Circular Gauge Research Articles

Virtual Gymnasium: Personalized Weight Perception Interface in Lifting Virtual Objects

This paper proposes a pseudo-haptic interface that depicts the virtual weights of dumbbells in a virtual gymnasium. When a user performs a dumbbell biceps curl, he/she fixes the elbow joint as a standard joint and lifts the dumbbell, with its movement trajectory represented as a circular arc. The trajectories and velocity of dumbbell bicep curls differ depending on human physiological characteristics. Therefore, the proposed system provides an adaptable exercise area and force visualization of virtual dumbbells using a velocity-based pseudo-haptic interface and computer vision-based tracking method. The system recognizes the position and rotation of joints related to a dumbbell biceps curl with the implementation of density-based spatial clustering of applications with noise (a clustering algorithm) and resizes the radius and angle of an integrated force circular gauge. Furthermore, when a user lifts a dumbbell, the system recognizes, using linear regression, the current position and lifting force of the virtual dumbbell and visualizes the current lifting force with a guided movement trajectory to match the lifting force. Experimental results show that the proposed pseudo-haptic interface increased weight perception and usability by up to 30% compared to conventional methods (p < 0.05).

Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids.

We consider a quantum spinless nonrelativistic charged particle moving in the plane under the action of a time-dependent magnetic field, described by means of the linear vector potential , with two fixed values of the gauge parameter : (the circular gauge) and (the Landau gauge). While the magnetic field is the same in all the cases, the systems with different values of the gauge parameter are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are circles for and straight lines for . We derive general formulas for the time-dependent mean values of the energy and magnetic moment, as well as for their variances, for an arbitrary function . They are expressed in terms of solutions to the classical equation of motion , with . Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions , when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. It appears that the adiabatic approximation fails when the magnetic field goes to zero. Moreover, the sudden jump approximation can fail in this case as well. The case of a slowly varying field changing its sign seems especially interesting. In all the cases, fluctuations of the magnetic moment are very strong, frequently exceeding the square of the mean value.

A Quantum Charged Particle under Sudden Jumps of the Magnetic Field and Shape of Non-Circular Solenoids

We consider a quantum charged particle moving in the x y plane under the action of a time-dependent magnetic field described by means of the linear vector potential of the form A = B ( t ) − y ( 1 + β ) , x ( 1 − β ) / 2 . Such potentials with β ≠ 0 exist inside infinite solenoids with non-circular cross sections. The systems with different values of β are not equivalent for nonstationary magnetic fields or time-dependent parameters β ( t ) , due to different structures of induced electric fields. Using the approximation of the stepwise variations of parameters, we obtain explicit formulas describing the change of the mean energy and magnetic moment. The generation of squeezing with respect to the relative and guiding center coordinates is also studied. The change of magnetic moment can be twice bigger for the Landau gauge than for the circular gauge, and this change can happen without any change of the angular momentum. A strong amplification of the magnetic moment can happen even for rapidly decreasing magnetic fields.

Squeezing of Relative and Center-of-Orbit Coordinates of a Charged Particle by Step-Wise Variations of a Uniform Magnetic Field with an Arbitrary Linear Vector Potential

We consider a quantum charged particle moving in the xy plane under the action of a time-dependent magnetic field described by means of the linear vector potential A = H(t) [−y(1 + β), x(1 − β)] /2 with a fixed parameter β. The systems with different values of β are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are ellipses for |β| 1. Using the approximation of the stepwise variation of the magnetic field H(t), we obtain explicit formulas describing the evolution of the principal squeezing in two pairs of noncommuting observables: the coordinates of the center of orbit and relative coordinates with respect to this center. Analysis of these formulas shows that no squeezing can arise for the circular gauge (β = 0). On the other hand, for any nonzero value of β, one can find the regimes of excitations resulting in some degree of squeezing in the both pairs. The maximum degree of squeezing can be obtained for the Landau gauge (|β| = 1) if the magnetic field is switched off and returns to the initial value after some time T, in the limit T → ∞.

Comparison of the Measuring Devices during the Evaluating of Circularity Deviation

The contribution deals with the comparison of devices for measuring and evaluation of circularity of deviation. The circularity of deviation was measure on the specific component using in practice. The deviation was measured with using standard circular gauge Formtester MMQ 44 CNC and 3D measuring device SCAN Max. The results were statistical evaluated in tables. Part of the results is the technical and economic evaluation too.

