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“Sensorless” measurement of the angle of rotation or speed of direct current motors using periodic oscillations in the electrical signals is usually very susceptible to errors. This is caused by the occurrence of frequencies in the signals that do not correspond to the expected frequency. In this article, a new method is presented that is robust against these influences and is thus able to provide a much more reliable angle or speed signal. For this purpose, the causes of the frequencies occurring in the electrical signals are discussed first. Based on general considerations incorporating these effects, the derivation of a general scheme and the associated requirements are presented. The algorithm is then developed in detail and implemented within the context of an application example using an electric parking brake of a motor vehicle. Finally, the process is experimentally validated using three different motor types under different operating conditions, and the specific properties of the method are discussed.

Advanced design methods offer not only a number of methods of modeling structures but also quite profound optimization approaches. The topology optimization is one of such advantageous methods. There are several implementations of this type of structural analysis, but the most common option is to deal with the material density as a generalized parameter. The development of 3D printing technologies increases the interest in algorithms of this type. However, it mostly refers to printing with metal or plastic, which implies the material isotropy. Advances in continuous fiber printing systems and automatic placement machines using composite tapes make it possible for engineers to control not only a material’s position, but also to choose the local orientation of reinforcing elements. Such systems require optimization algorithms taking into account additional parameters characterizing the material anisotropy. In this case the traditional problem of the topology optimization should first be modified for the model of an orthotropic material with restrictions on the value of the angle of rotation of the reinforcement lines along the print path. In this paper, an idea of such a topology optimization algorithm is proposed, which is implemented using the Abaqus finite element modeling facilities, and examples of solving typical problems are considered.

To compare the design, metallurgy, mechanical performance, and canal preparation of 5 rotary systems.A total of 735 25-mm NiTi instruments (sizes 0.17[0.18]/.02v, 0.20/.04v, 0.20/.07v, 0.25/.08v, 0.30/.09v) from ProTaper Gold, ProTaper Universal, Premium Taper Gold, Go-Taper Flex, and U-File systems were compared regarding overall geometry and surface finishing (stereomicroscopy and scanning electron microscopy), nickel and titanium ratio (energy-dispersive spectroscopy), phase transformation temperatures (differential scanning calorimetry), mechanical performance (torsional and bending tests), and unprepared canal surface (micro-CT). One-way ANOVA and Mood's median tests were used for statistical comparisons with a significance level set at 5%.Stereomicroscopic analysis showed more spirals and high helical angles in the Premium Taper Gold system. All sets of instruments had symmetrical spirals, no radial lands, no major defects, and an almost equiatomic ratio between nickel and titanium elements, while differences were observed in their tips' geometry and surface finishing. At room temperature (20 °C), DSC test revealed martensitic characteristics for ProTaper Gold and Go-Taper Flex, and mixed austenite plus R-phase for the Premium Taper Gold, while ProTaper Universal and U-Files had full austenitic characteristics. Overall, larger instruments had higher torque resistance and bending load values than smaller ones, while a lack of consistency and mixed values were observed in the angle of rotation. The 0.25/.08v and 0.30/.09v instruments of ProTaper Universal and U-File had the highest maximum torques, the lowest angles of rotation, and the highest bending loads than other tested systems (P .05). No significant difference was noted regarding the untouched root canal walls after preparation with the tested systems (P .05).Although differences observed in the overall geometry and phase transformation temperatures have influenced the results of mechanical tests, unprepared canal surface areas were equivalent among systems.Root canal preparation systems with similar geometries might present different mechanical behaviors but equivalent shaping ability.

The article is devoted to modeling and visualization of the formation of flat-nosed (snub-nosed) dodecahedron (snub dodecahedron). The purpose of the research is to model the snub dodecahedron (flat-nosed dodecahedron) and visualize the process of its formation. The formation of the faces of the flat-nosed dodecahedron consists in the truncation of the edges and vertices of the Platonic dodecahedron with the subsequent rotation of the new faces around their centers. The values of the truncation of the dodecahedron edges, the angle of rotation of the faces and the length of the edge of the flat-nosed dodecahedron are the parameters of three equations composed as the distances between the vertices of triangles located between the faces of the snub dodecahedron. The solution of these equations was carried out by the method of successive approximations. The results of the calculations were used to create an electronic model of the flat-nosed dodecahedron and visualize its formation. The task was generally achieved in the AutoCAD system using programs in the AutoLISP language. Software has been created for calculating the parameters of modeling a snub dodecahedron and visualizing its formation.

