The Newton-Euler formulation of the equations of motion of an open-loop kinematic chain is used within a dynamic computer simulation of a robotic mechanism. Four different methods are presented for obtaining the joint variable accelerations given the joint positions, velocities, and input torques or forces. Each of these methods was programmed in FORTRAN and then executed on a CYBER 175 digital computer. This paper contains a comparison of the computational complexity of these methods and the execution time of the programs which implement them.