The Effects of Stereoscopic Depth on Vigilance Task Performance and Cerebral Hemodynamics

The current study examined the effect of stereoscopic depth cues on vigilance performance and cerebral hemodynamics as reflected in cerebral bloodflow velocity (CBFV). During a 40 min continuous vigil, participants took the role of a flight engineer in a simulated fuel transfer task involving a circular gauge in which a vertical line was embedded. In a 2D condition, critical signals for detection were cases in which the vertical line was tilted slightly to the right. In a 3D condition, a stereoscopic display projected a 3D image in which critical signals were cases wherein the vertical line appeared to be located in front of the circular gage. The overall level of signal detections was greater in the 3D than in the 2D condition. Moreover, detection scores in the 2D condition showed the vigilance decrement, a temporal decline over time, while those in the 3D condition maintained relative stability. In both conditions, CBFV was greater in the right than in the left cerebral hemisphere and declined significantly over time. The results provide the the initial demonstration that 3D displays can enhance performance in tasks requiring sustained attention and that right hemispheric control may be involved in vigilance performance with both 2D and 3D stimuli.

Quantified Contours of Curvature in Female Index, Middle, Ring, and Small Metacarpophalangeal Joints

To study and quantify the morphology of the curvature of the surfaces of metacarpophalangeal metacarpophalangeal joints and to relate joint morphology to joint function. Forty metacarpophalangeal joints of the index, middle, ring, and small fingers from 5 right and 5 left hands were taken from female cadavers. The articulating surfaces of the metacarpal head and the base of the proximal phalanx were copied in a true-to-scale fashion. The hard plaster models were sliced in 7 sagittal and 7 transverse planes. The curvatures of the section contours were determined with circular gauges. Statistical analyses were performed by analysis of variance and paired Student t-tests. In the sagittal plane, the cartilaginous surface of the metacarpal head is divided into 2 functional regions and a third dorsal region that does not articulate with the base of the proximal phalanx. The articulating surface of the base of the proximal phalanx approximates a circle in the midsagittal plane. The mean median sagittal radius of curvature of the dorsal articulating aspect of the metacarpal head (6.9 mm) is 33% smaller than that of the base of the proximal phalanx (10.3 mm). The palmar articulating aspect of the metacarpal head (5.8 mm) is 44% smaller than that of the base of the proximal phalanx (10.3 mm). In the median transverse section, the mean radius of curvature of the metacarpal head (7.3 mm) is 18% smaller than that of the base of the proximal phalanx (8.9 mm). The data demonstrate the highly significant incongruity in the curvature of the articulating pair. This incongruity provides a joint space with its greatest dimension in the sagittal plane. From a mechanical perspective, the metacarpophalangeal joint mechanically represents a joint with 5 kinematic degrees of freedom: 2 for flexion and extension, 2 for abduction and adduction, and 1 for axial rotation.

OBTAINING DYNAMICAL GROUPS AND QUANTUM DEGREES OF FREEDOM BY USING NOETHER’S THEOREM: THE PLANAR LANDAU SYSTEM

The noncompact quantum dynamical group SU(2, 1) and the associated su(2, 1) spectrum-generating algebra of the nonrelativistic planar Landau system are constructively obtained from the classical theory, by considering time-dependent Noether symmetry transformations and along the lines of a procedure recently proposed by Castaños, Frank and López-Peña. For this nonconstrained system in the circular gauge, we have found an explicitly time-dependent Hermitian invariant operator, which is crucial for the correct identification of the number of quantum degrees of freedom.

Correcting for systematic errors of circular gauges

Correcting for systematic errors of circular gauges

Radius optimisation in an ultrasonic specimen with a circular gauge profile

When a hyperbolic cosine is used as an approximate profile function for a specimen with a circular gauge profile, it is shown that there is a unique profile radius Gamma which minimises the errors occasioned by the approximation.

The ultrasonic stress distribution in a specimen with a circular gauge profile

The ultrasonic particle displacement and stress amplitude along a solid body of revolution with a circular profile is obtained. In the calculation, a hyperbolic cosine function is approximated to the arc of circle profile, and it is shown that there is negligible error in this approximation. The results are used in the design of specimens for ultrasonic fatigue testing.