Oblique Cone Research Articles

Delineating Sight Occlusions of Head-On Traffic Signboards under Varying Available Sight Distances Using LiDAR Point Clouds

It is essential to delineate visual occlusions of head-on traffic signboards under varying available sight distances (ASDs) to improve road safety and guide maintenance. However, the status of sight occlusions in actual road scenarios is unclear because of the lack of an automatic and quantitative evaluation approach. This study presents a new cluster attention traffic-sign occlusion (CASO) method with a cluster attention traffic-sign network (CASNet) to automatically classify road infrastructures, and an occlusion delineating module to dynamically describe the occlusions of head-on traffic signboards using point clouds. CASNet consists of a cluster module to alleviate the interference of redundant object features and an attention module to focus on learning local features of small samples on road scenes. The occlusion delineating module is investigated to rapidly construct a signboard-related oblique cone and dynamically assess occlusions. The sight occlusions change with varying ASDs and are delineated by two indices: the degree of shaded signboard area, and the degree of occlusion volume from the driver’s dynamic perspective to the head-on signboard. Compared with the state-of-the-art networks, the experimental extraction results achieved for signboards show an overall improved performance. The degree of occlusion volumes toward head-on signboards fluctuates between 26.75% and 36.70%, and the degree of shaded areas on signboards increases from 22.75% to 59.63%, with ASDs varying from 20 to 75 m. This research contributes to evaluating road safety in intelligent transportation systems and accurately guiding the allocation of maintenance budgets to the heavily occluded road sections.

Precise Calibration of Binocular Vision System Based on Oblique Cone Projection Model

Precise Calibration of Binocular Vision System Based on Oblique Cone Projection Model

AXOIDS OF HOOKE’S JOINT

The analysis of literary sources devoted to the research and construction of cardan transmissions using the Hooke's joint showed that the peculiarities of the spherical movement of the cardan joint crosspiece are insufficiently covered. This is explained by the relatively small weight of the crosspiece, due to which it almost does not affect the dynamics of the cardan transmission. The need to take into account the mass-geometric parameters of the crosspiece and to analyze comprehensively its movement may arise during accurate calculations of high-speed cardan transmissions. In this case, it is convenient to consider the movement of the crosspiece as rolling without sliding of the moving axoid on the stationary axoid. This approach makes it possible to more fully investigate the peculiarities of the spherical movement of the crosspiece and gives a visual representation of the orientation of its instantaneous axis of rotation in fixed and moving coordinate systems. Based on this, this work is devoted to the construction of a kinematic model of the Hooke's joint crosspiece, the movement of which is considered as rolling without sliding of a moving axoid on a stationary one.
 As a result of the kinematic analysis of the Hooke's joint, the equations of the hodographs of the vector of the absolute angular velocity of the crosspiece in the fixed and moving coordinate systems were obtained, and the parameters of the fixed and moving axoids of the crosspiece of the cardan joint were determined. It is proved that the stationary axoid of the crosspiece of the Hooke's joint is an oblique elliptic cone with the apex in the center of the crosspiece, and its opposite generatrices, crossing the major axis of the guide ellipse, coincide with the axes of the drive and driven shafts of the joint. The moving axoid of the crosspiece is a closed conical surface with a variable opening angle, the maximum value of which is equal to twice the value of the interaxial transmission angle. With small values of the interaxial angle, which occur in the practice of using a single Hooke’s joint, a moving axoid can be approximately considered as a straight circular cone with a vertex in the center of the crosspiece and an opening angle equal to twice the value of the interaxial transmission angle. The error of this assumption increases rapidly with the increase of the interaxial transmission angle. The correctness of the obtained mathematical model was confirmed by computer modeling in the Autodesk Inventor environment.
 The obtained results can be used in the study of dynamic processes that occur in cardan transmissions using Hooke's joint.

Diaboloidal mirrors: algebraic solution and surface shape approximations.

