Simulation of flexible manipulators with elastic non-linearities

This article presents two simulators of the dynamics of flexible manipulators composed of slender elastic beams. Contrary to the standard dynamic modelling approaches the dynamic models proposed can model moderate deformations or some second order effects which appears in some limit cases as: high velocities, accelerations or tip forces and torques. The models are premised on an exact nonlinear Euler Bernouilli field and the expansion in perturbations is only achieved at the end of the dynamic modelling. This procedure allows one to obtain consistent linear and quadratic models. The two simulation algorithms are based on the NewtonEuler model of the dynamics. The first one is a global projective algorithm. The second one is a recursive one. Simulation results are reported for a long and thin four d.o.f. manipulator.