Historical Islamic ornaments include a fantastic treasury of geometric and mathematical algorithms. Inevitably, restoration of these ornaments in periodic patterns consisting of repeated elements has been faced following and substituting the other available similar ingredients instead of vanished parts. Still, the prediction of parametric, quasi, or non-periodic patterns, where components are not identical, needs to be carried out in a more challenging process than the periodic ones due to shape, scale, or angle of rotation alteration. Intelligent restoration could facilitate the forecasting of damaged parts in such geometric patterns that an algorithm has changed their geometric characteristics. In some architectural heritage, geometric patterns include a parametric algorithm like parametric patterns in the ceiling of Sheikh Lotfollahmosque in Isfahan, Iran, and the dominant structure of Persian domes Karbandi. In this article, the aim is to propose a new method for the smart restoration of the parametric geometric patterns in which, by having access to the image of the existing patterns, the vanished parts could be reconstructed spontaneously. Our approach is based on image processing by detecting boundaries of deterioration, finding every individual element, and extracting features of detected individual patterns via Zernike moments. The order of individual patterns starts from the farthest pattern to detected deterioration. Then by creating a time series, the Back-propagation neural network would be trained by extracted features, and the vanished patterns’ features could be predicted and reconstructed. Eventually, the reconstructed and real patterns are compared to determine differences between them by mean-squared error and to evaluate the performance of our method. To validate the process, a parametric geometric pattern is designed by the assumption that some parts are disappeared. The proposed method’s results, in this case, hold an efficient performance with the accuracy of 92.99%. Furthermore, Sheikh Lotfollah’s patterns and Naseredin Mirza mansion’s patterns as two real cases are tested by the proposed method, representing reliable and suitable performance results.

Three variants of the engineering solution of inverse problems regarding the strength of pipeline sections bent as a result of ground movements or during an earthquake are proposed. The feature of this approach consists in calculation of stresses not by the forces acting on the pipe, but by the displacements or deflections. Therefore, full-scale measurements of the detected deviation of the pipe position from the planned pipeline route should be taken as initial data for estimating the values of additional bending stresses. The first problem considered is the assessment of the risk of pipeline malfunction upon sagging or bulging of the supports of aboveground pipelines. The problem is solved in the beam approximation. The pipeline is considered a statically indeterminate beam, one of the supports of which is forcibly moved to a given distance. For a once statically indeterminate beam, a system of four equations — two equilibrium equations and two integral equations for deflections — was solved numerically. The calculated values of three reactions of the supports and the angle of rotation of the pipe section on the first support are used to calculate bending moments, stresses and deflection lines. The problem for a thrice statically indeterminate beam under strain loading was also solved. The second goal is to model the stress-strain state of the pipeline proceeding from the tables of experimental data on the values of pipe deflections and their coordinates. The problem was also solved numerically, using the procedures of smoothing, linear interpolation and sequential differentiation. It is shown that taking into account the possible ambiguous solution of the inverse problem, we should not rely on the calculated values of transverse forces and distributed loads. It is enough to limit ourselves to the second coordinate derivative of the deflection. The third goal is to prevent accidents at the design stage. It is proposed to create a list of normalized deflection functions for modeling possible emergency situations for pipeline sections placed in difficult ground-geological conditions and seismically dangerous zones. The examples of such functions are given.

A study of the operation of elastic joints with preset dependences of the restoring torque on the angle of rotation in the crank mechanism is presented. The principle of operation of the proposed joints is based on the movement of the elastic element between the guides of the calculated shape. The installation of such a joint with a preset characteristic between the strut and the crank enables obtaining a constant angular velocity of the crank. With the introduction of an elastic hinge between the crank and the connecting rod, the lateral force acting on the piston in the case of a constant angular velocity of the crank decreases significantly. By adding the counterweight properly, it is possible to obtain zero lateral force on the connecting rod for the entire crank revolution.

In this paper, mechanical models for FSW are developed for a square pin profile tool. The models express the oscillation of the forces over time and their mean values. The welding, transverse, radial, and tangential forces are modeled as a function of the rotational and welding speeds and the instantaneous angle of rotation. The models include the concept of a specific force, based on the mechanics of orthogonal cutting, to describe the relation between the forces and the area of the deformed material. Additionally, experimental measurements for the forces and torque are performed for different parameters to calibrate and validate the models. Due to the square profile of the tool pin, the welding, transverse, radial, and tangential experimental forces exhibit periodic variations along the tool advancing path. The maximum radial force occurs at 45° of the welding direction, and the mean welding and transverse forces present similar magnitudes in all experiments. The results show good agreement between the models and the experimental data with a correlation coefficient greater than 0.97. With increasing rotational speed, the torque decreases linearly, and the axial force is almost constant.

