Mechanical Engineering

Part 1 – Engineering Mechanics

Engineering Mechanics is one of the most important subjects in TNPSC CTS Mechanical Engineering examinations. It deals with the behaviour of bodies under the action of forces. It forms the foundation for Machine Design, Strength of Materials, Theory of Machines, and Structural Analysis.

Engineering Mechanics is divided into:

• Statics – deals with bodies at rest or moving with constant velocity.
• Dynamics – deals with bodies under acceleration.

Force

A force is a push or pull acting on a body which changes or tends to change its state of rest or motion.

Characteristics of Force

• Magnitude
• Direction
• Point of application
• Line of action

SI Unit

Newton (N)

Types of Forces

• External Force – Acts from outside the body. Examples: Load on beam, Weight, Wind force.
• Internal Force – Develops inside the body due to external loading. Examples: Tensile force, Compressive force.
• Concentrated Force – Acts at one point. Example: Weight suspended from a hook.
• Distributed Force – Acts over an area or length. Example: Pressure on a wall.

Newton's Laws of Motion

• First Law – A body remains at rest or continues in uniform motion unless acted upon by an external force. This law introduces Inertia.
• Second Law – Force is proportional to rate of change of momentum.

where F = Force, m = Mass, a = Acceleration

• Third Law – Every action has an equal and opposite reaction.

Examples: Walking, Swimming, Rocket propulsion.

Resolution of Forces

A force may be resolved into horizontal and vertical components. If force is P making angle θ:

This concept is widely used in trusses and inclined planes.

Resultant Force

The single force replacing several forces without changing the effect is called the resultant.

Methods

• Triangle law
• Parallelogram law
• Polygon law

Parallelogram Law of Forces

"If two forces acting simultaneously on a particle are represented by two adjacent sides of a parallelogram, then their resultant is represented by the diagonal."

Triangle Law of Forces

Useful for solving equilibrium problems involving three concurrent forces.

Polygon Law of Forces

Applicable when more than two forces act simultaneously.

Equilibrium

A body is said to be in equilibrium when the resultant force and resultant moment are zero.

Free Body Diagram (FBD)

A Free Body Diagram is a sketch showing all external forces acting on a body.

Importance

• Simplifies calculations
• Helps determine reactions
• Avoids missing forces

Moment of Force & Principle of Moments

Moment is the turning effect of a force. Unit: Newton metre (Nm)

Types: Clockwise moment, Anticlockwise moment.

Principle of Moments: For equilibrium, Clockwise Moments = Anticlockwise Moments. Widely used in beams and levers.

Couple

A couple is a pair of equal and opposite parallel forces separated by a distance.

Properties

• Produces rotation only
• No translation
• Resultant force is zero

Varignon's Theorem

"The moment of the resultant equals the sum of moments of individual forces." Useful for simplifying calculations.

Types of Supports

• Roller Support – Allows horizontal movement. Provides one reaction.
• Pin Support – Allows rotation. Provides horizontal and vertical reactions.
• Fixed Support – Restricts all movement. Provides horizontal, vertical and moment reactions.

Friction

Friction is the resisting force between two contacting surfaces.

Types

• Static friction
• Limiting friction
• Kinetic friction
• Rolling friction

Laws of Friction

• Friction opposes motion.
• Friction depends upon normal reaction.
• Independent of contact area.
• Sliding friction is less than limiting friction.

Angle of Friction: Angle between resultant reaction and normal reaction → tan θ = μ

Angle of Repose: Maximum angle before sliding starts → Angle of Repose = Angle of Friction

Centroid & Centre of Gravity

Centroid is the geometric centre of an area. Important shapes: Rectangle, Triangle, Circle, Semicircle, Trapezium.

Centre of Gravity is the point through which the total weight acts. For uniform bodies, Centroid = Centre of Gravity.

Moment of Inertia (Area)

Moment of inertia indicates resistance against bending. Units: mm⁴, cm⁴, m⁴.

