Closed form Newton–Euler dynamic model of flexible manipulators

In this paper, a closed-form dynamic model of flexible manipulators is developed, based on the Newton–Euler formulation of motion equations of flexible links and on the adoption of the spatial vector notation. The proposed model accounts for two main innovations with respect to the state of the art: it is obtained in closed form with respect to the joints and modal coordinates (including the quadratic velocity terms) and motion equations of the whole manipulator can be computed for any arbitrary shape of the links and any possible link cardinality starting from the output of several commercial (finite element analysis) FEA codes. The Newton–Euler formulation of motion equations in terms of the joint and elastic variables greatly improves the simulation performances and makes the model suitable for real-time control and active vibration damping. The model has been compared with literature benchmarks obtained by the classical multibody approach and further validated by comparison with experiments collected on an experimental manipulator.