Force, torque and pressure transducers complete the “transducers for industrial instrumentation” line of the GATE Robotics and Automation (RA) 2027 syllabus. All three measurands are usually converted first into a small elastic deformation (strain), which a secondary transducer — most often a strain gauge — turns into an electrical signal. This guide explains load cells, torque sensors and the elastic pressure elements (Bourdon tube, diaphragm, bellows), with governing equations, diagrams, worked examples and the exam pitfalls to watch for.
TABLE OF CONTENTS
Force transducers: the load cell
A load cell measures force by letting it strain an elastic element (a column, beam or ring) and reading the strain with bonded strain gauges arranged in a Wheatstone bridge. The applied force produces a stress σ = F/A and a proportional strain ε = σ/E, which the gauges convert into a resistance change:
where E is Young’s modulus and GF is the gauge factor. Using four active gauges (full bridge) maximises sensitivity and cancels temperature effects. Load cells are the backbone of industrial weighing, robot force/torque wrists and material-testing machines.
Figure 1. Column load cell: force strains the column; bonded strain gauges in a Wheatstone bridge give the output.
Torque transducers
Torque is measured from the shear strain in a shaft. From the torsion equation, the angle of twist and the surface shear stress are proportional to the applied torque T:
where J is the polar moment of inertia, τ the shear stress at radius r, G the shear modulus, θ the twist angle and L the shaft length. Strain gauges are bonded at ±45° to the shaft axis (the principal-strain directions in pure torsion) and wired as a full bridge. For a rotating shaft the bridge signal is carried out through slip rings or non-contact rotary/telemetry couplings. Reaction torque sensors instead measure the restraining torque on a stationary member.
Pressure transducers & elastic elements
Pressure measurement combines an elastic primary element that deflects with pressure and a secondary transducer that converts that deflection to an electrical signal. The three classic elastic elements are:
- Bourdon tube: a curved, flattened tube that tends to straighten under internal pressure; the tip movement drives a pointer or an LVDT/potentiometer. Best for medium-to-high pressures.
- Diaphragm: a thin membrane that bulges with pressure; deflection is read by bonded strain gauges, a capacitive plate, or piezoresistive elements. Ideal for low pressures and fast response.
- Bellows: an accordion-like element giving large axial motion for low-pressure and differential-pressure measurement.
Figure 2. Bourdon tube: internal pressure straightens the C-tube; the tip motion is the pressure signal.
Worked example: strain-gauge load cell
Example 1
A load cell has a steel column of cross-sectional area A = 200 mm² and E = 200 GPa. A force of 20 kN is applied. A strain gauge (GF = 2.0) is bonded axially. Find (a) the strain and (b) the fractional resistance change.
Solution. A = 200 × 10-6 m².
(a) σ = F/A = 20000/200e-6 = 100 MPa; ε = σ/E = 100e6/200e9 = 5 × 10-4 (500 µε).
(b) ΔR/R = GF·ε = 2.0 × 5e-4 = 1 × 10-3 = 0.1%.
Elastic elements compared
| Element | Pressure range | Typical use |
|---|---|---|
| Bourdon tube | Medium–high | Gauges, process pressure |
| Diaphragm | Low–medium | Fast response, electronic transmitters |
| Bellows | Low | Differential & absolute low pressure |
Key formulas
FORMULA SHEET
Stress & strain: σ = F/A, ε = σ/EGauge output: ΔR/R = GF·ε
Torsion: T/J = τ/r = Gθ/L
Polar moment (solid shaft): J = πd⁴/32
Pressure: P = F/A
Diaphragm deflection ∝ P (thin plate)
Common mistakes to avoid
- Placing torque strain gauges axially — in pure torsion the principal strains are at ±45°, so gauges must be oriented there.
- Forgetting the difference between gauge, absolute and differential pressure (reference matters).
- Using a single gauge instead of a full bridge — you lose sensitivity and temperature compensation.
- Ignoring the secondary transducer: a Bourdon tube alone gives motion, not an electrical signal.
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Enroll in the GATE RA Complete CourseFrequently asked questions
Why are torque strain gauges mounted at 45 degrees?
In a shaft under pure torsion, the maximum tensile and compressive (principal) strains occur along the ±45° helical directions, while the axial and circumferential strains are zero. Mounting the gauges at ±45° therefore captures the largest signal and lets a full bridge cancel bending and temperature effects.
What is the difference between gauge, absolute and differential pressure?
Gauge pressure is measured relative to local atmospheric pressure, absolute pressure relative to a perfect vacuum, and differential pressure is the difference between two applied pressures. The choice of reference determines which elastic element and porting arrangement are used.
How does a load cell achieve temperature compensation?
By using multiple strain gauges in a Wheatstone bridge. Because all gauges experience the same temperature, their resistance changes due to temperature cancel in the bridge, leaving only the strain-induced (force) signal.
Why is a diaphragm preferred over a Bourdon tube for low pressures?
A diaphragm has a large surface area and low stiffness, so it deflects measurably even at low pressures and responds quickly. A Bourdon tube needs higher pressure to produce useful tip motion, making it better suited to medium and high ranges.
This guide is part of the complete GATE RA 2027 Syllabus overview. Continue the sensor series with Displacement, Velocity & Acceleration Transducers and Resistive Sensors & Signal Conditioning.
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