GONIOMETER: HISTORY, PARTS, OPERATION, USES, TYPES - PHYSICAL - 2024

The goniometer is the device used to measure angles formed by two visuals. The name comes from two Greek words: gonios, which means angle and meters, referring to the fact of measuring. From there also derives goniometry, which is the science of measuring angles.

Angular quantities are an important part of disciplines such as astronomy, surveying, geology, medicine, mineralogy, architecture, engineering, and many more. Heights, distances, forces, and numerous physical properties have angles involved, so their measurement is relevant.

Figure 1. Universal goniometer. Source: F. Zapata,

History

In ancient times, someone had the idea of ​​dividing the circumference into 360 equal parts, called degrees. But it was not until 1538 that the Dutch physician Regnier Gemma Frisius first developed a goniometer, an instrument derived from the astrolabe (a device used to measure the elevations or depressions of an object).

Since an angle is defined as the region between two rays with a common point, which can be the center of said circle, one way to determine the measure of that region is by using a graduated circle.

So the basic design is a flat circle, graduated on a scale of 360º or half a circle, with 180º. A simple plastic protractor, like the ones used in school, is a very basic goniometer, if we stick to the definition.

The protractor is capable of measuring angles on a flat surface, such as a piece of paper or a board. So its range of motion is rather limited.

The goniometer is more sophisticated than a simple protractor. Some incorporate a vernier, for greater precision in the measurement, and rulers to measure distances. They also have arms to place them on non-flat surfaces.

That is why there are many varieties of goniometers, the use of which depends on the area in which you use. In terms of manufacturing materials, they are generally lightweight and strong, such as plastic, alloy steel, and aluminum.

What is the goniometer for?

As we have said, the goniometer is used to measure angles in a wide variety of situations, for example the angles made by the joints of the body, which are indicative of their mobility. Similarly, in construction it is necessary to measure the angles in ceilings, walls, doors and a multitude of elements.

This to mention only a few applications, as they are almost infinite, since angles are omnipresent entities in everything that surrounds us.

Sexagesimal system

The sexagesimal system consists of dividing the circumference into 360 equal parts called degrees (º). In turn, each degree is divided into minutes (´) and one minute is divided into 60 seconds (´´).

This system applies to angles and is also very familiar as a measure of time. In what follows we will refer exclusively to angles.

When an angle is expressed in degrees, minutes and seconds, it is said to be expressed in complex measure. But if you choose to leave everything in degrees and fractions of a degree, then it is a simple measure.

For example, an angle that measures 25º 38´ 12´´ is in complex measure, but the same angle in simple measure is 25.64º. Most scientific calculators convert from one to the other quickly.

Parts

Simple or traditional goniometer

A simple goniometer like the one shown in the following diagram consists of:

- A semicircular part that contains the graduated scale from 0 to 180º.

- The body, a piece that occupies a diameter, on which the semicircle with the scale rests.

- The sheet that ends in an indicator needle for reading.

Figure 2. Parts of a basic goniometer. Source: F. Zapata.

Precision Goniometer

A more sophisticated version is the precision goniometer, which has a sliding rule attached to the articulated arm of the goniometer.

The articulated arm goes on the rotating disc, which contains a vernier or vernier, and rotates on the fixed disc that has the main scale graduated in 1º units.

Attached to the fixed disk is the fixed ruler, which has a reference surface where the part to be measured is supported.

Figure 3. Precision goniometer and its parts. Source: F. Zapata.

Functioning

All varieties of goniometer have the same principle of operation, let's see:

The vernier, which goes on the rotating disk, has a scale graduated to both the right and the left, which allows measurements to be made both clockwise and counterclockwise.

It should be noted that the resolution or appreciation of this type of goniometer is 5 min of arc, which is shown numerically later.

In the center of the goniometer there is a screw that serves both as the axis of rotation and fixer of the angular position. Some precision goniometers have an additional wheel, to control the fine turn, so that it can be adjusted more precisely to the piece to be measured.

Said piece is placed between the variable rule and the fixed rule or square. Both the goniometer and the part already positioned are candled to make sure the fit is perfect.

Once any light path between the piece and the reference surface of the ruler or square has disappeared, the position is fixed with the articulation fixator or fixing screw. Finally, the measurement is carried out, the steps of which are detailed below:

How is the goniometer used?

