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The direct problem in gravimetry is one of the few areas of applied geophysics where complete, general and fully valid solutions are available. The common issue in the gravimetric direct problem is that there are several different solutions for even simple shaped bodies available throughout the literature. While the direct problem is single-valued, the general solutions (if possible to find analytically) are desired. The aim of the present paper is to bring clarity into the “information noise” which occurs in the literature for the case of the spherical shell/layer. We collected several different solutions and proved their equality (as special cases of the general solution). The differences between these solutions are caused by the symbolism used, but mostly by the different area of validity of each formula. The formulae are discussed and scored on several criteria. The general solutions for the gravitational potential and attraction on the rotational axis of the spherical shell are presented, as well as the solution for the biaxial ellipsoidal layer for comparison.

Design and development of a domino cyclative approach for the synthesis of new polycyclic γ-butenolides from β-aryl-Z-enoate propargylic alcohols, through the interception of an intermediate of the Z-enoate-assisted Meyer-Schuster rearrangement, has been reported. A systematic NMR analysis of various derivatives of this class revealed and supported the potential atropisomerism associated with them. These molecules represent first examples of butenolide ring-based atropisomeric compounds in organic chemistry. The synthetic process involves a synchronous construction of both rings with concurrent creation of the potential stereogenic rotational axis.

Tibiofemoral synchronization technique matches the rotational alignment of the tibial component to the femoral component during the total knee arthroplasty (TKA). The rotational axis of the proximal tibia can be changed by this technique, which affects tibial torsion postoperatively. The purpose of this study was to investigate whether the tibiofemoral synchronization technique affect the tibial torsion, and the lower limb rotation after primary TKA. It was hypothesised that the tibial torsion would change after primary TKA. Ninety-three posterior stabilised TKAs from 89 patients were included from January 2017 to December 2018. Mechanical hip–knee–ankle axis (mHKA), in plain radiographs, femoral anteversion, tibial torsion, femoral neck-malleolar angle (FNMA), and rotational alignment of the femoral and the tibial components in pre- and postoperative CT scans were measured by two blinded observers. The primary outcome was a postoperative change in femoral anteversion, tibial torsion and FNMA. Clinical outcomes were evaluated using the American Knee Society Knee Score (AKSKS)/Function Score (AKSFS), and Oxford Knee Score (OKS) preoperatively and at 1 year after TKA. Patients’ perception of changes in the foot progression angle after TKA was investigated. Statistical significance was set at p

A submerged oscillating heave plate is utilized as a mechanism in some marine structures for vibration reduction. Quantifying the hydrodynamic properties in axial (heave) oscillations has ...

The ability to verify the geometrical quality of a machined workpiece on the machine tool itself can be a crucial advantage in ultra-precision diamond turning. This paper presents a new positioning procedure for optical one-dimensional (1D) probes integrated on diamond turning machines with two horizontal linear axes and one rotational axis. A tilted flat, mounted onto the spindle, is used to determine the offsets between the probe and the spindle axis in order to minimize measurement deviations referred to probe alignment errors. An estimation of the positioning uncertainty, which can be specified to be less than 0.3 µm, is given.

Objectives The aim of this study was to determine the influence of short base lengths and supplemental grooves on surface area and rotational resistance in a simulated‐maxillary premolar. Materials and Methods Trigonometric calculations were done to determine the total surface area with and without supplemental grooves. Additional computations were done to determine the maximum wall angle needed to resist rotation displacement in a premolar‐sized model. Wall heights of 3.0, 4.0, and 5.0 mm were used in the surface area and rotational axis computations. The rotational axis was located on the lingual restoration margin to produce a buccal‐to‐lingual rotational displacement. Results Total surface area decreased with increasing four‐wall taper levels from 2° to 18° and decreasing preparation heights from 5 to 3 mm. Significant surface area improvements were found with the supplemental use of mesial and distal axial grooves compared with the same condition without grooves in all taper levels and preparation height categories. Resistance to rotational displacement was determined to occur at only at very low levels of opposing wall taper angles. The use of supplemental grooves on mesial and distal axial walls significantly improved both total surface area and rotational resistance. Conclusions The vertical wall taper angles, preparation heights, and supplemental grooves play a role in resistance form and restoration stability.

