It is known that cyclic configurations of a planar polygonal linkage are critical points of the
signed area function. In the paper we give an explicit formula of the Morse index for the …

We describe a nonconventional setting for studying cyclic polygons which provides a new
point of view at the conjectures formulated in 90-s by D. Robbins and studied by R …

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 …

Mechanical linkages (also known as hinge mechanisms, linkworks, bar-and-joint
mechanisms, and called systèmes articulés in French, Gelenkenmechanismen in German …

The article offers the authors' insights on their study on the critical points of a polygonal
linkage. The authors state that the polygonal linkage is interpreted as a positive number, in …

We consider the configuration space of planar n-gons with fixed perimeter, which is
diffeomorphic to the complex projective space CP n− 2. The oriented area function has the …

A polygonal linkage can be imagined as a set of $ n $ rigid bars connected by links
cyclically. This construction lies on a plane and can rotate freely around the links, with …

In this paper we study the area function of polygons, where the vertices are sliding along
curves. We give geometric criteria for the critical points and determine also the Hesse matrix …

It is known that a closed polygon P is a critical point of the oriented area function if and only if
P is a cyclic polygon, that is, P can be inscribed in a circle. Moreover, there is a short formula …

We present a number of observations on the complex geometry of quadrilateral linkages. In
particular, we show that, for each configuration of a planar quadrilateral linkage Q (a, b, c, d) …