• Rectangle: I = bd³/12
• Circle: I = πd⁴/64

Parallel Axis Theorem

where Ig = Centroidal MOI, A = Area, d = Distance

Radius of Gyration

Simple Machines

Simple machines help multiply force. Types: Lever, Pulley, Wheel and axle, Screw jack, Wedge.

Efficiency is always less than 100%.

Work, Power & Energy

1 HP = 746 W

Energy is the capacity to do work.

• Potential Energy: PE = mgh
• Kinetic Energy: KE = ½mv²

Conservation of Energy

Energy cannot be created or destroyed. It can only be transformed. Example: Hydroelectric plant – Potential → Kinetic → Mechanical → Electrical.

Impulse & Momentum

Projectile & Circular Motion

A body projected into air follows a parabolic path.

A body moving along a circular path experiences centripetal force:

Applications: Flywheel, Vehicle turning, Rotating machines.

Angular Motion

Engineering Mechanics – Applications & Tips

Engineering Mechanics is applied in: Machine Design, Crane Design, Bridges, Automobile Engineering, Manufacturing, Robotics, Structural Engineering, Pressure Vessels, Lifting Equipment, Construction Machinery.

Part 2 – Strength of Materials (Mechanics of Materials)

Strength of Materials (SOM) is one of the most important subjects in TNPSC CTS Mechanical Engineering examinations. It deals with the behavior of solid bodies when subjected to different types of loads. The objective is to determine the strength, stiffness, and stability of materials so that machine components and structures can safely withstand applied loads without failure.

The concepts of Strength of Materials are widely used in machine design, bridges, buildings, pressure vessels, automobile components, and industrial machinery.

Stress

Stress is the internal resisting force developed inside a material due to an externally applied load.

where σ = Stress (N/mm² or MPa), P = Applied Load (N), A = Cross-sectional Area (mm²)

SI Unit: Pascal (Pa). Engineering practice generally uses MPa and N/mm².

Types of Stress

• Tensile Stress – Occurs when a member is subjected to pulling force. Examples: Crane cable, Chain, Tie rod, Suspension bridge cable. Formula: σt = P/A
• Compressive Stress – Occurs due to pushing force. Examples: Building columns, Machine supports, Concrete pillars. Formula: σc = P/A
• Shear Stress – Acts parallel to the cross-section. Examples: Rivets, Bolts, Pins, Keys. Formula: τ = P/A
• Bearing Stress – Develops between two contacting surfaces. Examples: Pin joints, Riveted joints, Bolted joints.

Strain

Strain is the deformation produced per unit original dimension. It has no unit.

Types of Strain

• Tensile Strain – Increase in length.
• Compressive Strain – Decrease in length.
• Shear Strain – Angular deformation due to shear force.
• Volumetric Strain – Change in volume divided by original volume.

Hooke's Law & Elasticity

Within elastic limit, stress is directly proportional to strain.

where E = Young's Modulus. Hooke's law is applicable only within the elastic range.

Elasticity is the property by which a material regains its original size and shape after removal of load. Examples: Steel, Spring steel, Rubber (within limits).

Material Properties

• Plasticity – Property to undergo permanent deformation without breaking. Examples: Clay, Lead, Copper. Used in forging and rolling.
• Ductility – Ability to be drawn into wires. Examples: Copper, Aluminium, Mild steel. Measured by percentage elongation.
• Malleability – Ability to be rolled or hammered into sheets. Examples: Gold, Silver, Lead, Aluminium.
• Toughness – Ability to absorb energy before fracture. Examples: Mild steel, Structural steel. Applications: Railway rails, Hammer heads, Gears.
• Brittleness – Ability to fracture suddenly without significant deformation. Examples: Glass, Cast iron, Ceramics.
• Hardness – Resistance against scratching, wear, and indentation. Tests: Brinell, Rockwell, Vickers.
• Resilience – Ability to absorb energy within elastic limit. Applications: Springs, Shock absorbers.

Creep & Fatigue

Creep – Slow permanent deformation under constant load over a long period. Occurs mainly at high temperatures. Examples: Boiler tubes, Turbine blades, Steam pipes.

