  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 for the Morse index. Going further
in this direction, we extend these results to the case of open polygonal
chains, or robot arms. We introduce the notion of the oriented area for an open
polygonal chain, prove that critical points are exactly the cyclic
configurations with antipodal endpoints and derive a formula for the Morse
index of a critical configuration.
