A positioning device is disclosed which can include a base and a positioning element, which is configured to be adjusted with respect to six degrees of freedom relative to the base, wherein the positioning element is coupled to the base via at least three pairs of length-variable and electrically driven leg elements, and each leg element is connected, at its respective ends, to the base and the positioning element via an articulation element. A respective pair of legs projects through another pair of legs and each pair of legs is arranged perpendicular to the respective other pairs of legs. According to exemplary embodiments, each of the articulation elements associated with a leg element has only two axes of rotation (DA), which are arranged perpendicular to each other, so that the articulation elements allow pivotal movements of each respective leg element in precisely two planes that are perpendicular to each other and run through a longitudinal axis of the leg element, and at the same time prevent a rotational movement about a longitudinal axis of the leg element.