Mechatronics and Robotics

MECHATRONICS – BASIC CONCEPT

• Mechatronics: Integration of mechanical systems with electronics, sensors, actuators, computers and control systems.
• Basic chain: Physical system → Sensor → Signal conditioning → Controller → Actuator → Mechanical output.
• Main elements: Mechanical system + Electronics + Control + Computer + Sensors + Actuators.

Mechatronics System

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MICROPROCESSOR

Microprocessor: CPU implemented on a single integrated circuit. It generally requires external memory and I/O devices.

Basic Architecture

• ALU: Performs arithmetic and logical operations.
• Control Unit: Generates control signals.
• Registers: High-speed temporary storage.
• Program Counter (PC): Holds address of next instruction.
• Stack Pointer (SP): Points to top of stack.
• Instruction Register: Holds current instruction.
• Accumulator: Stores intermediate arithmetic/logic results in many architectures.
• Address bus: Carries address information.
• Data bus: Transfers data.
• Control bus: Carries control/timing signals.

Microprocessor vs Microcontroller

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MICROCONTROLLER

Microcontroller: Programmable embedded computer containing CPU, memory and peripheral interfaces on a single chip.

Typical Blocks

• CPU
• Program memory: ROM/Flash
• Data memory: RAM
• Digital I/O ports
• Timers/Counters
• Interrupt controller
• Serial communication interfaces
• ADC/DAC in many controllers
• Watchdog timer
• Clock/oscillator

Important Memory Types

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MICROPROCESSOR / MICROCONTROLLER PROGRAMMING

• Instruction: Command executed by processor.
• Opcode: Specifies the operation.
• Operand: Data/address on which operation acts.
• Instruction cycle: Fetch → Decode → Execute.
• Interrupt: Event that temporarily diverts processor execution to an interrupt service routine.

Common Programming Levels

• Machine language: Binary instructions directly understood by processor.
• Assembly language: Mnemonics representing machine instructions.
• High-level language: C/C++ and similar languages commonly used for embedded programming.

Common Instruction Categories

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I/O & COMPUTER INTERFACING

I/O: Communication between processor/controller and external devices.

Input Devices

• Sensors
• Switches
• Keyboards
• Encoders
• Analog transducers

Output Devices

• Motors
• Solenoid valves
• Relays
• Displays
• Actuators

Important Interfaces

• Digital I/O: Binary HIGH/LOW signals.
• ADC: Analog → Digital.
• DAC: Digital → Analog.
• PWM: Controls average voltage/power using pulse duty cycle.
• Interrupt: Allows immediate response to important events.
• Serial communication: Transfers data sequentially over communication lines.

ADC resolution: For an ideal n-bit ADC, number of quantization levels = 2ⁿ.

Ideal ADC LSB size: Approximately full-scale input range / 2ⁿ.

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PROGRAMMABLE LOGIC CONTROLLER (PLC)

PLC: Industrial digital controller designed to monitor inputs, execute a programmed logic sequence and control outputs.

PLC Block Diagram

Input devices → Input module → CPU/Memory → Output module → Actuators

PLC Main Components

• CPU: Executes control program.
• Memory: Stores program and data.
• Input module: Receives signals from sensors/switches.
• Output module: Drives actuators/relays/solenoids.
• Programming device: Used to create/download program.
• Power supply: Supplies required electrical power.

PLC Scan Cycle

Input scan → Program execution → Output update → Housekeeping/communication

PLC Programming Languages

• Ladder Diagram (LD)
• Function Block Diagram (FBD)
• Structured Text (ST)
• Sequential Function Chart (SFC)

Ladder logic: Widely used because its structure resembles relay-control circuits.

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SENSORS & TRANSDUCERS

Sensor: Device that detects/measures a physical quantity.

Transducer: Device that converts one form of energy/physical quantity into another, commonly into an electrical signal for measurement.

Classification

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PIEZOELECTRIC ACCELEROMETER

Principle: Piezoelectric effect — certain materials generate electric charge when mechanically stressed.

