{"id":187344,"date":"2019-07-08T09:40:15","date_gmt":"2019-07-08T07:40:15","guid":{"rendered":"https:\/\/www.elovis.com\/company\/measurement-technology-glosar\/"},"modified":"2019-07-21T21:05:32","modified_gmt":"2019-07-21T19:05:32","slug":"measurement-technology-glosar","status":"publish","type":"page","link":"https:\/\/www.elovis.com\/en\/company\/measurement-technology-glosar\/","title":{"rendered":"Measurement Technology Glosar"},"content":{"rendered":"\t\t
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Things to know about the topic of ELOVIS industrial measurement technology<\/h2>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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If you want to learn more about the basics of ELOVIS industrial measurement technology, you will find yourself on this page. Here, essential terms of ELOVIS measurement technology are explained, defined and, if possible, explained using simple practical examples. In addition to the explanations about length measurement technology on webs and strips with encoders or rotary encoders or laser encoders or laser Doppler systems,the section also deals with length measurement technology with explanations from the single light barrier, to light grids or even length-section light grids. The glossary was expanded to include the subject area “Spacing, Distance and Length” as well as the 7 basic units of the SI system. If you would like further information on measurement technology topics, we look forward to receiving your suggestions and contact. Simply use our contact form via the contact button.<\/p>\n

Enjoy the … further education!<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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KEYWORD<\/strong><\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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DEFINITION \/ IMPLEMENTATIONS \/*<\/strong><\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Encoder<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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An encoder is a technical element. The term can appear in both communications engineering and drive technology. The following section deals with encoders in drive technology:<\/p>\n

Encoders for signal formation from motion work optically, magnetically or mechanically with contacts. These are transducers or input devices that recognize the current position of a shaft or drive unit and output it as an electrical signal. There are two types of encoders: rotary and linear. Rotary encoders or rotary encoders are mounted on rotating components, for example on a motor shaft. Linear encoders are typically mounted on components with straight movements.<\/p>\n

Encoders have incremental, countable or absolute measuring standards in the form of line patterns (light barriers), magnetization or contacts. In the case of permanent magnetisation, the magnetic field modulation can be evaluated using AMR, GMR, Hall sensors or inductive sensors. For incremental inductive sensors, non-magnetic toothing is often sufficient.<\/p>\n

Absolute encoders work on the basis of measuring standards that assign a unique signal pattern to each position (see Absolute Encoders).<\/p>\n

Encoders that do not measure absolutely are called incremental encoders. They are used on motor shafts, but also as input devices on digitally operating devices, to set parameters (e.g. volume) or to control motor movements manually (e.g. on CNC controls).<\/p>\n

