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One of the key tasks for space debris removal is to estimate the rotation motion of non-cooperative targets. Many methods based on the Kalman filter have been proposed for motion estimation. However, they often need continuous tracking feature points, which conflicts with actual tracking conditions. Rodriguez formula can estimate rotation motion without continuous tracking feature points, while still facing the problem of poor estimation quality in the case of changing motion state. To overcome these problems, we propose a novel 3D point cloud sequence based algorithm to estimate the rotation motion parameters, which is composed of a phase of constructing double registration matrix and a phase of solving motion equation. With the point cloud sequence, the first phase proposes a double registration matrix to recover the local trajectory of the selected points, and the velocity information can be derived from the local trajectory. While in the second phase, the position information and velocity information of the local trajectory are substituted into the motion equation to solve the rotation axis direction and angular velocity of the non-cooperative target. Experimental results demonstrate the effectiveness and robustness of the proposed algorithm and its potential applicability for reality.

Twisted string actuators (TSAs) convert rotational motion from twisting into linear motion. They are known for high energy efficiency, and large linear strain and stress outputs. Although they have been successfully applied as the moving mechanism for different robot applications, their potential in soft robotics is mainly challenged by two aspects: First, the conventional strings of TSAs are stiff and strong but not compliant. Second, precise control of TSAs predominantly relies on external position or force sensors. Because of these, TSA-driven robots are often rigid and bulky. In this study, we propose the design, modeling, and robotic application of TSAs that are compliant, can produce large strain, and are capable of self-sensing during twisting-induced actuation. The design is realized by replacing conventional stiff strings with compliant, thermally activated, and conductive supercoiled polymer strings. Experiments show that the developed TSAs have normalized stiffness of50 N, strain30%, and position self-sensing capability during twisting. The quasi-static actuation and self-sensing properties are accurately captured by the Preisach hysteresis operators. In particular, both the twisting-induced actuation and thermally induced actuation are considered. Finally, the proposed TSAs are successfully demonstrated in a low-cost three-dimensionally printed compliant robotic gripper.

A 2-degree-of-freedom (2DoF) induction machine realizes rotary, linear, and helical motions, exhibiting the merits of integrated structure and high material utilization. Compared with traditional electric machines, one of the special factors affecting the electromagnetic performances is the helical motion coupling effect (HMCE). This article systematically investigates its production mechanism based on the proposed HMCE model first. Then, a comprehensive comparison of the torque performances between the rotary and linear motion parts is conducted to evaluate the HMCE in two motion parts, and then the results are verified by 3-D finite element model. Besides, resistant torque and force ratios are proposed and calculated to assess the extent of the HMCE. It can be concluded that the torque performances of the rotary motion component are weakened more than those of the linear motion component by the HMCE. Further, two methods to suppress the coupling effect, namely adjustment of linear motion slip ratio and change of linear motion frequency, are discussed. Experimental results have validated the analytical results and effectiveness of the suppression strategies.

Ultrawideband (UWB) radar can achieve ultrahigh-resolution inverse synthetic aperture radar (ISAR) imaging of noncooperative targets by transmitting UWB signals. However, the spatial-variant (SV) high-order migration through range cell (MTRC) and phase errors produced by the UWB radar system have seriously challenged the feasibility of conventional ISAR imaging algorithms. Moreover, maneuvering targets has exacerbated this problem compared with the steady ones. In this article, a UWB ISAR imaging algorithm of maneuvering targets with joint high-order motion compensation and azimuth scaling (JHOMCAS) is proposed. For the azimuth SV linear MTRC and 2-D SV high-order MTRC caused by the maneuvering rotational motion of the targets, the cascaded generalized keystone transform (GKT) is adopted for precise correction. It is worth noting that, when eliminating the SV MTRC by the cascaded GKT, the 2-D SV high-order phase errors induced by the maneuvering rotational motion must be accurately compensated, or MTRC correction will fail. The traditional autofocus methods usually only address the phase errors shared by the total target without due attention to the fine SV property. In response to this problem, this article first develops a joint 2-D SV autofocus and azimuth scaling algorithm (JSVAAS) to achieve the integration of SV high-order phase error compensation and azimuth scaling. A JHOMCAS algorithm is proposed to perform the joint processing of GKT and JSVAAS, ``GKT-JSVAAS-GKT.'' This approach helps accomplish the high-precision UWB ISAR imaging of maneuvering targets, and the well-focused and scaled UWB ISAR images obtained will build a sound foundation for target classification and recognition. Extensive experiments based on both scattering point simulation data and electromagnetic calculation data verify that the proposed algorithm outperforms conventional ISAR imaging approaches in UWB ISAR imaging of maneuvering targets.

The Rotary-Motion Extended Array Synthesis spacecraft is a dual-spin spacecraft with long tethers held in tension by the spin. This paper derives the free-space (not considering orbital effects) dy...

TEMPOL nitroxide radicals are frequently used as a polarizing agent for liquid-state Overhauser dynamic nuclear polarization. To achieve large signal enhancements at high magnetic fields (9.4 T), f...

Представлены особенности изменения параметров движения геосинхронного объекта 10294 SIRIO-1 №1977-080A по результатам оптических наблюдений в обсерваториях в Звенигороде, на пике Терскол и на горе Санглох республики Таджикистан. Пассивный итальянский научный космический аппарат SIRIO-1 представляет интерес тем, что он описывает классическую восьмерку вокруг точки либрации 75 ◦ в.д. без дрейфа по долготе и всегда доступен наблюдениям с наших пунктов. Это дает возможность детально исследовать поступательно-вращательное движение объекта, используя только результаты своих измерений. SIRIO-1 наблюдался нами для проверки аппаратуры и программного обеспечения как тестовый объект с очень устойчивой орбитой. В 2018 г. у этого объекта были обнаружены изменения в движении и в кривых блеска, не свойственные космическому мусору. Были зафиксированы небольшое скачкообразное изменение орбиты между 7 и 11 марта 2018 г. и изменение коэффициента отношения площади миделевого сечения объекта к его массе; кроме того перестал надежно определяться период изменения блеска и появилось характерное изменение блеска на одном и том же участке траектории с периодом, примерно равным звездным суткам. The features of changes in the motion parameters of the geosynchronous object 10294 SIRIO-1 No.1977-080A based on the results of optical observations at the observatories in Zvenigorod, Terskol Peak and Sanglokh Mountain in the Republic of Tajikistan are presented. The passive Italian scientific spacecraft SIRIO-1 is of interest to us because it describes the classic eight around the libration point of 75 ◦ E without longitude drift and is always available to observations from our observation points. This makes it possible to study in detail the translational-rotational motion of the object, using only the results of their measurements. SIRIO-1 was observed by us to test the hardware and software as a test object with a very stable orbit. In 2018, this object was found to have changes in motion and in the light curves that are not characteristic to space debris. A small abrupt change in the orbit between March 7 and 11, 2018, and a change in the area-to-mass ratio of the object were recorded. In addition, the period of change in the brightness was no longer reliably determined, and a characteristic change in the brightness appeared on the same part of the trajectory with a period approximately equal to the sidereal day.