A new type of optical element that can focus a cylindrical wave to a point focus (or vice versa) is analytically described. Such waves are, for example, produced in a beamline where light is collimated in one direction and then doubly focused by a single optic. A classical example in X-ray optics is the collimated two-crystal monochromator, with toroidal mirror refocusing. The element here replaces the toroid, and in such a system provides completely aberration free, point-to-point imaging of rays from the on-axis source point. We present an analytic solution for the mirror shape in its laboratory coordinate system with zero slope at the centre, and approximate solutions, based on bending an oblique circular cone and a bent right circular cylinder, that may facilitate fabrication and metrology.

Micromechanism of the Breakage of Two Spherical Gypsum Particles under Normal–Tangential Contact Conditions

Contact breakage of particles makes a large difference in the strength of coarse-grained soils, and exploring the characteristics within the process of the breakage is of great significance. Ignoring the influence of particle shape, the micromechanism of two spherical particles breaking under normal–tangential contact conditions was investigated theoretically and experimentally. Through theoretical analysis, the breakage form, the shape and size of the conical core, and the relationship between the normal and tangential forces at crushing were predicted. Particle contact tests of two gypsum spheres were carried out, in which the breakage forms, features of the conical cores and the normal and tangential forces at crushing were recorded for comparison with the predicted values. The test results and the theoretical predictions showed good agreement. Both the analysis and test demonstrate that the presence of tangential forces causes the conical core to assume the shape of an oblique cone, and the breakage form to change. Moreover, with increasing normal contact force, the tangential force needed for crushing increases gradually first and then decreases suddenly.

The Surface Area of a Scalene Cone as Solved by Varignon, Leibniz, and Euler

In a 1727 mathematical compendium, Pierre Varignon (1654-1722) published his solution to the problem of finding the surface area of a scalene (oblique) cone, one whose base is circular but whose vertex is off-center. The article after Varignon's in that publication was by Gottfried Leibniz (1646-1716), who proposed improvements and even extended the solution to a base with any curve. When Leonhard Euler (1707-1783) published on the subject [E133] in 1750, he gently pointed out an error in Leibniz's solution, which he corrected, after extending Varignon's solution in the case of circular base. Euler then used Leibniz's approach to solve the general problem. This paper examines all three articles, including English translations.

A Model of Diameter Measurement Based on the Machine Vision

If the shaft diameter can be measured in-situ during the finishing process, the closed-loop control of the shaft diameter processing process can be realized and the machining accuracy can be improved. Present work studies the measurement of shaft diameter with the structured light system composed of a laser linear light source and a camera. The shaft is a kind of part with rotationally symmetric structure. When the linear structured light irradiates the surface of the shaft, a light stripe will be formed, and the light stripe is a part of the ellipse. Therefore, the in-situ measurement of the shaft diameter can be realized by the light stripe and the rotational symmetry of the shaft. The measurement model of shaft diameter is established by the ellipse formed by the intersection of the light plane and the measured shaft surface. Firstly, in the camera coordinate system, normal vector of the light plane and the coordinates of the ellipse center are obtained by the calibration; then, the equation of oblique elliptic cone is established by taking the ellipse as the bottom and the optical center of the camera as the top. Next, the measurement model of shaft diameter is obtained by the established oblique elliptic cone equation and theoretical image plane equation. Finally, the accuracy of the measurement model of shaft diameter is tested by the checkerboard calibration plate and a lathe. The test results show that the measurement model of shaft diameter is correct, and when the shaft diameter is 36.162mm, the speed is 1250r/min, the maximum average measurement error is 0.019mm. The measurement accuracy meets the engineering requirement.

Ducting of upper-hybrid waves by density depletions in a magnetoplasma with weak spatial dispersion

The effects of wave trapping and ducting inside a plasma density depletion are studied in a large laboratory magnetoplasma in the upper-hybrid (UH) range of frequencies. A field-aligned density depletion is generated via localized rf plasma heating and subsequent plasma thermal diffusion. Test UH waves are emitted and detected by small-size electric monopole antennas. For a given set of experimental parameters, propagation of UH waves can be considered as collisionless. At the same time, wave surface topology in the UH range is determined by weak spatial dispersion, which is conditioned by the thermal motion of electrons and the ambient magnetic field. For various density depletion depths and diameters, ducting of UH waves belonging to different characteristic parts of the “dumbbell-shaped” wave surface can be observed. Particularly, quasiparallel Langmuir (L-mode) waves and oblique resonance cone (X-mode) waves can be ducted in different regimes. A qualitative explanation of ducting regimes is given based on ray tracing analysis.