• Measures vibration/acceleration.
• Mass + piezoelectric element + preload structure form the sensing system.
• Produces electrical output proportional to dynamic force/acceleration within its operating range.
• Very suitable for vibration monitoring and high-frequency measurements.
• Generally not suitable for measuring true static acceleration indefinitely because of charge leakage/electronic limitations.

Basic relation: F = ma

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HALL-EFFECT SENSOR

Principle: Hall effect — a transverse voltage develops across a current-carrying semiconductor when exposed to a magnetic field.

• Used for magnetic-field sensing.
• Used for position/proximity detection.
• Used for speed measurement and rotational sensing.
• Used in brushless DC motor commutation.
• Provides electrical isolation between sensing magnet and electronic circuit in many applications.

Hall voltage: V_H ∝ B

For a simple Hall element, V_H also depends on current, carrier concentration and geometry.

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OPTICAL ENCODER

Optical encoder: Converts shaft position/motion into electrical pulses using a patterned disc and optical sensing.

Types

• Quadrature output: Two phase-shifted channels determine direction and increase resolution.
• Used for position, speed and direction measurement.

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RESOLVER

Resolver: Electromagnetic rotary position sensor that produces sinusoidal/cosinusoidal signals related to shaft angle.

• Works on transformer action.
• Usually has one excitation winding and two output windings spatially displaced by 90°.
• Output amplitudes vary approximately as sinθ and cosθ.
• Robust and suitable for harsh environments.

Typical outputs:

• V_sin ∝ sinθ
• V_cos ∝ cosθ

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INDUCTOSYN

Inductosyn: Precision electromagnetic position transducer based on variable mutual inductance between patterned windings.

• Can measure linear or rotary displacement.
• Uses a scale and slider pattern similar in concept to a precision electromagnetic scale.
• Provides high accuracy and resolution.
• Used in precision machine tools and position measurement.

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ACTUATORS

Actuator: Device that converts control energy/signal into mechanical motion or force.

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PNEUMATIC ACTUATORS

Pneumatic actuator: Uses compressed air to produce mechanical motion.

• Single-acting cylinder: Air acts in one direction; return by spring/external force.
• Double-acting cylinder: Air controls motion in both directions.
• Clean, fast and relatively inexpensive.
• Suitable where very high force is not required.

Ideal cylinder force: F = pA

• p = gauge/working pressure
• A = effective piston area

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HYDRAULIC ACTUATORS

Hydraulic actuator: Uses pressurized liquid to produce mechanical motion.

• Provides high force/torque.
• Suitable for heavy-load applications.
• Good force control and stiffness.
• Common in presses, construction machinery and industrial systems.

Ideal hydraulic force: F = pA

Hydraulic motor torque: Approximately proportional to pressure difference × displacement per revolution.

Pneumatic vs Hydraulic

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STEPPER MOTOR

Stepper motor: Brushless motor that converts electrical pulse commands into discrete angular movements.

• Each input pulse produces a specified step.
• Position can be controlled by counting pulses.
• Direction is controlled by phase sequence.
• Speed depends on pulse frequency.
• Widely used in CNC machines, printers and positioning systems.

Number of steps/revolution: N_s = 360° / step angle

Step angle: α = 360°/N_s

Types

• Variable-reluctance stepper motor
• Permanent-magnet stepper motor
• Hybrid stepper motor

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CONTROL SYSTEMS

Control system: Arrangement of components designed to regulate a system output according to a desired input.

Open-Loop vs Closed-Loop

Basic Closed-Loop System

Reference input → Comparator → Controller → Plant → Output

↑ ↓

Feedback ← Sensor

Error: e(t) = r(t) − b(t)

• r(t) = reference input
• b(t) = feedback signal
• e(t) = error signal

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MATHEMATICAL MODELING OF PHYSICAL SYSTEMS

Mathematical modeling: Representing physical system behaviour using mathematical equations.