The article defines the general basic moment equation for a concave winged rotor with a vertical axis of rotation. The changing equation in the integral form is found depending on its position in the intervals.

To compare six reciprocating instruments regarding their geometric design, metallurgical characteristics, mechanical behaviour and ability to prepare root canals.A total of 246 new 25-mm NiTi instruments (41 per group) from six reciprocating systems (Reciproc, Reciproc Blue, One Files, One Files Blue, Reverso Silver, and WaveOne Gold) were evaluated throughout a multimethod approach regarding their design using stereomicroscopy (number of blades and helix angle) and scanning electron microscopy (blades symmetry, cross section and surface finishing), nickel-titanium composition, phase transformation temperatures, mechanical performance (cyclic fatigue, torsional and bending resistance) and unprepared canal surface area on anatomically matched mandibular molars assessed by micro-CT. One-way ANOVA and post hoc Tukey's or Mood's median tests were selected depending on sample distribution with significance level set at 5%.The instruments had similarities regarding their metal composition and unprepared canal area, whilst differences in phase transformation temperatures and geometric design (number of blades, surface finishing and tip geometry) were observed. Overall, no difference was observed regarding the maximum torque values (P 0.05), whilst One Files (72 s) and One Files Blue (414 s) had the shortest and longest times to fracture, respectively (P 0.05). Similar angles of rotation were observed in Reciproc (310°), One Files (285°) and Reverso Silver (318°) instruments (P 0.05), which were significantly lower than Reciproc Blue (492°), One Files Blue (456°) and WaveOne Gold (492°; P 0.05). Maximum bending load demonstrated that Reciproc Blue (201.3 gf) was significantly more flexible that the other instruments (P 0.05).Although there were similarities in metal composition and percentage of unprepared canal surface, the instruments had differences in the overall geometric design, phase transformation temperatures and in the four mechanical resistance parameters (time to fracture, maximum torque, angle of rotation and maximum bending load).

In this work, we proposed a novel Coordinate Rotation DIgital Computer (CORDIC) rotator algorithm that converges faster by performing radix-2,4 and 16 CORDIC iterations while maintaining the scale factor implicitly constant. A mixed-radix is used to achieve convergence faster to reduce the computational latency of the CORDIC algorithm. The main concern of the higher radix CORDIC algorithm is the compensation of a variable scale factor. To solve this problem, the Taylor series approximation of sine and cosine is proposed for a higher radix CORDIC algorithm to achieve the scaling-free rotation of the two-dimensional vector. The scaling-free rotation of the proposed CORDIC algorithm removes the read-only memory (ROM) needed to store scale factor of higher radix CORDIC algorithm. Further, the proposed CORDIC algorithm is designed in rotation mode and optimized by removing the Z datapath for the digital signal processing (DSP) applications for which the angle of rotation is known in advance. Finally, the multipath delay commutator (MDC) fast Fourier transform (FFT) algorithm is implemented with the proposed CORDIC algorithm based rotator on FPGA. The proposed design is compared with existing designs. In a comparison between the radix-16 CORDIC rotator based FFT implementation and our proposed implementation, it has been found out that implementation proposed in this article has used 17% fewer resources.

The article presents an analysis of the loading the milling working body of the disc cutting machine. The diagram of the current efforts on the working body of the disc cutting machine is presented. The process of loading a milling working body in a steady-state mode of movement is considered. It is established that in the steady state mode of operation of the cutter the feed force created by the weight of the working body and the force of the hydraulic cylinders of lifting and lowering will be equal to the resistance of movement along the y axis. The concept of an average cutter is proposed, its main characteristics are presented, the cutting angle, the back angle, the width of the wear site, the width of the cutter, the thickness of the cut chips, the angle of rotation. The diagram of the forces acting on the average cutter is presented, the thickness of the cut chips and the number of cutters installed on the working body are determined. It is established that the average cutter is affected by the force – caused by the action of the torque, and the result of the action of the traction force. These two forces determine the total active force. It is determined that the feed force is directly proportional to the area of the mill indentation and the number of cutters. The ground resistance to cutting, the resistance to moving the working body, and the feed force are considered. A system of equations is obtained that connects the components presented above. The torque and power generated by the drive for rotating the working body are determined.

