Feasible trajectories for a non-redundant robot at a singularity

At singular configurations, the form taken by the Jacobian matrix let one believe that no motion is possible along particular directions (called singular directions). For some singularities, however, a motion along a singular direction is possible if the timing law is properly chosen. In other cases the constraints on the trajectory are stronger, consequently the tangent to the path at the singular point cannot be arbitrary. In this paper, a classification of singularities is proposed and the set of all feasible trajectories is defined for each type of singularities. Different examples are provided