This study intended to help practitioners selecting the appropriate motion according to their level of expertise for glide path and complete root canal preparation of curved canals in terms of instrument fracture and preparation time. A total of 160 curved root canals (angle >30°, radius

Comparison of the dielectric relaxation (DR) behaviors of two polar rod-like low-mass molecules (LMs), cyanobiphenyl (CB) and 5-phenyl-2,3′-bipyridine (PBP), in antiplasticized polycarbonate (PC) revealed that rotations around the short and long axes of the LMs appeared from 60 to 125 °C (β region) and from −150 to −50 °C (γ region), respectively. The cooperativity between the local dynamics in PC, measured by dynamic mechanical analysis, and the rotation of the LMs around the short axis was examined based on the relaxation times and activation energies for the LMs (CB and PBP) and PC. The dynamic cooperativity involved the antiplasticization of PC. In contrast, the rotation of the LM (PBP) around its long axis was independent of the local motion in PC, resulting in no contribution to the antiplasticization phenomenon. Adding rod-like low-mass molecules (LMs) increases the elastic modulus of polycarbonate (PC). The anisotropy of the rotational dynamics of rod-like LMs in PC was investigated by dielectric relaxation and dynamic mechanical analysis. Two rotations of the LM around the short and long axes were separately observed at 80 °C and −100 °C, respectively. The rotation of the LM around the short axis was cooperative with the local dynamics of PC and. In contrast, the rotational motion around the long axis was independent of PC motions.

In applications of human-robot physical interaction, it is important to guarantee high accuracy not only in terms of the position of the end-effector, but also in terms of its orientation. While translational movements are easily understandable for a human, rotational ones do not have an immediate interpretation. This does not allow the operator to achieve an adequate positioning accuracy when a target orientation is set. In this work, a suitable strategy that facilitates the human in accomplishing rotational motion is proposed through the formulation of rotational virtual fixtures. This is obtained thanks to a clever description of the orientation that allows to draw an equivalence between the formulation of translational virtual fixtures and their rotational counterparts. To further improve the human comprehension of the best motion direction in the rotational world, a variable admittance control is also designed. We finally propose to jointly exploit these techniques to achieve the best possible performance in terms of positioning accuracy. The performance are evaluated by means of rotational point to point cooperative motions involving several subjects and an ABB IRB-140 robot.

The friction and wear characteristics of stainless steel diffused with Si-based ceramics were investigated using pin-and-disc configuration under reciprocation motion, rotational motion, and simultaneous motion. The pin material was diffused by the combination of 60% Ti2O3, 30% Al2O3, and 10% Si2O3. Experiments have been carried out both in diffused and non-diffused conditions. Both the friction coefficient and wear rate have been possible to reduce by diffused pin material. The effects of both friction coefficient and wear rate have been studied on ceramics composites at different pin-and-disc motions. Experiments were conducted underpin motions of 0.15–0.25 m/s, disc motions of 0.5–0.6 m/s, and normal loads of 2.5–3.5 N. A relation was found among friction, wear and surface hardness of the composite. The friction coefficient and wear resistance were improved of stainless steel diffused with ceramics. Scanning electron microscopic analysis was performed to observe the morphology of ceramic and pin material.

Vertical precision positioning is distinguished from positioning in horizontal plane due to the presence of gravitational forces that work differently in “lifting” and “lowering” modes. Vertical positioners also need a “locking mechanism” to avoid the unintentional lowering of the platform. We present a vertical precision positioner that works according to the “stick–slip” phenomenon. Using an adjustable offset coupling, the linear motion of a piezoelectric actuator is converted to the rotational motion of a low friction lead screw which results in the vertical motion of the screw. A microcontroller can adjust the grip, and hence the friction, between the coupling and the lead screw to ensure the uniformity of motion in lifting and lowering modes. The dynamic model of the mechanism is extracted, and simulations are performed to discover how the peak voltage and frequency of the saw-tooth signal affect the stick–slip motion of the mechanism. Additionally, equations are verified by comparing simulation results and experiments. They can be used in the control system design in future works.

Optical trap, a circularly polarized laser beam can levitate and control the rotation of microspheres in liquid medium with high stiffness. Trapping force performs as confinement while the trapped particle can be analog to a liquid floated gyroscope with three degree-of-freedom. In this work, we analyzed the feasibility of applying optically levitated rotor in the system. We presented the dynamic analysis and simulation of an ellipsoid micron particle. The precession motion and nutation motion of a rotating ellipsoid probe particle in optical tweezers were performed. We also analyzed the attitude changes of an optically levitated ellipsoid when there was variation of the external torque caused by deviation of the incident light that was provided. Furthermore, the trail path of the rotational axis vertex and the stabilization process of a particle of different ellipticities were simulated. We compared the movement tendencies of particles of different shapes and analyzed the selection criteria of ellipsoid rotor. These analytical formulae and simulation results are applicable to the analysis of the rotational motion of particles in optical tweezers, especially to the future research of the gyroscope effect.

This article considers the kinematic study of a planetary train for converting rotary motion to recurrent-rotary ensured by means of elliptical gears. Centroids of noncircular gears with inner teeth engaged with elliptical gears are drawn for various interaxial distances. The planetary train with a noncircular gear is exposed to kinematic analysis, which allows finding the functions of the position, velocity analogs, and accelerations of the output shaft of the mechanism.

