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Abstract-This paper presents a methodology for determining an optimal trajectory based on minimizing energy consumption. Firstly we analyze a work process of a robotic manipulator between two given configurations at a given time, and the effect of main factors on motor energy consumption is also analyzed. A mathematical model of torque is used for obtaining a mathematical expression of each joint's torque and angle relationships. More specifically, for a multi-variable, higher order total torque model, a variational principle is used to obtain many differential equations for a multi-DOF (degrees of freedom) robotic manipulator, and iterative optimization is used to determine the optimal trajectory. Finally, a simulation shows that the optimal trajectory can save energy compared with two other trajectories.