A mathematical model for determining the sucrose concentration in honey, based on the optical rotation of the plane of polarization in solutions, is described. The dependencies of the dispersion of the specific rotation in the main polysaccharides (sucrose, glucose and fructose) included in honey are obtained. A working hypothesis is put forward and experimentally tested to determine the angle of rotation of the plane of polarization of light passed through a cuvette with honey as an algebraic sum of the rotation angles for light that passed through individual components of honey. A prototype of a device for express analysis of honey has been developed and manufactured to determine the excess of sucrose concentration over its value in natural honey.

A comprehensive review on the approaches for synthesizing low side lobe concentric ring array (CRA) antennas is given. An Iterative Convex Optimization (ICO) based array layout synthesis technique is proposed for peak side-lobe level (PSLL) minimization over a given circular field-of-view in steerable uniform-amplitude concentric ring array (UA-CRA) antennas. For a given number of rings and number of uniformly-distributed elements in each ring, the ICO algorithm optimizes the ring radii and angle of rotation, with possible constraints on the minimum element separation and largest array size. As compared to the existing UA-CRA synthesis techniques, the proposed method presents unique features as it combines the capability of optimization of angle of rotation of the rings and PSLL minimization for multiple elevation scan angles in a computationally-efficient and easy-to-solve procedure. Through numerical design examples, it is demonstrated how the ICO technique can be effectively used (i) to synthesize sparse UA-CRA topologies generating low PSLL steerable beams, and (ii) to assess and improve the PSLL suppression performance of various known optimization algorithms. Based on the UA-CRA topologies synthesized via competitive methods in the recent literature, a new set of improved array topologies are presented.

This article discusses a method for calculating the operation of forces aimed at moving and turning the vehicle when performing an expert examination to establish the speed of movement of the research object before, at the time and after the accident. The authors present the results of comparing the calculation according to the proposed method and the calculation according to the generally accepted method with the data obtained in full-scale crash tests at the test site.

The article notes that the software of the complex used in the Russian troops to solve in a short time the actual problem of determining the possibility of safe passage of super heavy loads on girder road bridges has the following disadvantages: 1) it can only be used for split concrete bridges; 2) the decision to pass a large load through the bridge is made only by the value of the deflection in the center of the span, without taking into account the resulting stresses in the bridge span structure structures, and without taking into account the bearing capacity of the supports. In the article, in order to eliminate these shortcomings: 1) a strict formula is obtained for calculating the deflection in the middle of beam spans made of any structural materials from the angle of rotation of their support sections; 2) based on the use of the fundamental relationship between the relative heights of girder spans, the relative deformations of the edges of their cross sections and their relative deflections, it is proved that the maximum stresses in the edges of the cross sections of girder spans from any structural materials can be calculated by the maximum deflection value in the middle of their spans; 3) a method is established for determining the ability of beam bridge supports to ensure safe passage of a heavy vehicle by the nature of changing the rotation angles of the supporting cross sections of the span structures under the influence of the movement of the heavy vehicle layout. Taking these three results into account, when upgrading the software of the measurement system, ensures that the goal of the work is achieved.

A model of distributed information carriers in the form of stable spatially inhomogeneous structures in optical and fiber-optical communication systems is considered. We study the conditions for the occurrence of such stable spatially inhomogeneous structures of the light wave of the generator of the optical radiation. The formation of inhomogeneous structures that occur in a plane orthogonal to the direction of the wave propagation is provided by a thin layer of a nonlinear medium and a two-dimensional lagging feedback loop with the rotation operator of the spatial coordinates of the light wave in the emission plane of the optical generator. In the space of the main parameters of the generator (a control parameter, the angle of rotation of the spatial coordinates, and the magnitude of the delay), the areas of the generation of stable spatially inhomogeneous structures are constructed and the mechanisms of their occurrence are analyzed.

The paper presents the general concept of creating a system for cleaning main pipelines by a device with a roller drive using the energy of oil flow. The expediency of using cleaning devices with a roller brush drive has been analytically proved. Application of this system allows to reduce time and labor costs when carrying out cleaning works of the main pipelines. The effect is achieved due to the repeated action of the brushes moving along the helical trajectory. A new design of the in-tube device with a roller drive of brushes is offered. The drive allows you to use the energy of the oil flow to create the torque of the brush drive. Based on the equations of contact interaction mechanics and the theory of motion of wheeled vehicles, the equation of maximum power of a roller drive is established. The dependence analysis shows a sinusoidal dependence of the change in the power of the roller drive of the rotation of the rotor of the treatment device on the angle of rotation of the roller and linear on the sliding coefficient and speed.

