A Classification of Configuration Spaces of Planar Robot Arms for a Continuous Inverse Kinematics Problem

Using results on the topology of moduli space of polygons (Jaggi, Ph.D. Thesis, University of Bern, 1992; Kapovich and Millson, J. Differ. Geom. 42:133–164, 1994), it can be shown that for a planar robot arm with n segments there are some values of the base-length, z (i.e., length of line joining the base of the arm with its end-effector), at which the configuration space of the constrained arm (arm with its end effector fixed) has two disconnected components, while at other values it has one connected component. We first review some of these known results relating the value of z with the connectivity of the constrained configuration space.