With the help of the output signal of an encoder, a drive unit equipped with it can carry out reproducible movements and – in the case of an absolute encoder – move back exactly to the starting position (reference position) even after the machine has been switched off. Incremental encoders require an additional encoder, for example a limit switch, to find the reference position. An example of a linear incremental encoder is the optical scanning of a line pattern applied to a strip in a printer, which allows the print carriage to execute a defined movement along the line.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Measuring wheel encoder<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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The tactile measurement of linear movements directly on the measuring surface can be carried out with a measuring wheel or impeller which drives an encoder or rotary encoder:
\nMeasuring wheel systems pick up linear movements with a wheel and convert them into velocity or position values. The system does not require a reference point on the surface to be measured. This makes it suitable for measurements on different surfaces. In most cases, a spring integrated in the mounting arm for the measuring wheel ensures permanent pressure of the wheel on the surface and thus a measurement. A sufficient friction between the measuring wheel and the measuring surface is decisive for the good functioning of a measuring wheel system. If this friction is not guaranteed or if the measuring wheel leaves unwanted traces, the use of a laser encoder is recommended.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Laser Encoder<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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Laser encoders are ideally suited to replace measuring wheel driven encoders\/rotary encoders or length and speed measurement via the machine drive. Laser encoder length measurement systems and speed measurement systems work contactless and therefore without slippage, are maintenance-free, permanently accurate and work almost independent of material. Light, dark, black, glossy, matt, structured and uneven surfaces are all measured equally accurately. The higher price of laser encoders compared to measuring wheel encoders is usually quickly amortized by the higher measurement accuracy and in particular by the significantly longer service life of the laser encoders. Laser encoders also have self-monitoring and can signal error states. Laser encoders operate according to the principle of laser Doppler velocimetry and can output a parameterizable quadrature signal or an encoder pulse signal like regular rotary encoders\/encoders. Fieldbus couplers and other network interfaces are also available, making laser encoders often even easier to integrate into system controls than conventional rotary encoders\/encoders.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Doppler Effect<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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The simplest and therefore best known explanation of the Doppler principle is the siren of moving emergency vehicles. When an emergency vehicle moves towards the fixed location of an observer\/listener\/receiver, the siren sounds higher until the vehicle has reached the location. There you can hear the real sound. As the vehicle moves away from the listener’s location, the siren sound becomes lower and lower. The sound perceived by the receiver is a frequency with a certain number of oscillations per second. With a stationary sound source, the receiver reaches the true frequency of the sound. However, as soon as the sound source moves away from the receiver, the sound or frequency is transmitted from a growing distance. The frequency that reaches the receiver therefore becomes lower or the sound becomes lower. The so-called Doppler effect applies to sound waves and also to any other type of wave, such as light waves.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Laser Doppler Velocimetry<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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Laser Doppler Velocimetry is a method for non-contact measurement of the speed of moving surfaces. A laser beam with a constant wavelength is divided into two partial beams of equal intensity by means of a beam splitter. These two partial beams are cut at a defined angle by optical assemblies. When two laser beams of the same wavelength intersect, an interference stripe pattern of bright stripes is formed in the beam intersection. The special feature is that the distances of this strip pattern are defined exactly by the wavelength of the light and the angle at which the laser beams meet. This is the scale of a laser Doppler measuring system. A photodetector directed at the stripe pattern receives the Doppler frequency, i.e. the frequency caused by the movement of the material, with the backscattered light. It makes it easier to understand if one imagines a raised point in the microstructure of the moving surface, which passes through the stripe pattern. The raised point always reflects the laser light when it passes through a bright stripe and thus emits one light pulse after the other. The photodetector takes a flashing frequency and converts it into an electrical frequency, the Doppler frequency. An evaluation unit then converts the Doppler frequency by integration over time, e.g. into a length-proportional signal for output at the pulse output. Sensors that operate on the Doppler principle are also called laser encoders or laser surface velocimeters and therefore LSV sensors.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Light Barrier<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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In optoelectronics, a light barrier is a system that detects the interruption of a light beam and displays it as an electrical signal. In this way, automatic devices can detect moving objects without contact.<\/p>\n

Light barriers consist of a light beam source (the transmitter) and a sensor (the receiver) for this radiation.<\/p>\n

Light sources used include light-emitting diodes with a wavelength of 660 nm (visible red light) or infrared LEDs with 880-940 nm in the infrared range. Infrared light has the advantage of achieving a higher range on dark materials and is not visible to the human eye. The advantage of red light is the easier adjustment of the sensor system through the visible light spot. Light from a laser diode is generally used for particularly precise applications (small part detection, high repeat accuracy). The receiver is usually a photodiode or a phototransistor, rarely also a photo resistor.<\/p>\n

In order to make a photoelectric sensor insensitive to extraneous light, the radiation is modulated, especially in far-reaching models, so that it can be distinguished from the ambient light. In addition, an infrared filter that appears almost black to the human eye can be placed in front of the receiver to shield higher-frequency light, including the visible portion of daylight.<\/p>\n

To increase the range, most transmitters and receivers are equipped with an optically focussing system, such as a converging lens. In addition, the photodiodes and phototransistors can be mounted in a cylindrical sheet metal housing that blocks out side light and into whose circular opening a small lens made of plastic or glass is pressed in in a defined manner. The housings of small transmitters and receivers often consist entirely of black plastic, which is only transparent for IR.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Light Barrier Types<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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One-way Light Barrier<\/p>\n

