scholarly journals APPLICATION OF THE “FINITE ROTATION AND DISPLACEMENT” METHOD TO CONTROL THE PARABOLIC ANTENNA

2019 ◽  
pp. 162-169
Author(s):  
A. Danilov
Keyword(s):  
Vector Model ◽  
Small Displacement ◽  
Structural Constraints ◽  
Finite Rotation ◽  
Displacement Method ◽  
Generalized Coordinates ◽  
Sequential Structure ◽  
Parabolic Antenna ◽  
Source Data ◽  
Rotation Plane

The article deals with the application of the "finite rotation and displacement" method (FRDM) which can find the desired values of the generalized coordinates for the control system of a parabolic antenna. The special manipulator of a sequential structure with sufficient rigidity is used to control the parabolic antenna. The rigidity of this manipulator is ensured by use of links in the form of spherical shells and bearings located along the perimeter of each shell in the rotation plane of each link. It allows to optimally place the material of the manipulator's design and to obtain sufficient rigidity with minimal weight. The manipulator consists of four links connected by fifth class kinematic pairs with an arbitrary inclination of the axes. For this task the antenna's orientation is important without taking into account the small displacement of its position during the process of its orientation. The FRDM method provides both orientation and position. It is based on determining the precise and optimal iterative steps for each degree of mobility, providing maximum approximation to the specified orientation parameters of the parabolic antenna. According to the method's algorithm, the software is developed consisting of subprograms for organizing a general solution of the inverse kinematics for an arbitrary number of links and a particular one for a manipulator in the form of source data. The initial data are the vector model of the manipulator, the values of the structural constraints of the generalized coordinates, and the characteristics of kinematic pairs by type and class

scholarly journals TEST SIMULATION OF «FINITE ROTATION AND DISPLACEMENT» METHOD BY THE EUROPEAN ROBOTIC ARM PASSING THROUGH THE SINGULAR POINTS

2019 ◽  
pp. 128-138
Author(s):  
А. Данилов ◽  
A. Danilov
Keyword(s):  
Singular Points ◽  
Vector Model ◽  
Robotic Arm ◽  
Structural Constraints ◽  
Finite Rotation ◽  
Displacement Method ◽  
Generalized Coordinates ◽  
Sequential Structure ◽  
Source Data ◽  
The Given

The article consider the test simulation of the «finite rotation and displacement» method (FRDM) when the European Robotic Arm (ERA) manipulator is passing through the singular points. The test simulation confirms the method’s efficiency when passing through singular points and shows how to control the manipulator with various manifestations of the singularity. Depending on the type of singularities manifestation the manipulator is controlled in the vicinity of the singular point by means of small changes in its configuration or by limiting and setting specific values to generalized coordinates at the software and hardware level. The FRDM method is designed to solve the inverse kinematics (IK) for sequential-structure manipulators with an arbitrary number of links connected by fifth-class kinematic pairs. The method is based on determining the exact and optimal iterative steps that provide the maximum approximation to the given parameters of the final link for each degree of mobility. The software has been developed that consists of subprograms for organizing a general solution of the IK and a particular one for a particular manipulator in the form of source data according to the algorithm of the method. The initial data are the vector model of the manipulator, the values of the structural constraints of the generalized coordinates and signs of kinematic pairs by type and class.

scholarly journals THE ALGORITHM OF THE CROSS-SECTION OPTIMIZATION OF INELASTIC GEOMETRICAL NONLINEAR STEEL FRAME STRUCTURES

2009 ◽  
Vol 1 (1) ◽  
pp. 10-22 ◽  
Author(s):  
Romanas Karkauskas ◽  
Michail Popov
Keyword(s):  
Linear Theory ◽  
Cross Section ◽  
Cross Sections ◽  
Functional Relation ◽  
Steel Frame ◽  
Small Displacement ◽  
Plastic Collapse ◽  
Structural Constraints ◽  
The Cross ◽  
Maintenance Requirements

The purpose of the problem of optimization is introducing a project on the structure satisfying the limit requirements of the safety and usability conditions of the various eff ects of external actions. It can be provided by disposing comprehensive information about the real behaviour of construction under all working conditions and at any period of occurrence. Such problem cannot be solved applying the methods of the linear theory of structural mechanics because the form and dimensions of construction under assorted loads essentially change and the principle of small displacement becomes unreliable. In addition, starting from certain stress conditions, Hook’s law for majority materials is ineligible and changing by nonlinear relation. It is necessary to refuse the linear theory assumptions and change over to considerably wide and complex nonlinear theory generalizations. Abandoning calculation by unstrained condition tolerating small displacements allow changes in the infl uence of construction geometry on its defl ected mode, proceed to nonlinear tensions and relations with deformations and allow incipient plastic deformations because some materials of construction close to plastic collapse receive very large displacements and do not satisfy requirements for successful exploitation. Th ereby, the above mentioned causes must be allowed developing the mathematical models of solving the problems of construction optimization. A developed mathematical model and calculation algorithm with material inelastic properties as well as the evaluation of maintenance requirements are presented for the cross-sections optimization of geometrically nonlinear frames. Th e evaluation of dissipative features when employing inelastic steel stains results in a signifi cant reduction of reserve in carrying capacity in respect of the optimal elastic state of the structure. Maintenance requirements for the structure introduced to its operation time involve not only strength constraints but also stiff ness, stability and structural constraints defi ning minimal cross-section parameters and the ration of element slenderness. Th e aforementioned factors limit the free development of plastic stains, and therefore the optimal structure is considered in the state prior to plastic collapse. Th e used elastic response values are related to the optimal parameters of standard profi le cross-sections by nonlinear functional relation. Th erefore, this problem has to be solved using the iterative method. Th e procedure of forming a new beam element tangent stiff ness matrix considered by internal forces stimulated by diff erent element alterations is presented. Th e effi ciency of the developed algorithm exemplifi ed by calculating the optimal values of the cross-section involving 16-stroyed steel frame beam elements is obeyed by minimum volume requirements when node horizontal displacements are limited.

