Abstract: In this paper,an efficient method to linearize dynamic models about a nominaltrajectory for robot manipulators is developed from a straightforward Lagragian form-ulation.This method is very simple and systematic.It can be applied to compute thefeedforward control law(i,e.,the generalized forces/torques)about the desired nom-inal trajectory and to design the feedback controller that reduces or eliminates any dev-iations from the desired nominal trajectory.A conspicuous advantage of using this met-hod is that the number of computations for deriving complete linearized dynamic modelsfor a manipulator is so few that the real-time computation can be realized on a mini-computer or micro-computer.The total number of computations for deriving completelinearized dynamic models(including the computation of the generalized forces torques at the joint)about nominal trajectory for the manipulator with six degrees of freedom is at most 2600 multiplications and 2711 additions.Computationally,the proposedmethod is the fastest of all existing methods.