We study the integrability of a model of elastic satellite whose centre of mass moves in a circular Keplerian orbit around a gravity centre. The satellite is modelled by two point masses connected by an extensible massless spring that obeys Hooke’s law. It is assumed that the distance between point masses is much smaller than the radius of the orbit, so the orbital motion of the satellite is not perturbed by its rotational motion. The gravity potential of the satellite is expanded into a series with respect to its size up to quadratic terms which describe the gravity gradient torque acting on the satellite. Two cases are considered with Hooke’s centre localised in the centre of mass of the dumbbell and at an arbitrary point along a line connecting both masses. It is shown that the first case appears to be integrable and super-integrable for selected values of the parameter of the system. In the second case, model depends effectively only on one parameter and is non-integrable. In the proof, differential Galois integrability obstructions are used. For the considered sysem, these obstructions are deduced thanks to the recently developed symplectic Kovacic’s algorithm in dimension 4. According to our knowledge, this is the first application of this tool to a physical model.

Achieving sophisticated juxtaposition of geared molecular rotors with negligible energy-requirements in solids enables fast yet controllable and correlated rotary motion to construct switches and motors. Our endeavor was to realize multiple rotors operating in a MOF architecture capable of supporting fast motional regimes, even at extremely cold temperatures. Two distinct ligands, 4,4′-bipyridine (bipy) and bicyclo[1.1.1]pentanedicarboxylate (BCP), coordinated to Zn clusters fabricated a pillar-and-layer 3D array of orthogonal rotors. Variable temperature XRD, 2H solid-echo, and 1H T1 relaxation NMR, collected down to a temperature of 2 K revealed the hyperfast mobility of BCP and an unprecedented cascade mechanism modulated by distinct energy barriers starting from values as low as 100 J mol–1 (24 cal mol–1), a real benchmark for complex arrays of rotors. These rotors explored multiple configurations of conrotary and disrotary relationships, switched on and off by thermal energy, a scenario supported by DFT modeling. Furthermore, the collective bipy-ring rotation was concerted with the framework, which underwent controllable swinging between two arrangements in a dynamical structure. A second way to manipulate rotors by external stimuli was the use of CO2, which diffused through the open pores, dramatically changing the global rotation mechanism. Collectively, the intriguing gymnastics of multiple rotors, devised cooperatively and integrated into the same framework, gave the opportunity to engineer hypermobile rotors (107 Hz at 4 K) in machine-like double ligand MOF crystals.

In this paper, the researchers have described the development, design and characterization of a Switched Reluctance (SR) actuator, with a rotary motion, having a single-excitation activity. This SR actuator design consisted of a stator and rotor core and was based on the simplest SR actuator model design, with a Stator-to-Rotor pole ratio (S: R) of 6:4. In this design, the winding was coiled at Phase A, which enabled the single step motion characterization based on a single excitation. This SR actuator prototype showed a compact size, with a 36 mm stack length and a 60 mm outer diameter. This feature allowed small machine applications like the precision robotic machining, but required a low production cost, as it lacked a permanent magnet. On the other hand, the SR actuator consisted of highly non-linear characteristics and showed uncontrolled motion behavior. While achieving a very precise motion, it is important to suppress the non-linear characteristics of an actuator. Hence, the researchers designed the linearizer unit based on its characterization at Position 0°, which was related to the excitation current and the rotary angles for the various initial rotor positions. This initial position was chosen as it reflected the characteristics which indicated the self-starting characteristics. Thereafter, the researchers experimentally investigated the appropriate driving signal for this SR actuator as the normal step input signal showed a lower precision motion because of the discharging effect-related issues.

We present a hydrostatic teleoperator that provides physicians remote access inside the MRI bore and enables real-time MRI guided interventions such as liver biopsies. The device consists of a custom six-axis arm and a needle insertion end effector. The manipulator is passive and backdrivable with a near one-to-one mapping of motions and forces between the input and output. The six-axis arm translates and orients the needle during insertion and passively reflects respiratory motion while maintaining contact with the skin surface. Arm joints employ novel rotary rolling-diaphragms that provide stiff and low-friction rotational motion without the need for cables, belts, or gear mechanisms found in other solutions. We perform experiments to characterize the device’s force and position tracking and demonstrate its functionality with path following tasks. Our results find a system roll-off frequency at 20Hz and that teleoperation tasks are performed comparably to holding the output directly. We motivate the need for force transparency in MRI guided biopsies with a user study in which five radiologists perform phantom membrane puncture biopsies using the needle insertion mechanism. The results indicate a 50% reduction in scans and a 14.5% decrease in membrane overshoot when force feedback is present.

The diffusion of single micron-sized Brownian square platelets on cylindrical surfaces with different radii of curvature in the presence of depletion attractions was studied experimentally by video microscopy. The translational motion of a square is found to be diffusive along the axial direction of the cylinder but sub-diffusive along the circumferential direction due to the confinement induced by gravity, while its rotational motion displays a sub-diffusive behavior due to the confinement induced by orientation-dependent depletion attractions. Such a confinement effect decreases as the radius of curvature increases and can be tuned both through surface curvatures and/or depletion attractions. Our work provides a new way to control the translational and rotational dynamics of anisotropic particles through curved surfaces in the presence of depletion attractions.

Magnetic resonance imaging (MRI)-powered magnetic robotics aims to convert clinical MR scanners into a remote robotic manipulation platform to provide an alternative approach for interventional MRI procedures. The presence of the main magnetic field $(\mathbf {B_0})$ inside of MRI systems imposes magnetic constraints. Because of this static and strong magnetic field, many magnetic actuation techniques to orient or rotate magnetic objects are not feasible under MRI. Therefore, the robot design and actuation methods should consider these constraints for the intended medical applications. A free-to-rotate robot design could be utilized under MRI for providing rotational motion with magnetic pulling. However, the coupled translation with rotation induces difficulty in control of these robots, especially for camera pointing towards capsule endoscopy. In this study, we present a wireless magnetic robot that exploits a surface contact to create a rotation around a contact point with minimal translation. The proposed robot is integrated with a camera and an on-board battery for endoscopy purposes. The robot's tuned density also allows three-dimensional (3D) navigation to visually scan the workspace. We also demonstrate the open- and closed-loop actuation and control performance to explore the range of pitch angles accomplishable and closed-loop feedback control accuracy by using visual feedback. The closed-loop control experiments have shown 0.19 $^\circ$ of steady-state error with 1.9 seconds rise time and 20% overshoot. Thanks to the surface contact during orientation control, the worst-case undesired translation is found to be 6.7 mm. Such robot provides the first steps towards active capsule endoscopy actuated by MRI devices for combining physiological images from an MRI device and the auxiliary visual camera images via the capsule robot to diagnose certain diseases in the gastrointestinal (GI) tract.

