This research work focuses on finding an optimal trajectory for a robot manipulator taking into consideration the dynamics constraints of the manipulator. A 3-DOF planar robot was modeled using MATLAB/SIMULINK toolbox. The simulation of the robot manipulator was carried out using the Genetic Algorithm to find the optimal trajectory both in the workspace with and without obstacles. In both cases, the Genetic Algorithm (GA) generated optimal trajectories. The results of both environments were also compared. The increase in the simulation result in an obstacle existence environment made it possible for optimal trajectory devoid of collision with any obstacle in the working area. Thereafter, result comparison was done with a similar work and the GA method produced a more desired result in terms of execution time.