Translational Displacement Research Articles

A Reflective-Type Heterodyne Grating Interferometer for Three-Degree-of-Freedom Subnanometer Measurement

A heterodyne grating interferometer (HTGI) able to simultaneously measure the three-axis translational displacements of ultra-precision motion stages with a sub-nanometer resolution is demonstrated. The HTGI is composed of two main parts, a reflective planar grating with a uniform micron-scale period in two orthogonal directions, and a reading head. Thanks to the reflective grating, the reading head design manages to make main optical paths common and located on the same side of this compact structure, potentially resulting in low Abbe errors and environmental variations. Relying on a laboratory-made dual-frequency laser source at 780 nm, two heterodyne interferometric measurement modules for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> -/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</i> -direction motions and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -direction motion were realized based on first-order and zeroth-order diffraction, respectively. Experiments show that the proposed HTGI, in all three axes, can distinguish a 0.5 nm step or even better, perform an up to 2.5×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> 10linearity in a range of 80 μm, and hold a 5 nm stability within 300 s. These performances confirm that the proposed HTGI can greatly benefit nanoscience and technology, where multi-axis ultra-precision positioning is required, such as wafer stage in next-generation lithography machine, and so forth.

THE INFLUENCE OF SINGLY CHARGED IONS ON THE TRANSLATIONAL MOTION OF MOLECULES IN EXTREMELY DILUTE AMIDE SOLUTIONS

The type of short range solvation of Li+, Na+ K+, Rb+, Cs+, NH4+, Cl– , Br–, I–, ClO4– ions has been determined and analyzed in formamide (FA), N-methylformamide (MFA), N-dimethylformamide (DMF) at 298.15 K. In order to determine the type of ion solvation we used familiar-variable quantitative parameter (– ri), where is the translational displacement length of ion, ri is its structural radius. It was found that the difference (– ri) is equal to the coefficient of attraction friction (CAF) of ions normalized to the solvent viscosity and hydrodynamic coefficient. The sign of the CAF is determined by the sign of the algebraic sum of its ion-molecular and intermolecular components. In amide solutions the studied cations are cosmotropes (positively solvated ((– ri) &gt; 0), structure-making ions) and anions are chaotropes (negatively solvated ((– ri) &lt; 0 ), structure-breaking ions). In the amide series, regardless of the sign (– ri), the near-solvation enhances, which can be explained by the weakening of the specific interaction between the solvent molecules. The decrease of and respectively (– ri) with increasing cation radius in a given solvent is the result of weakening of its coordinating force due to the decrease of charge density in the series Li+–Na+–K+–Rb+–Cs+. The increase of (and (– ri), correspondingly) for the ions studied in the series FA- MFA-DMF can be explained by the weakening of intermolecular interactions in this series, which leads to the strengthening of solvation. It was found that for the halide ions in the series FA-MFA-DMF the regular growth of parameter is explained by the weakening of the solvent structure. It was shown that Li+ ion with the lowest diffusion coefficient among cations and the highest value forms kinetically stable complexes in amide solutions.

Quantifying the Sensitivity of Target Dose on Intrafraction Displacement in Intracranial Stereotactic Radiosurgery

