Moduli space of planar polygonal linkage: a combinatorial description

Panina, Gaiane

doi:10.48550/arxiv.1209.3241

Cited by 5 publications

(14 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• The topological type of the moduli space M(L) depends only on the chamber containing L [4]. • M(L) admits a structure of a regular cell complex [7]. The combinatorics is very much related (but not identical) to the combinatorics of the permutohedron.…”

Section: Moduli Spaces Of Planar Polygonal Linkagesmentioning

confidence: 99%

“…Description of the cell complex. Now we sketch the cell complex structure on the moduli space M(L), referring the reader to [7] for even more details and all the proofs. The cell structure comes from the following labeling of configurations.…”

Section: Moduli Spaces Of Planar Polygonal Linkagesmentioning

confidence: 99%

“…Our reconfiguring algorithm is based on a stratification of the moduli space into a cell complex, introduced in [7]. More precisely, we treat the one-skeleton…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Motion planning and control of a planar polygonal linkage

Panina

Siersma

2018

Journal of Symbolic Computation

Self Cite

View full text Add to dashboard Cite

For a polygonal linkage, we produce a fast navigation algorithm on its configuration space. The basic idea is to approximate the configuration space by the vertex-edge graph of its cell decomposition discovered by the first author. The algorithm has three aspects: (1) the number of navigation steps does not exceed 15 (independent of the linkage), (2) each step is a disguised flex of a quadrilateral from one triangular configuration to another, which is a well understood type of flex, and (3) each step can be performed explicitly by adding some extra bars and obtaining a mechanism with one degree of freedom.

show abstract

Section: Moduli Spaces Of Planar Polygonal Linkagesmentioning

confidence: 99%

Section: Moduli Spaces Of Planar Polygonal Linkagesmentioning

confidence: 99%

See 1 more Smart Citation

Motion planning and control of a planar polygonal linkage

Panina

Siersma

2018

Journal of Symbolic Computation

Self Cite

View full text Add to dashboard Cite

show abstract

“…Polygonal linkage: moduli space and the cell complex [12]. A polygonal n-linkage is a sequence of positive numbers L = (l 1 , .…”

Section: Preliminariesmentioning

confidence: 99%

“…The starting point of our construction is a cell decomposition of the moduli space constructed in [12] and reviewed in the next section. The number of cells is big: it exceeds the sum of Betti numbers very much.…”

Section: Introductionmentioning

confidence: 99%

Discrete Morse theory for moduli spaces of flexible polygons, or solitaire game on the circle

Panina¹,

Zhukova²

2015

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Coulomb Control of Polygonal Linkages

2014

View full text Add to dashboard Cite

Equilibria of polygonal linkage with respect to Coulomb potential of point charges placed at the vertices of linkage are considered. It is proved that any convex configuration of a quadrilateral linkage is the point of global minimum of Coulomb potential for appropriate values of charges of vertices. Similar problems are treated for the equilateral pentagonal linkage. Some corollaries and applications in the spirit of control theory are also presented.

show abstract

Moduli space of planar polygonal linkage: a combinatorial description

Cited by 5 publications

References 0 publications

Motion planning and control of a planar polygonal linkage

Motion planning and control of a planar polygonal linkage

Discrete Morse theory for moduli spaces of flexible polygons, or solitaire game on the circle

Coulomb Control of Polygonal Linkages

Contact Info

Product

Resources

About