A method of trajectory planning with regards to joint velocity and acceleration constraints for industrial 6 DOF manipulator is presented. The task of the robot is to move to specified location in the workspace passing through intermediate waypoints. The proposed algorithm can be used to plan the task of the robot by autonomous systems in smart factories eliminating human participation in the robot programing process. Opposite to similar approaches it does not assume the type of function describing the motion of the robot. The trajectories generated using the proposed approach are smooth and provide smooth velocities and continuous joint accelerations. The motion is planned in such a way to fulfill joint velocity and acceleration constraints. Fulfillment of velocity limitations is accomplished by perturbing the manipulator motion close to velocity limits. To satisfy acceleration constraints a trajectory scaling approach carried out in limited periods of time is used. The results of the research are illustrated by simulations and experiments, in which an analysis of the method of performing robot tasks carried out using built-in algorithms and presented methods are performed.