PurposeMask-immobilized stereotactic radiosurgery (SRS) using a gating window is an emerging technology. However, the amount of intracranial tumor motion that can be tolerated during treatment while satisfying clinical dosimetric goals is unknown. The purpose of this study was to quantify the sensitivity of target dose to tumor motion. Methods and MaterialsIn clinical SRS plans, where a nose marker was tracked as surrogate for target motion, translational and rotational target movements were simulated using nose-marker displacements of ±0.5 mm, ±1.0 mm, or ±1.5 mm. The effect on minimum dose to 99% of the target (D99) and percent target coverage by prescription dose was quantified using mixed-effect modeling with variables: displacement, target volume, and location. ResultsThe effect on dose metrics is statistically larger for translational displacements compared with rotational displacements, and the effect of pitch rotations is statistically larger compared with yaw rotations. The mixed-effect model for translations showed that displacement and target volume are statistically significant variables, for rotation the variable target distance to rotation axis is additionally significant. For mean target volume (12.6 cc) and translational nose-marker displacements of 0.5 mm, 1.0 mm, and 1.5 mm, D99 decreased by 2.2%, 7.1%, and 13.0%, and coverage by 0.4%, 1.8%, and 4.4%, respectively. For mean target volume, mean distance midpoint-target to pitch axis (7.6cm), and rotational nose-marker displacement of 0.5 mm, 1.0 mm, and 1.5 mm, D99 decreased by 1.0%, 3.6%, and 6.9%, and coverage by 0.2%, 0.8%, and 1.9%, respectively. For rotational yaw axis displacement, mean distance midpoint-target axis (4.2cm), D99 decreased by 0.3%, 1.2%, and 2.5%, and coverage by 0.1%, 0.2%, and 0.5%, respectively. ConclusionsSimulated target displacements showed that sensitivity of tumor dose to motion depends on both target volume and target location. Suggesting that patient- and target-specific thresholds may be implemented for optimizing the balance between dosimetric plan accuracy and treatment prolongation caused by out-of-tolerance motion.

Three-dimensional condylar displacement and remodelling following correction of asymmetric mandibular prognathism with maxillary canting

The aim of this study was to investigate the three-dimensional condylar displacement and long-term remodelling following the correction of asymmetric mandibular prognathism with maxillary canting. Thirty consecutive patients (60 condyles) with asymmetric mandibular prognathism >4 mm and occlusal canting >3 mm, treated by Le Fort I osteotomy and bilateral sagittal split ramus osteotomy, were included. Spiral computed tomography scans obtained at different periods during long-term follow-up (mean 17 ± 7.2 months) were gathered and processed using ITK-SNAP and 3D Slicer. The condyles were subjected to translational and rotational displacements immediately after the surgery (T2), which had not fully returned to the original preoperative positions at the last follow-up (T3). Condylar remodelling was observed at the last follow-up (T3), with the shorter side condyles subjected to higher surface resorption and overall condylar volume loss. The overall condylar volume on the shorter side was significantly reduced compared to the volume on the elongated side (−11.9 ± 90.6 vs −131.7 ± 138.2 mm3; P = 0.001). About 73%, 87%, 53%, and 54% of the shorter side condyles experienced resorption on the posterior, superior, medial, and lateral surfaces, respectively; in contrast, only 50% of the elongated side condyles showed resorption on the superior surface. Higher preoperative asymmetry was significantly correlated with increased postoperative condylar displacement (P < 0.05). The vertical asymmetry and the vector of condylar displacement were associated with the resultant remodelling process. It is concluded that condylar resorption of the shorter side condyle, which may affect the long-term surgical stability, has to be considered.

Analysis of the structural behavior of a historical mosque damaged due to an earthquake: Sofular mosque example

Since the earliest period of history, many civilizations have ruled our country. Historical structures, which we inherited from these civilizations, should be transferred safely to future generations. For this purpose, it is essential to clearly determine the behavior of these historical structures. In the present study, one of these historical structures, Sofular mosque located in Merzifon, was examined in detail by static and dynamic analysis. In the analysis, the mechanical properties of the material obtained by experimental studies were used. In the static analysis, the mosque was analyzed under its own weight, and it was obtained that the stresses have large values at the supports of the main dome. So, it can be said that the dome has to be supported at these points. The results of the modal analysis show that the mosque has translational displacements with great mass ratios through two orthogonal directions. This shows that the mosque will have out of plane deformation during an earthquake. Also, under the dynamic effects of seismic forces, it was identified that critical out of plane deformations could occur at the upper parts of the eastern and western facades. Also, it is clear that large stress and deformation values could occur at the narthex part. Moreover, it is determined that the dome portion is involved in translational motion and can be damaged during an earthquake.