This paper mainly addresses the formation control problem for a group of tail-sitters in transition flight between forward and vertical flight. A robust formation control method is proposed to achieve the aggressive time-varying formation subject to nonlinear dynamics and uncertainties. For each tail-sitter, the proposed control method results in a composite controller that includes a trajectory tracking controller and an attitude controller to achieve the translational and rotational motion control, respectively. It is proven that tracking errors of the proposed global closed-loop system can converge to a given neighborhood around the origin in a finite time. Finally, the simulation studies for multiple tail-sitters to accomplish the time-varying formation in transition flight are presented to show the effectiveness of the proposed control strategy.

Contrast maximization is an event camera application that can estimate angular velocity, depth, and optical-flow using a subset of events observed in a temporal window. In the estimation of rotational motion, we can compute the angular position by integrating the angular velocity. However, the accumulation of drift error degrades the accuracy of motion estimation. If the contrast maximization framework utilizes events measured before the temporal window, the performance of the framework will be improved, including the alleviation of drift error in motion estimation. In this work, we utilize the globally aligned event data and propose the rotational position and velocity estimation method using an event camera only. The proposed algorithm not only maximizes contrast of an image of events in a single temporal window but also maximizes the contrast image of events observed over time. Our algorithm works in real-time by reducing additional computations of the existing contrast maximization. We confirm the real-time operation with a single-core CPU on a laptop and show that the maximum error is within 3 degrees on public data sets and acquired real-world data sets. To contribute to the community, we provide the source code and the real-world data sets to the public.

The steady rotational motion of a spherical particle with frictionally slip surface about a diameter in a quiescent unbounded fluid is studied analytically for a small but finite Reynolds number R e . The Navier–Stokes equation governing the axisymmetric fluid flow around the particle is solved by using a regular perturbation method. The expansion expression for the retarding torque exerted by the fluid on the particle good to O ( R e 3 ) is obtained as a function of the scaled slip coefficient of the particle in closed form. This perturbation analysis shows that the perturbed fluid velocity field is of O ( R e ) , the same as that for the translation of the particle, but the first correction to the hydrodynamic torque occurs at O ( R e 2 ) , much weaker than that to the hydrodynamic drag force acting on a translating particle which is still of O ( R e ) . The hydrodynamic torque is found to be a monotonic increasing function of the Reynolds number and a monotonic decreasing function of the scaled slip coefficient, similar to the effect of fluid inertia on the hydrodynamic force on a slip particle undergoing translation. The inertial effect on the hydrodynamic torque, which can be a sensitive function of the slip coefficient and vanishes as the particle surface is fully slip, is generally negligible for the case of R e 3 but significant as R e is greater than about 10.

A nonlinear system of differential equations describing the rotational motion of a rigid body under the action of torque of potential and circular-gyroscopic forces is considered. For this torque, the system of differential equations has three classical first integrals: the energy integral, the area integral, and the geometric integral. For the analogue of the Lagrange case, when two moments of inertia coincide and the potential depends on one angle, an additional first integral is found and integration in quadratures is performed. A number of examples is considered where parametric families of exact solutions are considered. In these examples, polynomial or analytical functions were used as a potential. In particular, we construct families of periodic and almost periodic motions, as well as families of asymptotically uniaxial rotations. We also identified movements that have limit values of opposite signs for unlimited increase and decrease of time.

Numerical simulation of pulp flow in rotating and non-rotating grooves is carried out to investigate the effect of pulp rheological properties and groove geometry on the rotational motion of the pulp flow. The eucalyptus pulp suspension is considered as a working fluid in the present study whose apparent viscosity correlation is available from the experimental measurements reported in the literature. The simulations are carried out with OpenFoam for different values of pulp material, fiber concentrations, and groove cross-section. Helicity is introduced to measure the turnover rate of pulp flow in the groove due to the importance of such motion on the final properties of the pulp flow. A measurement of helicity magnitude and its distribution along the groove revealed that a change in the pulp material would significantly affect the flow structures within the groove. Further investigation on the effects of fiber concentration, c, showed that this parameter does not have a significant effect on the averaged helicity magnitude for c = 2.0 and 2.5, whereas the helicity distribution over the groove cross-section changes clearly for c = 1.5. The results showed that the helicity level is negligible for almost half of the cavity cross-section in the non-rotating groove simulations, which can be considered as a shortcoming of the original geometry of the groove. Therefore, a smaller cross-section for the groove is considered through which an enhancement in the helicity magnitude is observed.

The motion of a rigid molecule in a computer model can be described as the sum of the displacement of the center of mass of the molecule and the rotation of the molecule around an axis passing through this center. The interaction of a molecule with its environment leads to a correlation between these movements. Earlier in [1], we studied the distributions of angles between the directions of the displacement vectors and the axes of rotation of water molecules, as well as between them and the internal vectors of these molecules. This paper describes the correlation of the magnitudes of these displacements, that is, the lengths of the displacement vectors and angles of accompanying rotations. The correlation coefficients of these characteristics are calculated for intervals of different durations at different temperatures and pressures, and the character times of preservation of these correlations are determined. We believe that the times found by us represent the lifetimes of the local environments of molecules. For water molecules, a change in the local environment is accompanied by a change in the structure of the nearest section of the network of hydrogen bonds, and therefore the lifetimes of local environments are close to the lifetimes of these bonds.

