Vernier scale

The vernier (also Vernier ) is a movable length scale to increase the reading accuracy on angular and linear encoders, for example, a caliper, a marking gauge or a scale for mapping. At the head of a character Tear board is also a common vernier, which is used at this point for the precise measurement of angles. Occasionally, barometers are equipped with a vernier scale.

With the vernier it is possible to determine fractions of path lengths exactly.

The vernier scale was in 1631 by the French mathematician Pierre Vernier ( 1580-1637 ) introduced, according to which it is also named in many countries. The usual in German and other countries vernier name goes on the Portuguese astronomer, mathematician and geographer Pedro Nunes ( Latinized: Petrus Nonius, 1502-1578 ), who, however, has not invented the vernier.

• 4.1 Other scales

Method

The human eye can not be easily determined a slight offset. Without Nonius, it would therefore not possible with certainty to read route lengths that are smaller than the finest division of the main scale ( for example, the millimeter division on the centimeter ruler, see divisions).

Very much better can determine when two tick marks are sufficiently exactly opposite, however. This is achieved with the vernier. During the measurement process, it slides as movable Ableseskale to the fixed main scale past ( the scale ) and allows her to measuring sections with a precision of several thousandths of a centimeter.

Theoretically uses only the limited resolution of the human eye by 0.005 cm of accurately determining a limit. In fine lines thus a secure reading is reached at least 0.01 cm. Then additional tools to support the eye like a Ableselupe are required for subdivisions from 0.002 cm.

The measurement uncertainty is stated in addition to the scale (eg, 1 /20 mm ), is added to the reading error of the same order.

Comparator principle

A more accurate measurement would only be possible if the Abbe comparator principle is fulfilled: the test piece and the test instrument (or the scale ) must lie on an axis. In addition, the reading of the measured value must be perpendicular to the measurement scale in order to avoid parallax error in reading.

In the best-known application of the vernier, the vernier caliper, the Abbe comparator principle is not satisfied. However, he is due to its simplicity is still the cheapest and most widely used gauge of the mechanic and technician.

Example ( accurate measurement )

The picture on the right shows an enlargement of the vernier a vernier calliper from the image above. The reading is 3.58 mm. The 3 mm on the top scale will read that. 0.58 mm at the bottom, see red marks The measurement error is about 0.04 mm. Because the measurement uncertainty of the vernier of 0.02 mm is the reading error of the same order. In the example, it is not clear whether the right value is 3.58 or 3.60.

Earlier applications

Before the vernier has been widely used, for example, in the theodolite. These glass scales and measuring microscopes are used with micrometers since about 1930, which increases the accuracy to at least 1 % of the tick marks. More specifically, the reading by the double circle principle. Newer tachymeter usually have, as well as ( very reasonably priced ) Calipers optoelectronic reading devices ( with about 5 - to 10 -fold better accuracy than the simple vernier ).

Other applications

• Noniusverbinder enable tiered, highly accurate assembly of certain components.

Principle

The vernier itself is reduced in comparison with a unit of length () on the scale. The scale of the vernier usually has ten tick marks, so each of these parts is long. With each part on the vernier so missing just one hundredth to the nearest tenth on the scale.

Stated differently.

Therefore, a mark on the vernier only a mark of the scale exactly opposite when the reading mark, i.e., the zero mark of the vernier to has been moved to the corresponding difference. If the reading mark, for example, behind a tenth brand, so first comes the third mark of the vernier to cover with a graduation of the scale. The distance from the reading mark up to that mark on the vernier scale is in fact long. Because it is:

Other scales

To increase the reading accuracy, the vernier scale may be stretched on or etc..

Here it is possible to divide it into twenty or forty parts. The individual lines have a distance of or. The area in which now can be accurately measured increases to at forty ticks.

That there always is exactly one line on the vernier, which is opposed to a division on the main scale - provided the limits of accuracy - is related to the following property of Nine series, the vernier makes use of: the difference between a follower of nine series and the next higher Ten cycles through and in ascending order all the numbers from zero to nine.

In principle, therefore, it is possible to construct vernier scales that are based on the one -, three - or septenary.