This paper discusses the hardware structure of the human–machine interface of industrial exoskeletons and the corresponding mathematical models for selecting the optimal parameters of the human–machine interface and for developing the control algorithms. A four-stage algorithm for planning the angle of rotation of the operator’s back when performing a load lifting operation using polynomials of the seventh order is proposed. The movement of the human–exoskeleton system with a focus on the hip joint and lumbar spine was simulated. The effect of the parameters of the mathematical model of the human–exoskeleton system, including the operator’s muscular system, on the accuracy of reproducing operator’s movements by the exoskeleton is shown.

In 1891, Professor George H. Brian demonstrated the effect of standing wave precession in an elastic axisymmetric shell rotating about an axis of symmetry. To explain the effect, Brian turned to a mathematical description of elastic vibrations of a thin circular ring. As a result, he obtained a formula connecting the constant angular velocity of rotation of the ring in its plane with the speed of precession relative to it of a standing wave of elastic vibrations. Later, this formula was used to explain the effect of rotation of a standing wave in a hemispherical resonator when the resonator itself is rotated around its axis of symmetry. At the same time, the angular rate of rotation was no longer assumed to be constant, and Brian’s ratio between speeds was tacitly extended to the ratio between the angles of rotation. In fact, this meant the discovery of the effect of inertness of elastic waves. In the present study, an already complete spherical resonator is considered, and the plane rotation of the resonator is replaced by a spatial one. The generalized Brian effect is also spatial.

Background: Soft tissue defects in the hand can resultfrom a varietyof mechanisms including trauma, infection, andmalignant tumors. Propeller flaps have become an appealingoption for coverage of a large range of defects. The aim ofthis study is to determine the effect of dissected length of theperforator and its diameter and the angle of rotation or twistingof the flap on the blood flow in this chosen perforator andthe flap vascularity.Methods: Thirty cases of skin and soft tissue defects ofthe hand and wrist were reconstructed with a perforator-basedpropeller flap from the radial artery in the period from May2016 to November 2019. The age of patients ranged from 15to 60 years. The defects were on the dorsal or palmer aspectof the hand and wrist. We evaluated the viability of theflap,blood velocity and flow of the flap, survived area of theflap according to length and diameter of the chosen perforatorand the angle of rotation of the flap.

In this paper, we develop and validate an osteometry‐based mechanistic approach to calculation of available range of motion (aROM) in presacral intervertebral joints in sagittal bending (SB), lateral bending (LB), and axial rotation (AR). Our basic assumption was the existence of a mechanistic interrelation between the geometry of zygapophysial articular facets and aROM. Trigonometric formulae are developed for aROM calculation, of which the general principle is that the angle of rotation is given by the ratio of the arc length of motion to the radius of this arc. We tested a number of alternative formulae against available in vitro data to identify the most suitable geometric ratios and coefficients for accurate calculation. aROM values calculated with the developed formulae show significant correlation with in vitro data in SB, LB, and AR (Pearson r = 0.900) in the reference mammals (man, sheep, pig, cow). It was found that separate formulae for different zygapophysial facet types (radial (Rf), tangential (Tf), radial with a lock (RfL)) give significantly greater accuracy in aROM calculation than the formulae for the presacral spine as a whole and greater accuracy than the separate formulae for different spine regions (cervical, thoracic, lumbar). The advantage of the facet‐specific formulae over the region‐specific ones shows that the facet type is a more reliable indicator of the spine mobility than the presence or absence of ribs. The greatest gain in calculation accuracy with the facet‐specific formulae is characteristic in AR aROM. The most important theoretical outcome is that the evolutionary differentiation of the zygapophysial facets in mammals, that is the emergence of Tf joints in the rib cage area of the spine, was more likely associated with the development of AR rather than with SB mobility and, hence, with cornering rather than with forward galloping. The AR aROM can be calculated with the formulae common for man, sheep, pig, and cow. However, the SB aROM of the human spine is best calculated with different coefficient values in the formulae than those for studied artiodactyls. The most suitable coefficient values indicate that the zygapophysial articular facets tend to slide past each other to a greater extent in the human thoracolumbar spine rather than in artiodactyls. Due to this, artiodactyls retain relatively greater facet overlap in extremely flexed and extremely extended spine positions, which may be more crucial for their quadrupedal gallop than for human bipedal locomotion. The SB, LB, and AR aROMs are quite separate in respect of the formulae structure in the cervical region (radial facet type). However, throughout the thoracolumbar spine (tangential and radial with lock facets), the formulae for LB and AR are basically similar differing in coefficient values only. This means that, in the thoracolumbar spine, the greater the LB aROM, the greater the AR aROM, and vice versa. The approach developed promises a wide osteological screening of extant and extinct mammals to study the sex, age, geographical variations, and disorders.