In the case of One-way Light Barriers, the transmitter and receiver face each other. These include fork couplers and fork light barriers, in which the transmitter and receiver are pre-assembled at a certain distance (usually 3-120 mm) from each other. If the transmitter and receiver are in separate housings, they must be aligned and fine-tuned during installation. Of all types, through-beam photoelectric sensors have the longest range of typically up to 80 m.
\nRetro-reflective photoelectric sensor<\/p>\n

Transmitters and receivers of photoelectric reflex switches are located parallel to each other in a common housing. The light signal of the transmitter is reflected back at a side opposite the light barrier by means of a reflector or foil mark.<\/p>\n

The versions with reflector differ in the use of a polarisation filter. Versions with a polarization filter detect only a retroreflector or reflector, but not other reflective surfaces. This means that even a reflective surface is detected as an interruption; this creates additional safety. The use of retroreflectors and retro-reflective photoelectric sensors simplifies their installation considerably due to the reduced wiring effort and as no precise alignment of the reflector to the photoelectric sensor is required.<\/p>\n

Diffuse reflection light scanner<\/p>\n

The light signal is reflected back via the object to be detected. The switching distance therefore depends on the reflection properties of the object surface. Here, too, the transmitter and receiver are located parallel to each other in a common housing.<\/p>\n

In addition to purely energetic diffuse reflection light scanners, diffuse reflection light scanners with background suppression are of particular practical importance because they are capable of detecting dark objects against a bright background. If they are also capable of determining the distance, they are called distance sensors – they then usually work according to the principle of triangulation and contain a position-sensitive photodiode (PSD) instead of the phototransistor. These can be used to construct diffuse reflection light scanners that can distinguish between different objects (e.g. on a conveyor belt). There are also distance sensors with switching function which operate according to the principle of light transit time measurement. They achieve a longer range than diffuse sensors (typically up to 75 m).<\/p>\n

Light curtain<\/p>\n

In addition to the simple versions with only one light beam, there are also so-called light grids or light curtains that work with several parallel light beams. These can be used to monitor a large area, e.g. access to a machine or an alarm-secured room. With a light grid, openings of building lift cars are much better protected than with a single light barrier at ankle height, as was standard until 1970.<\/p>\n

Fiber optic light barrier<\/p>\n

There are also fiber-optic sensors in which optics and electronics are arranged separately and connected by means of fiber optics. They are used, for example, in confined installation conditions. Throughbeam and retro-reflective photoelectric sensors are possible here.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Length-Section Light Scanner\/Light Curtain<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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ELOVIS offers the worldwide unique LED length-section light scanner measurement technology, which can also be described by the term “optical micrometer” or “measuring light grid”. The ELOVIS series of length-section light grids bears the product name SLM for discrete part length measurement system. The parts to be measured pass through the SLM system without stopping in the longitudinal direction. As soon as the unit load is completely between the two sensor lines (one light transmitter line and one receiver line), a measurement is automatically triggered. Since the SLM system determines the shadow cast by the measuring object in transmitted light, there are virtually no material dependencies. Even numerous transparent materials with a certain opacity can be measured with this sensor technology. Length-Section Light scanners are used for high-precision, non-contact length measurement of profiles, tubes, hoses, plates, blanks, beams, bolts or winding cores made of various materials. Length-Section Light Scanner Discrete Part Length Measurement Systems are available in two versions. With the standard SLM system, parts up to approx. 5 m in length can currently be measured, depending on the system length. The two-part SLM\/2 systems are used for the re-measurement of parts with a length of up to approx. 15 m, or when no continuous SLM measuring lines can be used. ELOVIS Length-Section Light Scanners are maintenance-free, permanently calibrated and measure largely independent of material.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Meter<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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The meter is the basic unit of length in the International System of Units (SI) and other metric systems of units. The name “meter” is derived from the ancient Greek \u03bc\u03ad\u03c4\u03c1\u03bf\u03bd m\u00e9tron, German ‘Ma\u00df, L\u00e4nge’. A meter is defined as the length of the distance the light travels in a vacuum for a period of 1\/299 792 458 seconds. This current definition has been in force since 1983 (see below: Meter definition based on the speed of light). The unit sign of the meter is the lower case letter “m”. For decimal multiples and parts of the meter, the international prefixes for units of measurement are used.<\/p>\n

