Effect of vibrating feeder pan geometry on radiometric separator performance

The article offers justifies the optimized shape for the vibrating feeder pan of a radiometric separator, which ensures the maximum travelling speed and uniform flow of ore material in the zone of radiation and recording. Three shapes of pans are discussed: rectangular, parabolic and triangular. It is found that motion of ore material along an inclined rectangular-shape pan is straight-linear. Distribution of ore particles along the width of the channel, which governs the scatter of the motion trajectories relative to the central axis of the channel, depends on the runoff point of particles from the outlet feeder. Proposed for the description of the motion trajectory of ore particles along an inclined channel of parabolic shape, the mathematical model demonstrates the curved and pendulum-wise motion of an ore particle with the attenuating amplitude. The motion of an ore particle in an inclined pan with the triangular-shape channel features the minimized scatter of motion trajectories relative to the central axis of the channel. The analysis of ore motion along vibrating feeder pans with different shape channels is carried out in Rocky DEM environment with regard to interaction of ore particles with the pan surface and with each other. The simulation modeling has proved the conclusions on the efficiency of the triangularshape profile of the vibrating feeder pan as it ensures uniform single-row flow of ore particles along the straight-line trajectory. The triangular shape of the pan contributes to the increased travelling speed of ore particles and, accordingly, to the enhanced capacity of the separator. The radiometric separator efficiency can be increased 1.5 times by changing from the parabolicshape channels to the triangular-shape profiles of vibrating feeder pans at the other operating conditions of radiometric separators being equal.

Spatial Straight-Line Linkages by Factorization of Motion Polynomials

We use the recently introduced factorization of motion polynomials for constructing overconstrained spatial linkages with a straight-line trajectory. Unlike previous examples of such linkages by other authors, they are single-loop linkages and the end-effector motion is not translational. In particular, we obtain a number of linkages with four revolute and two prismatic joints and a remarkable linkage with seven revolute joints one of whose joints performs a Darboux motion.

Finding the Quickest Straight-Line Trajectory for a Three-Wheeled Omnidirectional Robot under Input Voltage Constraints

We provide an analytical solution to the problem of generating the quickest straight-line trajectory for a three-wheeled omnidirectional mobile robot, under the practical constraint of limited voltage. Applying the maximum principle to the geometric properties of the input constraints, we find that an optimal input vector of motor voltages has at least one extreme value when the orientation of the robot is fixed and two extreme values when rotation is allowed. We can find an explicit representation of the optimal vector for a motion under fixed orientation. We derive several properties of quickest straight-line trajectories and verify them through simulation. We show that the quickest trajectory when rotation is allowed is always faster than the quickest with fixed orientation.

Image Reconstruction Based on TV Minimization and OS-EM Method in Linear Scan CT

A straight-line trajectory computed tomography (CT) has been investigated in this paper and a high accuracy reconstruction algorithm based on TV minimization and OS-EM method has been put forward. This new algorithm, which is called TV-OS-EM, takes the advantage of both statistic iterative algorithm OS-EM and the total variation minimization technique, and has an efficient property of de-noising and restoration. The numerical experimental results show that the new method can achieve a remarkable improvement in image quality.

A Straight-Line Trajectory Tomography Method with Algebraic Iteration Reconstruction

A straight-line trajectory tomography method, based on multiple tilted X-ray cone-beams formed by multiple sources and detectors, is investigated. In this method, multiple cone-beams are fixed and tilted at different positions and only the object translates along a straight-line trajectory. This kind of imaging method may have potential applications in industry testing and security inspections. As is known, projection data from a straight-line trajectory based on single cone-beam are incomplete and their reconstruction suffers from a limited-angle problem. The proposed straight-line trajectory tomography method based on multiple tilted X-ray cone-beams can be used to compensate these deficiencies. To reconstruct images, algebraic reconstruction technique (ART) algorithm is deduced. Numerical simulations validate our method.

A Straight-Line Trajectory Tomography Method Based on Multiple Tilted X-Ray Cone-Beams

A straight-line trajectory tomography method, based on multiple tilted X-ray cone-beams formed by multiple sources and detectors, is investigated. In this method, multiple cone-beams are fixed and tilted at different positions and only the object translates along a straight-line trajectory. This kind of imaging method may have potential applications in industry testing and security inspections. As is known, projection data from a straight-line trajectory based on single cone-beam are incomplete and their reconstruction suffers from a limited-angle problem. The proposed straight-line trajectory tomography method based on multiple tilted X-ray cone-beams can be used to compensate these deficiencies. To reconstruct images, the filtered back-projection (FBP) reconstruction algorithm for the middle plane is first derived from the Fourier slice theorem. It is then extended to non-middle planes with the Feldkamp-Davis-Kress (FDK) approximation. Numerical simulations validate our method.