When a robot is at a singular configuration, i.e. when the Jacobian matrix of the system is not invertible, the classical control laws using the inverse or pseudo-inverse matrix of the Jacobian cannot be used. Nevertheless some tra-jectories can be followed with a finite input even along the degenerate direction. These trajectories, namely the feasible trajectories, are described and studied using the Singular Value Decomposition of the Jacobian matrix. This decomposition allows also to describe and to design the open loop control law which permits to leave the singular position. In a similar way a closed loop control law is given.