Magnetic Resonance Imaging Evaluation of Closed-Mouth TMJ Disc-Condyle Relationship in a Population of Patients Seeking for Temporomandibular Disorders Advice

Objective To characterize the closed-mouth temporomandibular joint (TMJ) disc-condyle relationship in a population of individuals who sought hospital services for temporomandibular disorders (TMD). Methods Two hundred and twenty-four TMJ magnetic resonance images (MRIs) of 112 patients were assessed in all spatial planes to classify disc position with respect to the condyle in a closed-mouth position. Results Disc displacement (DD) was present in 62.1% and superior disc position in 29.9% of the patients. Position could not be determined in 8% of the cases. Among DD, pure anteriorized position was the most common condition (34.4%), with different combined translational and rotational displacements in all the other joints (27.7%). Conclusion There is a wide biological variability in disc position in closed mouth among patients seeking for TMD advice. Getting deeper into the correlation with clinical symptoms is recommended to refine the potential relevance of any diagnostic and management strategies based on the imaging evaluation of TMJ disc position.

Translating Race on the French Stage

Translating Race on the French Stage

Blocking screw augmentation in intramedullary nailing for displaced surgical neck fractures of the proximal humerus

A displaced surgical neck fracture can be a good indication for antegrade intramedullary nailing. However, nail insertion may result in malreduction and translational displacement of the humeral head fragment because of muscle traction and size discrepancies between the diameters of the medullary canal and the intramedullary nail. We used blocking screw augmentation in 20 fractures with residual medial displacement of the distal fragment after nail insertion to anatomically reduce displacement of the fracture and to maintain the reduced position before bone union. A blocking screw was placed percutaneously at the lateral side of the canal. Next, a straight intramedullary nail was reinserted medial to the blocking screw. Finally, the nail was locked both proximally and distally. All cases showed bone union without fixation failure at the time of the final follow-up. Blocking screw augmentation with intramedullary nailing is feasible for the treatment of humeral surgical neck fractures and is thought to be helpful for fracture reduction during surgery and stable fixation after surgery.

Water Dynamics in Composite Aqueous Suspensions of Cellulose Nanocrystals and a Clay Mineral Studied through Magnetic Resonance Relaxometry.

1H spin-lattice relaxation time (T1) measurements were performed to probe the dynamic behavior of water in aqueous suspensions of cellulose nanocrystals (CNCs) and a layered smectite clay mineral with different degrees of concentration. 1H-T1 experiments were carried out over a wide frequency domain, ranging from a few kilohertz to 500 MHz, with the aid of conventional and fast field cycling nuclear magnetic resonance (NMR) techniques. The experimental relaxometry data illustrate differences between the dynamic behavior of bulk water and that confined in the vicinity of CNC-clay surfaces. Clay alone in moderate concentration was found to enforce almost no effect on the water dynamics, whereas introducing CNCs to the system presented a significantly enhanced relaxivity. The modeling of the relaxation dispersions allowed the determination of dynamical processes and variables explaining the dynamic behavior of water in CNC-clay suspensions. It turned out that reorientations mediated by translational displacements are a leading NMR relaxation mechanism for water interacting with the surfaces of CNC-clay particles in the low-frequency domain. In the high-frequency regime, however, the inner-sphere paramagnetic relaxation mechanism dominates, which is caused by the interaction of water protons with dissolved Fe ions.

Self-Bearing Machine Modeling Reflecting Rotor Position Induced Non-Linearity Based on 7-D Lookup Table

The rotor of self-bearing machines can be in an off-centered position as they lack of physical bearings. The air-gap length and effective area with respect to each phase become nonuniform, which results in inductance and back EMF non-linearities. Evaluation of self-bearing machines performance in time domain is inaccurate without a model that includes non-linear inductance and back EMF constants. To reflect non-linearities, finite element analysis (FEA) is often used. However, FEA requires large computational power to run in time-domain simulation. In this article, a 7-D lookup table (7-D LUT) model of inductance and back EMF constants, suspension forces, and torque is proposed for time-domain simulation, including non-linearity from the rotor translational and rotational displacement. Pre-evaluated FEA results are post-processed to construct the 7-D LUT model to enable fast and accurate time-domain simulation reflecting non-linearities from the input of rotary position (slotting effect), translational position in horizontal and vertical directions (unbalanced air-gap field effect), and magnetic saturation effect. A combined winding self-bearing machine is evaluated using the proposed method and verified with FEA and experimental results.

