This paper aims to approximate trajectories along any given paths for robot manipulators. Regarding the very large diversity of robot tasks, the algorithms presented here simply assigns a time-optimal motion law (w.r.t the given kinematic motion constraints) to the given path thus converts it into a trajectory, then the algorithm tries to approximate the trajectory with polynomial functions. In this paper, we compare 3rd, 4^th, and 5^th-degree polynomial functions in approximation of trajectories. Comparison results and experiments carried out with an industrial robot arm are also presented.