To use the goniometer, the object whose inclination angle is to be measured is wedged between the sheet and the disk of the goniometer, as shown in figure 4. The angle to be measured has been marked there in fuchsia.

Figure 4. How to measure an angle with a basic goniometer. source: F. Zapata.

Green and blue parallels have been drawn over the image to guide the reader. The fuchsia angle is opposite by the vertex to the yellow angle. When you have opposite angles through the vertex, they measure the same.

The angle in yellow measures the same as the orange, since they are between the green and blue lines, which are parallel. Once convinced of this, the reading is made immediately by observing the indicator on the sheet.

The angle of the piece to be measured is an acute angle and the reading is made from left to right. In the enlarged image they read 48º.

Figure 5. Enlarged view of the measure. Source: F. Zapata.

Of course, readings can be done from right to left, as there is a double scale for that. Doing it one way or the other depends on the object to be measured.

Appreciation error

All measuring instruments have an appreciation, which is the smallest division on the scale, and any measurement made, whether with the goniometer or any other, will always be affected by error.

For example, in the simple goniometer we have just seen, the smallest division corresponds to 1º.

The maximum error that can be made in a measurement made with this goniometer is more or less appreciation. According to this, the reading of the example is expressed as:

In general, the appreciation of a scale like this is calculated by selecting two arbitrary readings, and counting the number of divisions between them, like this:

Readings with the precision goniometer

The precision goniometer has a vernier: a second scale placed on a movable disk and that can be moved below the main scale. The vernier allows for finer readings.

As always, the measurement made with the main scale results in degrees and can be done clockwise (left to right) or counterclockwise (right to left), depending on convenience.

The reading on the main scale is carried out with the procedure described in the previous section. The 0 of the vernier acts as an indicator in this case.

Now we go to the final reading with the vernier, which will give us the minutes. Each division is equivalent to 5´ (angular minutes) and can also be read from left to right or right to left.

To find the measurement, the line of the vernier that best matches any of the lines of the fixed scale must be selected, and that will be the fraction in degrees that must be added to have the complete reading.

Reading example 1

As an example, let's see the reading of the figure, done counterclockwise. The 0 of the vernier indicates 64º (green line).

Figure 6. Example of reading from right to left. Source: F. Zapata.

Now let's look at the line of the vernier that best matches one of the main lines. In the figure it has been highlighted in fuchsia. It coincides with division number 30 on the vernier scale. So our angle measures:

As for the appreciation of this goniometer, it depends not only on the main scale, but on the vernier. Goniometers usually have 12 or 24 division verniers in each half. The one in the example has 12.

It is calculated as follows:

In this case, the smallest division is 1º = 60 ´, and the divisions are 12:

Therefore the reading is reported in this way:

Reading example 2

Now let's try a clockwise reading.

Figure 7. Goniometer reading taken from left to right. Source: F. Zapata.

The 0 of the vernier coincides with 42º (orange color), while the division of the vernier that best coincides with any of the divisions on the main scale (turquoise blue color) corresponds to 20´. Therefore the measured angle is:

The reader may wonder what happens if no division matches exactly. When the 0 of the vernier is in the middle of two main divisions, the division closest to 0 is taken as the degree reading. The rest of the measurement is done as already described

It is always up to the person making the measurement to select the divisions that best match. Two people taking the same measurement can disagree, but almost always on the fine measurement.

Types of goniometer

Universal Goniometer

There are of multiple designs. The one shown in figure 8 consists of two rotated metal or plastic rulers that rotate together with a graduated semicircle. The object whose angle is to be measured is placed between the rulers and read from the graduated semicircle.

The goniometer shown is widely used to determine the range of joint motion, or the distance a joint travels from its natural position to its maximum motion.

Figure 8. Goniometer of those used in medicine to measure the ability of joints to move. Source: Wikimedia Commons. Source: Voxymoron

Electrogoniometers

It is an instrument that transforms the angle to be measured into an electrical impulse. It is widely used to measure the range of motion of the joints.

Bubble goniometer

As its name implies, it has a leveling bubble, usually located at the end of one of the arms. Since many measurements need to align this arm with the horizontal, this allows for more reliable readings.

References

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4. 4) Encyclopaedia Britannica. Goniometer. Recovered from: britannica.com
5. Junta de Andalucía. Metrology. Recovered from: juntadeandalucia.es.
6. Mathematical laws and formulas. Angle measurement systems. Recovered from: ingemecanica.com.
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