Trajectory planning is one of the most studied topics in robotics. Among several methods, a sampling-based method, Rapidly-exploring Randomized Tree (RRT) algorithm, has become popular over the last two decades due to its computational efficiency. However, the RRT method does not suggest an exact way to obtain a smooth trajectory along the viapoints given by itself. In this paper, we present an approach using a time-optimal trajectory planning algorithm, specifically for robotic manipulators without using inverse kinematics. After the trajectory smoothing with cubic splines in an environment with obstacles considering not only velocity and acceleration but also jerk constraints; the study is simulated on a six degrees of freedom humanoid robot arm model and always finds a solution successfully if there is a feasible one.