Are pre- and postoperative true translational and angular displacement predictive of nonunion after intramedullary nail fixation of tibial shaft fractures?

To determine if there is an association between pre-/postoperative translational and angular displacement with nonunion after intramedullary nail (IMN) fixation of tibial shaft fractures. Retrospective review of 120 patients with tibial shaft fractures undergoing IMN at an urban level-one trauma center was performed. Demographics, injury characteristics, and pre-/postoperative translational and angular fracture displacement in the coronal and sagittal planes were recorded. True fracture translational and angular displacement (TTD and TAD) were calculated by combining sagittal and coronal displacement utilizing the Pythagorean theorem. 10.8% of patients (n = 13) developed nonunion with remaining patients serving as the control. Groups were similar across age, sex, and BMI. Univariate analysis revealed no difference in pre-/postoperative TAD between nonunion and union groups and an increased preoperative TTD (median difference (MD): 6.2mm, CI: 1.4-10.8mm) and postoperative TTD (MD: 1.8mm, CI: 0-3.7mm) in the nonunion group. On multivariate analysis, however, only tobacco use and type 2 or 3 open fractures were associated with nonunion (OR: 5.1, CI: 1.2-22.8 and OR: 4.9, CI: 1.2-19.2, respectively). True translational and angular displacement of tibial shaft fractures before and after IMN fixation were not independently associated with nonunion. Tobacco use and type 2 or 3 open fracture are independent factors for nonunion.

Optimum torsion axis in multistory buildings under earthquake excitation: A new criterion based on axis of twist

The elastic axis is essential for the definition of structural eccentricity, which significantly affects the torsional behavior of buildings. However, it can be determined straight-forwardly in single-story and some special cases of multi-story buildings. Therefore, for the majority of multi-story buildings, the notion of optimum torsion axis has been introduced, according to which, the torsion of the building is considered optimum when the sum of squares of the floor torsional angles is minimum under horizontal forces passing through this axis. The existing determination procedures refer to the application of static horizontal forces and static torsional moments at each story. The present study proposes a new criterion, which approaches the optimum torsion axis by the prism of axis of twist and requires the sum of floor translational displacements of the axis to be minimal. The criterion can be applied under: i) static torsional moments imposed at each story or ii) torsional ground motion excitation. In the latter case, the term of dynamic optimum torsion axis is introduced. Mathematical formulae are provided for the application of the new criterion as well as for the determination of the location of the optimum torsion axis, static or dynamic. It is mathematically proved that the coordinates of the static optimum torsion axis depend on the distribution of torsional moments along the building’s height. However, the coordinates of the dynamic optimum torsion axis are independent of the torsional base excitation and depend only on the mass moments of inertia at each floor level. The proposed method can be easily implemented, as it is based on data given by any structural program, either in terms of structural characteristics or in terms of response.

One-wing polymer micromachined transmission for insect-inspired flapping wing nano air vehicles

This paper presents a feasibility step in the development of an insect-inspired flapping wing nano air vehicle using advanced engineering technologies such as microelectromechanical systems (MEMS) technologies. To develop an insect-inspired flapping wing nano air vehicle, a one-wing polymer micromachined transmission is proposed in this paper. The novelty of this study includes (1) the use of the geometrically nonlinear bending deformation of a set of two parallel elastic hinges as the basis for the transmission mechanism, which produces a large rotational displacement from a small translational displacement, and (2) a complete 2.5-dimensional structure that can be fabricated using standard microfabrication techniques, including etching, photolithography, deposition, and curing, without any post-assembly. This design is also an improved version of our previous design, a two-wing polymer micromachined transmission. The transmission proposed here has a great advantage over other types of transmission mechanisms, including its low energy loss because no post-assembly is required (reduced friction loss); its low total weight; its capacity to be further miniaturized without difficulty; and its performance, i.e., ability to produce the necessary stroke angle of approximately 30° without resonance assistance.

