Finite Transformation Rigid Motion Mesh Morpher

Abstract Background Tumor motion may compromise the accuracy of liver stereotactic radiotherapy. In order to carry out a precise planning, estimating liver tumor motion during radiotherapy has received a lot of attention. Previous approach may have difficult to deal with image data corrupted by noise. The iterative closest point (ICP) algorithm is widely used for estimating the rigid registration of three-dimensional point sets when these data were dense or corrupted. In the light of this, our study estimated the three-dimensional (3D) rigid motion of liver tumors during stereotactic liver radiotherapy using reconstructed 3D coordinates of fiducials based on the ICP algorithm. Methods Four hundred ninety-five pairs of orthogonal kilovoltage (KV) images from the CyberKnife stereo imaging system for 12 patients were used in this study. For each pair of images, the 3D coordinates of fiducial markers inside the liver were calculated via geometric derivations. The 3D coordinates were used to calculate the real-time translational and rotational motion of liver tumors around three axes via an ICP algorithm. The residual error was also investigated both with and without rotational correction. Results The translational shifts of liver tumors in left-right (LR), anterior-posterior (AP),and superior-inferior (SI) directions were 2.92 ± 1.98 mm, 5.54 ± 3.12 mm, and 16.22 ± 5.86 mm, respectively; the rotational angles in left-right (LR), anterior-posterior (AP), and superior-inferior (SI) directions were 3.95° ± 3.08°, 4.93° ± 2.90°, and 4.09° ± 1.99°, respectively. Rotational correction decreased 3D fiducial displacement from 1.19 ± 0.35 mm to 0.65 ± 0.24 mm (P<0.001). Conclusions The maximum translational movement occurred in the SI direction. Rotational correction decreased fiducial displacements and increased tumor tracking accuracy.

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A Korn-type inequality in SBD for functions with small jump sets

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s021820251750049x ◽

2017 ◽

Vol 27 (13) ◽

pp. 2461-2484 ◽

Cited By ~ 10

Author(s):

Manuel Friedrich

Keyword(s):

Bounded Variation ◽

Elastic Strain ◽

Special Functions ◽

Type Inequality ◽

Rigid Motion ◽

Exceptional Set ◽

Finite Perimeter ◽

Functions Of Bounded Deformation ◽

Jump Set

We present a Korn-type inequality in a planar setting for special functions of bounded deformation. We prove that for each function in [Formula: see text] with a sufficiently small jump set the distance of the function and its derivative from an infinitesimal rigid motion can be controlled in terms of the linearized elastic strain outside of a small exceptional set of finite perimeter. Particularly, the result shows that each function in [Formula: see text] has bounded variation away from an arbitrarily small part of the domain.

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Time-Accurate Simulation of Longitudinal Flight Mechanics with Control by CFD/RBD Coupling

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.226-228.788 ◽

2012 ◽

Vol 226-228 ◽

pp. 788-792 ◽

Cited By ~ 4

Author(s):

Dong Guo ◽

Min Xu ◽

Shi Lu Chen

Keyword(s):

Computational Study ◽

Rigid Motion ◽

Rigid Body Dynamics ◽

Flight Mechanics ◽

Control Surface ◽

Free Flight ◽

Body Dynamics ◽

Computational Fluid Dynamics Cfd ◽

Coupled Solution ◽

Surface Deflections

This paper describes a multidisciplinary computational study undertaken to compute the flight trajectories and simultaneously predict the unsteady free flight aerodynamics of aircraft in time domain using an advanced coupled computational fluid dynamics (CFD)/rigid body dynamics (RBD) technique. This incorporation of the flight mechanics equations and controller into the CFD solver loop and the treatment of the mesh, which must move with both the control surface deflections and the rigid motion of the aircraft, are illustrated. This work is a contribution to a wider effort towards the simulation of aeroelastic and flight stability in regions where nonlinear aerodynamics, and hence potentially CFD, can play a key role. Results demonstrating the coupled solution are presented.

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A Numerical Study of Separation Performance of Vibrating Flip-Flow Screens for Cohesive Particles

Minerals ◽

10.3390/min11060631 ◽

2021 ◽

Vol 11 (6) ◽

pp. 631

Author(s):

Chi Yu ◽

Runhui Geng ◽

Xinwen Wang

Keyword(s):