Common Physical Domains

Mechanical Translational System

Equation: F(t) = Mẍ + Bẋ + Kx

• M = mass
• B = viscous damping coefficient
• K = spring stiffness
• x = displacement

Mechanical Rotational System

Equation: T(t) = Jθ̈ + Bθ̇ + Kθ

• J = moment of inertia
• B = rotational damping coefficient
• K = torsional stiffness
• θ = angular displacement

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TRANSFER FUNCTION

Transfer function: Ratio of Laplace transform of output to input, with zero initial conditions.

G(s) = C(s)/R(s)

Standard First-Order Form

G(s) = K/(τs + 1)

• K = system gain
• τ = time constant

Standard Second-Order Form

G(s) = ω_n² / [s² + 2ζω_ns + ω_n²]

• ω_n = natural frequency
• ζ = damping ratio

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CONTROL SIGNALS / STANDARD TEST INPUTS

Laplace Forms

• Unit step: 1/s
• Unit ramp: 1/s²
• Unit parabolic: 1/s³
• Unit impulse: 1

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CONTROLLABILITY & OBSERVABILITY

Controllability: Ability to drive the system state from an initial state to a desired state using suitable control input in finite time.

Observability: Ability to determine the internal state of a system from its measured outputs over a finite time interval.

State-Space Model

ẋ = Ax + Bu

y = Cx + Du

• x = state vector
• u = input vector
• y = output vector
• A = system matrix
• B = input matrix
• C = output matrix
• D = feedthrough matrix

Rank Conditions

Controllability matrix:

[ B AB A²B … Aⁿ⁻¹B ]

System is completely controllable if the controllability matrix has rank n.

Observability matrix:

[ C ; CA ; CA² ; … ; CAⁿ⁻¹ ]

System is completely observable if the observability matrix has rank n.

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ROBOTICS – BASIC CONCEPT

Robot: Automatically controlled, reprogrammable, multipurpose manipulator programmable in three or more axes in industrial applications.

Basic Robot Components

• Manipulator: Mechanical structure producing motion.
• Joints: Provide relative motion between links.
• Actuators: Drive robot joints.
• Controller: Executes motion/control program.
• End effector: Tool or gripper attached to robot wrist.
• Sensors: Provide position, force or environmental information.

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ROBOT CLASSIFICATION

Classification by Mechanical Configuration

Classification by Control

• Limited-sequence control
• Point-to-point (PTP) control
• Continuous-path control
• Intelligent/sensor-based control

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ROBOT SPECIFICATION

Important parameters used to specify a robot include:

• Number of axes / DOF: Independent motions available.
• Payload: Maximum permissible load at specified conditions.
• Reach: Maximum working distance from reference location.
• Work envelope: Total region accessible by the end effector.
• Accuracy: Closeness of achieved position to commanded position.
• Repeatability: Ability to return repeatedly to the same position.
• Resolution: Smallest programmable/controlled movement.
• Speed: Maximum or specified motion speed.
• Degrees of freedom: Number of independent coordinates needed to define configuration.

Important: Accuracy and repeatability are different. A robot can be highly repeatable but have systematic position error.

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ROBOT NOTATION

Robot kinematic structures are commonly represented using joint/link notation or standard Denavit–Hartenberg (D-H) parameters.

Common Joint Symbols

D-H parameters: θ, d, a, α

• θ: Joint angle
• d: Joint offset
• a: Link length
• α: Link twist

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DIRECT / FORWARD KINEMATICS

Forward kinematics: Determines position and orientation of the robot end effector from known joint variables and link dimensions.

Input: Joint variables + link parameters

Output: End-effector position + orientation

General Transformation

T = T₁ T₂ T₃ … Tₙ

The final transformation matrix gives the pose of the end effector relative to the reference frame.

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INVERSE KINEMATICS

Inverse kinematics: Determines joint variables required to achieve a specified end-effector position and orientation.

Input: Desired end-effector pose

Output: Joint angles/displacements

• May have multiple solutions.
• May have no solution if target is outside workspace.
• May become difficult near singular configurations.
• Generally more mathematically complex than forward kinematics.

Forward vs Inverse Kinematics

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HOMOGENEOUS COORDINATES

Homogeneous transformation: Matrix representation combining rotation and translation in a single transformation.

