  Spider mechanisms are the simplest examples of arachnoid mechanisms, they are
one step more complicated than polygonal linkages. Their configuration spaces
have been studied intensively, but are yet not completely understood. In the
paper we study them using the Morse theory of the squared distance function
from the "body" of the spider to some fixed point in the plane. Generically, it
is a Morse-Bott function. We list its critical manifolds, describe them as
products of polygon spaces, and derive a formula for their Morse-Bott indices.
We apply the obtained results to Hooke energy and Voronoi distance.
