Sensors and Actuators for Robotics

23RIPC210

Module 1: Motion, Position & Force Sensing

Force sensors- Strain gauges, force and tactile sensors, Accelerometers, Pressure sensors, Velocity sensing, Gyroscopes.

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Textbook 1: 6.1-6.7

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Textbooks:

1.Nathan Ida, Sensors, Actuators, and Their Interfaces A multidisciplinary introduction 2nd Edition,2020, IET, Control, Robotics and Sensors Series 127.

2.D. Patranabis, Sensors and Transducers, PHI Learning Pvt. Ltd.

The hand

• The human hand is the main organ used for interacting

with the environment.

• It functions as both:
• Actuator – performs movements and manipulates objects.
• Sensor – detects touch and pressure.
• The hand contains 27 bones:
• 14 phalanges (fingers)
• 5 metacarpals (palm)
• 8 carpals (wrist)
• Complex muscles, tendons, and joints provide
• high flexibility and dexterity

The hand

• The hand performs multiple articulations:
• Between finger bones
• Between fingers and palm
• Between palm and wrist
• Between wrist and arm
• With the elbow and shoulder, it forms a multi-axis actuator system capable of:
• Delicate movements (writing, grasping small objects)
• Powerful actions (lifting, holding tools).
• The hand is controlled by opposite brain hemispheres:
• Left brain → Right hand
• Right brain → Left hand.

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Sensing and the skin �

• The skin is the largest organ of the human body.
• Average characteristics:
• Thickness: 2–3 mm
• Surface area: ≈ 2 m²
• Main functions:
• Protection from microorganisms
• Prevents fluid loss
• Absorbs vitamin D
• Protection from UV radiation
• Chemical absorption and excretion.

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Sensing and the skin �

• The skin contains nerve receptors that detect:
• Heat
• Cold
• Pressure
• Vibration
• Pain or injury
• Sensitivity varies across the body; fingertips are the most sensitive.
• The skin allows accurate localization of stimuli, meaning we can identify where the touch occurs.
• This natural sensing ability inspires tactile sensors in robotics and automation systems.

Introduction �

• Mechanical sensors measure physical quantities related to motion, force, or deformation.
• Most mechanical sensing principles fall into four main categories:
• Force sensors – measure force, load, or weight.
• Accelerometers – measure acceleration or vibration.
• Pressure sensors – measure gas or fluid pressure.
• Gyroscopes – measure angular velocity or orientation.
• Mechanical sensors can also be used for indirect measurements.
• Example: Temperature measurement using gas expansion detected by a strain gauge.
• Some mechanical sensors do not require motion or force, such as the optical fiber gyroscope,

which measures rotation using light interference.

Some definitions and units �

Some definitions and units �

Some definitions and units �

Main units of pressure and conversion between them �

Force sensors �1.Strain gauges �

• The strain gauge is the primary sensor used for measuring force in mechanical sensing systems.
• It measures strain (deformation), which can be related to:
• Stress
• Force
• Torque
• Displacement
• Acceleration
• Position
• With suitable transduction methods, strain gauges can also measure:
• Temperature
• Liquid level
• Other physical quantities.

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Force sensors �1.Strain gauges �

• Strain gauges operate based on the change in electrical resistance of a material when it is stretched or compressed.
• When a conductor is strained:
• Length (L) changes
• Cross-sectional area (A) changes
• Resulting in a change in resistance (R).

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The resistance of the wire is �

Force sensors �1.Strain gauges �

• Change in Resistance due to Strain

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where g is the sensitivity of the strain gauge, also known as the gauge factor �

• The resistance of the strain gauge under strain �

Relation between Stress and Strain (Hooke’s Law)

Temperature Effect on Strain Gauge

Force sensors �1.Strain gauges �

Force sensors �1.Strain gauges �

A rudimentary wire strain gauge

(also called unbonded strain gauge) �

Common construction of a resistive strain gauge. �

Various configurations of strain gauges for different purposes �

Force sensors �2. Semiconductor strain gauges�

• Working Principle
• Operate similar to metal strain gauges but use semiconductor materials (usually silicon).
• Resistance changes significantly with mechanical strain due to change in conductivity.
• Key Characteristics
• Higher Gauge Factor: typically 40 – 200 (much higher than metal gauges: 2–6).
• Higher sensitivity but lower allowable strain.
• Smaller size and often embedded in sensors.

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Force sensors �2. Semiconductor strain gauges�

(a)Construction of a semiconductor strain gauge.

