In Ukraine it is called a "helicopter"...
The device with an installed straightedge I would assign to the category of control mandrels. With the help of this device, it is easy to check the perpendicular movement of the supports, tables and other nodes relative to the axis of the spindle. This article considers the device that I made for the repair of a lathe. For more details, see the process of manufacturing in the section MY_WORKS.
Overview.

Fig.1

Fig.1а

Fig.1б
The device Fig.1 (a, b) consists of: a straightedge (1), mounted with articulation screws (2), in the body (3). The body, in turn, is fixed to the instrumental cone (5). The set screws with a small pitch (4) serve to align the ruler perpendicular to the spindle axis.
The tool cone (5) can be of any type or the use of a transition sleeve is possible.
Tuning.
Adjustment of the device is reduced to using the adjusting screws to establish a straightedge perpendicular to the axis of rotation of the spindle. To do this, install a rack with an indicator on the cross slide and bring it to one of the ends of the straightedge. The indicator is set to zero. By turning the device on 180 degrees, the second end of the straightedge is fed to the measuring rod of the indicator. The difference in readings will give a non-perpendicularity of the straightedge to the axis of the spindle. Rotating the adjusting screws, set the straightedge so that on both its ends the indicator readings do not differ more than 0,005mm. In other words, the straightedge is verified with an accuracy of up to five microns. In practice, you can adjust the straightedge almost to zero at both ends. I used the indicator with the division price is 0.01 mm.
Measurements.
After the straightedge is installed, moving the slide along the straightedge, the indication of the indicator is marked at the beginning and at the end. The difference in readings will be the amount of non-perpendicularity of the displacement of the slide to the axis of rotation of the spindle Fig.2 and Fig.3.

Fig.2

Fig.3
A bibliography.
- "Технология ремонта металлорежущих станков."Пекелис Г.Д., Гельберг Б.Т. - Ленинград, "Машиностроение", 1970г.