Surface Energy ◽

Numerical Study ◽

Energy Levels ◽

Great Influence ◽

Rigid Motion ◽

Separation Performance ◽

Gravitational Acceleration ◽

Screening Process ◽

Vibration Intensity ◽

Screen Surface

Vibrating flip-flow screens (VFFS) are widely used to separate high-viscosity and fine materials. The most remarkable characteristic is that the vibration intensity of the screen frame is only 2–3 g (g represents the gravitational acceleration), while the vibration intensity of the screen surface can reach 30–50 g. This effectively solves the problem of the blocking screen aperture in the screening process of moist particles. In this paper, the approximate state of motion of the sieve mat is realized by setting the discrete rigid motion at multiple points on the elastic sieve mat of the VFFS. The effects of surface energy levels between particles separated via screening performance were compared and analyzed. The results show that the flow characteristics of particles have a great influence on the separation performance. For 8 mm particle screening, the particle’s velocity dominates its movement and screening behavior in the range of 0–8 J/m2 surface energy. In the feeding end region (Section 1 and Section 2), with the increase in the surface energy, the particle’s velocity decreases, and the contact time between the particles and the screen surface increases, and so the passage increases. When the surface energy level continues to increase, the particles agglomerate together due to the effect of the cohesive force, and the effect of the particle’s agglomeration is greater than the particle velocity. Due to the agglomeration of particles, the difficulty of particles passing through the screen increases, and the yields of various size fractions in the feeding end decrease to some extent. In the transporting process, the agglomerated particles need to travel a certain distance before depolymerization, and the stronger the adhesive force between particles, the larger the depolymerization distance. Therefore, for the case of higher surface energy, the screening percentage near the discharging end (Section 3 and Section 4) is greater. The above research is helpful to better understand and optimize the screening process of VFFS.

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Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains

Mathematics ◽

10.3390/math9080841 ◽

2021 ◽

Vol 9 (8) ◽

pp. 841

Author(s):

Toshiaki Hishida

Keyword(s):

Evolution Operator ◽

Large Time ◽

Rigid Motion ◽

Time Dependent ◽

Energy Relation ◽

Exterior Domains ◽

Decay Properties ◽

Decay Of Solutions ◽

Whole Space ◽

Expository Paper

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space Rn together with the energy relation imply the desired estimates in exterior domains provided n≥3.

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Discontinuous Non-Rigid Motion Analysis of Sea Ice using C-Band Synthetic Aperture Radar Satellite Imagery

10.1109/cvpr.2004.325 ◽

2005 ◽

Cited By ~ 5

Author(s):

M. Thomas ◽

C. Geiger ◽

C. Kambhamettu

Keyword(s):

Sea Ice ◽

Synthetic Aperture Radar ◽

Motion Analysis ◽

Satellite Imagery ◽

Rigid Motion ◽

Synthetic Aperture ◽

Radar Satellite ◽

Aperture Radar

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Satellite Attitude Control System Design Taking into Account the Fuel Slosh and Flexible Dynamics

Mathematical Problems in Engineering ◽

10.1155/2014/820586 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 7

Author(s):

Alain G. de Souza ◽

Luiz C. G. de Souza

Keyword(s):

Control System ◽

Attitude Control ◽

Center Of Mass ◽

Rigid Motion ◽

Linear Quadratic Regulator ◽

Comparative Investigation ◽

Attitude Control System ◽

Linear Quadratic ◽

Deformable Structure ◽

Fuel Slosh

The design of the spacecraft Attitude Control System (ACS) becomes more complex when the spacecraft has different type of components like, flexible solar panels, antennas, mechanical manipulators and tanks with fuel. The interaction between the fuel slosh motion, the panel’s flexible motion and the satellite rigid motion during translational and/or rotational manoeuvre can change the spacecraft center of mass position damaging the ACS pointing accuracy. This type of problem can be considered as a Fluid-Structure Interaction (FSI) where some movable or deformable structure interacts with an internal fluid. This paper develops a mathematical model for a rigid-flexible satellite with tank with fuel. The slosh dynamics is modelled using a common pendulum model and it is considered to be unactuated. The control inputs are defined by a transverse body fixed force and a moment about the centre of mass. A comparative investigation designing the satellite ACS by the Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) methods is done. One has obtained a significant improvement in the satellite ACS performance and robustness of what has been done previously, since it controls the rigid-flexible satellite and the fuel slosh motion, simultaneously.

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A Hexagonal Prism Folding for Membrane Packaging Based on Concepts of Finite Rigid Motion and Kinematic Synthesis

Volume 5B: 40th Mechanisms and Robotics Conference ◽

10.1115/detc2016-59293 ◽

2016 ◽

Author(s):

Kassim Abdul-Sater

Keyword(s):

Spatial Configuration ◽

Rigid Motion ◽

Building Blocks ◽

Computational Procedure ◽

Hexagonal Prism ◽

Linkage Mechanism ◽

Space Applications ◽

Kinematic Synthesis ◽

Kinematic Chains ◽

Position Synthesis

This paper discusses the use of concepts of finite rigid body kinematics as well as kinematic synthesis in non-rigid, engineering folding problems. The exemplary task consists in designing a folding pattern, which allows to fold a circular sheet from a flat unfolded state into a prescribed compact spatial configuration that forms a hexagonal prism. Other two-configuration design problems may be found for instance in space applications where membranes in tensegrity reflector antennas need to be stowed in a spacecraft. The folding motion could be actuated using an appropriately designed linkage mechanism attached to the membrane, which, however, is not considered in this paper. The specific result of this work is a creative but systematic and computational procedure for crease pattern design. The approach is essentially based on the relative kinematics equations of serial kinematic chains and the finite position synthesis of linkage building blocks. These techniques sucessively combine to segment a flat bounded surface, such that it can reach the prescribed spatial configuration.

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