(b–f) Various configurations of semiconductor strain gauges �

Force sensors �2. Semiconductor strain gauges�

• semiconductor strain gauges exhibit a quadratic (nonlinear) transfer function.
• Material and Construction
• Most commonly made of doped silicon.
• p-type (boron doped) and n-type (arsenic doped) materials used.
• Can show PTC or NTC behavior depending on the type.
• Applications
• Accelerometers
• Load cells
• Bridge load monitoring
• Engine shaft torque measurement
• Truck weighing systems

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Force sensors �2. Semiconductor strain gauges�

• Limitations & Errors
• High temperature sensitivity → requires temperature compensation.
• Limited operating temperature (< 150°C).
• Errors may occur due to temperature variation, lateral strain, bonding effects, and fatigue.
• Typical Performance
• Metal gauges: 100–1000 Ω resistance, gauge factor 2–5.
• Accuracy in bridge circuits: ≈ 0.2% – 0.5%.

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Force sensors �3. Other strain gauges�

• Optical Fiber Strain Gauges
• Use optical fibers to measure strain.
• Strain changes the length of the fiber, causing a phase shift in light.
• Phase change is measured directly or using interferometric methods.
• Extremely high sensitivity – capable of detecting very small strains.
• Limitation: Complex electronics and higher cost.
• Liquid Strain Gauges
• Use an electrolytic liquid inside a flexible container.
• Deformation changes the electrical resistance of the liquid.
• Used in some special measurement applications.
• Plastic Strain Gauges
• Made from graphite or carbon embedded in resin.
• Manufactured as thin ribbons or threads.
• Very high gauge factor (up to ~300).
• Limitations:
• Mechanical instability
• Lower accuracy
• Difficult to use in practice.

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Force sensors �4. Force and tactile sensors�

The basic structure of a force sensor �

• Strain Gauge Method (Most Common)
• Measures force indirectly through strain (deformation)
• Output calibrated in units of force
• Based on change in resistance
• Other Force Measurement Methods
• Acceleration-based: F=ma
• Spring displacement: F=kx
• Pressure measurement
• All are indirect methods of force measurement
• Transduction Principle
• Converts force into measurable electrical parameters:
• Resistance (strain gauges)
• Capacitance
• Inductance

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Force sensors �4. Force and tactile sensors�

The basic structure of a force sensor �

• Strain Gauge Force Sensor
• Measures tensile or compressive force
• Can be pre-stressed for compression sensing
• Used in:
• Machine tools
• Engine mounts
• Load Cell
• Most common practical force sensor
• Typically cylindrical with strain gauges
• Applications:
• Weighing scales
• Vehicle suspension systems
• Industrial presses

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Force sensors �4. Force and tactile sensors�

One type of load cell—the button load cell �

• Compression Load Cell Structure
• Operates in compression mode
• Includes a “button” element to transfer applied load
• Button may connect to:
• Cylindrical body
• Beam or other structural element
• Strain Gauge Arrangement
• Strain gauges bonded to sensing element
• Usually prestressed
• Under compression → stress reduces in gauges

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Force sensors �4. Force and tactile sensors�

One type of load cell—the button load cell �

• Configurations
• Wide variety of designs available
• Adaptable for different applications and force ranges
• Force Measurement Range
• From fraction of a Newton to hundreds of thousands of Newtons
• Typical Load Cell Setup
• Uses four strain gauges:
• 2 in compression
• 2 in tension
• Improves accuracy and sensitivity

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Force sensors �4. Force and tactile sensors�

Structure of load cells. (a) Bending beam load cell. (b) “Ring” load

cell. (c) The connection of the strain gauges in a bridge. Arrows

pointing up indicate tension, and arrows pointing down indicate

compression �

Force sensors �4. Force and tactile sensors�

Tactile sensors �

A piezoelectric film tactile sensor. The compression due to force changes the coupling between the lower and upper PVDF layers and hence the amplitude of the output �

A piezoelectric film sensor used to detect sliding motion due to breathing. The output is monitored for a pattern consistent with the breathing pattern and the shift in the center of gravityas a consequence �

Force sensors �4. Force and tactile sensors�

Tactile sensors �

FSR tactile sensor using conducting elastomers. (a) Principle and structure. (b) An array of tactile sensors. (c) The transfer function of FSRs �

Accelerometers ��

• Principle:�Based on Newton’s second law:

F=ma

Acceleration is measured by sensing the force acting on a mass.

