Apparatus comprising: a frame; a platform; a plurality of first connection elements which have one translational degree of freedom and up to one rotational degree of freedom, wherein the first connection elements are connected to the frame by means of second connection elements having at least one rotational degree of freedom, and are connected to the platform by means of third connection elements having at least one rotational degree of freedom; and a device; wherein two, three or more of the first connection elements are provided with orientation determination units; characterised in that the device is configured to determine a position of the platform relative to the frame on the basis of orientation data from the orientation determination units; and the device for determining the position of the platform relative to the frame is configured: to determine two non-parallel direction vectors which describe the respective orientation of first connection elements; to derive from the two direction vectors, respectively, a first and a second straight line parallel to the respective direction vector, wherein the first straight lines extend through first support points and the second straight lines extend through second support points, wherein a relative position of the first support points coincides with a relative position of the centres of rotation of the corresponding second connection elements, and a relative position of the second support points coincides with a relative position of the centres of rotation of the corresponding third connection elements; and to minimise or reduce below a limit value the distances between the first and second straight lines which are parallel in pairs, taking into account the relative position of the first support vectors and taking into account the relative position of the second support vectors, by shifting the first support points relative to the second support points. a frame; a platform; a plurality of first connection elements which have one translational degree of freedom and up to one rotational degree of freedom, wherein the first connection elements are connected to the frame by means of second connection elements having at least one rotational degree of freedom, and are connected to the platform by means of third connection elements having at least one rotational degree of freedom; and a device; wherein two, three or more of the first connection elements are provided with orientation determination units; characterised in that the device is configured to determine a position of the platform relative to the frame on the basis of orientation data from the orientation determination units; and the device for determining the position of the platform relative to the frame is configured: to determine two non-parallel direction vectors which describe the respective orientation of first connection elements; to derive from the two direction vectors, respectively, a first and a second straight line parallel to the respective direction vector, wherein the first straight lines extend through first support points and the second straight lines extend through second support points, wherein a relative position of the first support points coincides with a relative position of the centres of rotation of the corresponding second connection elements, and a relative position of the second support points coincides with a relative position of the centres of rotation of the corresponding third connection elements; and to minimise or reduce below a limit value the distances between the first and second straight lines which are parallel in pairs, taking into account the relative position of the first support vectors and taking into account the relative position of the second support vectors, by shifting the first support points relative to the second support points. to determine two non-parallel direction vectors which describe the respective orientation of first connection elements; to derive from the two direction vectors, respectively, a first and a second straight line parallel to the respective direction vector, wherein the first straight lines extend through first support points and the second straight lines extend through second support points, wherein a relative position of the first support points coincides with a relative position of the centres of rotation of the corresponding second connection elements, and a relative position of the second support points coincides with a relative position of the centres of rotation of the corresponding third connection elements; and to minimise or reduce below a limit value the distances between the first and second straight lines which are parallel in pairs, taking into account the relative position of the first support vectors and taking into account the relative position of the second support vectors, by shifting the first support points relative to the second support points.