In the industrial environment, several constraints affect the robot motion planning. These are imposed by manufacturing considerations, such as, e.g., to strictly follow a given path, or by physical constraints, such as, e.g., to avoid torque saturation. Among the others, limitation on the velocity, acceleration, and jerk at the joints is often required by the robot manufacturers. In this paper, a motion planning algorithm for open-chain robot manipulators that takes into account several constraints simultaneously is presented. The algorithm developed approaches the motion planning algorithm from a wide perspective, solving systematically the joint as well as the Cartesian motion, both for the point-to-point and the fly movements. The validation has been performed first by numerical simulations and then by experiments on two different industrial manipulators, with different size, with and without the presence of a payload, by imposing demanding trajectories where all the constraints have been excited.