Theory of Machines and Vibrations MCQs 2026

A kinematic chain becomes mechanism when

1. A all links move freely without frame ✓
2. B no relative motion exists ✓
3. C one link is fixed to ground frame ✓
4. D only gears are present ✓

Degrees of freedom of plane mechanism given by Kutzbach equation is

1. A F = L + j only ✓
2. B F = 3(L-1) - 2j - h ✓
3. C F = 2L always ✓
4. D F = j - h only ✓

Four-bar linkage has

1. A three links and five pairs ✓
2. B only prismatic pairs ✓
3. C no coupler link ✓
4. D four links connected by four revolute pairs ✓

Grashof law states for continuous relative rotation

1. A all links equal length always ✓
2. B shortest plus longest link length ≤ sum of other two ✓
3. C only sliding pairs allowed ✓
4. D coupler must be longest always ✓

Slider-crank mechanism converts

1. A heat directly to electricity only ✓
2. B hydraulic pressure to sand mould ✓
3. C welding arc to lathe feed ✓
4. D reciprocating slider motion to rotary crank motion ✓

Instantaneous centre of rotation is

1. A always at geometric centre of mass ✓
2. B fixed for all time always ✓
3. C point about which body appears to rotate at given instant ✓
4. D only for gears never links ✓

Velocity of point on link equals

1. A angular velocity times radius to I-centre ✓
2. B only linear speed of slider always ✓
3. C zero at all pins always ✓
4. D product of masses only ✓

Acceleration in mechanism analysis includes

1. A only static weight ✓
2. B tangential and normal components relative to I-centre ✓
3. C only thermal expansion ✓
4. D only sand shrinkage ✓

Coriolis component appears in

1. A pure rotation about fixed centre only ✓
2. B sliding motion on rotating link ✓
3. C static equilibrium only ✓
4. D heat conduction only ✓

Lower pair has

1. A surface contact between elements ✓
2. B point or line contact only always ✓
3. C no contact ever ✓
4. D fluid film only in gears ✓

Higher pair example is

1. A pin in hole revolute joint ✓
2. B gear teeth mesh or cam-follower point contact ✓
3. C slider in slot prismatic ✓
4. D welded fixed joint ✓

Kinematic inversion changes

1. A tooth profile of gears only ✓
2. B material of links only ✓
3. C motor voltage only ✓
4. D which link is fixed without altering relative motions ✓

Double slider crank chain forms

1. A Oldham coupling or Scotch yoke mechanisms ✓
2. B only simple pendulum ✓
3. C only flywheel energy store ✓
4. D only governor spring ✓

Cam-follower mechanism converts

1. A cam rotation into prescribed follower translation or oscillation ✓
2. B electricity to refrigerant ✓
3. C sand to molten iron ✓
4. D rolling torque to billet only ✓

Disk cam with knife-edge follower has

1. A point contact and high wear ✓
2. B surface contact lower pair ✓
3. C no pressure angle concern ✓
4. D constant velocity always ✓

Roller follower reduces

1. A cam lift amplitude to zero ✓
2. B need for cam profile ✓
3. C friction and wear compared to knife-edge follower ✓
4. D all dynamic forces to zero ✓

Pressure angle in cam is angle between

1. A cam shaft and crank throw only ✓
2. B normal to profile and follower motion direction ✓
3. C gear helix and axis only ✓
4. D welding torch and plate only ✓

Base circle of cam is

1. A smallest circle centred on cam axis touching profile ✓
2. B pitch circle of gear ✓
3. C root circle of gear ✓
4. D lathe chuck diameter ✓

Simple harmonic motion cam profile gives

1. A infinite jerk everywhere ✓
2. B constant velocity throughout dwell ✓
3. C random displacement ✓
4. D smooth acceleration at start and end of stroke ✓

Dwell in cam motion means

1. A maximum velocity segment ✓
2. B follower oscillates rapidly ✓
3. C follower stationary while cam rotates ✓
4. D cam stops rotating ✓

