APPSC AMVI cheat sheet

Gruebler's/Kutzbach criterion for planar mechanisms: DOF = 3(N − 1) − 2J − H, where N = links, J = lower pairs (1-DOF), H = higher pairs (2-DOF).

Four-bar Grashof condition: s + l ≤ p + q gives at least one full rotation link; if the shortest link is the frame, it is a double-crank (drag-link) mechanism.

Quick-return ratio = time of cutting stroke / time of return stroke = (360° − α)/α, where α is the crank angle of the return stroke.

Gear trains: velocity ratio = product of teeth on driven gears / product of teeth on driving gears; for a simple train, ratio = T driven / T driver.

Epicyclic gear train: use the tabular method (arm fixed, then arm moved) or the relative velocity equation N_s − N_arm over N_p − N_arm = −T_p/T_s for external mesh.

Flywheel: ΔE = I·ω²·C_s for a given coefficient of fluctuation of speed C_s = (ω1 − ω2)/ω_mean; energy stored E = ½Iω².

Balancing: for a rotating mass m at radius r, centrifugal force F = mω²r; primary unbalanced force in a reciprocating engine varies with crank angle θ, secondary with 2θ.

Vibrations: natural frequency of a spring-mass system f = (1/2π)√(k/m); damping ratio ζ = c/(2√(km)); resonance occurs when excitation frequency equals natural frequency.

Friction: limiting friction F = μN; for a screw jack, torque to raise load T = W·r·tan(α + φ), where tan φ = μ and α is the helix angle.

Clutch capacity: torque transmitted T = μ·W·n·r_m, where n = number of friction surfaces (2 for a single-plate clutch) and r_m is the mean radius; uniform wear uses r_m = (r1 + r2)/2.

Manual gearbox ratio: overall ratio = gear pair ratio × final drive ratio; tractive effort = engine torque × overall ratio × transmission efficiency / wheel radius.

Automatic transmission: torque converter multiplication is maximum at stall (turbine stationary); coupling point occurs when turbine speed approaches impeller speed and slip is minimal.

Differential: with the ring gear fixed, ω_ring = (ω_left + ω_right)/2, so the average of the two wheel speeds equals the crown wheel speed.

Brakes: braking force F = μ·P·(pedal ratio) × (wheel cylinder area / master cylinder area); disc brake torque T = 2·μ·P·A·r_eff·n_pads.

Weight transfer under braking: ΔW = (m·a·h)/L, where h = CG height and L = wheelbase; front brakes therefore do more work than rear brakes.

Steering: Ackermann condition cot δ_o − cot δ_i = w/L; turning circle radius R = L/sin δ for small angles; caster and camber affect self-centering and tyre wear.

Suspension: spring rate k = W/δ; ride frequency f = (1/2π)√(k/m); a typical passenger car ride frequency is about 1.0-1.5 Hz.

Tyres: slip angle produces cornering force; peak longitudinal friction occurs at roughly 10-20% slip; ABS modulates slip to stay near that peak.

Otto cycle efficiency η = 1 − 1/r^(γ−1), where r = compression ratio and γ = cp/cv (about 1.4 for air); Diesel cycle adds cut-off ratio dependence.

Engine performance: indicated power IP = (P_mep × L × A × N × k)/60, where k = 1 for a two-stroke and ½ for a four-stroke; mechanical efficiency = BP/IP.

Air-fuel ratio: stoichiometric petrol ≈ 14.7:1 by mass; rich mixture (λ < 1) gives more power, lean (λ > 1) gives better economy but risks misfire and high NOx.

Octane number rates petrol anti-knock quality; cetane number rates diesel ignition quality (higher cetane = shorter ignition delay); both are measured against reference fuels.

Emissions: CO and HC rise with rich mixtures; NOx peaks at slightly lean, high-temperature combustion; PM rises with diesel over-fueling; EGR reduces NOx by lowering peak temperature.

Battery: capacity in Ah; cranking current depends on cold cranking amps (CCA); charging voltage for a 12 V lead-acid system is about 13.8-14.4 V.

Starting and charging: the starter motor draws high current through a solenoid; the alternator's output is rectified by a diode bridge and regulated by the voltage regulator.

Ignition: spark timing advance before TDC increases with engine speed; too much advance causes knock, too little causes overheating and power loss; coil-on-plug eliminates the distributor.

Sensors and actuators: MAP/MAF meters air mass, lambda sensor trims fuel (closed loop), knock sensor retards timing; OBD-II codes P0xxx denote powertrain faults.

Motor Vehicles Act, 1988: Section 3 covers licensing of drivers; Section 4 sets age limits (18 years for a motor vehicle, 16 for a motorcycle up to 50 cc with guardian consent).

Section 19 empowers the licensing authority to disqualify a licence holder; Section 20 covers court-ordered disqualification; Section 22 deals with suspension of a licence for offences.

Section 39 requires registration of a motor vehicle before it is driven in a public place; Section 41 covers the certificate of registration; Section 47 covers transfer of ownership.

Section 51 mandates insurance; Section 146 prohibits use of a vehicle without a valid third-party insurance policy; Section 147 specifies the policy's mandatory coverage.

Section 185 (drunk driving) uses the breath analyser limit of 30 mg of alcohol per 100 mL of blood; Section 184 covers dangerous driving; Section 183 covers speeding.

Section 129 requires a helmet for a rider and pillion on a two-wheeler; Section 128 restricts seating capacity; Section 134 places a duty on the driver after an accident to report and render aid.

Section 166 provides for compensation claims before the Motor Accident Claims Tribunal (MACT); Section 161 covers hit-and-run relief; Section 173 provides for appeals.

Section 194B penalises not wearing a seat belt; Section 194C penalises driving without a valid licence; Section 194D penalises driving without insurance; penalties were raised by the Motor Vehicles (Amendment) Act, 2019.

Transport authorities: the State Transport Authority and Regional Transport Authority issue permits under Sections 66-72; national permits are issued under Section 88; the CMVR, 1989, contains the detailed rules.

Traffic flow: q = k·v (flow = density × speed); the fundamental diagram shows free-flow, capacity, and congested regimes; capacity is the maximum flow on a lane.

Speed parameters: time mean speed is the arithmetic average of spot speeds; space mean speed is the harmonic mean and is used in flow-density relations.

Stopping sight distance SSD = 0.278·V·t + V²/(254·f), where V is in km/h, t is reaction time (about 2.5 s) and f is the longitudinal friction coefficient.

Overtaking sight distance OSD = 0.278·V·t + 0.278·V·T + 2s, adding the opposing vehicle's travel during the overtaking manoeuvre; safe passing requires OSD.

Accident analysis: use the collision diagram, skid marks and momentum conservation; pre-impact speed from skid length v = √(2·μ·g·d), with μ the friction coefficient.

Accident severity indices: fatality rate per 10,000 vehicles, accident rate per million vehicle-kilometres, and black-spot identification by frequency and severity.

Traffic control: a Webster optimum cycle C_o = (1.5L + 5)/(1 − Y), where L is total lost time and Y is the sum of critical flow ratios.

Road safety countermeasures: speed humps and chicanes for traffic calming; rumble strips, crash barriers, and delineators for rural roads; pedestrian crossings with refuge islands.

Accident investigation procedure: secure the scene, preserve evidence, record positions and skid marks, interview witnesses, and reconstruct using momentum and energy methods.