Dynamic modeling of flexible robotic manipulators

Abstract

The futuristic design as well as control applications of flexible manipulators depend solely on accurate dynamic model. In this paper, elastic behavior of flexible manipulators is modeled using Euler–Bernoulli beam theory and equations of motion are derived using the Lagrange approach. First of all, the elemental kinetic energy as well as potential energy of each link are determined to find the elemental mass and stiffness matrices. Thereafter, global mass and stiffness matrices are obtained. Discretization of the flexible links is done with finite element method (FEM). The case study of a two-link flexible manipulator is taken and its complete dynamic model is developed and validated in both the frequency domain and in the time domain. The results, in terms of natural frequencies and flexural displacements are found in close agreement with those reported in the published literature.