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An efficent Lagangian formulation of manipulator dynamics has been developed. The efficiency derives from recurrence relatons for the velocities, accelerations, and generalized forces. The number of additons and multiplicatins varies linearly with the number of joint, as opposed to past Lagrangian dynamics formulations with an n4 dependence. Wih this formulation it should be possible in principle to compute the Lagrangian dynamics in real time. The computational complexities of this and other dynamics formulations including rect Newton-Euler formulations and tabular formulations are compared. It Is concluded that recursive formultions based either on the Lagrangian or Newton-Euler dynamics offer the best method of dynamns calculation.