The meter was defined in 1799 as the length of the original meter, a prototype made of platinum. According to the measurements taken at the time, its length corresponded to the ten millionth part of the distance from the North Pole to the equator.<\/p>\n

The unit of length “meter” has been in use since the end of the 18th century. The origin of this unit of length goes back to a decision of the French National Assembly to define a uniform measure of length. This was preceded by several proposals for the definition of a unit of length which, unlike traditional measures of length, was not derived from the length of human limbs (finger width, inch, hand width, hand span, ulna, foot, crotch and fathom). In 1668 Abb\u00e9 Jean Picard proposed the second pendulum as the unit of length – i.e. the length of a pendulum that has a half period of one second. In the gravitational field of Europe, such a pendulum would have a length of about 0.994 m and would come quite close to the current definition of the metre. However, the decisive factor for the new unit of length was not the seconds pendulum, but the earth figure. In 1735, the Paris Academy of Sciences sent two expeditions to Ecuador and Lapland to determine the exact dimensions of the Earth. In 1793, the French National Convention set a new measure of length in addition to a new calendar: the metre was to be the 10 millionth part of the Earth’s quadrant on the meridian of Paris – the ten millionth part of the distance from the North Pole via Paris to the equator. A prototype of this meter was cast in brass in 1795.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Original Meter<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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Between 1792 and 1799, Delambre and M\u00e9chain redefined the length of the meridian arch between Dunkirk and Barcelona. A combination with the Ecuador-Lapland results resulted in a new value of 443,296 Parisian lines, which was declared binding in 1799 and realized as a platinum rod, the original meter. In the 19th century, however, more precise measurements of the earth came to the conclusion that the original meter was about 0.02% too short. Nevertheless, the meter defined in 1799 was retained – with the result that the Earth meridian quadrant is not 10,000 km but 10,001.966 km long. This length applies to the meridian of Paris, other meridians can have other lengths. A side effect was that it was recognized that the Earth is not an exact rotational ellipsoid, but has an irregular shape. The earth thus proved unsuitable for the definition of the meter. Until 1960 the meter was therefore fixed as the length of a concrete object – first the original meter, since 1889 then the international meter prototype (see below). All later definitions aimed to correspond as closely as possible to this length.<\/p>\n

In 1889, the International Bureau of Weights and Measures (BIPM) introduced the International Meter Prototype as a prototype for the unit meter. It was a rod with a cross-shaped cross-section. A platinum-iridium alloy with a ratio of 90:10 was chosen as the material. The length of the metre was defined as the distance between the centre lines of two groups of lines on the bar, which was kept at a constant temperature of 0 \u00b0C. The length of the metre was determined as the distance between the centre lines of two groups of lines on the bar, which was kept at a constant temperature of 0 \u00b0C. The length of the metre was determined as the distance between the centre lines of two groups of lines on the bar. 30 copies of this prototype were made and handed over to national calibration institutes.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Meter definition based on the wavelength of spectral lines<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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Although great importance had been attached to durability and unchangeability during the production of the meter prototypes, it was clear that they were basically transient. The making of copies inevitably led to deviations and – just as regular comparisons of the copies with each other and with the original – to the risk of damage.<\/p>\n

