Mechatronics · Module 2 of 10
Sensors and Transducers
A sensor turns a physical quantity into an electrical signal. Choosing one means reading its static characteristics: range, sensitivity, resolution, and linearity, and knowing whether it reports a level or counts increments.
Readiness check
This module builds the sensing block. Tick only what you can do closed-notes.
- Compute a slope as output span divided by input span.
- Recall that a sensor maps a physical quantity to a signal.
- Divide a full circle into equal parts.
- Recall the difference between accuracy and precision.
- Read a straight-line calibration graph.
The core idea
A sensor maps an input quantity onto an output signal. An analog sensor reports a level, and its sensitivity is the output span divided by the input span. An incremental encoder instead counts equal steps, so its resolution is a full revolution divided by the counts per revolution.
sensitivity = output span / input spancounts per rev = lines × 4 (quadrature)resolution = 360° / counts per revA transducer converts energy from one form to another; a sensor is a transducer used to measure. What matters in practice are the static characteristics. The range is the span of input it accepts; the sensitivity is how much output it gives per unit input, the slope of its calibration line; the resolution is the smallest change it can distinguish; and the linearity is how close that calibration is to a straight line. Accuracy, how close the reading is to truth, is separate from precision, how repeatable it is. Analog position sensors such as the potentiometer, the LVDT, and the strain gauge report a continuous level, and their sensitivity is simply output span over input span. A digital, incremental sensor such as an optical encoder works differently: it emits pulses as it moves, and two tracks in quadrature let the electronics count four edges per line and also sense direction. Its resolution is then a full revolution divided by those counts, and finer resolution just means more lines. Recognising which kind of sensor you have decides how you read it.
The skills, taught in order
Five skills let you read a datasheet and pick a sensor with intent.
2.1 Sensor and transducer terms
A transducer converts one energy form to another; a sensor is a transducer chosen to measure a quantity of interest. An actuator is the opposite, a transducer that converts a signal into action. Using the words precisely keeps a design readable.
2.2 Static characteristics
Range, sensitivity, resolution, linearity, hysteresis, and repeatability describe how a sensor behaves in steady state. Accuracy is closeness to the true value; precision is closeness of repeated readings to each other. A sensor can be precise yet inaccurate.
2.3 Displacement and position sensors
The potentiometer gives a voltage proportional to position; the LVDT gives an AC amplitude proportional to core displacement; the strain gauge changes resistance with strain; the capacitive sensor changes capacitance with a gap. Each trades range, resolution, and robustness differently.
| Sensor | Measures | Output |
|---|---|---|
| Potentiometer | linear or angular position | voltage |
| Strain gauge | strain, hence force | resistance change |
| Optical encoder | angular position and speed | pulse count |
A few workhorse sensors and the signal each produces. The output type sets the conditioning that follows.
2.4 The optical encoder and quadrature
An incremental encoder has a slotted disk and light gate that emit pulses as it turns. Two tracks offset by a quarter cycle, channels A and B, let the electronics count four edges per line and read direction from which channel leads. An absolute encoder instead reports a unique code for each position.
2.5 Choosing a sensor
Match the range to the motion, the resolution to the smallest change that matters, and the output to the electronics downstream. A finer sensor than needed wastes conditioning and money; a coarser one loses the signal.
Engineering connection: a servo motor's shaft encoder both closes the position loop and, by counting pulses per unit time, measures speed, doing two jobs from one sensor.
Worked example 1: a linear potentiometer
A linear potentiometer gives 5 V across its full 100 mm travel. Find its sensitivity and the output voltage when the wiper is at 30 mm.
- ProblemFind the sensitivity and the 30 mm output for the potentiometer in Figure 1.
- Given / find5 V over 100 mm travel. Find sensitivity and output at 30 mm.
- AssumptionsLinear track, negligible loading current on the wiper.
- ModelSensitivity = output span / input span; output = sensitivity × position.
- EquationsS = 5 V / 100 mmV = S × x
- SolveS = 5/100 = 0.05 V/mm. At x = 30 mm, V = 0.05 × 30 = 1.5 V.
- Check30 mm is 30 percent of travel, and 30 percent of 5 V is 1.5 V, so the two routes agree.
