584 research outputs found
The Kinematic Image of 2R Dyads and Exact Synthesis of 5R Linkages
We characterise the kinematic image of the constraint variety of a 2R dyad as
a regular ruled quadric in a 3-space that contains a "null quadrilateral".
Three prescribed poses determine, in general, two such quadrics. This allows us
to modify a recent algorithm for the synthesis of 6R linkages in such a way
that two consecutive revolute axes coincide, thus producing a 5R linkage. Using
the classical geometry of twisted cubics on a quadric, we explain some of the
peculiar properties of the the resulting synthesis procedure for 5R linkages.Comment: Accepted for publication in the proceedings of the IMA Conference on
Mathematics of Robotics, Oxford, 201
Equivalent birational embeddings II: divisors
Two divisors in are said to be Cremona equivalent if there is a
Cremona modification sending one to the other. We produce infinitely many non
equivalent divisorial embeddings of any variety of dimension at most 14. Then
we study the special case of plane curves and rational hypersurfaces. For the
latter we characterise surfaces Cremona equivalent to a plane.Comment: v2 Exposition improved, thanks to referee, unconditional
characterization of surfaces Cremona equivalent to a plan
Equivariant Degenerations of Plane Curve Orbits
In a series of papers, Aluffi and Faber computed the degree of the
orbit closure of an arbitrary plane curve. We attempt to generalize this to the
equivariant setting by studying how orbits degenerate under some natural
specializations, yielding a fairly complete picture in the case of plane
quartics.Comment: 33 pages, comments welcom
A Worldsheet Description of Planar Yang-Mills Theory
We extend previous work by developing a worldsheet description of non-abelian
gauge theory (Yang-Mills). This task requires the introduction of Grassmann
variables on the world sheet analogous to those of the Neveu-Schwarz-Ramond
formulation of string theory. A highlight of our construction is that once the
three gluon vertices of Yang-Mills Feynman diagrams are given a worldsheet
description, the worldsheet formalism automatically produces all of the quartic
vertices.Comment: 18 pages, 15 figures, reference added, paragraph added to section
3.3, erroneous statement in section 4 corrected, typos correcte
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