Dynamic Modelling of a Two-link Flexible Manipulator System Incorporating Payload

This paper presents dynamic modelling of a twolink
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.