To Solution of Contact Problem for Elastic Half-Strip

Contact problems for elastic stripes have been well studied and published in domestic scientific literature. This is partly due to the fact that normative documents on the foundation structure it is recommended to use this elastic foundation model for simulation of a “structure – foundation – soil foundation” system. Two variants of boundary conditions at the contact between a half-strip and a rigid non-deformable base are usually considered. The first boundary condition nullifies the vertical displacements and tangential stresses, the second one nullifies vertical and horizontal displacements. Contact problems for an elastic half-strip are much less investigated. The paper considers this contact problem when the first boundary condition for zeroing of vertical displacements and tangential stresses at the contact of a half-strip with a rigid, nondeformable base. When performing calculations in the traditional formulation without taking into account tangential stresses in the contact zone, the Zhemochkin method has been used, which reduces the solution of the contact problem of solid mechanics to the solution of a statically indeterminate problem by the mixed method of structural mechanics. Therefore, at first, we have found the displacements of the upper edge of the half-strip from the unit load uniformly distributed over the edge section. The resulting expression is used to compose a system of equations for the Zhemochkin method. The case of translational displacement of the die has been considered, and the graph of contact stress distribution under the die's sole has been given in the paper.

Numerical Simulation of Interaction between Kr+ Ion and Rotating C60 Fullerene towards for Nanoarchitectonics of Fullerene Materials

Dynamics of charged fullerene in a surface layer of fullerite is studied under the influence of neutral or charged particles of the gas phase surrounding the fullerite material. The translational displacements of the nodes of the crystal lattice structure are determined by the equations of motion of the centers of mass of fullerenes. Central fullerene, which is described as a discrete set of sixty carbon atoms, plays a special role in the presented mathematical model. Angular oscillations and rotations of the central fullerene are described by the dynamic Euler equations. All other fullerenes have a centrally symmetric field of the potential of interaction with the surrounding atoms and molecules. In this regard, we use the hybrid discrete–continuous mathematical model with four potentials that describe the interactions between the surrounding fullerenes, smoothed fullerene and an atom, a pair of atoms, and electric charges. The results of a numerical study of influence of the Coulomb interaction on the rotational and translational motion of the C60 fullerene are presented.

A Multilevel Model for Calculating the Motion of Rocks

The presence of a large number of loose rocks, often accompanied by giant rocks, which are highly destructive to the surface are an important factor in geological hazard risk assessment. In rocks moving along a slope, the scale of movement and the scale of deformation differ substantially in magnitude owing to their movement characteristics of large moving distance, fast rotation speed, and small deformation. A multilevel model for rock motion calculation is established to separate the rigid displacement and deformation displacement of the rock. The total rock movement displacement comprises translational displacement, rotational displacement, and deformation displacement. Three corresponding coordinate systems are set up. These include the translational coordinate system, which is used to describe the translational displacement of the rock, the rotational coordinate system, which is used to describe the rotational displacement of the rock, and the co-rotational coordinate system, which is used to describe the deformation displacement of the rock. The origin and the direction of the coordinate axis of the co-rotational coordinate system change with the movement of the rock. Lagrange’s principle establishes the equations of motion, which is solved by an explicit approach in the framework of the Continuum-discontiuum element method. Several numerical cases verify that this method can accurately calculate the rotational movement of the rock.

Mechanically transduced immunosorbent assay to measure protein-protein interactions.

Measuring protein-protein interaction (PPI) affinities is fundamental to biochemistry. Yet, conventional methods rely upon the law of mass action and cannot measure many PPIs due to a scarcity of reagents and limitations in the measurable affinity ranges. Here, we present a novel technique that leverages the fundamental concept of friction to produce a mechanical signal that correlates to binding potential. The mechanically transduced immunosorbent (METRIS) assay utilizes rolling magnetic probes to measure PPI interaction affinities. METRIS measures the translational displacement of protein-coated particles on a protein-functionalized substrate. The translational displacement scales with the effective friction induced by a PPI, thus producing a mechanical signal when a binding event occurs. The METRIS assay uses as little as 20 pmols of reagents to measure a wide range of affinities while exhibiting a high resolution and sensitivity. We use METRIS to measure several PPIs that were previously inaccessible using traditional methods, providing new insights into epigenetic recognition.