• Basic Concept:
• At rest → acceleration = 0 → force = 0
• When accelerated → force ∝ mass × acceleration
• Force is typically measured using strain gauges
• Alternative Sensing Methods:
• Capacitive (Electrostatic): Change in capacitance due to displacement
• Magnetic: Variation in magnetic field with movement of a magnetic mass
• Thermal methods (less common)

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Accelerometers ��

(a) Mechanical model of an accelerometer based on sensing the force

on a mass. (b) Free body diagram of the accelerometer in (a) �

• Mechanical Model of Accelerometer:
• Components: Mass (m), Spring (k), Damper (b)
• Governing equation:

ma=kx−b(dx/dt)​

• Displacement xxx indicates acceleration
• Key Idea:
• Uses a proof (inertial) mass
• Measures its displacement relative to housing
• Requires a displacement sensor (position/proximity)
• Applications:
• Vibration measurement
• Motion tracking
• Robotics and control systems

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Accelerometers ��

1.Capacitive accelerometers �

Three basic capacitive acceleration sensors. (a) Moving plate against a spring.

(b) Beam-suspended plate. (c) Sideways moving plate against a spring �

Two basic forms of producing accelerometers. (a) Cantilever

(supported on the left). (b) Bridge support �

Accelerometers ��

2.Strain gauge accelerometers �

Accelerometers ��

3. Magnetic accelerometers �

(a) An inductive accelerometer in which the horizontal motion of the mass is sensed by a change in the inductance of a coil. (b) An accelerometer in which the position of the mass is sensed by a Hall element �

Accelerometers ��

4. Other accelerometers�

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• Gas heated inside a cavity to equilibrium
• Two thermocouples placed equidistant from heater
• At rest → same temperature → zero differential output
• During acceleration:
• Gas shifts opposite to motion
• Temperature difference occurs
• Output calibrated to acceleration

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• Magnetic (mass–spring–coil system)
• Optical / Optical fiber based
• Vibrating reed (frequency variation)

Pressure sensors � ��

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• In gases and fluids, direct force measurement is difficult
• Pressure is used to determine:
• Force
• Temperature
• Power
• Other related quantities
• Pressure = Force / Area
• Sensed by measuring: Displacement Strain of a sensing element
• Mechanical (diaphragm, Bourdon tube)
• Electrical (strain gauges, capacitive sensors)
• Thermal methods Magnetic methods
• Automobiles
• Weather forecasting (barometers)
• HVAC systems
• Industrial and consumer devices

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Pressure sensors � ��

1.Mechanical pressure sensors �

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• Early pressure sensing used purely mechanical devices
• Direct conversion: Pressure → Mechanical displacement
• Still widely used due to simplicity and low cost
• Invented by Eugene Bourdon (1849)
• C-shaped tube expands with pressure
• Drives dial via linkage mechanism
• Suitable for high-pressure applications

• Diaphragm → Flexible membrane deformation
• Bellows → Expansion/contraction under pressure
• Piston-based sensors

(a) The bourdon tube pressure sensor. The bourdon tube (C-shaped

portion) expands with pressure, turning the dial (below the bezel,

not seen) through a leverage arm and gear mechanism.

(b) The diaphragm pressure sensor �

Pressure sensors � ��

1.Mechanical pressure sensors �

(a) The thin plate. (b) The membrane �

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• Sealed chamber with flexible wall
• Expands/contracts with pressure difference
• Used in barometers

Membrane (Negligible Thickness)

Thin Plate (Finite Thickness)

where P is the applied pressure, r is its radius, and t is its thickness E is the modulus of elasticity and v is Poisson’s ratio � � �,

Pressure sensors � ��

1.Mechanical pressure sensors �

Pressure sensors � ��

2. Piezoresistive pressure sensors�

• A piezoresistor = semiconductor strain gauge
• Preferred over conductor strain gauges because:
• Higher sensitivity
• Easy miniaturization (MEMS technology)
• Better integration with electronics

Conductor strain gauges used only for:

• High-temperature applications
• Specialized environments
• Diaphragm often made of silicon
• Embedded piezoresistors on diaphragm surface Enables:
• On-chip temperature compensation
• Signal conditioning circuits Amplifiers
• Pressure → Stress on diaphragm
• Stress → Change in resistance

