Dynamic Analysis of Flexible Robotic Manipulators Constructed of Functionally Graded Materials

In this paper, the motion equations of n-flexible-link robotic manipulators constructed of functionally graded materials, whose properties vary continuously along the axial direction and also along the thickness, are investigated. Gibbs–Appell formulation and Timoshenko beam theory based on the assumed mode method are used to derive the motion equations and to model the flexible characteristics of links, respectively. In mathematical modeling the effects of torsion, longitudinal deformation, bending in two directions and gravity effects are also considered. Subsequently, the effect of power law index on the vibration behavior 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 significant influence on the vibrational behaviors of the mentioned system; and that by choosing an appropriate power law index, system vibrations can be reduced substantially in a passive way. Finally, to verify the accuracy of the numerical simulations, the results of this work are compared with the previous works and the reliability of the results of numerical simulations is investigated for the cases in which manipulators are constructed of materials with constant mechanical properties.