General 4 × 4 transformation matrix:

• Upper-left 3 × 3 matrix → rotation.
• Last column → translation.
• Bottom row → homogeneous-coordinate convention.

Homogeneous Point

P = [x y z 1]^T

P′ = T P

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FOUR-AXIS SCARA ROBOT

SCARA: Selective Compliance Assembly Robot Arm.

• Commonly a 4-axis robot.
• Typical joint arrangement: R-R-P-R.
• First two rotary joints provide planar X-Y positioning.
• Third joint provides vertical Z motion.
• Fourth joint provides wrist rotation about vertical axis.
• High speed and repeatability make SCARA suitable for assembly, pick-and-place and material handling.

Typical SCARA Joint Variables

• θ₁ = first rotary joint angle
• θ₂ = second rotary joint angle
• d₃ = vertical displacement
• θ₄ = wrist rotation

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FOUR-AXIS SCARA ARM EQUATIONS

For a standard planar two-link SCARA geometry with link lengths L₁ and L₂:

x = L₁ cosθ₁ + L₂ cos(θ₁ + θ₂)

y = L₁ sinθ₁ + L₂ sin(θ₁ + θ₂)

z = z₀ ± d₃

φ = θ₁ + θ₂ + θ₄

• x, y = horizontal end-effector coordinates.
• z = vertical coordinate.
• φ = end-effector orientation about vertical axis.
• Sign of d₃ depends on the chosen positive Z direction and coordinate convention.

SCARA Arm Matrix Concept

T₀⁴ = T₀¹ T₁² T₂³ T₃⁴

The resulting homogeneous matrix contains:

• End-effector orientation in the 3 × 3 rotation portion.
• End-effector x, y, z coordinates in the translation portion.

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SCARA INVERSE KINEMATICS – HIGH-YIELD FORM

For the planar two-link section:

D = (x² + y² − L₁² − L₂²)/(2L₁L₂)

θ₂ = ± cos⁻¹(D)

θ₁ = atan2(y,x) − atan2(L₂ sinθ₂, L₁ + L₂ cosθ₂)

θ₄ = φ − θ₁ − θ₂

d₃ is obtained from the desired vertical coordinate according to the selected Z-axis convention.

Important: The ± sign in θ₂ represents the two common planar configurations, often described as elbow-up and elbow-down.

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SINGULARITY

Singularity: Robot configuration at which the Jacobian loses rank and certain end-effector motions/forces cannot be produced or resolved normally.

• May cause loss of one or more instantaneous degrees of freedom.
• Can lead to very large joint velocities for a commanded Cartesian velocity.
• Important in robot trajectory planning.

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HIGH-YIELD COMPARISON TABLE

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⚡ ONE-MINUTE REVISION

• Mechatronics: Mechanical + Electronics + Control + Computing.
• Microprocessor: Mainly CPU; external memory/I/O commonly used.
• Microcontroller: CPU + memory + peripherals on one chip.
• ADC: Analog → Digital.
• DAC: Digital → Analog.
• PLC: Input scan → Program execution → Output update.
• Piezoelectric: Mechanical stress → electrical charge.
• Hall: Magnetic field → Hall voltage.
• Encoder: Motion/position → digital pulses/code.
• Resolver: Rotary angle → sinθ/cosθ signals.
• Stepper: One pulse → one specified step.
• Pneumatic: Air powered.
• Hydraulic: Liquid powered.
• Open loop: No feedback.
• Closed loop: Feedback.
• Transfer function: Output/Input with zero initial conditions.
• Controllability: Control the state.
• Observability: Observe/determine the state.
• Forward kinematics: Joint → pose.
• Inverse kinematics: Pose → joint variables.
• Homogeneous matrix: 4 × 4; combines rotation + translation.
• SCARA: Selective Compliance Assembly Robot Arm; typically 4-axis R-R-P-R.
• SCARA X: L₁cosθ₁ + L₂cos(θ₁+θ₂).
• SCARA Y: L₁sinθ₁ + L₂sin(θ₁+θ₂).