A zirconium metal-organic framework with a difluorophenylene rotator bearing a permanent electric dipole of ∼3.2 D was synthesized, and its rotational motion was analyzed by temperature- and frequency-dependent broadband dielectric spectroscopy. While solid-state NMR confirms fast rotation qualitatively, the dissipation factors measured between 113 and 153 K suggested an activation energy Ea = 2.6 kcal/mol, but deviations from a single Debye relaxation suggested a dynamic process that cannot be accounted for by a well-defined potential with a single activation barrier. The dynamic heterogeneity of the dipolar rotor was confirmed by analysis in terms of a Cole-Cole relaxation, which suggested a mean barrier of ∼1.9 kcal/mol, with a heterogeneity that decreases as temperature increases. Based on the single-crystal structure, we propose that the kinetic heterogeneity results from a temperature-dependent potential where rotation motion is mediated by the escape of the rotator from an energy well created by a double Ph-H···F-Ph hydrogen bond.

This paper continues the authors’ previous work and presents a coplanar averaged ellipsoid–ellipsoid model of synchronous binary asteroid system (BAS) plus thermal and tidal effects. Using this model, we analyse the break-up mechanism of the synchronous BAS. Different from the classical spin-orbit coupling model that neglects the rotational motion’s influence on the orbital motion, our model considers simultaneously the orbital motion and the rotational motions. Our findings are as follows: (1) Stable region of the secondary’s synchronous state is mainly up to the secondary’s shape. The primary’s shape has little influence on it. (2) The stable region shrinks continuously with the increasing value of the secondary’s shape parameter aB/bB. Beyond the value of $a_B/b_B=\sqrt{2}$, the planar stable region for the secondary’s synchronous rotation is small but not zero. (3) Considering the BYORP torque, our model shows agreement with the 1-degree-of-freedom adiabatic invariance theory in the outwards migration process, but an obvious difference in the inwards migration process. In particular, our studies show that the so-called ‘long-term’ stable equilibrium between the BYORP torque and the tidal torque is never a real equilibrium state, although the BAS can be captured in this state for quite a long time. (4) In case that the primary’s angular velocity gradually reduces due to the YORP effect, the secondary’s synchronous state may be broken when the primary’s rotational motion crosses some major spin-orbit resonances.

Purpose To enable SWI that is robust to severe head movement. Methods Prospective motion correction using a markerless optical tracker was applied to all pulse sequences. Three-dimensional gradient-echo and 3D EPI were used as reference sequences, but were expected to be sensitive to motion-induced B0 changes, as the long TE required for SWI allows phase discrepancies to accumulate between shots. Therefore, 2D interleaved snapshot EPI was investigated for motion-robust SWI and compared with conventional 2D EPI. Repeated signal averages were retrospectively corrected for motion. The sequences were evaluated at 3 T through controlled motion experiments involving two cooperative volunteers and SWI of a tumor patient. Results The performed continuous head motion was in the range of 5-8° rotations. The image quality of the 3D sequences and conventional 2D EPI was poor unless the rotational motion axis was parallel to B0 . Interleaved snapshot EPI had minimal intraslice phase discrepancies due to its small temporal footprint. Phase inconsistency between signal averages was well tolerated due to the high-pass filter effect of the SWI processing. Interleaved snapshot EPI with prospective and retrospective motion correction demonstrated similar image quality, regardless of whether motion was present. Lesion depiction was equal to 3D EPI with matching resolution. Conclusion Susceptibility-based imaging can be severely corrupted by head movement despite accurate prospective motion correction. Interleaved snapshot EPI is a superior alternative for patients who are prone to move and offers SWI which is insensitive to motion when combined with prospective and retrospective motion correction.

Using a space robot to capture a non-cooperative spacecraft with high-speed rotation is significantly challenging since any collision generated during capturing will have great impact on both. To reduce the risk in capturing operations, it is crucial to slow down the rotation velocity of the target before capturing. Hence, this paper studies a collision control strategy for using a robotic arm to detumble a non-cooperative spacecraft. The goal of this strategy is to maintain contact between the robot and the target and to apply continuous detumbling force on the target to slow down its rotational motion. To achieve that, first the mechanism analysis of the two balls for a central collision scenario is performed. Then an overdamping control method is proposed to avoid the separation of the balls after the central collision based on the overdamping property of the mass-spring-damper system, the effectiveness of which is validated theoretically. Finally, to use this overdamping control method in the detumbling missions of space robots, a position-based overdamping control strategy is introduced. In this strategy, the relative dynamic behavior between the robotic arm tip and the contact surface of the target during detumbling is approximated to that of a mass-spring-damper system. Owing to the proposed overdamping control method, the contact between the robot and the target can be maintained, and the space robot can apply continuous control torque to slow down the rotational velocity of the target. Numerical simulations are performed to demonstrate the validity of the proposed control strategy.

Problem. During the reconstruction of the circumstances of road traffic accidents with vehicles overturning, difficulties arise with determining the parameters of vehicles in the process of their overturning. This is due to the fact that the recommended calculation methods are often simplified. The main focus of such techniques is to determine the minimum speed of vehicles, which leads to their overturning. In fact, the speed of vehicles before overturning can be significantly higher. Goal. This paper is dedicated to developing mathematical model of overturning vehicles that makes possible to determine not only the conditions for overturning vehicles, but also other parameters of the vehicle movement in the process of overturning. Methodology. The overturning of the vehicle occurs as a result of the action of inertial forces after collision with an immovable side obstacle. In this case, the moment from the force of gravity of the vehicle keeps it from overturning. In the process of overturning the vehicle, the moment from the force of gravity decreases due to the decrease in the arm of the force of gravity. To compile a mathematical model, the basic equation of dynamics during rotational motion was used. The mathematical model of a vehicle overturning is written in the form of a nonlinear homogeneous second order differential equation. An analytical solution of this equation is obtained. Results. Developed mathematical model makes possible to determine not only the conditions for overturning vehicles, but also other parameters of the vehicle movement from the moment the center of mass begins to rise to the moment of its maximum rise in the process of overturning. For a particular case, when the critical speed of a vehicle during its overturning is determined, the developed mathematical model fully corresponds to the mathematical model based on the law of conservation of energy. For a specific vehicle, numerical results were obtained that fully correspond to the physics of the overturning process.

