Let  be the configuration space of equilateral polygon linkages with nvertices, each edge having length 1 in the Euclidean plane  modulo orientation preserving isometry group. The space  is a codimension-two subspace of  which is the configuration space of a robot arm.

On the other hand, Gottlieb studied the configuration space of a robot arm in  which is homeomorphic to  In this paper, we define a hypersurface of  and study its topology.

robot arm, configuration space, polygon space.