Dynamic modelling of a two-link flexible manipulator system incorporating payload

This paper presents dynamic modelling of a two-link flexible manipulator based on closed-form equations of motion. The kinematic model is based on standard frame transformation matrices describing both rigid rotation and modal displacement, under small deflection assumption. The Lagrangian approach is used to derive the dynamic model of the structure. Links are modelled as Euler-Bernoulli beams with proper clamped-mass boundary conditions. A dynamic model of the system, incorporating structural damping, hub inertia and payload, is developed using finite assumed mode methods. Explicit equations of motions are detailed by assuming two modes of vibration for each link. Moreover, effects of payload on the response of the flexible manipulator are discussed. Extensive results that validate the theoretical derivation are presented in the time and frequency domains.