Displacement and Position Sensing
LINEAR DISPLACEMENT

Motion control systems typically require a sensor in a
feedback loop to ensure that the moving member orcomponent reaches its commanded position. Position
sensors are typically used on machine-tool controls,
elevators, liquid-level assemblies, forklift trucks, automobile throttle controls, and numerous other applications. Position sensors measure either absoluteor incremental displacement, and are made with avariety of different materials. Also, when the sensor’spower fails, some retain the measured position data,and other types lose the information.
One common device is a resistive position sensor orpotentiometer. It may be a single-turn or a multi-turnrotary sensor with an element made of carbon or any
one of a number of more durable, high-temperature,
conductive-plastic film materials. Some types of potentiometers connect to the moving member througha rigid or flexible coupling while others are actuatedwith a string wrapped around its output shaft. Yetother position sensors include LVDT’s (linear variable
differential transformers), sonically operated devices,Figure 9.01 A
Figure 9.01 B
and digital encoders.

String-Potentiometer Position Sensor
Wire Wound

Direction oflinear motion
Direction of rotation
String or cable

Coil spring
Potentiometer

String-Potentiometer Transducers

String-type potentiometers are basically rotational
devices that typically measure linear motion as shownin Figure 9.01. Because a cable connects between themoving member and the potentiometer, the cablemust be preloaded with a spring, have a low coefficient of expansion under wide ranges of temperature(-65 to +125˚C), and have little tendency to stretch.
Because of these constraints, its accuracy is somewhat
less than that of a more rigid, shaft-coupled sensor.

Figure 9.01 C

Most modern potentiometers are extremely linear
and are made with special alloys or precious metal
wipers and conductive plastic resistive elements towithstand as many as 100 million revolutions. They
are usually part of a voltage divider and provide anoutput voltage proportional to displacement, but they
may also drive analog-to-digital converters to feed
microprocessor-based instruments directly. However,when digital outputs are needed, a more common
practice uses digital encoders that inherently supply
higher accuracy.

FilmThreaded
drum

Fig. 9.01. String potentiometers occupy relatively
little overall space in a machine installation ordevice under test. In some applications where asensor cannot be mounted on the device being measured, the potentiometer may be conveniently
located some distance from the test bed without
sacrificing accuracy or repeatability.

LVDT: Linear Variable Differential
Transformers

LVDTs are electronic devices comprised of a specialtransformer with a movable metal actuator in its hollowcore. The transformer contains two differentially woundsecondary windings on either side of a primary winding.
As the actuator in the core moves in and out, it couples

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LVDT Position Sensor
Physical Construction
S1

Excitation and Output Signals
Primaryexcitation
Sec. 1
output

LVDT

PS2

Sec. 2
outputCore motion
Zero output at null

Sec. 1 +Sec. 2

Winding Positions
Secondary 1

Primary coil

Secondary 2

Schematic
Primary coilCore motionCore motion

Figure 9.02 C

Secondary 1

Secondary 2

Fig. 9.02. LVDT sensors provide distance and direction information with extremely high accuracy. But a drawback for someinstallations is their relatively long length. The minimum length of the sensor is its body, and the core can extend only as far as
the length of the body.

Magnetostrictive Position Sensor

Figure 9.02 B
Interrogation:• Return wire
• Wave guide

The magnetic field generated
by the interrogation pulse
encompasses the entire
waveguideInteraction of magnetic fields
causes wave guide to generate
a strain pulse

Protective sheath

Pulse
outputEnd cap
Magnetic field
generated byposition magnet

Strain pulse
detector

Wave guide
Movable position magnet

Distance

Fig. 9.03. Magnetostrictive position sensors have a high signal-to-noise ratio, shock and vibration resistance, and accuracy. They arerugged devices that deliver from 30 to 400 mV signals at their output terminals and require little or no additional signal conditioning.
A possible disadvantage for some applications, however, is its wave-guide, which must be at least as long as the measured stroke.