“Grinding Mechanism having Advanced Secondary Rotational Axis” is one of the newer plane surface grinding methods that has an uncommon abrasion mechanism. Unlike conventional methods, in Grinding Mechanism having Advanced Secondary Rotational Axis, there are two rotations of a wheel. The first rotation is the same as the conventional grinding methods, which is the circumferential rotation. The other rotation is the newly developed axial rotation, where the wheel rotates around itself perpendicular to its radial axis. In the grinding process, the grinding force, energy, power, and temperature are directly related to the material removal rate. In this article, the chip model in Grinding Mechanism having Advanced Secondary Rotational Axis was addressed and material removal rate was reformulated. The new chip ratio formula was adapted to the grinding force, energy, power, and temperature in the conventional plane surface grinding method. The chip formed in the conventional plane surface grinding method consists of two-dimensional xy plane. In Grinding Mechanism having Advanced Secondary Rotational Axis, on the other hand, the chips consist of three-dimensional xyz plane. The reason behind this is the second rotation obtained in Grinding Mechanism having Advanced Secondary Rotational Axis (axial rotational motion). The chip model was obtained from the combination of two rotations in Grinding Mechanism having Advanced Secondary Rotational Axis. As a result, the resulting chip model increased the material removal rate only slightly and this increase was negligible. Accordingly, an increase in grinding force, energy, power, and temperature was observed at negligible rates.

In the present study, the physical meaning of vorticity is revisited based on the Liutex-Shear (RS) decomposition proposed by Liu et al. in the framework of Liutex (previously called Rortex), a vortex vector field with information of both rotation axis and swirling strength (Liu et al. 2018). It is demonstrated that the vorticity in the direction of rotational axis is twice the spatial mean angular velocity in the small neighborhood around the considered point while the imaginary part of the complex eigenvalue (λci) of the velocity gradient tensor (if exist) is the pseudo-time average angular velocity of a trajectory moving circularly or spirally around the axis. In addition, an explicit expression of the Liutex vector in terms of the eigenvalues and eigenvectors of velocity gradient is obtained for the first time from above understanding, which can further, though mildly, accelerate the calculation and give more physical comprehension of the Liutex vector.

We aimed to evaluate whether there is a consensus among bi- (2D) and three-dimensional (3D) evaluations of mandible condyle position and its rotation center. Also, if this data can be replicated in orthognathic surgery planning. The survey was carried out on the major databases (PubMed, SCOPUS, Embase, Cochrane). Human or human bio models evaluations in 2D or 3D of mandibular condylar position concerning its fossa and rotational axis for orthognathic surgery planning were eligible. The heterogeneity of the studies and uncertainties in methodological biases did not allow us to identify the superiority of 2D or 3D methodology in determination of the condylar rotational axis. There is a lot of divergences in the definition of occlusal relationships among dental specialties. Although there was no consensus regarding condylar position in relation to the fossa, the most reported axis of rotation was positioned posterior-inferior. Weak scientific evidence and divergences in dental vocabulary shows the need for clinical studies with more accurate and transparent methodological design to standardize concepts. Despite we cannot affirm, we can suggest that the centric relation (CR) is not the condylar position when clinically manipulated in the posterior superior direction. This condylar position is the retruded contact position (RCt) while CR is the functional position of the condyle. In this way, the orthognathic surgery has two occlusal relationships during planning and execution. The ideal axis of rotation for orthognathic surgery planning must be fixed, permit individualization for each condyle and be reproducible. The 2D planning is obsolete as cannot provide all the necessary tools for an accurate planning.