A research on thickness distribution of oblique cone in dieless shear spinning

In order to shorten the preparation period, dieless shear spinning is widely used in various industrial fields with advantage of economy of materials and easy control. Controlling roller path is one of the main methods for changing thickness distribution. A new discretization method is proposed by theoretical derivation in dieless shear spinning. It will generate a virtual axis by inclining the flange of the workpiece. And, the roller path is derived for spinning machine combined with the sine law in shear spinning. The derived path should be applied after the range of forming reaches the certain height. The thickness distribution of formed workpiece is basically in agreement with the theoretical value. It also illustrates that roller nose radius and axial feed will influence the surface quality.

A mathematical method for precisely calculating the radiographic angles of the cup after total hip arthroplasty

We established a mathematical method to precisely calculate the radiographic anteversion (RA) and radiographic inclination (RI) angles of the acetabular cup based on anterior–posterior (AP) pelvic radiographs after total hip arthroplasty. Using Mathematica software, a mathematical model for an oblique cone was established to simulate how AP pelvic radiographs are obtained and to address the relationship between the two-dimensional and three-dimensional geometry of the opening circle of the cup. In this model, the vertex was the X-ray beam source, and the generatrix was the ellipse in radiographs projected from the opening circle of the acetabular cup. Using this model, we established a series of mathematical formulas to reveal the differences between the true RA and RI cup angles and the measurements results achieved using traditional methods and AP pelvic radiographs and to precisely calculate the RA and RI cup angles based on post-operative AP pelvic radiographs. Statistical analysis indicated that traditional methods should be used with caution if traditional measurements methods are used to calculate the RA and RI cup angles with AP pelvic radiograph. The entire calculation process could be performed by an orthopedic surgeon with mathematical knowledge of basic matrix and vector equations.

The Design of New Cycloid Gear with Variable Cross Section and the Research of End Milling in Five-Axis Machine Tool

In order to improve the transmission efficiency and the service life of ordinary cycloid gear, 5 kinds of new cycloid gears with variable cross section are devoleped based on the principles of traditional cycloid drive. These new cycloid gears include concave cycloid gear, drum cycloid gear, spherical cycloid gear, oblique cycloid gear and cone cycloid gear. The general mathematical equations of these new cycloid gears are obtained and the characteristics of these new cycloid gears in transmission applications are analyzed in detail. A new method on the end milling tooth profile surfaces of cycloid gear using ball end mill is proposed. 5 axis numerical control simulations of these cycloid gears are conducted and the tool paths of machining cycloid gear are obtained. 5 kinds of cycloid gear with variable section are machined on five-axis CNC machining center, which verifies the correctness of the NC program. The study will provide a new way of designing and machining cycloid gear.

SU‐F‐T‐649: Dosimetric Evaluation of Non‐Coplanar Arc Therapy Using a Novel Rotating Gamma Ray System

Purpose:Stereotactic intra and extra‐cranial body radiation therapy has evolved with advances in treatment accuracy, effective radiation dose, and parameters necessary to maximize machine capabilities. Novel gamma systems with a ring type gantry were developed having the ability to perform oblique arcs. The aim of this study is to explore the dosimetric advantages of this new system.Methods:The rotating Gamma system is named CybeRay (Cyber Medical Corp., Xian, China). It has a treatment head of 16 cobalt‐60 sources focused to the isocenter, which can rotate 360° on the ring gantry and swing 35° in the superior direction. Treatment plans were generated utilizing our in‐house Monte Carlo treatment planning system. A cylindrical phantom was modeled with 2mm voxel size. Dose inside the cylindrical phantom was calculated for coplanar and non‐coplanar arcs. Dosimetric differences between CybeRay cobalt beams and CyberKnife 6MV beams were compared in a lung phantom and for previously treated SBRT patients.Results:The full width at half maxima of cross profiles in the S‐I direction for the coplanar setup matched the cone sizes, while for the non‐coplanar setup, FWHM was larger by 2mm for a 10mm cone and about 5mm for larger cones. In the coronal and sagittal view, coplanar beams showed elliptical shaped isodose lines, while non‐coplanar beams showed circular isodose lines. Thus proper selection of the oblique angle and cone size can aid optimal dose matching to the target volume. Comparing a single 5mm cone from CybeRay to that from CyberKnife showed similar penumbra in a lung phantom but CybeRay had significant lower doses beyond lung tissues. Comparable treatment plans were obtained with CybeRay as that from CyberKnife.ConclusionThe noncoplanar multiple source arrangement of CybeRay will be of great clinical benefits for stereotactic intra and extra‐cranial radiation therapy.

