This work focuses on additive manufacturing by Directed Energy Deposition (DED) using a 6-axis robot. The objective is to generate an optimized trajectory in the joint space, taking into account axis redundancy for parts of revolution produced with a coaxial deposition system. To achieve this goal, a new layer-by-layer method coupled with a trajectory constrained optimization is presented. The optimization results are theoretically compared to a non-optimized trajectory and a point-by-point optimized trajectory. The layer-by-layer generation of optimized trajectories is validated experimentally on a 6-axis robot using a PLA extrusion system. Experimental results show that the layer-by-layer trajectory optimization strategy applied to parts of revolution provides better geometrical accuracy while improving the efficiency of the manufacturing device compared to non-optimized solutions.