Purpose How to model blind image deblurring that arises when a camera undergoes ego-motion while observing a static and close scene. In particular, this paper aims to detail how the blurry image can be restored under a sequence of the linear model of the point spread function (PSF) that are derived from the 6-degree of freedom (DOF) camera’s accurate path during the long exposure time. Design/methodology/approach There are two existing techniques, namely, an estimation of the PSF and a blind image deconvolution. Based on online and short-period inertial measurement unit (IMU) self-calibration, this motion path has discretized a sequence of the uniform speed of 3-DOF rectilinear motion, which unites with a 3-DOF rotational motion to form a discrete 6-DOF camera’s path. These PSFs are evaluated through the discrete path, then combine with a blurry image to restoration through deconvolution. Findings This paper describes to build a hardware attachment, which is composed of a consumer camera, an inexpensive IMU and a 3-DOF motion mechanism to the best of the knowledge, together with experimental results demonstrating its overall effectiveness. Originality/value First, the paper proposes that a high-precision 6-DOF motion platform periodically adjusts the speed of a three-axis rotational motion and a three-axis rectilinear motion in a short time to compensate the bias of the gyroscope and the accelerometer. Second, this paper establishes a model of 6-DOF motion and emphasizes on rotational motion, translational motion and scene depth motion. Third, this paper addresses a novel model of the discrete path that the motion during long exposure time is discretized at a uniform speed, then to estimate a sequence of PSFs.

Reciprocating rotary motion of the impeller in a mixer is produced by a planetary mechanism with elliptical gears. The forces in the planetary mechanism are analyzed. Equations of kinetostatic equilibrium are derived and solved for each component of the mechanism. The angular position of the mechanism’s input shaft affects the reaction in the kinematic pairs and the balancing torque. This influence is described by mathematical formulas. The results obtained here may be used in the synthesis and analysis of machines with a planetary mechanism of the type considered.

This paper presents a piezoelectric energy harvester with rotational magnetic excitation. Through the rotation of the rotating body, the intermittent magnetic force between the driving magnet and the tip magnetic mass drives the piezoelectric element to vibrate nonlinearly to generate electrical energy. The working principle and vibration model of the proposed energy harvester are studied theoretically and experimentally. With two driving magnets, 5-g tip magnetic mass, and 8-mm radial excitation distances, the piezoelectric energy harvester captures energy efficiently. The results demonstrate that the piezoelectric energy harvester produces three resonance frequencies of 5 Hz, 8 Hz, and 10 Hz. When the rotation frequency is 8 Hz, the maximum open-circuit voltages of the primary and auxiliary piezoelectric beam is 63.24 V and 30.38 V, respectively. The primary and auxiliary piezoelectric beam gets the maximum average power with external resistance is 125 KΩ and 75 KΩ, respectively. The maximum average power of the primary and auxiliary piezoelectric beam is 12.24 mW and 3.92 mW, respectively. At the maximum power of the primary and auxiliary piezoelectric beam, the voltage across the resistance is 39.12 V and 17.12 V, respectively.

A nonstationary two-body problem is considered such that one of the bodies has a spherically symmetric density distribution and is central, while the other one is a satellite with axisymmetric dynamical structure, shape, and variable oblateness. Newton’s interaction force is characterized by an approximate expression of the force function up to the second harmonic. The masses of the central body and the satellite vary isotropically at different rates and do not occur reactive forces and additional rotational moments. The nonstationary axisymmetric body have an equatorial plane of symmetry. Thus, it has three mutually perpendicular planes of symmetry. The axes of its intrinsic coordinate system coincide with the principal axes of inertia and they are directed along the intersection lines of these three mutually perpendicular planes. This position remains unchangeable during the evolution. Equations of motion of the satellite in a relative system of coordinates are considered. The translational- rotational motion of the nonstationary axisymmetric body in the gravitational field of the nonstationary ball is studied by perturbation theory methods. The equations of secular perturbations reduces to the fourth order system with one first integral. This first integral is considered and three-dimensional graphs of this first integral are plotted using the Wolfram Mathematica system.

Particle methods for high-viscous free-surface flows are of great use to capture flow behaviors which are intermediate between solid and liquid. In general, it is important for numerical methods to satisfy the fundamental laws of physics such as the conservation laws of mass and momentum and the thermodynamic laws. Especially, the angular momentum conservation is necessary to calculate rotational motion of high-viscous objects. However, most of the particle methods do not satisfy the physical laws in their spatially discretized system. The angular momentum conservation law is broken mostly because of the viscosity models, which may result in physically strange behavior when high-viscous free-surface flow is calculated. In this study, a physically consistent particle method for high-viscous free-surface flows is developed. The present method was verified, and its performance was shown with calculating flow in a rotating circular pipe, high-viscous Taylor–Couette flow, and offset collision of a high-viscous object.

In this research work we investigate the performance of golf ball with 256 circular arc dimples on golf ball. The turbulence characteristics and flow pattern over golf with various velocities investigated by computational fluid dynamics in suitable turbulence model, in addition that the distance covered by a ball and rotational motion characteristics also investigated with same turbulence model

In this paper, two novel methods to mitigate lever arm effect in Redundant Inertial Measurement Units (RIMUs) are proposed with different approaches. With the presence of a lever arm for each sensing axis, the unexpected accelerations such as Euler and centrifugal accelerations are added to the measurements through rotational motion, resulting in an estimation error of linear acceleration. Therefore, it was previously considered as the best option to minimize the length of the lever arm and compensate the lever arm effect from the accelerometer measurements. However, this approach cannot completely remove the estimation error as the compensated value is based on the estimated angular rates, where the magnitude of the error becomes more apparent with a RIMU composed of low-grade gyroscopes that shows a higher noise level. In order to solve this problem, we propose two methods that can mitigate estimation error using the specific arrangement of the lever arm vectors and the concentrated likelihood method-based nonlinear least squares (NLS). By the proposed methods, the accuracy in compensating the lever arm effect can be increased by placing the lever arm vectors symmetrically or using the information from accelerometers when estimating angular rates. Besides, the suggested methods each have their own advantages in computational efficiency and overall navigation performance, compared to previous method. The effectiveness of the proposed methods is verified through simulations including misalignments of each redundant sensor.

