Abstract: The present invention relates to a method and a device for displacing a moving body (4) on a base (2) mounted elastically with respect to the ground (S), the moving body (4) being displaced linearly with a predetermined displacement under the action of a controllable force (F). According to the invention: a) a mathematical relationship illustrating the movements of the entity formed by the base (2) and the moving body (4) is defined; b) using said mathematical relationship there is determined a force (F) which, applied to the moving body (4), produces a combined effect on the moving body (4) so that it performs said predetermined displacement, and on the base (2) at least so that it is immobile at the end of the displacement of the moving body (4); and c) the force (F) thus determined is applied to the moving body (4).