This paper proposes a computational method for solving the dynamic equations of motion of manipulator-robots, using the integration methods. The proposed algorithm is conceived using Mathematica software, which allows the integration of differential system equations by his functions, assuring in this way the result correctness and a high computational speed. The software may be used for the 2-D or 3-D robotsmanipulators, which contain an open kinematics chain with rotation and translation joints. The software allows also for the calculation of the timevariation curves of the degrees of freedom, having as initial data the values of joints generalized forces, the mass and inertia of the robot links, the inertia of the actuators and the initial conditions for joints coordinates and speeds