Position, Displacement and Speed Sensors

Potentiometers, LVDTs, magnetostrictive and laser sensors, linear scales, Hall sensors and speed measurement.

Choosing a position sensor

Position, displacement and length sensors report where something is (an analog or digital value), unlike the switches in Proximity Sensors that only say whether it is present. The choice depends on the stroke, the resolution, the speed, whether contact is allowed and the environment. Rotary position (angle) and the encoders on motors are covered in Encoders, Resolvers and Feedback.

SensorTypical strokeResolution / accuracyStrengthsLimits
Potentiometer10 mm to 1 mGood for the cost: 0.1 to 1 percentCheap, simpleWear of the wiper; noise; loading error
Draw-wire (string pot)Up to 50 m0.1 to 0.5 percent of rangeLong strokes, easy mountingWire and spring wear; not for fast motion
LVDT±0.5 mm to ±500 mmResolution limited by the electronics; 0.1 to 0.5 percentNo contact, infinite life, rugged, high resolutionNeeds excitation and conditioning; length of coil
Magnetostrictive25 mm to 20 m1 to 10 µm; 0.01 to 0.05 percentAbsolute, long strokes, in hydraulic cylindersCostly; the head and the magnet need space
Linear scale (optical or magnetic)20 mm to many meters0.1 to 5 µmHighest accuracy, fastCost; dust, coolant and mounting
Laser triangulation2 to 1 000 mm range0.1 µm to 100 µmNon-contact, fast, high resolutionSurface finish and angle; cost
Eddy-current0.5 to 20 mmNanometersTiny, extremely precise on metalMetal targets only; short range
Ultrasonic5 cm to 10 mAbout 0.1 to 1 mmAny surface, simpleTemperature and soft targets (see Proximity Sensors)

Potentiometers and draw-wire sensors

A potentiometer is a resistive track with a wiper: the output voltage is a fraction of the supply proportional to the position. Conductive-plastic tracks last for millions of cycles; wire-wound and carbon tracks wear faster. A draw-wire sensor (string pot) winds a wire on a drum, coupled to a potentiometer, an encoder or a resolver, with a spring for return.

Worked example: the loading error of a potentiometer

A 10 kΩ potentiometer on a 5 V supply with its wiper at mid-travel should give 2.5 V. If the input it feeds has an impedance of 100 kΩ, the lower half (5 kΩ) is shunted by the load: 5 kΩ ∥ 100 kΩ = 4.76 kΩ, so the output is 5 × 4.76 ÷ (4.76 + 5) = 2.439 V, an error of 1.22 percent of full scale. Keep the load at least 100 times the track resistance (or use a buffer), and use a low-resistance track for long cables.

  • Use the wiper as a voltage divider, with the track fed from a stable supply, not as a variable resistor (a poor contact then makes noise or a break).
  • Linear (hybrid) potentiometers have a limited life (106 to 108 cycles) and a micro-motion limit: do not use them for a constant, tiny vibration that wears one spot.

LVDTs

A linear variable differential transformer has a primary coil excited with an AC signal and two secondary coils wired in opposition. A magnetic core (attached to the moving part, with no contact) couples the primary to the secondaries: at the center both secondaries give equal and opposite voltages, so the output is zero; moving the core makes one stronger, giving an output proportional to the displacement, with the phase showing the direction. A demodulator converts it to a DC voltage or current.

LVDT construction and outputS1S2Pcoreprimary P (AC excitation, 1 to 10 kHz)secondaries S1 and S2, wired in opposition02.557.510-101core position (mm; center at 5)outputnullThere is no contact between the core and the coils, so the life is practically unlimited, and the resolution is limited only by the electronics.
An LVDT: the coil arrangement and the linear output through zero at the center.

Worked example: sensitivity and resolution

  • A ±10 mm LVDT gives ±3 V at full stroke with 3 V rms excitation: the sensitivity is S = 3 ÷ 3 ÷ 10 = 0.10 V/V per mm (100 mV/V/mm).
  • At a displacement of 2.5 mm the output is 0.10 × 3 × 2.5 = 0.75 V (positive on one side, negative on the other).
  • The output has a slope of 0.30 V/mm. Read with a 16-bit converter over ±3 V (a step of 0.092 mV), the resolution is 0.092 mV ÷ 300 mV/mm = 0.31 µm: the electronics, not the sensor, set the resolution.
  • Conditioning: the sensor needs a sine-wave oscillator (1 to 10 kHz) and a phase-sensitive demodulator, or an LVDT-to-digital converter chip; ready-made sensors with the electronics built in (DC-LVDTs) run from a 24 V supply and give 0 to 10 V or 4 to 20 mA.
  • Strengths: frictionless, almost infinite life, resolution limited only by noise, good in dirt, oil and radiation, and rugged against shock.
  • Limits: the core must be aligned with the bore, the body is as long as the stroke, and a magnetic mounting or nearby steel can disturb the reading.

Magnetostrictive sensors

A magnetostrictive sensor has a long waveguide tube with a head at one end and a ring magnet on the moving part. The head sends a current pulse along the waveguide; where the pulse meets the magnet’s field a torsion pulse is created and travels back at about 2 800 m/s. The delay measures the distance: absolute position, with no contact between the magnet and the tube. This construction survives inside hydraulic cylinders at hundreds of bar.