As a remedy, Albert A. Michelson suggested at the beginning of the 20th century that the meter be defined by the wavelength of spectral lines. In 1951 Ernst Engelhard and Wilhelm K\u00f6sters at the Physikalisch-Technische Bundesanstalt in Braunschweig developed the Krypton 86 spectral lamp, which produced orange-red light with the then most stable and reproducible wavelength and exceeded the accuracy of the original meter. In 1960, the meter was officially redefined: One metre was now 1,650,763.73 times the wavelength of the radiation emitted by atoms of the 86Kr nuclide at the transition from the 5d5 state to the 2p10 state, propagating in a vacuum. The numerical value was chosen in such a way that the result corresponded to the meter valid until 1960 within the measurement uncertainty at that time. Understanding this definition only required knowledge of atomic physics. If this and the necessary equipment were available, the length of one meter could be reproduced at any location. The meter was thus the first basic unit based on a natural constant and could be realized independently of measuring standards and measuring regulations.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Meter definition on the basis of the speed of light<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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With the Kypton lamp the meter could be defined with an accuracy of 10-8. With the discovery of the laser, however, ever more stable light sources and measuring methods were developed in the following years. In particular, the speed of light could be determined with an accuracy of 1 m\/s, and the definition of the meter became the limiting factor. Therefore, at the 15th General Conference on Weights and Measures (CGPM) in 1975, it was recommended that the numerical value of the speed of light should no longer be measured, but rather numerically determined, and that the unit of length should henceforth be defined on the basis of the speed of light. The 17th CGPM adopted this definition on 20 October 1983. The meter was defined as the distance that light travels in a vacuum within a time interval of 1\/299 792 458 seconds. With the redefinition of the SI in 2019 by the 26th General Conference on Weights and Measures, only the wording of the definition was adapted to that of the other SI base units.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Length<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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Length is a physical quantity that indicates the extent of physical objects and their distances from each other. The symbol of the length is the lower case letter “l”, its SI unit is the meter “m”. For the length of paths and curves, “s” is usually used as the formula character. In the SI system, length is a basic quantity.<\/p>\n

The length is measured by comparing the length to be measured with scales of known length. The length of distances between two points or a scale is considered constant in classical physics. In the special theory of relativity, however, the length is dependent on the relative state of motion of the respective observer, one speaks of a relativistic length contraction.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Distance (also space or seperation)<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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The distance, also the distance or the distance of two points is the length of the shortest connection of these points.<\/p>\n

In Euclidean space, this is the length of the straight line between the two points. The distance between two geometric objects is the length of the shortest connecting line between the two objects, i.e. the distance between the two nearest points. If not the nearest points of two objects are considered, so this is explicitly indicated or results from the connection, as for example the distance of the geometrical centers or the centers of gravity.<\/p>\n

The area of mathematics that deals with distance measurement is the metric.<\/p>\n

The distance, the distance, the distance between two values of a quantity or between two points in time is determined by forming the absolute value of their difference, i.e. by subtracting them from each other and forming the absolute value from the result. The measured distance is independent of the selected reference point of the coordinate system, but not of its scaling.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Euclidean Distance<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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In the Cartesian coordinate system, the distance (Euclidean distance) between two points is calculated using the Pythagorean theorem:<\/p>\n

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The distance between two points in the plane<\/div>\n<\/div>\n<\/div>\n
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d ( A , B ) = \u2211 i = 1 n ( a i \u2212 b i ) 2 , wobei\u00a0 A = ( a 1 , \u2026 , a n ) \u2208 R n \u00a0und\u00a0 B = ( b 1 , \u2026 , b n ) \u2208 R n <\/span>\"{\\displaystyle<\/span><\/sup><\/dd>\n<\/dl>\n

For the plane ( A , B \u2208 R 2 )<\/span><\/span>:<\/p>\n

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For the 3-dimensional space ( A , B \u2208 R 3)<\/span><\/span>:<\/p>\n

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The distance of a point from a straight line or a flat surface is the distance from the base of the plumb bob dropped on it, the distance from a curved line is always a distance from one of its tangents.<\/p>\n

Calculation possibilities for the distances of points to straight lines or planes are listed in the formula collection of analytical geometry.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Position Sensor<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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A displacement sensor is used to measure the distance between an object and a reference point or changes in length. The change in distance is converted into a standard signal. Other terms for this are displacement measuring system, displacement sensor, distance sensor, position sensor or distance sensor. This article provides an overview of the functional principles from the field of automation technology. Apart from these, there are other methods \u2192 see distance measurement. A detailed description can be found in the linked articles.<\/p>\n

In contrast, proximity switches generate a switching signal when approaching an object.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Function principles for position sensors<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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Resistance change<\/span><\/span><\/h3>\n