On the area of constrained polygonal linkages
Publication date
2018-04-01
Authors
Panina, Gaiane
Siersma, D.
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Document Type
Article
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Abstract
Consider a mechanical linkages whose underlying graph is a polygon with a diagonal constraint, or more general, a partial two-tree. We show that (with an appropriate definition) the oriented area is a Bott–Morse function on the configuration space of the linkage. 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).
Keywords
Critical point, Morse index, Partial two-tree, Pitchfork bifurcation, Two-terminal series-parallel graph, Taverne, Geometry and Topology
Citation
Panina, G & Siersma, D 2018, 'On the area of constrained polygonal linkages', Topology and its Applications, vol. 238, pp. 32-44. https://doi.org/10.1016/j.topol.2018.02.004