The dynamics of rigid-arm manipulators are characterised by a system of a non-linear, coupled, ordinary differential equations, but manipulators with flexible links, being continuous (distributed) dynamical systems, are governed by non-linear, coupled, ordinary and partial differential equations. In this lecture we describe the assumed modes and finite element models to approximate the flexibility of links. We consider only the bending vibrations of flexible links. We use Euler-Bernoulli beam theory to represent the dynamics of flexible links, and the kinematics of such manipulators are represented utilising 4 x 4 homogeneous transformation matrices. The computations then resulting from Lagrangian formulation of dynamics are used to derive the closed-form equations of motion.

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