The change in resistance of the two piezoresistors is �

A piezoresistive pressure sensor. (a) Placement of the

piezoresistances. (b) Construction showing the diaphragm

and vent hole (for gauge pressure sensors) �

Pressure sensors � ��

2. Piezoresistive pressure sensors�

• Gauge Sensor → One side vented to atmosphere
• Sealed Gauge Sensor → Reference pressure P0 sealed inside
• Differential Sensor → Measures pressure difference between two ports Single strain gauge with current flow
• Pressure applied perpendicular to current
• Output measured as voltage change
• Silicon (most common)Metals → structural strength
• Ceramics → corrosive environments
• Glass → protective coatings

Construction of a differential pressure sensor. The diaphragm is

placed between the two ports �

Pressure sensors � ��

2. Piezoresistive pressure sensors�

A direct-sensing piezoresistance pressure sensor. The potential

across the resistor is a measure of pressure. Pressure is applied

perpendicular to the current �

Various pressure sensors. (a) Pressure sensors of various sizes. The smallest is 2 mm in diameter, the largest is 30 mm in diameter. Note the connectors. All are sealed gauge pressure sensors. (b) Small sensors in stainless steel housings (absolute pressure sensors). (c) Miniature surface-mount digital pressure sensors (from top-left, clockwise: two 14 bar sensors, two 7 bar sensors, 1 bar sensor, two 12 bar sensors and 1 bar sensor) sealed gauge sensors �

Pressure sensors � ��

3. Capacitive pressure sensors�

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• Diaphragm + fixed plate form a capacitor
• Pressure → diaphragm deflection
• Deflection → change in plate (distance)
• Capacitance varies with pressure

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• Very effective for low-pressure sensing
• Small strain → large capacitance change
• Can be used in oscillator circuits → frequency change improves sensitivity

• High sensitivity at low pressures
• Low temperature dependence
• Can withstand high overpressure (100–1000× rated pressure)
• Mechanical stops prevent damage

Pressure sensors � ��

4. Magnetic pressure sensors�

• Use magnetic principles for pressure measurement
• Types:
• LVDT / Inductive sensors → for large deflection
• Variable reluctance sensors → for low pressure

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• Diaphragm made of ferromagnetic material
• Forms part of magnetic circuit
• Pressure → changes air gap
• Air gap change → change in reluctance & inductance
• Output measured as current/inductance variation

• High sensitivity (small deflection → large inductance change)
• Low temperature sensitivity
• Suitable for harsh environments

• Optoelectronic sensors → Fabry–Perot cavity (light-based)
• Pirani gauge → measures heat loss in gases (vacuum sensing)

A variable reluctance pressure sensor. (a) Structure and operation. (b) Equivalent circuit in terms of reluctances. (c) Operation with an AC source. The core and diaphragm are circular �

Velocity sensing

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• Velocity sensing is more complex than acceleration sensing because velocity is relative and needs a reference
• Direct measurement of velocity is difficult; indirect methods are commonly used
• Velocity can be inferred from rotational speed (e.g., wheels, motor shafts)
• GPS can be used to measure velocity based on position change over time
• In aircraft, velocity is estimated using pressure or temperature changes (airflow effects)
• Measuring something proportional to velocity is often more practical than direct sensing
• Direct velocity sensors (standalone) are challenging to design and implement
• One method uses electromagnetic induction with a moving magnet and stationary coil
• Constant velocity cannot be measured easily with this method due to lack of relative motion
• A restoring force (spring) is needed to create relative motion between magnet and coil
• For changing velocity (non-zero acceleration), induced emf can be generated
• The induced emf is governed by Faraday’s law of electromagnetic induction

A velocity sensor. The induced emf in the coils is proportional to the velocity of the magnet �

Velocity sensing

Flow velocity sensor. (a) The downstream temperature sensor (2) is shielded from the flow but measures the air (or fluid) temperature. (b) The downstream sensor (2) is also in the flow, but is cooled less because of the heat transfer from the up tream sensor (1). (c) A fluid velocity sensor showing four deposited thermistors on a ceramic substrate (right-hand side of the picture). Flow is from top to bottom and the sensors are connected in a bridge configuration. A reference

thermistor is placed on the reverse side of the substrate along with a temperature sensor �

• Vehicle speed can be measured relative to ground using practical techniques
• Fluid and gas velocities are easier to measure compared to solid objects
• Aircraft and watercraft measure velocity relative to surrounding fluid
• Thermistor-based sensors measure cooling effect of flowing fluid

Velocity sensing

• Speed can be measured using pressure difference in a fluid
• Moving fluid creates higher pressure at the front (Pitot tube)
• Faster flow → higher pressure difference
• Total pressure = static pressure + dynamic pressure
• Pitot tube is commonly used in aircraft to measure airspeed
• Simple, reliable, and widely used method