Accurate and robust calibration is crucial to a multisensor fusion-based system. The calibration of heterogeneous sensors is particularly challenging because of the huge difference of the captured sensor data. On the other hand, many calibration approaches ignore temporal calibration that is in fact as important as spatial calibration. In this article, we focus on the temporal calibration of heterogeneous sensors, and the corresponding extrinsic rotation is also derived. Most existing methods are specialized for a certain sensor combination, such as an inertial measurement unit (IMU) camera or a camera-Lidar system. However, heterogeneous multisensor fusion is a tendency in the robotics area, so a unified calibration method is desired. To this end, we leverage the 3-D rotational motion feature for calibration, and auxiliary calibration boards are not needed since multiple odometry methods are available to capture 3-D sensor motion. Using a high-frequency IMU as the calibration reference, an IMU-centric scheme is designed to achieve a unified framework that adapts to various target sensors that can independently estimate 3-D rotational motion. By combining independent IMU-centric calibration pairs, an arbitrary pair of sensors can also be calibrated using the same reference IMU. Due to a novel 3-D motion correlation quantification and analysis mechanism, the temporal offset can be first estimated in real time. Given temporally aligned sensor motion, the extrinsic rotation can be derived in closed-form in the same 3-D motion correlation mechanism. Experimental results of certain sensor combinations show the accuracy and robustness of the proposed method through comparison with state-of-the-art calibration approaches, and the calibration result of a heterogeneous multisensor set demonstrates the scalability and versatility of our method.

Previous gyro-free inertial measurement units (GF-IMU) usually suffered from installation errors induced by mutual placements and mutual sensing directions of accelerometers, and underlying mechanism for eliminating the effect of position change in the center of gravity (PCGC) was not presented clearly. This paper reports a GF-IMU compensating for the effect of PCGC and installation errors by using two parallel mounted accelerometers as a group in designing accelerometer array configuration. The underlying kinematics is first developed and indicates that subtraction of accelerations within a group can remove the effect of PCGC. Nine acceleration subtractions from nine independent groups with irrelevant sensing directions and arbitrary installation distances can determine the square of angular velocity and angular acceleration directly, which does not induce installation errors. Then three configurations fitting different requirements are proposed based on three accelerometer placement rules. The motion quantities at the center of gravity (GC) can also be obtained if mutual installation distance among different groups is known. The validity and performance of schemes are finally verified by SimMechanics simulations. The rotational motion measurement scheme proposed in this paper does not need to know mutual placement information of accelerometers as well as the GC position, which greatly simplifies its installation, and make it possible to develop a convenient product for the rotational motion measurement with only accelerometers.

The separation behavior of two bodies was experimentally investigated in a shock tunnel. Simple-shaped bodies, including a cylinder, cube, and sphere, with a size of 3 or 5 mm were used as the test models. The two contact models with a plane-exposed configuration were mounted using a thin wire, and the separation behavior was observed and analyzed using the shadowgraph technique. The surface roughness effect on the separation of two spheres was also considered. Particularly, attention was given to the lateral velocity. It was found that the spheres had a constant final lateral velocity after the shock interaction, whereas the velocities of the cylinders and cubes were determined by the rotational motion of the body. Based on the experimental data, a reentry trajectory analysis was conducted using Monte Carlo simulation. The results showed large ground footprint and downrange differences depending on the characteristics of the body, implying the importance of separation behavior for a reentry analysis.

Purpose Magnetic resonance imaging (MRI)-guided transperineal prostate biopsy has been practiced since the early 2000s. The technique often suffers from targeting error due to deviation of the needle as a result of physical interaction between the needle and inhomogeneous tissues. Existing needle guide devices, such as a grid template, do not allow choosing an alternative insertion path to mitigate the deviation because of their limited degree-of-freedom (DoF). This study evaluates how an angulated needle insertion path can reduce needle deviation and improve needle placement accuracy. Methods We extended a robotic needle-guidance device (Smart Template) for in-bore MRI-guided transperineal prostate biopsy. The new Smart Template has a 4-DoF needle-guiding mechanism allowing a translational range of motion of 65 and 58 mm along the vertical and horizontal axis, and a needle rotational motion around the vertical and horizontal axis ± 30 ∘ and a vertical rotational range of - 30 ∘ , + 10 ∘ , respectively. We defined a path planning strategy, which chooses between straight and angulated insertion paths depending on the anatomical structures on the potential insertion path. We performed (a) a set of experiments to evaluate the device positioning accuracy outside the MR-bore, and (b) an in vivo experiment to evaluate the improvement of targeting accuracy combining straight and angulated insertions in animal models (swine, n = 3 ). Results We analyzed 46 in vivo insertions using either straight or angulated insertions paths. The experiment showed that the proposed strategy of selecting straight or angulated insertions based on the subject's anatomy outperformed the conventional approach of just straight insertions in terms of targeting accuracy (2.4 mm [1.3-3.7] vs 3.9 mm [2.4-5.0] {Median IQR } ); p = 0.041 after the bias correction). Conclusion The in vivo experiment successfully demonstrated that an angulated needle insertion path could improve needle placement accuracy with a path planning strategy that takes account of the subject-specific anatomical structures.

Driveshafts are the driveline elements that transfers torque and rotational motion which is received from the engine to the rear axles. In order to meet the high torque handling requirements, driveshaft components are usually made up of steel. Weight reduction in steel parts can often be limited due to the boundary conditions of geometries. For this reason, applications developed with low density parts such as aluminum gain importance. Within the scope of this study, engineering calculations for aluminum cardan shaft for pick-up style light commercial vehicle applications were performed and the calculations were verified with finite element analysis. As a result of the corrections, deviation of 1% for strength calculations and 8% for natural frequency calculations was calculated between the two methods, and it was determined that the deviation values were acceptable. The yield limits and safety coefficients of the aluminum material used were calculated for the unit parts with the results obtained with finite elements. It has been determined that the safety coefficients obtained are suitable for driveshafts., Kardan milleri, motordan aldığı torku ve dönme hareketini arka akslara ileten bir aktarma organı elemanıdır. Yüksek tork taşıma gerekliliklerini karşılamak amacıyla, hafif ticari araç uygulamalarında kullanılan kardan milleri çelik malzeme kullanılarak üretilmektedir. Çelik malzeme kullanılarak üretilmiş kardan mili ve parçalarında ağırlık azaltma, geometrilerin sınır koşulları nedeniyle çoğu zaman kısıtlı olabilir. Bu nedenle alüminyum gibi düşük yoğunluklu malzemeler kullanılarak geliştirilen uygulamalar önem kazanmaktadır. Bu çalışma kapsamında pick-up tarzı hafif ticari araç uygulamalarında kullanılmak üzere alüminyum kardan mili için mühendislik hesapları gerçekleştirilmiş ve sonlu elemanlar analizleri ile hesaplar doğrulanmıştır. Doğrulmalar sonucunda iki yöntem arasında dayanım hesaplarında %1, doğal frekans hesaplarına %8 sapma hesaplanmıştır ve sapma değerlerinin kabul edilebilir olduğu belirlenmiştir. Birim parçaların, için sonlu elemanlar ile elde edilen sonuçlar kullanılan alüminyum malzemenin akma limitleri ile güvenlik katsayıları hesaplanmıştır. Elde edilen güvenlik katsayıları kardan milleri için uygun olduğu tespit edilmiştir.

