The reproduction of hand movements by a robot remains difficult and conventional learning methods do not allow us to faithfully recreate these movements because it is very difficult when the number of crossing points is very large. Programming by demonstration gives a better opportunity for solving this problem by tracking the user s movements with a motion capture system and creating a robotic program to reproduce the performed tasks. This paper presents a programming by demonstration system in a trajectory level for the reproduction of hand/tool movement by a manipulator robot; this was realized by tracking the user s movement with the ArToolkit using a normal camera (low cost) and reconstruct the trajectories by using the constrained cubic spline, which gives better results comparing the conventional cubic spline interpolation. And finally the obtained trajectories will be simulated in a virtual environment on a robot (Puma 600) based on a computed torque controller.