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arXiv · 1702.07468

On the area of constrained polygonal linkages

Gaiane Panina·Dirk Siersma
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Abstract

We study configuration spaces of linkages whose underlying graph are polygons with diagonal constrains, or more general, partial two-trees. We show that (with an appropriate definition) the oriented area is a Bott-Morse function on the configuration space. Its critical points are described and Bott-Morse indices are computed. This paper is a generalization of analogous results for polygonal linkages (obtained earlier by G. Khimshiashvili, G. Panina, and A. Zhukova).

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Gaiane Panina, Dirk Siersma. 2017-02-24. On the area of constrained polygonal linkages. https://doi.org/10.1016/j.topol.2018.02.004

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