Fatigue – Failure due to repeated or fluctuating loading below ultimate strength. Examples: Crankshaft, Connecting rod, Aircraft wings, Springs. Fatigue failure is one of the most common failures in machine parts.

Stress-Strain Curve of Mild Steel

Important points: Proportional limit, Elastic limit, Yield point, Ultimate tensile stress, Breaking point.

• Elastic Region – Material returns to original shape.
• Plastic Region – Permanent deformation occurs.

Working Stress & Factor of Safety

Higher FOS gives greater safety but increases cost.

Thermal Stress & Poisson's Ratio

where α = Coefficient of thermal expansion.

Typical value for steel: 0.25–0.30.

Elastic Constants

• Young's Modulus (E) – Resistance to longitudinal deformation. Steel ≈ 200 GPa.
• Shear Modulus (G) – Resistance against shear deformation.
• Bulk Modulus (K) – Resistance against volume change.

Composite Bars & Varying Sections

Composite bars consist of two or more different materials joined together. Examples: Reinforced concrete, Steel-aluminium members. Condition: Both materials undergo equal deformation.

Bars of varying sections – Different cross-sectional areas produce different stresses. Each section must be analysed separately. Frequently asked numerical topic.

Principal Stress & Mohr's Circle

Principal stress – Maximum and minimum normal stresses acting on a plane. Occurs where shear stress becomes zero. Applications: Pressure vessels, Shafts, Machine elements.

Mohr's Circle – Graphical method used for determining principal stress, maximum shear stress, and plane orientation. Important for objective questions.

Shear Force & Bending Moment

Shear Force – Algebraic sum of vertical forces acting on one side of a section. Unit: Newton (N).

Bending Moment – Moment produced by external loads about any section. Unit: N-m.

Important relation: Maximum bending moment occurs where shear force changes sign.

• Shear Force Diagram (SFD) – Graph showing variation of shear force along beam length.
• Bending Moment Diagram (BMD) – Graph showing bending moment variation. Important in beam design.

Types of Beams & Loading

Types of Beams

• Simply Supported Beam – Supported at both ends.
• Cantilever Beam – Fixed at one end only. Examples: Balcony, Traffic signal arm.
• Overhanging Beam – Beam extends beyond support.
• Fixed Beam – Both ends fixed.
• Continuous Beam – More than two supports.

Types of Loading

• Point Load
• Uniformly Distributed Load (UDL)
• Uniformly Varying Load (UVL)
• Applied Moment

Bending Stress & Deflection

where M = Bending moment, y = Distance from neutral axis, I = Moment of inertia.

Neutral Axis – The axis where bending stress is zero. Material above and below undergoes compression and tension respectively.

Higher section modulus means higher bending strength.

Beam Deflection – Displacement of a beam due to loading. Factors affecting deflection: Load, Span, Elastic modulus, Moment of inertia.

Torsion

Twisting of circular shafts under torque. Applications: Motor shafts, Transmission shafts, Propeller shafts.

where T = Torque, J = Polar moment of inertia, τ = Shear stress, R = Radius, θ = Angle of twist.

Springs

Springs absorb shocks and store energy. Types: Helical spring, Leaf spring, Spiral spring, Disc spring. Applications: Vehicle suspension, Clutches, Valves.

Columns, Struts & Cylinders

A column carries compressive load. Failure occurs mainly due to buckling. Types: Short column, Long column.

Rankine Formula – Applicable for both short and long columns. Frequently asked in competitive examinations.

Thin Cylinders – Used in boilers, air receivers, water tanks. Types of stress: Hoop stress, Longitudinal stress. Hoop stress is twice the longitudinal stress.

Thick Cylinders – Stress distribution is non-uniform. Lame's equations are used. Applications: Hydraulic cylinders, Gun barrels, High-pressure vessels.

Riveted & Welded Joints

Riveted Joints – Types: Lap joint, Butt joint. Failure may occur by Shearing, Crushing, Tearing.

