45,822 research outputs found
Compliance error compensation technique for parallel robots composed of non-perfect serial chains
The paper presents the compliance errors compensation technique for
over-constrained parallel manipulators under external and internal loadings.
This technique is based on the non-linear stiffness modeling which is able to
take into account the influence of non-perfect geometry of serial chains caused
by manufacturing errors. Within the developed technique, the deviation
compensation reduces to an adjustment of a target trajectory that is modified
in the off-line mode. The advantages and practical significance of the proposed
technique are illustrated by an example that deals with groove milling by the
Orthoglide manipulator that considers different locations of the workpiece. It
is also demonstrated that the impact of the compliance errors and the errors
caused by inaccuracy in serial chains cannot be taken into account using the
superposition principle.Comment: arXiv admin note: text overlap with arXiv:1204.175
Non-Smooth Spatio-Temporal Coordinates in Nonlinear Dynamics
This paper presents an overview of physical ideas and mathematical methods
for implementing non-smooth and discontinuous substitutions in dynamical
systems. General purpose of such substitutions is to bring the differential
equations of motion to the form, which is convenient for further use of
analytical and numerical methods of analyses. Three different types of
nonsmooth transformations are discussed as follows: positional coordinate
transformation, state variables transformation, and temporal transformations.
Illustrating examples are provided.Comment: 15 figure
Cooperative surmounting of bottlenecks
The physics of activated escape of objects out of a metastable state plays a
key role in diverse scientific areas involving chemical kinetics, diffusion and
dislocation motion in solids, nucleation, electrical transport, motion of flux
lines superconductors, charge density waves, and transport processes of
macromolecules, to name but a few. The underlying activated processes present
the multidimensional extension of the Kramers problem of a single Brownian
particle. In comparison to the latter case, however, the dynamics ensuing from
the interactions of many coupled units can lead to intriguing novel phenomena
that are not present when only a single degree of freedom is involved. In this
review we report on a variety of such phenomena that are exhibited by systems
consisting of chains of interacting units in the presence of potential
barriers.
In the first part we consider recent developments in the case of a
deterministic dynamics driving cooperative escape processes of coupled
nonlinear units out of metastable states. The ability of chains of coupled
units to undergo spontaneous conformational transitions can lead to a
self-organised escape. The mechanism at work is that the energies of the units
become re-arranged, while keeping the total energy conserved, in forming
localised energy modes that in turn trigger the cooperative escape. We present
scenarios of significantly enhanced noise-free escape rates if compared to the
noise-assisted case.
The second part deals with the collective directed transport of systems of
interacting particles overcoming energetic barriers in periodic potential
landscapes. Escape processes in both time-homogeneous and time-dependent driven
systems are considered for the emergence of directed motion. It is shown that
ballistic channels immersed in the associated high-dimensional phase space are
the source for the directed long-range transport
Steinitz Theorems for Orthogonal Polyhedra
We define a simple orthogonal polyhedron to be a three-dimensional polyhedron
with the topology of a sphere in which three mutually-perpendicular edges meet
at each vertex. By analogy to Steinitz's theorem characterizing the graphs of
convex polyhedra, we find graph-theoretic characterizations of three classes of
simple orthogonal polyhedra: corner polyhedra, which can be drawn by isometric
projection in the plane with only one hidden vertex, xyz polyhedra, in which
each axis-parallel line through a vertex contains exactly one other vertex, and
arbitrary simple orthogonal polyhedra. In particular, the graphs of xyz
polyhedra are exactly the bipartite cubic polyhedral graphs, and every
bipartite cubic polyhedral graph with a 4-connected dual graph is the graph of
a corner polyhedron. Based on our characterizations we find efficient
algorithms for constructing orthogonal polyhedra from their graphs.Comment: 48 pages, 31 figure
On the negative spectrum of the Robin Laplacian in corner domains
For a bounded corner domain , we consider the Robin Laplacian in
with large Robin parameter. Exploiting multiscale analysis and a
recursive procedure, we have a precise description of the mechanism giving the
ground state of the spectrum. It allows also the study of the bottom of the
essential spectrum on the associated tangent structures given by cones. Then we
obtain the asymptotic behavior of the principal eigenvalue for this singular
limit in any dimension, with remainder estimates. The same method works for the
Schr\"odinger operator in with a strong attractive
delta-interaction supported on . Applications to some Erhling's
type estimates and the analysis of the critical temperature of some
superconductors are also provided
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