All the protractors

Theory A protractor is a printed schematic that helps aligning your turntable's cartridge in order to minimize distortion when playing a record.
Indeed, when cutting a record, the stylus moves tangentially; it is always perpendicular to the record's radius and its tip travels through this radius.

On the other hand, when a record is played with a pivoting tone arm, the tip of the cartridge traces an arc of a circle and the cantilever of the cartridge can only be tangent at a maximum of two points (which is not the case with a tangential arm, as it is always tangent by definition and you therefore do not need a protractor!).

At the points where the cantilever is tangent, the reading distortion is zero. Elsewhere, it is not.

The aim of the game is to choose these two points (they are defined by their distances R and r at the center of the circle) in order to minimize the distortion.
Fortunately for you, some have already addressed the problem and several types of alignment have already won their spurs:
Baerwald / Loefgren A : R = 120.9 mm, r = 66 mm. The distortion values at the beginning, middle and end of the record are equal. This is the most common alignment.
Loefgren B : R = 116.6 mm, r = 70.3 mm. The distortion is minimized over the entire record.
Stevenson : R = 117.42 mm, r = 60.325 mm. The distortion being more important at the end of the record than at the beginning, one of the null points is set at the end of the record.
UNI-DIN : R = 112.5 mm, r = 63.3 mm. A recent alignment in comparison with the others.
You can also choose the R and r values for new experiments!

The mounting distance of your turntable (distance between the axis of rotation of the arm and the axis of the record) and your selection of null points will define the geometry of the protractor:
- Offset: the angle between the cartridge and the arm.
- Effective length: the distance between the axis's arm and the stylus. This is the radius of the arc of a circle traveled by the stylus.
- Overhang, effective length - mounting distance
The resulting protractor will allow you to align your cartridge.

If your cartridge is not aligned, there is a good chance that the cantilever will never be tangent to the groove and that the angle between the two will take exaggerated values. This can obviously cause a lot of distortion but also mechanical tension on the cantilever of your cartridge and the stylus itself and wear down the grooves of your records.