Worked example: time of flight

At 2 800 m/s a magnet 1.0 m from the head gives a delay of 1.0 ÷ 2 800 = 357 µs. Timing with a 100 MHz clock resolves 0.028 mm per tick; interpolation and averaging give a few micrometers. Outputs are analog (0 to 10 V, 4 to 20 mA) or digital (SSI, CANopen, EtherCAT), and the sensor can report several magnets at once (for example the position and the level float).

Linear scales and encoders

A linear scale is the straight version of an encoder: an optical glass or a magnetic strip with a fine pattern read by a head. It is the most accurate way of measuring position, used on machine tools and measuring machines, with resolutions of 0.1 µm and better. It measures the load directly, avoiding the errors of a screw, a belt or a gearbox (see Encoders, Resolvers and Feedback for the signals, the decoding and the interfaces). Magnetic tapes are more tolerant of dirt, optical scales more accurate; both need protection from coolant and chips.

Laser, eddy-current and other non-contact sensors

  • Laser triangulation: a laser spot is imaged onto a line sensor from an angle; the spot position shifts with the distance. High speed and resolution for thickness, height, flatness and vibration, with surface finish, color and angle that matter. Use a blue or a red laser to suit the target.
  • Confocal and white-light sensors measure transparent and shiny surfaces to sub-micron resolution.
  • Time-of-flight laser rangefinders measure long distances (meters to hundreds of meters) with millimeter accuracy for cranes, vehicles and stores.
  • Eddy-current displacement sensors measure the gap to a metal target with nanometer resolution over a few millimeters: shaft position and runout in turbines, and thin films.
  • Inclinometers measure the angle to gravity with MEMS accelerometers: crane booms, solar trackers, leveling.
  • Analog Hall and magnetoresistive sensors give a position signal from a magnet over a short stroke: pedals, valves, lever positions.

Measuring speed

Speed can be derived from position: count the pulses of an encoder or of a gear-tooth sensor over a known time (frequency counting), or time the interval between pulses (period measurement). Frequency counting is best at high speed; period measurement is best at low speed. A tachogenerator gives a DC voltage proportional to speed; Doppler radar and laser sensors measure the speed of a surface (vehicles, conveyors, webs) without contact.

Worked example: speed resolution

  • A wheel with 60 pulses per revolution is counted over a 100 ms gate: the smallest speed step is 60 ÷ (60 × 0.1) = 10 rpm. At 1 500 rpm the pulse rate is 1 500 ÷ 60 × 60 = 1 500 Hz and the count per gate is 150, which means a ±1 count error of 0.7 percent.
  • A longer gate or more pulses per turn improves the resolution but slows the response. At low speed the period method times one interval (1 ms at 1 500 Hz) with a fast clock, giving a much finer reading.
  • Zero-speed detection (for example, safe standstill) uses a sensor that responds to a stationary target, since a pickup coil gives no output at rest.

Outputs and interfacing

OutputNotes
0 to 10 V, 4 to 20 mACommon; scale with the Analog Scaling Tool. Mind the resolution of the input card.
SSI, BiSSSynchronous serial absolute position; clock from the controller; fast; differential RS-422 lines
CANopen, EtherCAT, PROFINET, IO-LinkFieldbus sensors with configuration and diagnostics (see Fieldbuses and Device Networks)
Quadrature pulses (A, B, Z)Incremental scales; need a counter and homing
Start/stop pulsesOlder magnetostrictive systems measure the interval with a timer module

Troubleshooting

SymptomLikely causeCheck
Noisy or jumping readingElectrical noise on the cable, a poor connection, a worn potentiometer trackShielding and grounding (see Installing and Troubleshooting Sensors), the supply ripple, replace a worn pot
Reading offset or not linearCore or magnet misaligned, a magnetic part nearby, wrong calibrationRe-align; keep steel away; recalibrate zero and span
No outputNo excitation or supply, a broken wire, a failed conditionerMeasure the supply and the excitation at the sensor
Drift with temperatureThermal expansion of the mounting, a cable or electronics driftMount on a stable frame; allow warm-up; use the temperature-compensated type
Lost position after power-offAn incremental deviceUse an absolute sensor, or home at start-up
Wrong speed readingGate time too short, a missed pulse, wrong pulses per revolutionCheck the settings and the counter input rating

Related

FAQ

LVDT or linear potentiometer?

A potentiometer is cheaper and simpler for low-duty positioning. An LVDT has no contact and so a far longer life, a better resolution and is much more rugged in dirt and shock, at the cost of the electronics.

How accurate is a draw-wire sensor?

Typically 0.1 to 0.5 percent of the range: very good for the cost, especially on long strokes, but not for precision work. The wire needs to run straight, without side pull.

Absolute or incremental?

Absolute devices know the position at power-up; incremental ones count and must be referenced. For long strokes or critical positions an absolute sensor avoids a homing move.

What limits the resolution of an analog position sensor?

The input converter and the noise: a 12-bit input on a 100 mm sensor resolves about 25 µm at best, while a 16-bit input resolves 1.5 µm if the sensor and wiring are quiet enough.

References

  • Fraden, J., Handbook of Modern Sensors, Springer (LVDTs, magnetostrictive and optical sensors).
  • MTS Sensors, Temposonics and Heidenhain and Renishaw linear encoder technical information; TE Connectivity / Measurement Specialties, LVDT application notes.
  • Doebelin, E. O., Measurement Systems: Application and Design, McGraw-Hill.

Last reviewed: October 2026. Sensor figures are typical; use the manufacturer’s specifications for real accuracy and resolution.