Experimental research on oblique cone die-less shear spinning

In order to break through the limitation of traditional axisymmetric spinning, a discretization method is made to form an oblique cone by die-less shear spinning technique. Due to the characteristics of asymmetric spinning, the roller feed should harmonize with the spindle rotation, and the roller path is derived through a discretization method. The thickness variation of oblique cone in different directions is coincident with the sine relation in axisymmetric shear spinning. The surface quality, especially the surface smoothness (the distribution of arrises) and surface roughness of the spun part, is discussed by analyzing the roller motion and important spinning parameters, and a smaller axial feed rate f and a smaller angle increment Δ α can improve the surface quality.

Fabrication of Comb Shape of Leading Edge Wing of Dragonfly

Research on Micro air vehicle (MAV) has been carried out by many researchers to gather information in environmental monitoring, security and so on. When the earthquake, fire, smoke take place, it is difficult for human beings to investigate the detail because of dangerous condition. However, MAV has possibility to investigate the detail because MAV can fly freely around. Recently, dragonfly is highly focused by many researchers because dragonfly has high flight performances those are high efficiency flight, unintended acceleration, rapid turn and hovering. In general, these characteristics have root that wing is corrugation shape. We focus on microstructures on wing and its aerodynamic characteristics because there are many unique microstructures. We focused on micro spikes on dragonfly wing. Over three thousands of spikes exist on two sides of wing. The length and shape of spikes are 10 to 100 micron meters and oblique circular cone. It is important to clear the aerodynamic effect of the oblique circular cone. Artificial wing was fabricated by following processes. We fabricated micro spikes utilizing electro polishing. Fabricated micro spikes were set on plate utilizing micro spot bonding. We investigated the flow around the artificial wing and found that the flow around wing was controlled by micro spikes on wing. In this paper, we focused on comb shape of leading edge of wing. Comb shape is fabricated utilizing micro-EDM. We investigate flow characteristics of comb shape.

Proposal of a Planar Directional UWB Antenna for Any Desired Operational Bandwidth

A novel planar directional UWB antenna is proposed. The antenna design evolves from an oblique elliptic cone antenna by applying the planar-solid correspondence to two axes. Through a simple equation, this antenna can be designed, to operate at a specific lower cutoff frequency with a bandwidth larger than 10 GHz for a reflection coefficient magnitude lower than −10 dB. This characteristic provides the antenna with a good versatility. The directional radiation pattern has an average gain of 6 dBi.

Geometrical Analysis of Localization Error in Stereo Vision Systems

Determining an object location in a specific region is an important task in many machine vision applications. Different parameters affect the accuracy of the localization process. The quantization process in charge-coupled device of a camera is one of the sources of error that causes estimation rather than identifying the exact position of the observed object. A cluster of points, in the field of view of a camera are mapped into a pixel. These points form an uncertainty region. In this paper, we present a geometrical model to analyze the volume of this uncertainty region as a criterion for object localization error. The proposed approach models the field of view of each pixel as an oblique cone. The uncertainty region is formed via the intersection of two cones, each emanating from one of the two cameras. Because of the complexity in modeling of two oblique cones' intersection, we propose three methods to simplify the problem. In the first two methods, only four lines are used. Each line goes through the camera's lens, modeled as a pinhole, and then passes one of the four vertices of a square that is fitted around the circular pixel. The first proposed method projects all points of these four lines into an image plane. In the second method, the line-cone intersection is used instead of intersection of two cones. Therefore, by applying line-cone intersection, the boundary points of the intersection of the two cones are determined. In the third approach, the extremum points of the intersection of two cones are determined by the Lagrangain method. The validity of our methods is verified through extensive simulations. In addition, we analyze effects of parameters, such as the baseline length, focal length, and pixel size, on the amount of the estimation error.

