Title: On the area of constrained polygonal linkages,
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).