To ensure the high-precision location of the navigation system of the rescue equipment delivery vehicle, a method has been developed for forming the decisive function of the correlation-extreme navigation system. It is proposed to use a multichannel correlation-extreme navigation system in which the formation of private decision functions is carried out in a channel corresponding to a given angle of rotation of the reference image according to the brightness and contrast parameter or their combination. To assess the degree of blurring of the current image, a quantitative measure of image quality is determined, its sharpness and contrast are estimated. The conditions under which the maximum coefficient of mutual correlation of the current and reference images are achieved are also determined. During the rotation of the projectile around the longitudinal axis, a mismatch of the current image (CI) with respect to the pre-formed reference image (RI) occurs. The elimination of such a mismatch can be achieved by eliminating distortions caused by blurring of the contours of objects and backgrounds of CI on the surface of sight. To assess the degree of blur, a quantitative measure of image quality is determined. This value is the degree of sharpness. To give an absolute assessment of the image, its sharpness and contrast were evaluated. To achieve the required results, a multi-channel correlation-extreme navigation system is considered as an improved navigation system. The formation of private decision functions takes place in each channel, which corresponds to a given angle of rotation, according to the brightness and contrast parameter. According to the results of studies of statistical modeling using CI on the surface of sight of different quality and background - object composition, the values ​​of the measure of sharpness and the angle of rotation at which it becomes impossible to link are established. In this case, it is necessary to apply the method of restoring the distorted images.

Objective: The aim of this study was to evaluate the cyclic fatigue, torsional behavior and bending resistance of EdgeTaper Platinum [ETP (tip 25, taper 0.06)], Flex Gold [FG (tip 25, taper 0.08)], Pro-T [PT (tip 25, taper 0.08)] and ProTaper Gold [PTG (tip 25, taper 0.08)] systems. Methods: Rotary instruments of ETP, PT, FG, and PTG were used (n=30). Cyclic fatigue tests were performed using an artificial stainless-steel canal with a 60o angle and a 5-mm radius of curvature at body temperature (35°±1°C). The time and number of cycles to fracture (NCF) was recorded. The torsional test evaluated the torque and angle of rotation to failure at 3 mm from the tip according to ISO 3630-1. The fractured surface of each fragment was observed by using scanning electron microscopy (SEM). The bending test evaluated the torque required to bend the instruments at an angular deflection of 60°. Data were analyzed using one-way ANOVA and Tukey tests, and the level of significance was set at 5%. Results: The ETP had highest time until fracture and NCF than all the groups (P

The skipper must be well aware of the maneuverability of his vessel, as well as the capabilities of the ship's controls to perform a particular maneuver. In the» Information «about the parameters of turnability, which is available on the ship, there is no data on the performance of such an important maneuver as «turn in place», which is often used in a confined area of water. Some assumptions have been taken in this article and the solution of the system of equations of the motion of the vessel in relation to the considered maneuver is proposed. The author obtained analytical expressions for calculation of angular speed and the angle of turn of the vessel at the time of the maneuver of «acceleration», the rotation by inertia and active damping rotational inertia. Using the obtained expressions, the calculation of the parameters of the turnover of the project 507 ship was performed. Graphs of the dependence of the angular speed and the angle of rotation of the vessel on the maneuver time are given.