The Pitot tube. (a) The original use was to measure water velocity and flow rates in rivers. (b) The modern adaptation to measure airspeed in an aircraft or the relative speed in a fluid. What is measured is the total (stagnant) pressure in the tube �

• Pt​: total (stagnation) pressure measured when fluid is brought to rest
• Ps​: static pressure (pressure of fluid at rest, e.g., atmospheric pressure)
• Pd​: dynamic pressure caused by motion of fluid

Velocity sensing

• 𝜌: fluid density (air or water), may be known or measured
• Higher pressure difference → higher velocity
• Air density depends on pressure and temperature

• RRR: gas constant, TTT: absolute temperature
• Density decreases with increase in altitude
• Static pressure changes with height (altitude)
• Pressure decreases as altitude increases

• Used in altimeters and aircraft systems
• Pitot tube measures both total and static pressure to calculate velocity

Velocity sensing

The Prandtl tube. A differential pressure sensor measures the

difference between the total pressure and the static pressure.

The tube moves to the right at a velocity v in a fluid (air) �

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• Prandtl tube (Pitot-static tube) measures both total and static pressure
• Has two openings: front (total pressure) and side (static pressure)
• Differential pressure sensor finds the difference between these pressures
• This pressure difference is used to calculate velocity
• Measures velocity relative to fluid (e.g., aircraft airspeed, not ground speed)
• Widely used in aircraft, ships, and submarines
• Small openings can get blocked by ice (icing problem in aircraft)
• Icing can give wrong speed readings and cause serious accidents
• To prevent this, Pitot tubes are heated
• Simple, reliable, and widely used method for speed measurement

Velocity sensing

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• Velocity can be measured using ultrasonic, electromagnetic, or optical methods
• These methods use waves and their reflections
• Speed is found by measuring time taken by waves (time of flight)
• Doppler effect measures change in frequency due to motion
• Frequency change gives velocity
• Used in radar, weather monitoring, and speed detection systems

Inertial sensors: gyroscopes �

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• Gyroscopes are used as stabilizing devices in aircraft, spacecraft, and satellites
• Used in autopilots, smart weapons, and attitude/position control systems
• Function as a navigation tool, similar to a magnetic compass
• Help maintain direction and orientation (attitude) of a system
• Used in applications like tunnel construction and mining due to high accuracy
• Increasing miniaturization → use in cars, consumer devices, toys, and drones
• Basic principle: conservation of angular momentum
• Angular momentum remains constant if no external forces act on the system
• Term “gyroscope” derived from Greek words meaning “rotation” and “to see”
• Concept popularized by Leon Foucault (1852) to demonstrate Earth’s rotation
• Principle known earlier (around 1817) through Johann Bohnenberger

Inertial sensors: gyroscopes �

1.Mechanical or rotor gyroscopes �

The rotating mass gyroscope �

Mechanical gyroscope consists of a rotating mass (wheel) on an axis

Spinning mass creates angular momentum

Applying torque causes precession motion

Precession is perpendicular to rotation axis and applied torque

Precession rate is proportional to applied torque and inertia

Relationship:𝑇=𝐼𝜔Ω,Ω=𝑇/𝐼𝜔

​Output (precession) used to measure orientation and direction

Used in aircraft, satellites, and navigation systems

Can be extended to two-axis and three-axis gyroscopes

Inertial sensors: gyroscopes �

1.Mechanical or rotor gyroscopes �

Limitations: large size, heavy, complex construction

Requires high-speed rotation and precise balancing

Friction and mechanical wear reduce reliability

Advanced versions use:

Vacuum operation

Magnetic/electrostatic suspension

Gas bearings

Modern gyroscopes:

Smaller rotating mass + high-speed motors

Sensitive detection systems

Alternative: Coriolis-based (MEMS) gyroscopes

Based on Coriolis effect → motion in rotating frame produces perpendicular acceleration

Uses vibrating mass → rotation generates measurable force

Advantages: compact, low cost, widely used in modern electronics

Inertial sensors: gyroscopes �

2.Optical gyroscopes

1. The Sagnac effect in an optical fiber ring rotating at an angular frequency W.
2. Implementation of the ring resonator using mirrors to “close” the ring �

A resonating ring optical fiber gyroscope �

Inertial sensors: gyroscopes �

2.Optical gyroscopes

A coil optical fiber gyroscope �