Here we report two new multicomponent supramolecular rotors (1 and 2) based on 2,7-diphenyl-9H-carbazole stators and two rotators brought together by a non-innocent C-H…O interaction. This hydrogen bond serves a dual function: it constitutes the rotational axis for THF and acts as a ‘brake’ for the motion of DABCO. Dynamic characterization of 1 by VT 2H NMR experiments supports that DABCO rotates about its supramolecular axis with jumps of 120º (3-fold) and a krot >10 MHz at 300 K, but interestingly, this motion is reduced to 5 MHz at 150 K. Concurrently, the THF experiences an atypical motion on an axis that is perpendicular to that of DABCO, experiencing 180º jumps in the fast regime even at 175 K. 1H(T1) relaxometry studies show that DABCO has an Ea=3.5 kcal/mol, while for THF, an Ea=2.3 kcal/mol was computed by periodic DFT. Fast and organized mobility of two constituents within crystals is extremely infrequent and could have strong implications for future applications of multicomponent solids with regulated dynamics.

This study investigated the principal translational or rotational axis that evokes the most severe cybersickness by detecting constant velocity and acceleration thresholds on the onset of cybersickness. This human subject experiment with 16 participants used a 3D particle field with movement directions (lateral, vertical, yaw, or pitch) and motion profiles (constant velocity or constant acceleration). The results showed that the threshold of pitch optical flow was suggestively lower than that of the yaw, and the vertical threshold was significantly lower than the lateral. Still, there was no effect of scene movement on the level of cybersickness. In four trials, the threshold increased from the first to the second trial, but the rest remained the same as the second one. However, the level of cybersickness increased significantly between the trials on the same day. The disorientation-related symptoms occurred on the first trial day diminished before the second trial day, but the oculomotor-related symptoms accumulated over the days. Although there were no correlations between the threshold and total cybersickness severity, participants with a lower threshold experienced severe nausea. The experimental findings can be applied in designing motion profiles to reduce cybersickness by controlling the optical flow in virtual reality.

A microrobot system comprising an untethered tumbling magnetic microrobot, a two-degree-of-freedom rotating permanent magnet, and an ultrasound imaging system has been developed for in vitro and in vivo biomedical applications. The microrobot tumbles end-over-end in a net forward motion due to applied magnetic torque from the rotating magnet. By turning the rotational axis of the magnet, two-dimensional directional control is possible and the microrobot was steered along various trajectories, including a circular path and P-shaped path. The microrobot is capable of moving over the unstructured terrain within a murine colon in in vitro, in situ, and in vivo conditions, as well as a porcine colon in ex vivo conditions. High-frequency ultrasound imaging allows for real-time determination of the microrobot&rsquo, s position while it is optically occluded by animal tissue. When coated with a fluorescein payload, the microrobot was shown to release the majority of the payload over a 1-h time period in phosphate-buffered saline. Cytotoxicity tests demonstrated that the microrobot&rsquo, s constituent materials, SU-8 and polydimethylsiloxane (PDMS), did not show a statistically significant difference in toxicity to murine fibroblasts from the negative control, even when the materials were doped with magnetic neodymium microparticles. The microrobot system&rsquo, s capabilities make it promising for targeted drug delivery and other in vivo biomedical applications.

In recent machining processes, 5-axis controlled machine tool is widely used for machining complicated workpiece shape with curved surface. In such process, to achieve high productivity, planning method of cutting conditions to satisfy both following the commanded tool feed rate in machining process and realization of good surface roughness are required. In conventional study, it is known that lead angle of tool posture against local machined surface influence the surface roughness. Then, common commercial CAM systems have already functioned to avoid interference and control the lead angle in each cutter location. However, in the generated cutter locations by the conventional algorithms, when the tool posture changes rapidly, there is a problem that actual feed rate does not reach the command value and machining time becomes longer than expected. In this paper, we propose the new tool posture correction algorithm. In the proposed method, first, the rotational axis that causes the feed speed rate decline is specified by preliminary experiments. And, the jerk value that is the threshold for the feed speed decline is investigated. After that, for the NC program, the command value of the target axis is modified within a range where interference of cutting tool does not occur, thereby preventing a decline in the actual feed rate. This paper describes an outline of the proposed modification method and the effect of the modification of the target axis positions on the lead angle and the actual feed rate.

