Explicit dynamic modeling of a planar two-link flexible manipulator

An explicit, complete, and accurate dynamic model for lightweight flexible arms is presented. A planar two-link flexible arm with rotary joints subject only to bending deformations in the plane of motion is considered (torsional effects are neglected). A payload is added at the tip of the outer link, while hub inertias are included at the actuated joints. Links are modeled as Euler-Bernoulli beams of uniform density with clamped-mass boundary conditions. A finite-dimensional model of link flexibility is obtained with two assumed modes for each link. The standard Lagrangian approach is followed, and the resulting dynamic equations are given