Module m of spur gear equals

1. A circular pitch divided by pi only ✓
2. B pitch circle diameter divided by number of teeth ✓
3. C addendum only ✓
4. D pressure angle in degrees ✓

Circular pitch p of gear is

1. A module divided by π ✓
2. B π times module ✓
3. C teeth divided by diameter ✓
4. D pressure angle cosine only ✓

Addendum of gear tooth is

1. A depth of dedendum only ✓
2. B whole face width ✓
3. C helix angle ✓
4. D radial height from pitch circle to tooth tip ✓

Dedendum is measured from pitch circle to

1. A tip circle only ✓
2. B base circle always as addendum ✓
3. C root of tooth ✓
4. D outside helix ✓

Law of gearing requires for constant velocity ratio

1. A teeth must be rectangular ✓
2. B common normal at contact passes through pitch point ✓
3. C only helical gears qualify ✓
4. D pressure angle must be 90° ✓

Involute tooth profile is generated by

1. A extruding metal through die ✓
2. B sand casting pattern only ✓
3. C unwrapping string from base circle ✓
4. D resistance welding spot ✓

Contact ratio in gears should be

1. A zero for quiet operation ✓
2. B negative for strength ✓
3. C exactly 0.5 always ✓
4. D greater than one for continuous smooth transmission ✓

Undercutting in spur gears occurs when

1. A tip of mating gear cuts into root below base circle ✓
2. B pressure angle is too large only always ✓
3. C module is too large always ✓
4. D face width is excessive ✓

Helical gears differ from spur by

1. A having no pitch circle ✓
2. B teeth cut at helix angle to axis ✓
3. C meshing only in vertical plane always ✓
4. D using only plastic always ✓

Helix angle in helical gear is measured at

1. A root circle only ✓
2. B addendum circle only ✓
3. C lathe bed guide ✓
4. D pitch cylinder relative to gear axis ✓

Herringbone gear eliminates

1. A net axial thrust of double helical arrangement ✓
2. B all tooth loading ✓
3. C need for lubrication ✓
4. D pitch diameter definition ✓

Bevel gears transmit motion between

1. A parallel axes only always ✓
2. B non-intersecting skew axes without hypoid ✓
3. C intersecting axes usually at 90 degrees ✓
4. D fixed ratio belt only ✓

Worm gear pair has

1. A high speed reduction and self-locking tendency possible ✓
2. B only parallel axis layout ✓
3. C equal size pinion and gear always ✓
4. D no sliding contact ever ✓

Gear train velocity ratio is product of

1. A modules only ✓
2. B pressure angles only ✓
3. C driven teeth divided by driver teeth for each stage ✓
4. D face widths only ✓

Idler gear in train changes

1. A direction of rotation without affecting ratio magnitude ✓
2. B overall velocity ratio value ✓
3. C centre distance law only ✓
4. D module standard ✓

Epicyclic gear train has

1. A one or more gears rotating on moving arm ✓
2. B only fixed axis gears ✓
3. C no planet gears ever ✓
4. D only belt drives ✓

Reverted gear train has

1. A input and output shafts coaxial ✓
2. B parallel offset shafts only ✓
3. C intersecting axes only ✓
4. D no idler allowed ever ✓

Governor maintains

1. A constant fuel tank level ✓
2. B constant tyre pressure ✓
3. C near-constant speed of engine despite load changes ✓
4. D constant sand moisture ✓

Watt governor is

1. A hydraulic piston only ✓
2. B electronic ECU map only ✓
3. C pendulum type with flyballs on arms near spindle ✓
4. D turbocharger wastegate only ✓

Porter governor has

1. A no controlling force element ✓
2. B only hydraulic dashpot from start ✓
3. C central spring supporting flyball arms ✓
4. D fixed mass without arms ✓

Proell governor extends flyballs

1. A inward toward spindle only ✓
2. B outward on extended links for greater speed rise effect ✓
3. C eliminates all sensitivity ✓
4. D replaces throttle completely ✓