- ConclusionThe potentiometer reads 0.05 V per millimetre, giving 1.5 V at the 30 mm position.
Worked example 2: an optical encoder
An incremental optical encoder has 500 lines and is read in quadrature. Find the counts per revolution, the angular resolution, and the count for a 90 degree rotation.
- ProblemFind counts per revolution, resolution, and the count for 90 degrees for the encoder in Figure 2.
- Given / find500 lines, quadrature reading. Find counts/rev, resolution, and counts at 90 degrees.
- AssumptionsClean quadrature edges, no missed counts.
- Modelcounts/rev = lines × 4; resolution = 360°/counts; counts = (angle/360°) × counts/rev.
- EquationsN = 500 × 4r = 360° / N
- SolveN = 2000 counts/rev; r = 360/2000 = 0.18°; at 90 degrees, (90/360) × 2000 = 500 counts.
- Check90 degrees is a quarter turn, and a quarter of 2000 is 500, consistent with the resolution.
- ConclusionThe encoder resolves 0.18 degrees per count and reports 500 counts for a quarter revolution.
Misconceptions and diagnostics
| Mistake | Symptom | Diagnostic question | Correction |
|---|---|---|---|
| Forgetting quadrature | Counts one quarter of the truth | "Am I counting edges or lines?" | Quadrature gives four counts per line. |
| Resolution read as accuracy | Trusting a reading to the last count | "Is this the smallest step or the true error?" | Resolution is not accuracy; check calibration. |
| Confusing accuracy and precision | Repeatable but consistently offset | "Repeatable, or close to truth?" | Precision is repeatability; accuracy is truth. |
| Range and sensitivity mixed up | Signal clips or is too small | "Does the range cover the motion?" | Set range to the motion, then read sensitivity. |
Practice ladder
A rotary potentiometer gives 10 V over 270 degrees. What is its sensitivity, and what does it read at 90 degrees?
Show answer
Sensitivity = 10/270 = 0.037 V/degree; at 90 degrees, 0.037 × 90 = 3.33 V.
An encoder has 1024 lines read in quadrature. Find the counts per revolution and the resolution in degrees.
Show answer
1024 × 4 = 4096 counts/rev; resolution = 360/4096 = 0.088 degrees.
A temperature sensor outputs 4 to 20 mA over 0 to 200 degrees Celsius. Find its sensitivity and the current at 75 degrees.
Show answer
Sensitivity = (20 − 4)/200 = 0.08 mA/degree; at 75 degrees, 4 + 0.08 × 75 = 10 mA.
Pick a sensor to measure a robot elbow angle over 0 to 120 degrees to about 0.1 degree. State the type and the resolution you would specify.
What good work looks like
An incremental encoder needing at least 3600 counts over 120 degrees, so 360 counts per revolution scaled to the joint, or roughly 900 lines in quadrature across a full turn; a good answer states counts/rev and checks 360/counts is below 0.1 degrees.
Working with AI, and proving it yourself
Use AI as an examiner, not a solver
Portfolio task
Take one real sensor datasheet and write its range, sensitivity, resolution, and linearity in your own words, then predict a reading.
Retrieval and spaced review
Closed notes. Answer out loud, then reveal.
1. Define sensitivity.
Output span divided by input span, the slope of the calibration line.
2. How many counts per line does quadrature give?
Four, from the four edges of the two offset channels.
3. Accuracy versus precision?
Accuracy is closeness to truth; precision is repeatability.
4. Write encoder resolution.
360 degrees divided by counts per revolution.
5. Incremental versus absolute encoder?
Incremental counts steps and needs a reference; absolute reports a unique code per position.
Textbook mapping
This module follows William Bolton, Mechatronics, 6th edition. Use these references to read further.
| Topic in this module | Where to read more |
|---|---|
| Sensor terms and static characteristics | Bolton, Chapter 2, Performance terminology |
| Displacement and position sensors | Bolton, Chapter 2, Displacement, position and proximity |
| Encoders and quadrature | Bolton, Chapter 2, Optical encoders |
Chapter numbers refer to Bolton's Mechatronics, 6th edition. Any edition with the same chapter titles is equivalent for study.