six-membered screw groups. Three-membered screw groups correspond to progressively guiding mechanisms, to spherical mechanisms, and to planar mechanisms. The four-membered group corresponds to the motion of the SCARA robot. The six-membered group includes all possible motions. From the works of A.P. Kotelnikov, F.M. Dimentberg, it is known that closed fifth-order screw groups do not exist. The article presents examples of the mechanisms corresponding to the given groups.

Design of 2-degrees-of-freedom (DOF) planar translational mechanisms with parallel linear motion elements for an automatic docking device

A class of kinematic chains assembled from parallel linear motion elements were investigated using screw theory. Based on a consideration of kinematic screws, two types of kinematic chain were identified, and the singularities were determined. By synthesizing these kinematic chains, 2-degree-of-freedom (DOF) planar translational mechanisms with three limbs were designed. Furthermore, the kinematics and stiffnesses of these mechanisms were studied. The mechanisms were used in an automatic docking device, designed for joining two water pipes in a water sample collection system aboard an unmanned surface vehicle. Simplified equations for the maximum displacement and driving force of this device were also derived. Simulations of the 2-DOF planar translational mechanisms and the docking procedures were carried out. Finally, a prototype was manufactured to verify the mobility and motion feasibility of these mechanisms.

Application of the Theory of Kinematic Motion Control of a Rigid Body

The theory of the kinematic control of the rotational (angular) motion of a rigid body and the spatial motion of a free rigid body used in the article is based on the quaternion and biquaternion kinematic models of the rigid body motion. In this theory, the kinematic equations of the rotational and (or) translational motion of a body are considered as the mathematical models of a rigid body motion, and the vectors of the angular and (or) translational velocities of a body or kinematic screws are used as the controls. The goal of the kinematic control is transfer of a rigid body from its assigned initial position to the desired final position by applying the required (program) angular and (or) linear velocities to the body. Also, the goal of the kinematic control can transfer a rigid body from its given initial position to any selected program path and, further, to an asymptotically stable motion along the program path with the required program angular and linear velocities by applying the required stabilizing angular and linear velocities to the body. In the article the authors present a review of the papers dedicated to the following applications of the theory of the kinematic control of a rigid body motion in the mechanics of a space flight, inertial navigation and mechanics of the robot manipulators: two-circuit control of the rotational motion of a rigid body (spacecraft) using a strapdown inertial navigation system; adjustable strapdown systems for orientation and navigation of the moving objects; TSP-Argus motion control platform complex for Mars-94 space project; optimal reorientation of the orbit, of the orbital plane and correction of the angular elements of the orbit of the spacecraft by means of a reactive acceleration, orthogonal to the plane of the orbit of the spacecraft; solving of the inverse problems of the kinematics of the robot manipulators using the biquaternion theory of the kinematic control; kinematic control for the mechanics of the robotic manipulators (independent program motion speed control).

Определение взаимного соответствия кинематического винта выходного звена и винта-градиента в особом положении механизма параллельной структуры

Определение взаимного соответствия кинематического винта выходного звена и винта-градиента в особом положении механизма параллельной структуры