Sensitiveness of governor is ratio of

1. A power output to fuel flow only ✓
2. B flywheel energy to torque only ✓
3. C range of speed to mean speed ✓
4. D gear ratio to module ✓

Hunting in governor means

1. A stable immediate stop ✓
2. B zero response to load ✓
3. C continuous speed oscillation about mean ✓
4. D fixed throttle always ✓

Flywheel stores energy as

1. A chemical fuel energy only ✓
2. B rotational kinetic energy smoothing cyclic fluctuation ✓
3. C elastic spring potential in governor only ✓
4. D electrical capacitor charge only ✓

Coefficient of fluctuation of speed is

1. A flywheel weight only ✓
2. B gear pressure angle ✓
3. C cam lift divided by base circle ✓
4. D (ω1 - ω2)/ω_mean ✓

Flywheel rim has most mass at periphery because

1. A centre hub stores more energy always ✓
2. B spokes alone sufficient always ✓
3. C bearing friction requires it ✓
4. D moment of inertia increases with radius squared ✓

Turning moment diagram plots

1. A velocity versus time only always ✓
2. B stress versus strain only ✓
3. C crank torque versus crank angle for one cycle ✓
4. D pressure versus volume only ✓

Static balancing of rotating masses requires

1. A couple in plane must be maximum ✓
2. B only single mass considered always ✓
3. C gear teeth must be involute ✓
4. D resultant centrifugal force in any plane is zero ✓

Dynamic balancing requires

1. A only force balance in one plane ✓
2. B resultant force and resultant couple both zero ✓
3. C no consideration of axial length ✓
4. D welding symmetry only ✓

Balancing machine measures

1. A only hardness HRC ✓
2. B only surface Ra ✓
3. C only cam lift ✓
4. D vibration or force due to unbalance at supports ✓

Primary unbalance in reciprocating engine is

1. A first-order force along line of stroke at crank speed ✓
2. B only constant torque always ✓
3. C only gear mesh frequency ✓
4. D zero at all speeds ✓

Secondary unbalance occurs at

1. A half crank speed only ✓
2. B twice crank speed in four-stroke inline engines ✓
3. C zero frequency always ✓
4. D cam shaft speed only for all orders ✓

Gyroscope resists change in

1. A linear speed along road only ✓
2. B fuel octane number ✓
3. C sand binder type ✓
4. D axis of rotation due to angular momentum ✓

Precession angular velocity of gyro is

1. A Iω divided by T ✓
2. B T times ω only ✓
3. C zero for all applied torque ✓
4. D T / (Iω) ✓

Velocity diagram in relative motion shows

1. A only scalar gear teeth count ✓
2. B only temperature entropy ✓
3. C only weld pool width ✓
4. D vector addition of absolute velocities of links ✓

Kennedy theorem states I-centres of three bodies

1. A form equilateral triangle always ✓
2. B coincide at mass centre always ✓
3. C lie on a straight line ✓
4. D are unrelated ✓

Rubbing velocity at pin joint equals

1. A angular velocity times pin radius if one link fixed locally ✓
2. B sum of link lengths ✓
3. C product of modules ✓
4. D zero always at all joints ✓

Toggle mechanism at dead centre has

1. A zero force transmission always ✓
2. B mechanical advantage approaching infinity theoretically ✓
3. C maximum velocity ratio always ✓
4. D no fixed link ✓

Peaucellier linkage generates

1. A exact straight line motion from rotation ✓
2. B parabolic cam profile only ✓
3. C helical gear teeth only ✓
4. D random vibration path ✓

Whitworth quick return used in

1. A lathe headstock only ✓
2. B CNC tool changer only ✓
3. C car differential only ✓
4. D shaper and slotting machines ✓

Geneva mechanism provides

1. A constant smooth rotation only ✓
2. B linear welding seam ✓
3. C intermittent rotary motion from continuous input ✓
4. D hydraulic pump flow ✓

