The invention concerns an apparatus (1) comprising a chassis (10) supported on the ground (S), a mobile platform (44) supporting a subject, and motorized means (30, 32, 38) for driving the platform relative to the chassis. In order to put the subject off balance while moving its lifting polygon, so as to act on the subject'body according to advanced kinematics, the driving means are capable of moving the platform off-center relative to a substantially vertical fixed axis (Z-Z) and of driving the platform in rotation about said axis when the platform is off-center, whereas the platform is provided with peripheral mobile supporting means (60, 62) on corresponding bearing means (64) secured to the chassis (10), said supporting means being capable of resting the platform on the chassis by adjustably inclining same relative to the horizontal in a plane passing through the fixed axis and a central region of the platform when the driving means move the platform off-center relative to said axis. The apparatus thus generates remarkable neuro-biomechanical actions, while having a reliable lightweight and compact structure.