A Spherical Near-to-far-Field Transformation Using a Non-Redundant Voltage Representation Optimized for Non-Centered Mounted Quasi-Planar Antennas

This research falls in the antenna measurements related topic, and deals with the problem occurring in the classical spherical near-to-far-field (NTFF) transformation, when it becomes unpractical to mount the antenna under test (AUT) with its center at the center of the scanning sphere. This issue reflects in a growth of the number of near-field (NF) samples to be acquired, since this number depends on the radius of the minimum sphere, which contains the antenna, and is centered at the scanning sphere center. The non-redundant sampling representations of the electromagnetic field are conveniently exploited, to develop an effective spherical NTFF transformation for non-centered AUTs with quasi-planar geometry, requiring a minimum amount of NF samples, and nearly the same as that for a centered mounting of the AUT. Then, the NF data needed to perform the classical NTFF transformation are determined in efficient way from the acquired non-redundant NF samples by employing an accurate 2-D sampling interpolation scheme. Thus, it is possible to significantly save measurement time. Some simulation and laboratory results are reported to show the effectiveness of the developed technique, which takes into account a non-centered AUT mounting.

X-ray Computed Tomography InstrumentPerformance Evaluation, Part I: Sensitivity to Detector Geometry Errors

X-ray computed tomography (XCT), long used in medical imaging and defect inspection, is now increasingly used for dimensional measurements of geometrical features in engineering components. With widespread use of XCT instruments, there is growing need for the development of standardized test procedures to verify manufacturer specifications and provide pathways to establish metrological traceability. As technical committees within the American Society of Mechanical Engineers (ASME) and the International Organization for Standardization (ISO) are developing documentary standards that include test procedures that are sensitive to all known error sources, we report on work exploring one set of error sources, instrument geometry errors, and their effect on dimensional measurements. In particular, we studied detector and rotation stage errors in cone-beam XCT instruments and determined their influence on sphere center-to-center distance errors and sphere form errors for spheres located in the tomographically reconstructed measurement volume. We developed a novel method, called the single-point ray tracing method, that allows for efficient determination of the sphere center-to-center distance error and sphere form error in the presence of each of the different geometry errors in an XCT instrument. In Part I of this work, we (1) describe the single-point ray tracing method, (2) discuss optimal placement of spheres so that sphere center-to-center distance errors and sphere form errors are sensitive to the different detector geometry errors, and (3) present data validating our method against the more conventional radiograph-based tomographic reconstruction method. In Part II of this work, we discuss optimal placement of spheres so that sphere center-to-center distance errors and sphere form errors are sensitive to error sources associated with the rotation stage. This work is in support of ongoing standards development activity within ASME and ISO for XCT performance evaluation.

X-ray Computed Tomography Instrument Performance Evaluation, Part II: Sensitivity to Rotation Stage Errors

The development of standards for evaluating the performance of X-ray computed tomography (XCT) instruments is ongoing within the American Society of Mechanical Engineers (ASME) and the International Organization for Standardization (ISO) working committees. A key challenge in developing documentary standards is to identify test procedures that are sensitive to known error sources. In Part I of this work, we described the effect of geometry errors associated with the detector and determined their influence through simulations on sphere center-to-center distance errors and sphere form errors for spheres located in the tomographically reconstructed measurement volume. We also introduced a new simulation method, the single-point ray tracing method, to efficiently perform the distance and form error computations and presented data validating the method. In this second part, also based on simulation studies, we describe the effect of errors associated with the rotation stage on sphere center-to-center distance errors and sphere form errors for spheres located in the tomographically reconstructed measurement volume. We recommend optimal sphere center locations that are most sensitive to rotation stage errors for consideration by documentary standards committees in the development of test procedures for performance evaluation.

Loci of Points Equally Spaced From Two Given Geometrical Figures. Part 3

The loci (L) equally spaced from a sphere and a straight line, and from a conic surface and a plane, are considered. The following options have been considered. The straight line passes through the center of the sphere (a = 0), at the same time completely at spheres’ positive radiuses a surface of rotation is obtained, forming which the parabola is, and a rotation axis – this straight line. The parabola’s top forms the biggest parallel on the site points of intersection of the parabola’s forming with the rotation axis. Let's call such paraboloid a perpendicular paraboloid of rotation. The straight line crosses the sphere, but does not pass through the center (0 < a < R/2) – a perpendicular paraboloid, at that the surface is also completely obtained at radiuses’ positive values. The straight line is tangent to the sphere (a = R/2) – a surface which projections are parabolas, lemniscates and circles, and a piece from a tangency point to the sphere center – at radiuses positive values; a beam from the sphere center, perpendicular to this straight line – at radiuses negative values, at that the beam and the piece belong to one straight line. The straight line lies out of the sphere (α > R/2) – two different surfaces, having the general properties with a hyperbolic paraboloid, are obtained, one of which is obtained at radius positive values, and another one – at radius negative values. It has been noticed that loci, equally spaced from a sphere and a straight line, and from a cylinder and a point, coincide at equal radiuses and distances from axes to points and straight lines if to take into account the surfaces obtained both at positive, and negative values of radiuses. Locus, equally spaced from the conic surface of rotation and the plane, are two elliptic conic surfaces which in case 7.4.1 degenerate in the conic surfaces of rotation. In cases 7.4.3 and 7.4.4 one elliptic conic surface degenerates in a plane and a parabolic cylinder respectively.

Loci of Points Equally Spaced From Two Given Geometrical Figures. Part 1

Loci of points (LOP) equally spaced from two given geometrical figures are considered. Has been proposed a method, giving the possibility to systematize the loci, and the key to their study. The following options have been considered. A locus equidistant from N point and l straight line. N belongs to l. We have a plane that is perpendicular to l and passing through N. N does not belong to l – parabolic cylinder. A locus equidistant from F point and a plane. In the general case, we have a paraboloid of revolution. The F point belongs to the given plane. We get a straight line perpendicular to the plane and passing through the F point. A locus equidistant from a point and a sphere. The point coincides with the sphere center. We get the sphere with a radius of 0.5 R. The point lies on the sphere. We get the straight line passing through the sphere center and the point. The point does not coincide with the sphere center, but is inside the sphere. We get the ellipsoid. The point is outside the sphere. We have parted hyperboloid of rotation. A locus equidistant from a point and a cylindrical surface. The point lies on the cylindrical surface’s axis. We get the surface of revolution which generatix is a parabola. The point lies on the generatrix of the cylindrical surface of rotation. We get a straight line, perpendicular to that generatrix and passing through the cylinder axis. The point does not lie on the axis, but is located inside the cylindrical surface. We get the surface with a horizontal sketch line – the ellipse, and a front sketch lines – two different parabolas. The point is outside the cylindrical surface. A locus consists of two surfaces. The one with the positive Gaussian curvature, and the other – with the negative one.

Kinematics of a Novel Type Positioning Table for Cast Alignment on Machine Tool

The paper presents a study into the kinematics of a novel type of a rotary positioning table based on the constrained parallel mechanism. Fixture and leveling a workpiece on a machine tool table is an essential stage in machining or layout process. In this study, a compact low-height rotary table is presented for automated leveling, which can be mounted directly on the machine tool table without a significant decrease of the workspace. The authors propose a modification of parallel mechanism by introducing four extensible leg design with specific geometrical constraint for workpiece positioning and in order to achieve higher rigidness. The table is driven by four hydraulic linear actuators which are integrated in the linkages. The designed model allows to rotate the table about the sphere center about three independent axis. Procedures using meta-heuristic methods were implemented to optimize the geometrical dimensions of the entire mechanism for the required workspace.