Biomechanical aspects of the initial stability of instrumental fixation in the treatment of subaxial cervical dislocations: an experimental study

Objective. To study the influence of thoracic inlet angle (TIA) and the fracture of the articular process on the initial strength of the fixation of the spinal segment during its anterior and circular instrumental surgical stabilization in an experiment on a model of the lower cervical spinal segment.Material and Methods. The material of the study was assembled models of C6–C7 spinal segments made using addictive technologies by 3D printing. After preliminary instrumentation, spinal segments were installed on the stand testing machine using specially manufactured equipment. A metered axial load simulating the native one was applied along the axis of the parameters SVA COG–C7 and C2–C7 SVA, which values were close to the value of 20 mm, at a rate of 1 mm/min until the shear strain was reached. The system’s resistance to displacement was measured, and the resulting load was evaluated. Four study groups were formed depending on the modeling of the T1 slope parameter, the integrity of the facets, and the type of instrumentation. Three tests were conducted in each group. The graphical curves were analyzed, and the values of the parameters of the neutral and elastic zones, the yield point, time to yield point, and the value of the applied load for the implementation of shear displacement were recorded. The data were subjected to comparative analysis.Results. In Group 1, anterior shear displacement of the C6 vertebra could not be induced in all series. In groups 2, 3, and 4 a shear displacement of ≥4 mm was noted in all series. In Group 3 where a fracture of the articular process was additionally modeled, the average value of the yield point was 423.5 ± 46.8 N. Elastic zone, the time to the onset of the yield point, the time at the end point or at a shear of C6 ≥4 mm did not differ significantly. In Group 4, a translational displacement of ≥4 mm was observed, though the average yield point was 1536.0 ± 40.0 N.Conclusion. The direction of the load applied to the fixed spinal segment, as well as the presence of damage to the articular processes, play a crucial role in maintaining resistance to shear deformation of the spinal segment during its instrumental stabilization. At high values of TIA (T1 slope) and the presence of fractures of the articular processes, the isolated anterior stabilization is less effective, circular fixation of 360° under these conditions gives a high initial stability to the spinal segment.

Vision‐based displacement and joint rotation tracking of frame structure using feature mix with single consumer‐grade camera

A monocular vision-based response tracking method is proposed for simultaneously identifying translational floor displacement and rotational joint deformation of frame structures at multiple locations. The framework incorporates subpixel-level feature matching and tracking and is designed by introducing the feature-mix concept and feature quality evaluation for the initialization and postprocessing stage, respectively. The necessity of monitoring frame joint rotation is presented with the damage observations. A large-scale reinforced concrete frame structure is employed to investigate the proposed response estimation method through comprehensive shaking table tests by using a consumer-grade camera. The initial feature population, time-history agreement, overall estimation accuracy, survival feature ratio, and measurement uncertainty are further analyzed. In addition, the potential values and advantages of the proposed response tracking method for dynamic measurement and seismic evaluation are discussed illustratively.

Dynamics of a vibration-driven single disk

Granular particles exhibit rich collective behaviors on vibration beds, but the motion of an isolated particle is not well understood even for uniform particles with a simple shape such as disks or spheres. Here we measured the motion of a single disk confined to a quasi-two-dimensional horizontal box on a vertically vibrating stage. The translational displacements obey compressed exponential distributions whose exponent beta increases with the frequency, while the rotational displacements exhibit unimodal distributions at low frequencies and bimodal distributions at high frequencies. During short time intervals, the translational displacements are subdiffusive and negatively correlated, while the rotational displacements are superdiffusive and positively correlated. After prolonged periods, the rotational displacements become diffusive and their correlations decay to zero. Both the rotational and the translational displacements exhibit white noise at low frequencies, and blue noise for translational motions and Brownian noise for rotational motions at high frequencies. The translational kinetic energy obeys Boltzmann distribution while the rotational kinetic energy deviates from it. Most energy is distributed in translational motions at low frequencies and in rotational motions at high frequencies, which violates the equipartition theorem. Translational and rotational motions are not correlated. These experimental results show that the random diffusion of such driven particles is distinct from thermal motion in both the translational and rotational degrees of freedom, which poses new challenges to theory. The results cast new light on the motion of individual particles and the collective motion of driven granular particles.