This work presents the problem of trajectory generation based on the use of artificial potential fields associated to articulated robotic manipulators, in order to find a trajectory so that a manipulator reaches a goal from an initial position without colliding with obstacles within its workspace. The search of a continuous sequence of collision-free configurations between an initial configuration and the final position implies the exploration of a non-linear solution space which can be described and solved with an optimization approach. It does not take into account the use of complex mathematics in an analytical or numerical solution of the inverse kinematics, where are shown manifolds solutions as a result of the angular displacements of each joint of the robot. The genetic algorithm used as strategy, reduces the complexity of the problem, because the geometric connection equations are obtained systematically. In addition, the artificial potential field simulates the attraction and repulsion forces between the goal and the obstacles, where the goal is identified as the global minimum and the obstacles as restricted points. Altogether the potential field and the genetic algorithm generate trajectories for the robot among the obstacles through the design of an appropriate fitness function that effectively drives the manipulator to the desired while avoiding collide with the obstacles.