In-phase self-synchronization of two eccentric rotors with common rotational axis is hardly implemented in far-resonance system. In this article, a dual motor coaxially coupling with a torsion spring is proposed to obtain in-phase synchronization between the eccentric rotors. To explore the dynamic and synchronous characteristics of the proposed system, the mechanical model is first established with Lagrangian formulation. Second, the steady response of the system is calculated based on differential motion equations. Subsequently, the synchronous mechanism between the eccentric rotors is discussed by averaged small parameter method. Finally, some numerical computations are further implemented to verify correctness of theoretical analysis. The result shows that the synchronous state is determined by stiffness of torsion spring, masses of eccentric rotors, and distance between the motors. When axial distance between the motor is smaller, “critical stiffness of in-phase synchronization” is gradually enlarged as the masses of the eccentric rotors are increased and approached to equality, but in-phase synchronization is permanently maintained when the axial distance of the motor is far; in this situation, the synchronous state is hardly affected by variation of stiffness of torsion spring and masses of eccentric rotors. When the stiffness of the torsion spring is smaller, “critical distance [Formula: see text] of in-phase synchronization” is also enlarged as the masses of the eccentric rotors are increased and approached to equality; otherwise, the synchronous state is always locked in in-phase synchronization. When the stiffness of the torsion spring is smaller, “critical distance [Formula: see text] of anti-phase synchronization” is decreased as the masses of eccentric rotors are increased and approached to equality; otherwise, the synchronous state is always locked in in-phase synchronization.

PURPOSE: Magnetic resonance imaging (MRI) was used to determine the effect of axial length (AL) on globe rotational axis and horizontal extraocular muscle (EOM) leverage during horizontal duction. DESIGN: Prospective observational case series. METHODS: At a single academic center, 36 orthophoric adults with a wide range of ALs underwent high-resolution axial orbital MRI in target-controlled adduction and abduction. ALs were measured in planes containing maximum globe cross-sections. Area centroids were calculated to determine globe centers. Rotational axes in orbital coordinates were calculated from displacements of lens centers and globe-optic nerve attachments. Lever arms were calculated as distances between published EOM insertions and rotational axes. RESULTS: ALs averaged 26.3±0.3mm (standard error, range 21.5-33.4mm). Rotational axes from adduction to abduction averaged 1.1±0.2mm medial and 1.1±0.2mm anterior to the globe’s geometric center in adduction. Linear regression demonstrated no significant correlation between AL and rotational axis horizontal (R(2)=0.06) or anteroposterior (R(2)= 0.07) position. Medial rectus (MR) lever arms averaged 12.0±0.2mm and lateral rectus (LR) lever arms averaged 12.8±0.2mm. Both MR (R(2)=0.24, p

In the field of modern manufacturing, probes have been playing a more and more crucial role. However, contact probes are unfit for measuring objects with soft surfaces or very tiny cavities and require radius compensation of stylus. In comparison, noncontact probes such as optical probes do not have to consider these problems and are well-performed in measurement. However, existing optical probes (triangulation) may fail to detect objects with rich spatial structures (due to the occlusion effect) and highly reflective curved surfaces (due to existence of highlight spots). Considering the problems, an optical probe based on discrete rotational symmetric triangulation is proposed in this paper. The emitting laser beam of the probe is the rotational axis and the five receiving optical paths (lenses and mirrors) are rotationally symmetrically distributed around the laser axis and are coimaged on a CMOS camera. Results of simulations and experiments show that the new-established prototype is designed with good robustness under various conditions such as different surface characteristics and different inclination degrees. The probe enables conducting real-time on-machine measurement without directional dependency with a resolution of 39 μm and repeatability accuracy of 0.72 μm.

Left ventricular rotational motion is a feature of normal and diseased cardiac function. However, classical torsion and twist measures rely on the definition of a rotational axis which may not exist. This paper reviews global and local rotation descriptors of myocardial motion and introduces new curl-based (vortical) features built from tensorial magnitudes, intended to provide better comprehension about fibrotic tissue characteristics mechanical properties. Fifty-six cardiomyopathy patients and twenty-two healthy volunteers have been studied using tagged magnetic resonance by means of harmonic phase analysis. Rotation descriptors are built, with no assumption about a regular geometrical model, from different approaches. The extracted vortical features have been tested by means of a sequential cardiomyopathy classification procedure; they have proven useful for the regional characterization of the left ventricular function by showing great separability not only between pathologic and healthy patients but also, and specifically, between heterogeneous phenotypes within cardiomyopathies.