A condition for determining the sufficient reliability of nanoscale surface topography measurements using atomic force microscopy (AFM) for relatively small cantilever inclination angles is proposed. Relationships between the basic geometrical parameters of surface roughness, geometric deviations of the probe, the angles of the cantilever and the inclination of the side faces of the probe, as well as the dimensions of the nonlocal point of the probable contact of its side faces with protrusions of roughness, were established. The requirement to determine the smallness of the ratio of the sizes of a nonlocal point to the distance between neighboring nonlocal points as a necessary condition for the sufficient reliability of surface topographical measurements using AFM, is asserted. Publications in which nanoscale surface topography measurement fails to indicate the roughness of the sample surface and the probe, the angles at the tip of the probe and the inclination of the cantilever, as well as the best resolution (smallest increment) at which the study is carried out, cannot be accepted as reliable, due to the probabilistic character of results thus obtained. Moreover, surface images obtained using AFM without proper justification for the resolution (value of the measurement increment) represent only a qualitative picture, providing an insufficient basis for carrying out computational manipulations. In order to increase the reliability of measurements of nanoscale surface topography measurements using AFM, it is necessary to radically increase probe manufacture precision, as well as to use probes with the smallest possible angle at the apex. In addition, it is necessary to make changes in the design of AFM apparatus. In particular, the microscope stage should be designed to employ automatic rotation. It should provide closeness the probe axis direction to the normal to the average plane of the sample. This “integral” angle of rotation of the microscope stage is easily iteratively determined at the stage of preliminary investigation of the surface topography of the sample. In this case, it will be necessary to geometrically increase the length of the cantilever so that the base extends beyond the limits of the sample.

A significant part in the structure of production costs associated with restoring the current operability of locomotive wheels by processing on the KJ20 machine is amounted by tool costs. The cost of the tool, especially hard-alloy, is constantly increasing. The restoration of the working capacity of hard-alloy cutting elements is carried out by turning them in the tool holder (knife) at a certain angle around the axis of this element. The new technique for the effective use of special shaped mills is based on determining the rational angle of rotation of the cutting elements. A promising direction for the use of cutting elements is also the restoration of the properties of worn elements for their reuse. EDM processes are especially effective in tool production in the manufacture of special tools. The authors developed and proposed a technology for restoring the working capacity of cutting elements that have already worked out their resources. The technology proposed by the authors makes it possible to introduce a system of cost-effective and rational operation for the use of part of worn out, but suitable for restoration, replaceable cutting elements, for their reuse in the repair of the working surface of wheelsets of rail vehicles on KJ20 machines.

The article considers the structure and principle of operation of the weapon stabilization system, which is technically a set of sensors and a computer system connected to the gun drive. The stabilization system ensures the constancy of the angles between the axes of the fixed coordinate system and the axes rigidly connected to the object of stabilization. It is established that the quality of armament stabilization systems is evaluated by the following indicators, both in stabilization mode and in guidance mode: stability, accuracy of weapon stabilization, stabilization quality, guidance speed and nature of distribution on the angle of rotation of the control panel, stabilizer time, continuous operation stabilizer, reliability of operation and the nature and timing of transients when working out the angles of inconsistency. The accuracy of stabilization is the main indicator that characterizes the operation of the fire control system in stabilization mode. External disturbances caused by continuous random oscillations of the hull by mobile light armored vehicles cause deviation of the stabilized armament from the specified direction of guidance. A new piezoelectric sensitive element of the weapon stabilization system and the expediency of using the two-channel method to increase its accuracy are considered. It is established that due to the use of additionally introduced into the design of the sensitive piezoelectric element of the second measurement channel, there is no error in its output signal from the influence of vertical acceleration, from residual non-identical designs of identical piezoelectric plates and masses, from temperature, humidity and external pressure environment (i.e. instrumental errors), which can be significant.

Background In transposition flaps, thicker tissue and higher degrees of rotation are associated with increased pivotal restraint; however, limited experimental data exist quantifying the degree to which these affect flap biomechanics. The use of artificial skin models in conjunction with digital image correlation technology allows for investigation into biomechanical properties of skin flaps. Objective To quantify the effects of tissue thickness and rotational angles on pivotal restraint within transposition flaps using artificial skin models. Methods Ninety degree bilobed and trilobed flaps were used to close defects in artificial skin models of increasing thicknesses. Digital image correlation was used to quantify strain. Quantitative and qualitative differences in strain were assessed in increasing flap thicknesses and between flap designs. Results Increasing flap thickness was associated with decreasing strain. In the bilobed flap, increasing thickness was associated with displacement of the flap pivot point away from the distal flap edge. Comparatively, lower angles of rotation in the trilobed flap were not associated with migration of the flap pivot point. Conclusion Increased pivotal restraint observed in higher degrees of rotation is due to migration of the flap pivot point. This model supports the common practice of decreasing flap angles to compensate for pivotal restraint.

In this paper, we study kinematics of the motion of a two-wheeled caster board. Using the theory of finite rotations, we propose an elementary derivation of the formula connecting the angles of slope of the decks of the caster board with the angles of rotation of the wheels.

