Dynamic modeling of multi-link flexible robotic manipulators

This paper presents a linearized dynamic model for multi-link planar flexible manipulators which can include an arbitrary number of flexible links. The elastic deformation of each link is modeled by using the assumed-mode method. Flexible links are treated as Euler–Bernoulli beams and the rotary inertia and shear deformation are thus neglected. The Lagrange approach is adopted to establish equations of motion for the total robotic manipulator system. The motion of each link is decomposed as the nonlinear gross rigid body motion upon which small elastic deformations are superimposed. The rigid-body motion and elastic deformations are decoupled by linearizing the equations of motion around the rigid-body reference trajectory. The proposed method can be used in both dynamic simulation and controller design. Numerical simulations of two-link flexible robotic manipulators are included to verify the proposed method.