In this paper, we present a method that uses a combination of experimental and modeled data to assess properties of x‐ray beam measured using a small‐animal spectral scanner. The spatial properties of the beam profile are characterized by beam profile shape, the angular offset along the rotational axis, and the photon count difference between experimental and modeled data at the central beam axis. Temporal stability of the beam profile is assessed by measuring intra‐ and interscan count variations. The beam profile assessment method was evaluated on several spectral CT scanners equipped with Medipix3RX‐based detectors. On a well‐calibrated spectral CT scanner, we measured an integral count error of 0.5%, intrascan count variation of 0.1%, and an interscan count variation of less than 1%. The angular offset of the beam center ranged from 0.8° to 1.6° for the studied spectral CT scanners. We also demonstrate the capability of this method to identify poor performance of the system through analyzing the deviation of the experimental beam profile from the model. This technique can, therefore, aid in monitoring the system performance to obtain a robust spectral CT; providing the reliable quantitative images. Furthermore, the accurate offset parameters of a spectral scanner provided by this method allow us to incorporate a more realistic form of the photon distribution in the polychromatic‐based image reconstruction models. Both improvements of the reliability of the system and accuracy of the volume reconstruction result in a better discrimination and quantification of the imaged materials.

PURPOSE The aim of this cross-sectional study was to assess maximum restraining lip force (MLF), maximum voluntary bite force (MBF), and patient-related parameters to evaluate their influence on masticatory function in four groups of participants with different dental states. METHODS Participants were recruited and assigned to one of four different groups depending on dental status: complete removable dental prostheses (CRDP group); edentulous with two-implant overdentures (IOD group); Kennedy Class I partial removable dental prostheses (PRDP group); or fully dentate (control group). A dental examination was performed and history taken. MLF was measured as the maximum withstood pulling force with three sizes of oral screens, MBF was evaluated using a digital force gauge, and masticatory performance was assessed using a two-color mixing ability test. Linear regression was used to determine the predictive effects of covariates on masticatory performance. Global and pairwise comparisons were also carried out. RESULTS A total of 68 participants with an average age of 69.3 ± 7.7 years were recruited. MLF depended on the screen size (P = .0004; Kruskal-Wallis) and increased with CRDP use, especially in challenging tasks, such as restraining the smallest screen. The highest MBF was found in dentate participants (P < .0001; Mann-Whitney). Analysis of variance (ANOVA) showed a global significant difference in masticatory performance between groups, with PRDP patients chewing better than CRDP patients. Dental state, time lapse since last tooth loss, and MBF predicted masticatory function. CONCLUSION Tooth loss significantly affects MBF and masticatory performance. Free-end saddles with a rotational axis in two-implant IODs and Kennedy Class I PRDPs may limit MBF and consequently masticatory performance. CRDP design should facilitate perioral muscular function.

The main purpose of the present study is to prove the usability of a mechanism with a common rotational axis during twisting manipulation using a multi-fingered robotic hand where two fingers and two other fingers can independently rotate in inner and outer circles with a dual turning mechanism. Although various types of conventional multi-fingered hands have potential capability to achieve twisting manipulations such as opening a bottle cap from within a hand, it is well-known that such tasks are difficult to execute quickly due to limited working space of the fingers and complexity of control. The proposed hand with a common rotational axis is effective in rotational manipulation around a particular axis, where each joint role assignment is completely decoupled into internal force control for grasping an object and velocity control around the axis for rotating the object. We prove the usability of this mechanism with a common rotational axis through the use of a control scheme, and show experimental results involving manipulation tasks where twisting manipulation is dominant.

