Position Encoders

Many different types of transducers can be used, in conjunction with peripheral equipment, to determine the position of an object in one, two, or three dimensions. The number of transducers in creases as the number of dimensions increases; e.g., we can expect that it will require more devices to locate a satellite in space as opposed to determining the linear separation between two objects.

In this section we will examine several types of position en coders. The examples given here are just a small cross section of all the different methods of position encoding.

ACOUSTIC MEASUREMENT OF DISTANCE

ill. 27-1. A primitive method of determining distance by acoustic means. The distance d is proportional to the delay n for the echo to return.

ill. 27-2. A more sophisticated method of distance determination by means of sound.

Electro-acoustic transducers (speakers, microphones, and variations) can be used to determine the distance between two points, the location of an object on land or at sea, or the position of an object in the air or under water. Generally, these types of position encoder make use of the fact that acoustic waves in various media travel at a fairly constant, known speed.

Perhaps you have stood at the top of a cliff in a so-called “echo canyon” and listened to your shouts come back to you. Sound waves travel at about 1100 ft/sec in the atmosphere of our planet. Thus, if the sound returned to you in, say, 3 sec., you would know that the echo barrier was 1.5 “sound seconds,” or about 1650 feet, away.

In general, an echo delay of n seconds would mean a distance d, in feet, of

d = 1100 x n/2

This is shown in ill. 27-1 above.

A more sophisticated method of distance measurement by means of sound echoes is shown at ill. 27-2. Transducers are used to transmit and receive an acoustic pulse. A precision electronic timer provides exact measurement of the time between the transmission and the reception of the pulse. A microcomputer de vice interprets the information and sends the appropriate signal to the readout. If the speed of sound is known (for the particular altitude and weather conditions) to a high degree of accuracy, the distance to a far-off object can be found to within better than 1 percent.

The apparatus of ill. 27-2 tells us nothing about the location of the acoustic reflector; it only provides one-dimensional information. In order to precisely locate the point of reflection in space, it's necessary to use three different transmitting/receiving stations located some distance apart (ill. 27-3A). If the terrain is flat, then only two transducers are needed (ill. 27-3B).

ill. 27-3. At A, three-dimensional acoustic location scheme (side view). At B, two-dimensional acoustic location scheme (top view, level terrain). Transmit ting/receiving stations are represented by X, Y, and Z.

In the three-dimensional case (ill. 27-3A) the three transmit ting/receiving stations must be located sufficiently far apart from each other that a clear intersection point can be found and calculated. This will be the intersection among three spheres in space. In the two-dimensional case the point of the reflecting object is found by the intersection of two or three circles. The spheres or circles have radii that are determined according to the preceding distance formula. The three-dimensional case is somewhat difficult to illustrate. Figure 27-4 shows the principle for the two- dimensional case.

ill. 27-4. Intersecting-circle method of acoustic location in two dimensions. (This method will work in some cases but not, in general, if stations X and V are an opposite sides of the object.)

Similar techniques can be used to locate objects or to deter mine distances under water. The sonar device is probably the most well-known position encoder for use under water. The depth of the lake, river, or ocean is determined by measuring the time between transmission and reception of an acoustic pulse. (Some aircraft make use of similar devices, known as sonic altimeters, to ascertain the actual altitude above the ground surface.)

Somewhat less familiar is the so far technique for locating a wrecked ship. Radio contact is made with the vessel, and then depth charges are set off. Receiving transducers and amplifiers located at three widely separated shore points are used to determine the distance to the ship (ill. 27-5). The intersection point of the three circles is the location of the wreck.

ill. 27-5. Location of a wrecked ship from land-based stations. Three stations allow unambiguous determination of the ship’s position.

ELECTROMAGNETIC POSITION ENCODING

Distances can be measured by using electromagnetic waves in the same way as acoustic waves. Radio signals, infrared radiation, visible light, and even ultraviolet rays can be employed. Lasers are commonly used for this purpose because of their long-distance, narrow-beam propagation qualities. Electromagnetic radiation travels through space at a precisely known speed of 186,282 milsec (299,792 km/sec). This is true in the atmosphere and in a vacuum such as outer space.

ill. 27-6. A laser and photocell can be used to measure the distance to a reflecting object.

A visible-light (laser) apparatus for distance measurement is shown in ill. 27-6. A pulse is sent out by the laser, and the instant of this pulse marked by an oscilloscope or high-speed timer. A photoelectric or photovoltaic cell detects the return (reflected) pulse. The time difference is determined; if the delay is n seconds, the distance d to the object is given by

d = 186,282 x n/2

in miles. If n is given in microseconds, the distance d in miles is

d = 0.186282 x n12

As is the case with acoustic waves, two transmitting/receiving setups are needed to locate a point in a plane, and three stations are necessary to uniquely locate a point in space. In the three- dimensional case the three stations and the point to be located must be non-coplanar; that is, they must not all lie in a single plane.

Another commonly used method of locating objects by electromagnetic means is the familiar radar system. This device re quires only one transmitting/receiving station and locates the position of an object or objects in two dimensions with a high degree of accuracy. A polar-coordinate scheme is used. The distance (range) and direction (bearing) of the object are determined. The distance is found according to the time required for a pulse to propagate to and from the distance object. The direction is found by means of a rotating antenna emitting frequent pulses in a narrow beam at a short wavelength.

Two radar sets can be used—one in the horizontal plane, and the other in the vertical plane—to determine the location of an object in three-dimensional space. The range and bearing are found by using horizontal radar. Then the vertical radar is operated in a plane passing through the line representing the bearing as indicated by the horizontal radar (ill. 27-7). Such a system can be useful, e.g., for locating satellites in space. The celestial coordinate system might be used; the “horizontal” radar would be operated in the plane of the celestial equator, and the “vertical” radar in a perpendicular plane, corresponding to the right ascension of the object as found by the “horizontal” radar.

ill. 27-7. Determination of exact position in three dimensions, using two radar sets.

An object equipped with tricorner reflectors can be located with extreme accuracy if lasers are used. The distance can be found to within a tiny fraction of 1 percent from three different transmit ting/receiving stations. (Using lasers, scientists have ascertained the distance to the moon to within a few inches.)

OTHER POSITION SENSORS

The potentiometer is commonly employed for deter mining angular position (see Section 3). Capacitors are sometimes employed for determining position on a small scale (Section 5). Inductors can be employed in a similar way on a small scale with ferrous materials (Section 9, ill. 9-3).

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