Sensors, Signals and Measurement
Comprehensive university textbook unit covering fundamental principles, governing relationships, and engineering applications of Sensors, Signals and Measurement.
§2.1 Incremental encoders and position resolution
**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 2: Sensors, Signals and Measurement.** Educational draft for university study; no hardware-specific safety certification is implied.
§2.2 Strain gauges and bridge conditioning
**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 2: Sensors, Signals and Measurement.** Educational draft for university study; no hardware-specific safety certification is implied.
§2.3 Inertial measurement and sensor fusion
**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 2: Sensors, Signals and Measurement.** Educational draft for university study; no hardware-specific safety certification is implied.
§2.4 Anti-alias filters and sampling
**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 2: Sensors, Signals and Measurement.** Educational draft for university study; no hardware-specific safety certification is implied.
§2.5 Calibration, uncertainty and measurement quality
**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 2: Sensors, Signals and Measurement.** Educational draft for university study; no hardware-specific safety certification is implied.
Step-by-Step Mechatronics Engineering Solutions
Three original questions connect calculations, definitions and interpretation. Open each solution to follow the reasoning.
Problem Statement: At 2,048 counts per revolution, one count is about 0.003068 rad or 0.176 degrees. Rewrite the given numbers before substitution; explicitly carry their units through the equation. Compare the answer to a rough mental estimate and state a sensible number of significant figures. Do not interpret the displayed precision as measured accuracy. The calculation is synthetic unless independently verified against a particular device.
Worked Engineering Derivation:
**Sensitivity experiment.** Repeat the calculation after changing one controlling quantity by +10% while keeping other stated inputs fixed. For a linear relationship, expect a proportional response in the appropriate variable; for a nonlinear one, compute the actual change and compare it with the local slope. Explain whether the chosen perturbation is realistic for the application. **Dimensional audit.** Convert angles, voltages, forces, lengths and time to an explicitly declared convention before putting them in code. A numerical answer with the wrong units is not a small editorial error: it can change the actual machine motion or power demands by large factors. Record the conversion and the numerical rounding separately.
Problem Statement: At gauge factor 2.1 and strain 400 microstrain, the fractional resistance change is 0.00084. Rewrite the given numbers before substitution; explicitly carry their units through the equation. Compare the answer to a rough mental estimate and state a sensible number of significant figures. Do not interpret the displayed precision as measured accuracy. The calculation is synthetic unless independently verified against a particular device.
Worked Engineering Derivation:
**Sensitivity experiment.** Repeat the calculation after changing one controlling quantity by +10% while keeping other stated inputs fixed. For a linear relationship, expect a proportional response in the appropriate variable; for a nonlinear one, compute the actual change and compare it with the local slope. Explain whether the chosen perturbation is realistic for the application. **Dimensional audit.** Convert angles, voltages, forces, lengths and time to an explicitly declared convention before putting them in code. A numerical answer with the wrong units is not a small editorial error: it can change the actual machine motion or power demands by large factors. Record the conversion and the numerical rounding separately.
Problem Statement: A 0.2 degrees/s rate bias accumulates 12 degrees of angular error in one minute if left uncorrected. Rewrite the given numbers before substitution; explicitly carry their units through the equation. Compare the answer to a rough mental estimate and state a sensible number of significant figures. Do not interpret the displayed precision as measured accuracy. The calculation is synthetic unless independently verified against a particular device.
Worked Engineering Derivation:
**Sensitivity experiment.** Repeat the calculation after changing one controlling quantity by +10% while keeping other stated inputs fixed. For a linear relationship, expect a proportional response in the appropriate variable; for a nonlinear one, compute the actual change and compare it with the local slope. Explain whether the chosen perturbation is realistic for the application. **Dimensional audit.** Convert angles, voltages, forces, lengths and time to an explicitly declared convention before putting them in code. A numerical answer with the wrong units is not a small editorial error: it can change the actual machine motion or power demands by large factors. Record the conversion and the numerical rounding separately.
Problem Statement: A 200 Hz acquisition rate has a 100 Hz Nyquist frequency, which is not a guarantee of useful accuracy at 99 Hz. Rewrite the given numbers before substitution; explicitly carry their units through the equation. Compare the answer to a rough mental estimate and state a sensible number of significant figures. Do not interpret the displayed precision as measured accuracy. The calculation is synthetic unless independently verified against a particular device.
Worked Engineering Derivation:
**Sensitivity experiment.** Repeat the calculation after changing one controlling quantity by +10% while keeping other stated inputs fixed. For a linear relationship, expect a proportional response in the appropriate variable; for a nonlinear one, compute the actual change and compare it with the local slope. Explain whether the chosen perturbation is realistic for the application. **Dimensional audit.** Convert angles, voltages, forces, lengths and time to an explicitly declared convention before putting them in code. A numerical answer with the wrong units is not a small editorial error: it can change the actual machine motion or power demands by large factors. Record the conversion and the numerical rounding separately.
Problem Statement: Independent standard uncertainties of 0.10 mm and 0.20 mm combine to approximately 0.224 mm. Rewrite the given numbers before substitution; explicitly carry their units through the equation. Compare the answer to a rough mental estimate and state a sensible number of significant figures. Do not interpret the displayed precision as measured accuracy. The calculation is synthetic unless independently verified against a particular device.
Worked Engineering Derivation:
**Sensitivity experiment.** Repeat the calculation after changing one controlling quantity by +10% while keeping other stated inputs fixed. For a linear relationship, expect a proportional response in the appropriate variable; for a nonlinear one, compute the actual change and compare it with the local slope. Explain whether the chosen perturbation is realistic for the application. **Dimensional audit.** Convert angles, voltages, forces, lengths and time to an explicitly declared convention before putting them in code. A numerical answer with the wrong units is not a small editorial error: it can change the actual machine motion or power demands by large factors. Record the conversion and the numerical rounding separately.