How Likely is the Variety of Singularities of a Serial Manipulator a Smooth Manifold?

It is commonly assumed that the singularities of serial manpulators constitute generically smooth manifolds. This assumption has not been proved yet, nor is there an established notion of of genericity. In this paper two different notions of generic properties of forward kinematic mappings are discussed. Serial manipulators are classified according to the type of end-effector motion and feasible manipulator geometries. A sufficient condition for that generically singularities form locally smooth manifolds is presented. This condition admits to separately treat the individual classes. As an example it is shown that the singularities of 3-DOF manipulators form generically smooth manifolds.