Ratchet and pawl allows

1. A bidirectional equal torque ✓
2. B variable gear module ✓
3. C cam dwell elimination ✓
4. D rotation in one direction only ✓

Belt drive velocity ratio depends on

1. A only belt colour ✓
2. B only sand grain size ✓
3. C only lathe feed rate ✓
4. D diameters of driver and driven pulleys if no slip ✓

Creep in belt drive is

1. A total belt fracture ✓
2. B zero tension condition ✓
3. C welding arc instability ✓
4. D relative slip due to elastic stretch difference tight and slack sides ✓

Chain drive compared to belt has

1. A no slip and suitable for short centre distance high load ✓
2. B only elastic stretch transmission ✓
3. C must always be vertical ✓
4. D cannot work in oil ✓

Synchronizing mesh in manual gearbox uses

1. A only open dog clutch always without sync ✓
2. B friction cones or blocker rings to match shaft speeds ✓
3. C hydraulic torque converter only ✓
4. D CVT rubber belt only ✓

Frictional clutch transmits torque by

1. A gear tooth only always ✓
2. B hydraulic fluid shear only in manual plate clutch ✓
3. C normal force times coefficient of friction on mating surfaces ✓
4. D electromagnetic flux in plate clutch only always ✓

Universal joint transmits motion between

1. A perfectly constant velocity always alone ✓
2. B parallel non-intersecting axes without CV joint ✓
3. C inclined intersecting shafts with varying angular velocity ✓
4. D fixed welding only ✓

Oldham coupling connects

1. A intersecting bevel gears only ✓
2. B parallel shafts with small misalignment using sliding middle disc ✓
3. C coaxial shafts only always ✓
4. D reciprocating piston to crank only ✓

Ackermann steering geometry ensures

1. A all wheels turn equal angle ✓
2. B rear wheels steer more than front ✓
3. C inner front wheel turns sharper than outer in a turn ✓
4. D only differential slip controls turn ✓

Differential in automobile allows

1. A both rear wheels locked always ✓
2. B front wheels to steer automatically ✓
3. C engine flywheel to stop ✓
4. D outer drive wheel to rotate faster in turn ✓

Cam shaft speed in four-stroke engine is

1. A twice crank speed ✓
2. B equal to wheel speed always ✓
3. C same as alternator belt only ✓
4. D half crankshaft speed ✓

Valve overlap period occurs when

1. A both intake and exhaust valves slightly open near TDC ✓
2. B only intake open at BDC ✓
3. C no valves open ever ✓
4. D flywheel removed ✓

Mechanical advantage of lever is

1. A input distance divided by output distance inverted for MA ✓
2. B output force divided by input force ✓
3. C always less than one ✓
4. D gear module ratio ✓

Efficiency of machine equals

1. A output work divided by input work ✓
2. B velocity ratio only ✓
3. C mechanical advantage squared ✓
4. D always 100 percent ✓

Pair of higher order in cam-follower is

1. A revolute pin joint ✓
2. B cam and follower line contact pair ✓
3. C prismatic slider guide ✓
4. D fixed welded bracket ✓

Transmission angle in four-bar should be kept

1. A between about 40 and 140 degrees for good force transmission ✓
2. B near zero for maximum torque ✓
3. C always 180 degrees ✓
4. D irrelevant to performance ✓

Coupler curve of four-bar is path traced by

1. A fixed frame link only ✓
2. B ground only ✓
3. C point on coupler link ✓
4. D motor shaft only without motion ✓

Chebyshev spacing for precision points in synthesis

1. A minimizes maximum structural error ✓
2. B maximizes backlash always ✓
3. C ignores boundary conditions ✓
4. D uses only two points always ✓

Angular velocity ratio of bevel gears equals

1. A pitch cone angle only ✓
2. B teeth on driven divided by teeth on driver ✓
3. C addendum only ✓
4. D helix hand only ✓