scholarly journals STABILIZATION OF THE SPATIAL POSITION OF THE MANIPULATOR OF A PARALLEL-SEQUENTIAL STRUCTURE

2021 ◽  
pp. 17-21
Author(s):  
N. S. Vorob’eva
Keyword(s):  
Boundary Conditions ◽  
Spatial Position ◽  
Control Law ◽  
Terminal Control ◽  
Generalized Coordinates ◽  
Control Functions ◽  
Sequential Structure

A method for constructing terminal control based on the representation of control functions relative to time is considered. The parameters of the functions are determined from the condition of satisfying the boundary conditions at the ends of the trajectory of the generalized coordinates of the manipulator. On the basis of the obtained program movements, a control law with feedbacks is constructed.

A Device for Magnification Measurement

1972 ◽  
Vol 30 ◽  
pp. 622-623
Author(s):  
J.A. Eades ◽  
A. van Dun
Keyword(s):  
Electron Microscope ◽  
Small Displacement ◽  
Private Communication ◽  
Piezoelectric Crystal ◽  
Double Exposure ◽  
Standard Methods ◽  
Elegant Method ◽  
The Right ◽  
Piezo Electric

The measurement of magnification in the electron microscope is always troublesome especially when a goniometer stage is in use, since there can be wide variations from calibrated values. One elegant method (L.M.Brown, private communication) of avoiding the difficulties of standard methods would be to fit a device which displaces the specimen a small but known distance and recording the displacement by a double exposure. Such a device would obviate the need for changing the specimen and guarantee that the magnification was measured under precisely the conditions used.Such a small displacement could be produced by any suitable transducer mounted in one of the specimen translation mechanisms. In the present case a piezoelectric crystal was used. Modern synthetic piezo electric ceramics readily give reproducible displacements in the right range for quite modest voltages (for example: Joyce and Wilson, 1969).

Observation of faint contrast at planar faults in alloys

1978 ◽  
Vol 36 (1) ◽  
pp. 340-341
Author(s):  
K. Kuroda ◽  
Y. Tomokiyo ◽  
T. Kumano ◽  
T. Eguchi
Keyword(s):  
Reciprocal Lattice ◽  
Beam Theory ◽  
Al Alloys ◽  
Small Displacement ◽  
Electron Microscopic ◽  
Lattice Vector ◽  
Fringe Contrast ◽  
Planar Fault ◽  
Lattice Displacement ◽  
The Many

The contrast in electron microscopic images of planar faults in a crystal is characterized by a phase factor , where is the reciprocal lattice vector of the operating reflection, and the lattice displacement due to the fault under consideration. Within the two-beam theory a planar fault with an integer value of is invisible, but a detectable contrast is expected when the many-beam dynamical effect is not negligibly small. A weak fringe contrast is also expected when differs slightly from an integer owing to an additional small displacement of the lattice across the fault. These faint contrasts are termed as many-beam contrasts in the former case, and as ε fringe contrasts in the latter. In the present work stacking faults in Cu-Al alloys and antiphase boundaries (APB) in CuZn, FeCo and Fe-Al alloys were observed under such conditions as mentioned above, and the results were compared with the image profiles of the faults calculated in the systematic ten-beam approximation.

Superstructures and ordering phenomena in ceramic superconductors

1996 ◽  
Vol 54 ◽  
pp. 710-711
Author(s):  
R. Gronsky
Keyword(s):  
Domain Growth ◽  
Small Displacement ◽  
Small Scale ◽  
Ceramic Superconductors ◽  
Oxygen Sublattices ◽  
Tweed Contrast ◽  
Diffraction Patterns ◽  
Representative Image ◽  
Static Lattice ◽  
Modulation Wavelength

It is now well established that the phase transformation behavior of YBa2Cu3O6+δ is significantly influenced by matrix strain effects, as evidenced by the formation of accommodation twins, the occurrence of diffuse scattering in diffraction patterns, the appearance of tweed contrast in electron micrographs, and the generation of displacive modulation superstructures, all of which have been successfully modeled via simple Monte Carlo simulations. The model is based upon a static lattice formulation with two types of excitations, one of which is a change in oxygen occupancy, and the other a small displacement of both the copper and oxygen sublattices. Results of these simulations show that a displacive superstructure forms very rapidly in a morphology of finely textured domains, followed by domain growth and a more sharply defined modulation wavelength, ultimately evolving into a strong <110> tweed with 5 nm to 7 nm period. What is new about these findings is the revelation that both the small-scale deformation superstructures and coarser tweed morphologies can result from displacive modulations in ordered YBa2Cu3O6+δ and need not be restricted to domain coarsening of the disordered phase. Figures 1 and 2 show a representative image and diffraction pattern for fully-ordered (δ = 1) YBa2Cu3O6+δ associated with a long-period <110> modulation.

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