Goal. To explore theoretically and experimentally the increase of stability of the pivot connection of the technological and power modules of a new design of the modular machine-tractor unit. Methods. Theoretical studies were carried out using the main provisions of the higher mathematics, theoretical mechanics, theory of automatic control. Experimental studies were carried out in field conditions on a real modular machine-tractor unit. Results. The new construction of the pivot connection of the technological module with the power module (tractor) of the modular machine-tractor unit is developed. To ensure satisfactory maneuverability of technological module when cornering it is equipped with vertical and horizontal joints. Limitation of turning ability of technological module relative to the power one in the horizontal plane through this vertical hinge is provided by a hydraulic cylinder, which over- and under-piston cavities are connected through a restrictor with the coefficient of hydraulic resistance at the level of 1.03×106 N·m·s·rad–1. Based on the equivalent power circuit, a mathematical model was created of movement of the unit, allowing to investigate theoretically its stability. As the energizing impact was taken the turning moment, created by external forces. Output parameters of the model were the angle of rotation of the technological module relative to the energy in the horizontal plane, and the heading angle of the latter. The theoretical study is confirmed experimentally. Conclusions. As a result of mathematical modeling, the change of speed of the unit from 2 to 5 m·s–1 does not lead to a deterioration of the stability of motion, neither technological nor, especially, the power modules. The values of the coefficients of resistance of the introduction of wheel tires of power module do not affect its development of fluctuations of the energizing moment. However, the value of the coefficient of resistance of the introduction of the tire of each wheel of the technological module of modular traction vehicle should be not less than 160 kN·rad–1.

The motion of an artificial Earth satellite in different variants of the solar orientation mode in the low Earth orbit is investigated. The satellite is close in shape to a cylinder with two solar arrays. Nonrotating solar arrays are located symmetrically relative to it along the satellite’s longitudinal axis. In the solar mode normal to the plane of the satellite’s solar arrays invariably directed toward the Sun, the longitudinal axis lies near the plane of the orbit and the absolute angular velocity of the satellite is very small. A gyro system (a set of reaction wheels or gyrodines) is used as the decision-making centers of the satellite’s control system. Two versions of the law controlling the angular momentum of the gyro system are considered. The first variant provides only the attenuation of the disturbed motion of the satellite in the vicinity of the rest position at the required speed. The second variant further limits the growth of the accumulated angular momentum of the gyro system by controlling the angle of rotation of the satellite around the normal to the plane of the solar arrays.

A method of studying the error of a laser dynamic goniometer by a cross-calibration method with the use of a created calculation algorithm is proposed. The algorithm is based on the method of sequential rotations of a polygon relative to a ring laser from the goniometer structure. The results of the application of the specified calculated algorithm to estimate the error of a laser dynamic goniometer are presented. The dominant source of error of this goniometer is defined: the nonuniformity of the angle scale of the ring laser, which is caused by the slope of the scale to the angle of rotation of the spindle of the goniometer. Adjustment corrections are computed and introduced into the calculation algorithm, which made it possible to reduce the systematic error of the goniometer to 0.03″.

The dynamic characteristics of a saw gin as a subsystem with lumped and distributed parameters are considered in the paper. On the basis of investigation of the machine assembly, graphs are drawn that allow establishing the maximum values of the angle of relative rotation and the angle of rotation of the saw cylinder shaft under torsion.

The analysis of various designs (both traditional and alternative) for outboard bearing housing joints with cylinders of steam turbines of medium and high power. Taking into account the identified similarities in the interaction of elements of the considered structures, a generalized kinematic model of the thermal expansion system of a steam turbine is presented. In the assumed model, the thermal expansion system is presented in the form of a multi-link hinged system consisting of one or more “basic” modules. Based on the developed model, the stability conditions (the absence of self-braking on the guiding longitudinal keys) against external influences are studied for the thermal expansion system of a steam turbine. According to the simulation results, it is shown that the magnitude of the turbine cylinder rotation angle change relative to the bearing housing in the junction must be limited. It was revealed that for stability of a system with one outboard bearing housing, it is sufficient that the maximum rotation angle at the junction of the turbine cylinder and the bearing housing does not exceed the maximum rotation angle of the bearing housing relative to the longitudinal keys. For stability of a system with several sequentially moving outboard bearing housings (multi-cylinder turbine), it is necessary that the limiting angle of rotation at all junctions of the turbine cylinders with bearing housings does not exceed the value of the smallest limiting angle of rotation for all bearing housings. The results of the study can be applied in the design of new steam turbines and in the reconstruction of thermal expansion systems for equipment in operation.