Surface development of oblique circular cone with SolidWorks re-development

Because the unfolded process of three-way conical pipe is complex,the development drawing cannot be completed automatically.This paper introduced a general analytic algorithm about the development of curve oblique based on the thought of symbolic-graphic combination.The equation of two conical intersection line was established by exploring the mathematical model of the skew intersection to the axis of the cone.The intersecting lines in the SolidWorks interface were created by means of VB progamming and were verified through SolidWorks.After setting up flattening curve equation,the development drawing was carried out in the SolidWorks.Thus,the expansion plan of two cones with arbitrary size and skew axises was designed by parametric means on the SolidWorks interface.The unfolding method is reliable and it makes automatic development drawing practical.The results and relevant data also reveal that the algorithm is of fast speed,high precision and strong universality,which can be used for the expansion mapping of a variety of sheet metal parts to facilitate the manufacture of sheet metal parts.

Collisionless tool orientation smoothing above blade stream surface using NURBS envelope

In five-axis machining, tool orientation above a blade stream surface may lead to tool collision and a decrease in workpiece rigidity. Hence, collisionless tool orientation smoothing (TOS) becomes an important issue. On the basis of a constant scallop height tool path, the triangular facets in the faces, vertices format are constructed from cutter contact (CC) using the Voronoi incremental algorithm. The cutter location (CL) points candidate set is represented by an oblique elliptic cone whose vertex lies at CC using NURBS envelope. Whether the CL point is above its CC is judged by the dot product between the normal vector and the point on triangulation nearest to the CL point. The curvatures at CC are obtained by fitting a moving least square (MLS) quadratic patch to the local neighborhood of a vertex and calculating eigenvectors and eigenvalues of the Hessian matrix. Triangular surface elastic energy is employed as the weight in selection from the NURBS envelope. The collision is judged by NURBS surface intersection. TOS can then be expressed by selecting a CL point for each CC point and converted into a numerical control (NC) code automatically according to the postprocessor type of the machine center. The proposed method is verified by finishing of a cryogenic turboexpander impeller of air separation equipment.

The Theory and Observational Evidence for Streamlets: A New Velocity-Based Feature Model of Jet Streams and Eddies in the Oceans

The aim of this study is the verification of a new velocity-based feature model, called streamlets, proposed recently for objective analysis of the three-dimensional velocity structure of jet streams and eddies in the oceans. Streamlets are continuously imbedded shearing vortex solenoids having two forms: cylindrical (for jets) or toroidal (for eddies, considered as self-closed jets). Both these forms comprise stream coordinates based on streamlines of maximum velocity as an axis and vertical velocity cross-sections defined as an oblique cone with elliptical base. Assimilation of velocity measurements is accomplished by fitting this cone to available data using the well-known Nelder-Mead simplex downhill algorithm for finding the minimum of nonlinear parametric functions. Advantages of the streamlet model are discussed emphasizing its functional integrity. The focus is on velocity data assimilation based on coherency of synoptic scale features as opposed to usual pointwise assimilation methods such as averaging or optimal interpolation. Case studies present synoptic features of a different origin and scale including surface-intensified and subsurface baroclinic examples as well as deep barotropic ones demonstrating universality of the model. The theory of streamlets is also addressed in this paper, since it further sustain the streamlet model.

Application of CAD/CAM Technology in the Development and Lofting of Complex Sheet Metal Parts

For a development and lofting of complex sheet metal parts, the traditional work is hard and lack of accuracy. Using CAD/CAM to aid development and lofting needs neither lofting site nor mathematic models, but can achieve high quality and efficiency. The development and lofting of multi-tapered conical tube with 90º elbows as an example, the paper describes the methods of development and lofting of complex sheet metal parts based on CAD​/CAM technology, such as drawing view of four sections of tapered conical tube with 90º elbow, drawing graphic model and developed view of frustum conical tube, checking the coordination situation of each section oblique cone tube model, and blanking programming using CAXA wire EDM V2 software.