Welded Joints – Advantages: High efficiency, Leak-proof, Light weight. Types: Butt weld, Fillet weld, Groove weld.

Strength of Materials – Applications & Tips

Applied in: Machine Design, Bridge Design, Building Construction, Pressure Vessel Design, Railway Engineering, Automobile Engineering, Aerospace Components, Heavy Machinery, Industrial Equipment.

Part 3 – Theory of Machines (TOM)

Theory of Machines is one of the highest-scoring subjects in TNPSC Combined Technical Services (CTS) Mechanical Engineering examinations. It deals with the study of mechanisms, machines, motion, force transmission, balancing, and power transmission. The concepts are extensively used in automobiles, manufacturing industries, robotics, power plants, textile machinery, and machine design.

Machine & Mechanism

A machine is a combination of resistant bodies arranged to transmit or modify force and motion to perform useful work. Examples: Lathe machine, Drilling machine, Pump, Engine, Compressor.

Characteristics of a Machine

• Consists of one or more mechanisms.
• Transmits power.
• Converts one form of energy into another.
• Performs useful work.

A mechanism is a combination of links connected together to produce a definite motion. Examples: Slider-crank mechanism, Four-bar mechanism, Cam and follower, Gear train.

Kinematic Link & Kinematic Pair

A link is a resistant body that connects different machine parts and transmits motion.

Types of Links

• Rigid Link – Does not undergo appreciable deformation. Examples: Connecting rod, Crank, Frame.
• Flexible Link – Undergoes slight deformation. Examples: Belt, Rope, Chain, Cable.
• Fluid Link – Uses fluid pressure for transmitting motion. Examples: Hydraulic brake, Hydraulic press, Hydraulic jack.

Two links joined together to permit relative motion are called a kinematic pair.

• Lower Pair – Surface contact. Examples: Nut and bolt, Shaft and bearing, Piston and cylinder.
• Higher Pair – Point or line contact. Examples: Gear teeth, Cam and follower, Ball bearing.

Types of Motion & Kinematic Chain

Types of Motion

• Rotary Motion
• Linear Motion
• Oscillating Motion
• Reciprocating Motion
• Helical Motion

A combination of links connected together to produce constrained motion is called a kinematic chain. Examples: Bicycle chain mechanism, Four-bar chain, Slider crank chain.

Four-Bar Chain

Consists of four rigid links connected by four turning pairs. Applications: Pumping mechanism, Automobile steering linkage, Door closer, Coupling rod of locomotive.

Slider Crank Mechanism

Converts rotary motion into reciprocating motion and vice versa. Applications: IC Engine, Air Compressor, Reciprocating Pump.

Main Parts: Crank, Connecting rod, Piston, Cylinder.

Inversion & Quick Return Mechanism

Inversion of mechanism – Obtained by fixing different links of the same kinematic chain. Examples: Crank and slotted lever mechanism, Whitworth quick return mechanism, Oscillating cylinder engine.

Quick Return Mechanism – Used where return stroke must be faster than forward stroke. Applications: Shaper machine, Slotter machine. Advantages: Saves machining time, Increases productivity.

Belt, Chain & Rope Drives

Belt Drives

Belts transmit power between rotating shafts. Types: Flat Belt, V-Belt, Circular Belt, Timing Belt.

Advantages: Simple construction, Low maintenance, Quiet operation, Low cost. Disadvantages: Slip occurs, Lower efficiency compared to gears. Applications: Fans, Blowers, Machine tools, Conveyors.

Slip – Relative movement between belt and pulley. Causes: Low tension, Oil on pulley, Overloading. Creep – Occurs due to elastic stretching and contraction of belt.

Chain Drives

Power is transmitted through metallic chains. Advantages: No slip, High efficiency, Constant velocity ratio. Applications: Bicycle, Motorcycle, Conveyor systems.

Rope Drives

Used for transmitting power over long distances. Applications: Mine hoists, Cranes, Elevators.

