In this article, the dynamic equations of multiple flexible links robotic manipulators fabricated of functionally graded materials (FGM), whose properties vary continuously along the axial direction and also along the thickness, are examined. Gibbs-Appell methodology and Timoshenko Beam Theory according to the Assumed Mode Method are utilized to obtain the equations of motion and to model the flexible characteristics of links, respectively. Subsequently, the influence of power law index on the vibration response of a two-link functionally graded robotic manipulator is studied for two cases in which the mechanical properties of links vary once along the axial direction and again along the thickness direction of each link. By introducing a parameter called signal energy, it is shown that the power law index has a substantial effect on the vibrational behaviors of the mentioned system; and that by choosing a proper power law index, system vibrations can be reduced considerably in a passive way.