An accurate prediction of the translational and rotational motion of particles suspended in a fluid is only possible if a complete set of correlations for the force coefficients of fluid-particle interaction is known. The present study is thus devoted to the derivation and validation of a new framework to determine the drag, lift, rotational and pitching torque coefficients for different non-spherical particles in a fluid flow. The motivation for the study arises from medical applications, where particles may have an arbitrary and complex shape. Here, it is usually not possible to derive accurate analytical models for predicting the different hydrodynamic forces. The presented model is designed to be applicable to a broad range of shapes. Another important feature of the suspensions occurring in medical and biological applications is the high number of particles. The modelling approach we propose can be efficiently used for simulations of solid-liquid suspensions with numerous particles. Based on resolved numerical simulations of prototypical particles we generate data to train a neural network which allows us to quickly estimate the hydrodynamic forces experienced by a specific particle immersed in a fluid.

Initial value problems with various boundary conditions at the ends are studied for the beam vibration equation taking into account the beam rotational motion under bending. An energy inequality is established, which implies the uniqueness of the solution of the four initial–boundary value problems posed. In the case of hinged ends, theorems on the existence and stability of the solution of the problem in the classes of regular and generalized solutions are proved.

Capturing large space debris with complex rotational motion is extremely challenging. A de-tumbling phase before capturing may be necessary to reduce the risk of collision with debris. This paper proposes a new noncontact de-tumbling method using a two-satellite electromagnetic formation, in which two small electromagnetic satellites, each having a high-temperature superconducting coil, generate control torques to reduce the rotation rate of debris prior to making any physical contact. The electromagnetic interaction of the target-satellite system is analyzed. A relative translational dynamics of the target–satellite system and the attitude dynamics of the target are established. Simulation results show that the proposed method effectively eliminates the rotational motion of the target. It can be safely concluded that the noncontact method for de-tumbling space debris using a two-satellite electromagnetic formation is feasible and potentially applicable to on-orbit capture.

The rotational motion of an axisymmetric artificial satellite with a constant magnet under an effect of a torque produced by the Earth’s magnetic field (EMF) influence on the magnet is studied. The orbital motion of a satellite is calculated taking into account the noncentral nature of the Earth’s gravitational field and the atmospheric drag; the proper magnetic moment of a satellite is parallel to the axis of symmetry. The steady-state motions of a satellite are constructed, in which the axis of symmetry makes a small angle with the EMF intensity vector. The IGRF model is used as the EMF model. It is shown that such motions can be approximated by a sequence of periodic solutions of modified equations of motion. Steady-state motions contain two basis frequencies—the orbital and angular velocity of the Earth’s rotation. Periodic solutions have an orbital period, but the spectrum of the approximating sequence composed of them virtually coincides with the spectrum of the original steady-state mode.

The uncontrolled rotational motion of the Progress M-24M and M-25M cargo spacecraft in the mode of one-axis solar orientation (the so-called “spin on the Sun”) has been reconstructed. The initial conditions of motion in this mode are the spinning of the spacecraft with an angular velocity of 2.2–2.4°/s around the normal to the sunward plane of the solar arrays. The duration of the mode is several orbits. The reconstruction was carried out using an integral statistical method based on telemetric values of the current taken from its solar arrays. As a result, the rotational motion of the spacecraft relative to the Earth–Sun direction is determined. A study of the spectrum of current oscillations during spinning was carried out, which explains the possibility of reconstruction based on such, at first sight, little informative data.

This paper has analyzed the equation of motion in terms of stresses (Navier), as well as its two special cases for an incompressible viscous current. One is the Stokes (Navier-Stokes) equation, and the other was derived with fewer restrictions. It has been shown that the Laplace equation of linear velocity can be represented as a function of two variables ‒ the linear and angular speed of particle rotation. To describe the particle acceleration, all motion equations employed a complete derivative from speed in the Gromeka-Lamb form, which depends on the same variables. Taking into consideration the joint influence of linear and angular velocity allows solving a task of the analytical description of a turbulent current within the average model. A given method of analysis applies the provision of general physics that examines the translational and rotational motion. The third type of mechanical movement, oscillatory (pulsation), was not considered in the current work. A property related to the Stokes equation decomposition has been found; a block diagram composed of equations and conditions has been built. It is shown that all equations for viscous liquid have their own analog in a simpler model of non-viscous fluid. That makes it easier to find solutions to the equations for the viscous flow. The Stokes and Navier equations were used to solve two one-dimensional problems, which found the distribution of speed along the normal to the surface at the flow on a horizontal plate and in a circular pipe. Both solution methods produce the same result. No solution for the distribution of speed along the normal to the surface in a laminar sublayer could be found. A relevant task related to the mathematical part is to solve the problem of closing the equations considered. A comparison of the theoretical and empirical equations has been performed, which has made it possible to justify the assumption that a rarefied gas is the Stokes liquid

This article identifies deficiencies in the article of Bernauer et al. (2020) in performing and describing shake table and numerical (synthetic) testing of newly designed seismic instruments for recording complex translational and rotational motion. In my opinion, this is a result from a deficiency in referencing previously published peer-reviewed papers in this area. I also disagree with Bernauer et al. (2020) interpretation of the origin of errors in a vertical sensor’s recording because the sensitivity of a vertical pendulum type sensor to small tilts is much lower than that of the horizontal. Complete differential equations of pendulum-type horizontal and vertical seismometers are presented and examples of previously performed numerical and shake table tests of seismic instruments are shown.