Dynamic modeling of multi-flexible-link planar manipulators using curvature–based finite element method

Abstract

In conventional displacement-based finite element formulation, the nodal transverse deflections and slopes of a beam element are used to approximate its transverse deflection distribution. In this paper, a curvature-based finite element formulation is presented for dynamic modeling of planar multi-link flexible manipulators. This formulation approximates the curvature distribution of the Euler-Bernoulli beam element by using its nodal curvatures. Therefore, in the curvature-based finite element formulation, fewer numbers of total elastic degrees of freedom for the system are needed. In addition, while the displacement-based finite element formulation yields discontinuous bending stresses at the inter-element nodes, this modeling provides continuous bending stress at those nodes. The proposed modeling will be verified and the dynamic behavior of the flexible planar manipulators will be studied.