Figure 9.03

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Two-Channel Linear Position Encoder

Rack and Pinion Encoder Assembly

Stationary plate
number 1

Movingplate

Light sensor number 1

Directionof motion

Light sensor number 2

Stationary plate
number 2 (180˚ out ofphase with number 1)

Lens
LightsourceEncoder
Adjustable springloaded mountto accommodate runout

Lightrays

Alternating opaque and transparent
lines interrupt light from source to sensors

Fig. 9.04. Two-channel encoders provide step and direction
vectors with an output signal that can be a sinewave, squarewave, or a series of equally spaced pulses generated at regularintervals on the waveform.

Fig. 9.05. A rack and pinion sensor assembly should have aflexible mount to compensate the combined runout error. In amachine application, the sensor should be protected from metal
chips and other foreign objects to ensure measurement accuracy.

a signal from primary to secondary in proportion to the displacement. Being differentially wound, LVDTs also can provide directionalsignals with the appropriate signal conditioning circuits. With theactuator at the center position, the output signal is null or zero. As
the actuator moves out in one direction, the signal is positive, andwhen it moves in the opposite direction from null, the signal isnegative. (See Figure 9.02.)

magnet and the pulse generator. Resolution is about 0.002 mm,durability is high, and the stroke ranges from 5 to 20,000 mm.
Higher resolutions require additional interpolating circuits. The
output signal, which is proportional to displacement, can be either
analog or digital, and it can represent both position and velocity.

Figure 9.05

Absolute Contact Encoder Disc

LVDTs require electronic circuits to provide an ac signal to excite
the primary and a demodulator to convert the output to a dc
signal with directional polarity. Some LVDTs contain the electronics onboard and only require power to obtain an output, whileothers require separate signal conditioners or modules. The LVDTs
themselves are rugged devices and have a MTBF of as much as
3 million hours. The main limitation is the displacement rangeof the core to ensure high linearity.

20212223

4-bit binary
word

B0

Shaft

B1
B2
B3

Ultrasonic Sensors

141312Another relatively new type of position sensor is based on the theoryof operation of the interaction of two magnetic fields on magnetostrictive materials. The major components of the sensor include
an external permanent magnet, integral sensing and output signal
conditioning circuits, a sensor tube, and a wave-guide element. The
permanent magnet fastens to the movable object, and the housing
remains attached to a stationary reference point. (See Figure 9.03.)

1110

The output signal conditioning circuit generates a current pulse
and magnetic field which travel down the waveguide. When thetransmitted field reaches the permanent magnet field, the combination induces a strain pulse in the magnetostrictive tube. The
strain pulse, in turn, travels down the waveguide to the head of
the sensor where it is detected. The time measured between theapplication of the interrogation pulse and the arrival of the strain
pulse determines the precise, absolute distance between the movableFigure 9.06

915 0 12.

87653
4

Contact
tracksFig. 9.06. The disc pattern on the contacting encoder is adigital word, which represents the absolute position of theencoder shaft.

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Rotary Position Encoder
L.E.D. light source

PC board

Optical disk

Detector

ReticleCollimated light
Signal andpower

Fig. 9.07. The shutter is one of the most critical components of the encoder assembly. The sensor’s resolution and accuracy hingeon the quality of the vendor’s manufacturing and assembly processes.

ROTATIONAL POSITION

LinearEncoders
Figure9.07

Linear encoders have evolved over the years to provide extremely
accurate position information. Their principle of operation
depends upon sensing position from precision graduations(position codes) etched on a linear scale. They come in both contacting and non-contacting types, and their length is primarily
limited to their temperature-sensitive coefficient of expansion
to preserve accuracy. Most modern scales are glass, and opticalsensors detect the graduations. (See Figure 9.04.) The benefitof a non-contacting type is typically longer life because it uses
optical components instead of brushes or a contacting wiper.
All optical encoders contain a light source, light detector, code
wheel or scale, and signal processor.

Rotational position may be measured with potentiometers, coupled
to a rack and pinion assembly or gear trains to obtain a suitable ratioof potentiometer revolutions to measured component rotation ormovement. (See Figure 9.05) Potentiometers commonly come insingle turn to as many as 25 turns and fit numerous applications.
But, most rotational measurements, whether they are velocity,rpm, or position, are best handled with digital encoders. Like linearencoders, several types have been used over the years including
both contacting (see Figure 9.06) and non-contacting. They containa disc (code wheel) or a plate made with alternating opaque andtransparent segments that move between a light source such as
an LED, and a photo-detector. (See Figure 9.07.)

