In a device for the translatory positioning of a platform (1), in particular a tool mount, with articulated rods (2a, 2a9 of invariable length, whose first ends are hinged to he platform (1), and whose second ends are coupled with respectively independent rail-mounted slide blocks (3), wherein the coupling points (9) on the platform (1) and coupling points (11) on the sliding blocks (3) respectively do not lie on a straight line, and the articulated rods (2a, 2a) do not run parallel to either each other or a shared plane, only three independent sliding blocks (3) and accompanying initial articulated rods (2a, 2a) are present. In a first variant, at least one of the coupling points (11) on the sliding blocks (3) is offset relative to the rail axis (4a), and all sliding blocks (3) are arranged on the same rail (4). In a second variant, all sliding block (3) are arranged on the same side horizontally next to the space provided for postioning the platform (1), and essentially run parallel to each other. Three restrictive guides (2b; 23-27) are formed for the platform (1), which are each secured to a sliding block (3) or the accompanying first articulated rod (2a, 2a), and each permit one rotation of the platform (1) relative to the sliding block (3) only around two rotational axes, while preventing rotation around a third rotational axis, wherein the respective third rotational axes do not run parallel to each other, and do not lie in a shared plane.