Displacement, Speed, Force & Strain Measurement

Measuring motion and force for machines and structures: potentiometers, LVDTs, capacitive and eddy-current proximity probes, optical encoders (incremental/absolute, quadrature), tachogenerators, accelerometers and vibration monitoring, strain gauges and Wheatstone bridges (quarter/half/full), temperature compensation and load cells.

Robots, CNC machines, turbines and bridges all need to know where things are, how fast they move and what forces they carry. Encoders close servo loops; accelerometers watch bearings; load cells weigh tanks and trucks; strain gauges test aircraft wings.

Many of these sensors produce tiny signals — a strain gauge changes its resistance by less than 0.1% — so bridge circuits and careful amplification are essential.

An analogy

A strain gauge is like a rubber band with ink lines: stretch it and the lines get longer and thinner, raising its resistance. A Wheatstone bridge is the precise balance scale that notices that tiny change.

Displacement and position

Potentiometers are cheap and simple but wear. LVDTs (linear variable differential transformers) are contactless with infinite resolution. Capacitive and eddy-current probes measure tiny gaps (turbine shaft vibration). Optical and magnetic encoders give digital position: incremental encoders output A/B quadrature pulses (direction from phase), absolute encoders output a unique code (often Gray) for every position.

Speed, vibration and acceleration

Motion sensors for machines:

Strain gauges and bridges

A foil gauge bonded to a part changes resistance with strain: ΔR/R = GF·ε. At 500 µε a 350 Ω gauge changes by only 0.35 Ω. The Wheatstone bridge converts this to a voltage and rejects common changes: quarter bridge (1 active gauge + dummy for temperature), half bridge (bending: one in tension, one in compression), full bridge (4 active, maximum output and compensation).

Load cells and practical measurement

Load cells are machined elements (beam, S-type, canister) with a full bridge; output is quoted in mV/V (e.g. 2 mV/V at rated load). Remote sensing (6-wire) compensates cable drop in excitation. Ratiometric ADCs use the excitation as reference so supply drift cancels. Creep, off-axis loading, temperature gradients and shunt calibration are practical concerns in weighing and structural testing.

Formulas

Worked example: Encoder resolution

Given: 1024 PPR incremental encoder, quadrature decoding

Find: Angle per count.

Answer: 0.088°

Worked example: Stress from strain

Given: Steel E = 200 GPa, ε = 500 µε

Find: Stress.

Answer: 100 MPa

Worked example: Load-cell output

Given: 2 mV/V, 10 V excitation, 500 kg cell with 200 kg load

Find: Output.

Answer: 8 mV

Strain-gauge bridge configurations

# Quarter / half / full Wheatstone bridge with strain gauges, GF = 2.0
GF, Vex, eps = 2.0, 5.0, 500e-6                 # gauge factor, excitation V, 500 microstrain
for name, arms in (("quarter", 1), ("half", 2), ("full", 4)):
    Vout = Vex * GF * eps * arms / 4
    print(f"{name:7s} bridge: {Vout*1e3:.3f} mV")
# Required amplifier gain to map full-bridge 5 mV to a 0-5 V ADC
print(f"gain for full bridge -> 5 V: {5 / (Vex*GF*eps):.0f}")
# quarter bridge: 1.250 mV
# half    bridge: 2.500 mV
# full    bridge: 5.000 mV
# gain for full bridge -> 5 V: 1000

A full bridge gives 4× the signal of a quarter bridge and cancels temperature effects because all gauges drift together. Even so the output is only millivolts — an instrumentation amplifier with gain ≈ 1000 is required.

Common mistakes

Applications

Key takeaways

Going further