The invention concerns an apparatus (1) comprising a chassis (10) supportedon the ground (S), a mobile platform (44) supporting a subject, and motorizedmeans (30, 32, 38) for driving the platform relative to the chassis. In order toput the subject off balance while moving its lifting polygon, so as to act on thesubjects body according to advanced kinematics, the driving means arecapable of moving the platform off-center relative to a substantially verticalfixed axis (Z-Z) and of driving the platform in rotation about said axis when theplatform is off-center, whereas the platform is provided with peripheral mobilesupporting means (60, 62) on corresponding bearing means (64) secured to thechassis (10), said supporting means being capable of resting the platform onthe chassis by adjustably inclining same relative to the horizontal in a planepassing through the fixed axis and a central region of the platform when the drivingmeans move the platform off-center relative to said axis. The apparatus thusgenerates remarkable neuro-biomechanical actions, while having a reliablelightweight and compact structure.