38,831 research outputs found
Noncircular rolling joints for vibrational reduction in slewing maneuvers
A rolling joint is provided for obtaining slewing maneuvers for various apparatus including space structures, space vehicles, robotic manipulators, and simulators. Two noncircular cylinders, namely a drive and a driven cylinder, are provided in driving contact with one another. This contact is maintained by two pairs of generally S-shaped bands, each pair forming a generally 8-shaped coupling tightly about the circumferential periphery of the noncircular drive and driven cylinders. A stationarily fixed arm extends between and is rotatably journalled with a drive axle and a spindle axle respectively extending through selected rotational points of the drive cylinder and of the driven cylinder. The noncircular cylinders are profiled to obtain the desired varying gear ratio. The novelty of the present invention resides in using specifically profiled noncircular cylinders to obtain a desired varying gear ratio
About the Algebraic Solutions of Smallest Enclosing Cylinders Problems
Given n points in Euclidean space E^d, we propose an algebraic algorithm to
compute the best fitting (d-1)-cylinder. This algorithm computes the unknown
direction of the axis of the cylinder. The location of the axis and the radius
of the cylinder are deduced analytically from this direction. Special attention
is paid to the case d=3 when n=4 and n=5. For the former, the minimal radius
enclosing cylinder is computed algebrically from constrained minimization of a
quartic form of the unknown direction of the axis. For the latter, an
analytical condition of existence of the circumscribed cylinder is given, and
the algorithm reduces to find the zeroes of an one unknown polynomial of degree
at most 6. In both cases, the other parameters of the cylinder are deduced
analytically. The minimal radius enclosing cylinder is computed analytically
for the regular tetrahedron and for a trigonal bipyramids family with a
symmetry axis of order 3.Comment: 13 pages, 0 figure; revised version submitted to publication
(previous version is a copy of the original one of 2010
Extraction of cylinders and cones from minimal point sets
We propose new algebraic methods for extracting cylinders and cones from
minimal point sets, including oriented points. More precisely, we are
interested in computing efficiently cylinders through a set of three points,
one of them being oriented, or through a set of five simple points. We are also
interested in computing efficiently cones through a set of two oriented points,
through a set of four points, one of them being oriented, or through a set of
six points. For these different interpolation problems, we give optimal bounds
on the number of solutions. Moreover, we describe algebraic methods targeted to
solve these problems efficiently
Vortex motion around a circular cylinder above a plane
The study of vortex flows around solid obstacles is of considerable interest
from both a theoretical and practical perspective. One geometry that has
attracted renewed attention recently is that of vortex flows past a circular
cylinder placed above a plane wall, where a stationary recirculating eddy can
form in front of the cylinder, in contradistinction to the usual case (without
the plane boundary) for which a vortex pair appears behind the cylinder. Here
we analyze the problem of vortex flows past a cylinder near a wall through the
lenses of the point-vortex model. By conformally mapping the fluid domain onto
an annular region in an auxiliary complex plane, we compute the vortex
Hamiltonian analytically in terms of certain special functions related to
elliptic theta functions. A detailed analysis of the equilibria of the model is
then presented. The location of the equilibrium in front of the cylinder is
shown to be in qualitative agreement with the experimental findings. We also
show that a topological transition occurs in phase space as the parameters of
the systems are variedComment: 17 pages, 8 figure
Multi-Dimensional, Compressible Viscous Flow on a Moving Voronoi Mesh
Numerous formulations of finite volume schemes for the Euler and
Navier-Stokes equations exist, but in the majority of cases they have been
developed for structured and stationary meshes. In many applications, more
flexible mesh geometries that can dynamically adjust to the problem at hand and
move with the flow in a (quasi) Lagrangian fashion would, however, be highly
desirable, as this can allow a significant reduction of advection errors and an
accurate realization of curved and moving boundary conditions. Here we describe
a novel formulation of viscous continuum hydrodynamics that solves the
equations of motion on a Voronoi mesh created by a set of mesh-generating
points. The points can move in an arbitrary manner, but the most natural motion
is that given by the fluid velocity itself, such that the mesh dynamically
adjusts to the flow. Owing to the mathematical properties of the Voronoi
tessellation, pathological mesh-twisting effects are avoided. Our
implementation considers the full Navier-Stokes equations and has been realized
in the AREPO code both in 2D and 3D. We propose a new approach to compute
accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a
finite volume solver of the Navier-Stokes equations. Through a number of test
problems, including circular Couette flow and flow past a cylindrical obstacle,
we show that our new scheme combines good accuracy with geometric flexibility,
and hence promises to be competitive with other highly refined Eulerian
methods. This will in particular allow astrophysical applications of the AREPO
code where physical viscosity is important, such as in the hot plasma in galaxy
clusters, or for viscous accretion disk models.Comment: 26 pages, 21 figures. Submitted to MNRA
Metric for attractor overlap
We present the first general metric for attractor overlap (MAO) facilitating
an unsupervised comparison of flow data sets. The starting point is two or more
attractors, i.e., ensembles of states representing different operating
conditions. The proposed metric generalizes the standard Hilbert-space distance
between two snapshots to snapshot ensembles of two attractors. A reduced-order
analysis for big data and many attractors is enabled by coarse-graining the
snapshots into representative clusters with corresponding centroids and
population probabilities. For a large number of attractors, MAO is augmented by
proximity maps for the snapshots, the centroids, and the attractors, giving
scientifically interpretable visual access to the closeness of the states. The
coherent structures belonging to the overlap and disjoint states between these
attractors are distilled by few representative centroids. We employ MAO for two
quite different actuated flow configurations: (1) a two-dimensional wake of the
fluidic pinball with vortices in a narrow frequency range and (2)
three-dimensional wall turbulence with broadband frequency spectrum manipulated
by spanwise traveling transversal surface waves. MAO compares and classifies
these actuated flows in agreement with physical intuition. For instance, the
first feature coordinate of the attractor proximity map correlates with drag
for the fluidic pinball and for the turbulent boundary layer. MAO has a large
spectrum of potential applications ranging from a quantitative comparison
between numerical simulations and experimental particle-image velocimetry data
to the analysis of simulations representing a myriad of different operating
conditions.Comment: 33 pages, 20 figure
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