The dynamical performance of robot manipulators is greatly affected by the different payloads handled by the end-effector (hand). Hence, it is very important, especially for industrial applications, to study the different interconnected relationships between the manipulator's joints, speeds, loads and actuation forces. In the paper, a simplified semicustomised symbolic formulation of robot dynamics, based on the Lagrangian, is presented, with emphasis on the Coriolis and centripetal effects. The accuracy and computational efficiency of this new formulation is demonstrated by simulation of the Stanford and PUMA 560 robot manipulators. Useful quantitative measurements and error analysis are also included on the significance of Coriolis and centripetal terms, under different load and speed conditions.