It has been demonstrated that the torsional patterns of the metatarsal heads are associated with the presence or absence of the medial longitudinal arch in hominoid feet. The relatively untwisted second metatarsal is unique in humans, but that of the African apes is much more inverted, suggesting that the torsion of the second metatarsal might represent the overall shape and flatness of the foot. Some clinical studies have recently argued that the onset of foot pathologies such as hallux valgus might be related to the torsional pattern of the metatarsals. However, to date, no studies have systematically investigated the morphological variations of the torsional patterns of human metatarsals. In this study, therefore, the aim was to clarify the age- and sex-associated variations in the torsional patterns of human metatarsals using three-dimensional computed tomography. The torsion angles of the five metatarsals were calculated by defining the dorsopalmar vector of the metatarsal base and the vector corresponding to the rotational axis of the metatarsal head. The present result demonstrated that the second metatarsals of females were significantly more inverted with increasing age. Flat foot is known to be most common in elderly women. Whether there is a cause-effect relationship between second metatarsal torsion and flattening of the medial longitudinal arch has yet to be answered, but this study suggested that torsion of the second metatarsal might possibly be used as an indicator for the early diagnosis of flat foot and associated foot pathologies. Clin. Anat. 30:1058-1063, 2017. © 2017 Wiley Periodicals, Inc.

Inner-and-outer steel flange has gained many attentions in China. This type flange has both inner and outer rings, as well as bolts. To gain insight into the intrinsic characteristics of the flange, an experimental study is conducted, taking into account that the tension and bending loads are imposed simultaneously. The varying of relative displacement between two adjacent flange planes with external loading is surveyed. It is indicated that the deformation is almost linearly increased with the external loads, if there is no yielded bolt. Strain gauges are employed to capture the strain distribution in the ribs as well as the tube. The internal tension force of bolt is also measured in the test. It is revealed that the failure mode of the flange is the breaking of the outer bolts. Moreover, the existence of the tension load would reduce the bending bearing capacity of the flange, and prying force could be ignored. It is concluded that the plane-section assumption holds approximately. Accordingly, formulas are given to compute the bearing capacity of the flange. It is found that the computing method is quite conservative if the position of rotation axis takes a value of 0.8 times of the diameter of the steel tube.

Parallel mechanisms (PMs) having three translational (T) and one rotational (R) movement capability draw continuous attention from academia and industry. The existing 3T1R PMs can only generate Schoenflies motion and bifurcation of Schoenflies motion. This paper proposes a new 3T1R motion that features one rotation about a varying axis plus three pure translations. Drawing mainly on finite screw theory, a hierarchical approach for type synthesis of limb structures of the PMs having 3T1R motion with variable rotational axis is presented by developing the basic limb bonds first and then their equivalent substitutions using the properties of screw triangle product. The assembly conditions for the PMs of this kind are discussed. Consequently, numerous novel PMs consisting of four identical limbs are synthesized using this technique.

Simultaneous 5-axis control machining is used to machine components in complex, deep grooved shapes. In order to maintain actual feed rates in this kind of machining, it is vitally important to secure continuity in the movement of the rotational axis. When the tool reverses its direction of travel, however, its axis of rotation is liable to make sudden movements. In this study, therefore, we first derive candidate tool postures that can meet the conditions for relative postures to machined surfaces while avoiding tool interferences. We then develop a method for automatically planning continuous changes in the command values of the rotating axial angles in the machine coordinate space.

Surgeon-dependent factors such as optimal implant alignment of the tibial component are thought to play a significant role in the outcome following primary total knee arthroplasty (TKA). In addition, tibial component malrotation is associated with pain, stiffness, and altered patellofemoral kinematics in TKA. However, measuring tibial component rotation after TKA is difficult. Therefore, the purpose of this study was to find a reliable method for positioning the tibial component in TKA. To investigate the morphology of the tibial plateau, 977 patients' knees (829 females and 148 males) were evaluated using MRI. The relationships between the femoral transepicondylar axis (TEA), Akagi line, posterior tibial margin (PTM), medial third of the tibial tubercle (MTT), and anatomical tibial axis (ATS) were investigated in this study. In addition, gender difference in tibial rotational alignment were evaluated. Relative to the TEA, the MTT and ATS were externally rotated by 0.5° ± 4.4° and 0.5° ± 5.4°, respectively, while Akagi line and PTM were internally rotated by 3.7° ± 4.5° and 9.9° ± 6.1°, respectively. Gender differences were found in MTT, Akagi line and ATS (P