Gear Drives

Gears transmit motion without slip. Advantages: Positive drive, High efficiency, Constant speed ratio. Applications: Automobiles, Gearboxes, Clocks, Industrial machinery.

Types of Gears

• Spur Gear – Teeth are straight, parallel shafts. Applications: Gearboxes, Machine tools.
• Helical Gear – Teeth are inclined, smooth and quiet operation. Applications: Automobile transmission.
• Bevel Gear – Intersecting shafts. Applications: Differential gear.
• Worm Gear – Shafts are at 90°. Applications: Hoists, Elevators, Conveyor drives.
• Rack and Pinion – Converts rotary motion into linear motion. Applications: Steering mechanism, CNC machines.

Gear Terminology

Important terms: Pitch circle, Module, Pressure angle, Addendum, Dedendum, Circular pitch, Tooth thickness, Face width.

Gear Train

Types: Simple Gear Train, Compound Gear Train, Reverted Gear Train, Epicyclic Gear Train. Applications: Clocks, Automobiles, Gearboxes.

Flywheel vs Governor

Flywheel stores rotational energy and reduces speed fluctuations. Applications: IC engines, Punch presses, Rolling mills.

Governor controls engine speed automatically when load changes. Types: Watt, Porter, Proell, Hartnell. Applications: Diesel engines, Steam engines, Turbines.

Difference: Flywheel stores energy; Governor regulates speed.

Cam and Follower

Cam converts rotary motion into reciprocating or oscillating motion. Applications: IC Engine valve mechanism, Automatic machines, Textile machines.

Types of Followers: Knife edge, Roller, Flat-faced, Mushroom.

Friction, Brakes & Clutch

Friction is the resisting force between contacting surfaces. Types: Static, Kinetic, Rolling. Friction is useful in: Brakes, Clutches, Belt drives.

Brake is used to stop or reduce speed. Types: Drum Brake, Disc Brake, Band Brake, Internal Expanding Brake. Applications: Cars, Bikes, Cranes, Elevators.

Clutch connects and disconnects power transmission. Types: Single Plate Clutch, Multi Plate Clutch, Cone Clutch, Centrifugal Clutch. Applications: Automobiles, Machine tools.

Dynamometer, Balancing & Vibration

Dynamometer measures power transmitted by rotating shafts. Types: Absorption Dynamometer, Transmission Dynamometer.

Balancing removes unbalanced centrifugal forces. Types: Static Balancing, Dynamic Balancing. Applications: Turbines, Rotors, Fans, Wheels, Crankshafts.

Vibration is the oscillatory motion of a body. Types: Free Vibration, Forced Vibration, Damped Vibration. Causes: Unbalance, Misalignment, Resonance.

Resonance – Occurs when exciting frequency equals natural frequency. Effects: Excessive vibration, Noise, Structural failure. Examples: Bridges, Machine foundations, Rotating shafts.

Power Transmission Comparison

IC Engine Basics

Internal Combustion (IC) Engine converts chemical energy into mechanical energy. Types: Petrol Engine (SI Engine), Diesel Engine (CI Engine).

Four-Stroke Engine

• Suction Stroke
• Compression Stroke
• Power Stroke
• Exhaust Stroke

Two-Stroke Engine

Completes one cycle in two strokes. Advantages: Simpler construction, Higher power-to-weight ratio. Disadvantages: Lower fuel efficiency, Higher emissions.

Turning Moment, Efficiency & SHM

Turning Moment Diagram – A graph showing variation of crankshaft torque during one engine cycle. Importance: Determines flywheel size, Analyzes speed fluctuation.

Always less than 100%.

Simple Harmonic Motion (SHM) – A periodic motion where restoring force is directly proportional to displacement and acts toward the mean position. Applications: Springs, Pendulums, Vibrating systems.

Theory of Machines – Applications & Tips

Applied in: Automobile Engineering, Robotics, Manufacturing Industries, Machine Tools, Textile Machinery, Power Plants, Aerospace Engineering, Packaging Machines, CNC Machines, Industrial Automation.