A Quantitative Evaluation of the Non-Minimum Phase Phenomenon for a Robot ARM

The non-minimum phase phenomena of a robot´s arm modelled by a set of Euler-Bernoulli beams clamped on a moving cart is demonstrated. Modal analysis is used to derive the exact eigensolutions which verify the described geometric boundary conditions. The equations of motion are determined using the assumed mode method. The influence of geometrical and mechanical parameters such as the thickness of the cross sections of the beams, or the beam length, is discussed using numerical simulations. The overall results, with an application to a real robot, show that one has to take the non-minimum phase problem into consideration when designing a flexible mechanical structure