Absolute Encoders

Two-Channel Quadrature Output

Absolute encoders typically contain several detectors and slots
on a revolving wheel to provide a unique output binary codefor each shaft position within its range of resolution. Therefore,
the shaft position can be determined absolutely. Moreover, thecorrect position is always retained before and after a powerfailure. The tracks on the encoder wheel may be arranged toprovide a 0.5 bit maximum error. Absolute encoders come insingle and multi-turn versions.

Channel A
Channel B
eMAX
pp

p

p

pp

eMIN

ppp

Plate
movement

Incremental Encoders

Incremental encoders usually provide two channels of squarewave output signals. Each pulse represents an increment of rotation of relative position. These encoders often contain a thirdslot called the reference slot used to calibrate the encoder. Dualchannel encoders are more accurate than single channel types.
They register direction, and when a code wheel stops on the edgeof a slot, incident vibrations cannot generate an error count, as
it does for single-channel sensors.

One line width displacement

Fig. 9.08. The two light sensors in a dual channel linear position encoder are connected in a push-pull configuration andtrack one another, so equal changes in the input produce equalchanges in the output.

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In some cases, encoder misalignment errors can be calculated.
For example, a linear sensor often incorporates a glass scale tosense linear displacement. When the scale is bent or bowed, thecurvature introduces an error that is proportional to the displacement d, as shown in Figure 9.09. When d is small relative to S,
the concave surface of the scale is shortened by ∆, and the convex
surface is elongated by ∆, where ∆ = 4td/S.

Misalignment Error in Glass Scales
Top view ofglass scale

SdFor example, when:t

S = 8 in.
t = 0.20 in.
d = 0.0010 in,then:∆ = (4 x 0.20 x 0.0010)/8 = 0.0001 in.

Fig. 9.09. The top view of an exaggerated bow in linear
scale illustrates the errors that could undermine measurement accuracy. The error in this case is proportional to thedisplacement “d.”Quadrature Encoders

Lines etched on the convex side produce an error of +0.0001
in., and lines on the opposite side produce an error of -0.0001
in./foot.

The two channels, A and B, of a dual output incremental encoder
are usually displaced by 90 degrees from each other. Therefore,
the spacing between pulses is one-half the line width. When thedisc contains 1024 lines and 1024 spaces, the sensor generates
4 x 1024 = 4096 pulses per revolution; hence the output signals are delivered in quadrature. (See Figure 9.08.) The angularmovement in this arrangement resolves to 5.27 minutes of arc.

Power supply stability and freedom from electrical interference
are critical requirements for encoders. Both anomalies can produce intermittent and random operation, which are frequentlydifficult to diagnose.

Signal conditioning circuits generate the output signal waveformand complementary signals, sense their direction, and filter theoutput. The amplitude of the input voltage controls two stable
output states of a shaper circuit. The shaper output feeds several
gates, which in turn generate the pulses that mark the encoder’szero-signal crossings. The circuits also sense whether channel A
leads or lags channel B to provide direction information.

Temperature has minimal influence on today’s encoder electronics, although the maximum operating temperature at rated powerfor LEDs is 150˚F compared to 200˚F for incandescent lamps. But
LEDs have more than double the expected life of lamps, and theywork with superior signal conditioning circuits, so they are usedalmost exclusively. Temperature fluctuations affect linear glassscales more significantly. For example, a ±150˚F temperaturechange can produce an error of ±0.0008 in./ft.

ErrorsThe mechanical coupling to the moving member should suitthe application, considering axial and radial loads, acceleration,
velocity, vibration, accuracy, and resolution. The proper coupling
reduces errors and increases the encoder’s life.

Encoder manufacturers endeavor to minimize device errors,
but users must be concerned with total system errors. Encoder
errors consist of instrument and quantization errors, as wellas manufacturing and assembly errors. For example, the lightsources must be closely matched and the code wheel must have
low disc eccentricity.
Encoder error is relatively easy to quantify, whereas total error
depends upon each application and is a little more difficult topin down. Several sources contribute to total error, including
manufacturing and assembly tolerances, LED characteristics,
scale and disc alignment, and power supply stability. Others
include electrical interference, temperature variations, mechanicalcoupling, and mechanical vibration.

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