THEORY OF MACHINES (ME-403) - Important Questions

Determine velocity and acceleration of the slider / piston / reciprocating block in a slider-crank mechanism for a given configuration.

Explain the inversions of a single slider-crank mechanism with neat sketches and examples/applications.

Explain the concept of inversions and illustrate the different inversions of a four-bar mechanism.

Determine angular velocity and angular acceleration of the connecting rod in a slider-crank / reciprocating engine mechanism for a given crank position, speed and acceleration.

Numerical to determine the ratio of connecting rod length to crank radius in a slider-crank mechanism.

Write and explain the inversions of the double slider crank chain/mechanism with neat sketches.

Determine the type / class of a four-bar mechanism using Grashof's criterion.

Design a Whitworth quick return motion mechanism for given stroke, time ratio and crank length.

Define mechanisms and machines, differentiate between them, and explain the concept of degree of freedom in a mechanism.

Derive an expression for the magnitude and direction of the Coriolis component of acceleration.

Write a short note on any Two

Determine angular velocity of the oscillating link CD in a four-bar chain ABCD for a given crank angle.

State and explain D'Alembert's principle and its application in dynamic analysis of mechanisms.

Differentiate between number synthesis and motion analysis. Explain the analytical and graphical methods used for dynamic motion analysis, highlighting their advantages and limitations.

Synthesize a four-bar linkage using Freudenstein's equation for prescribed position, velocity and acceleration.

Describe the process of kinematic synthesis of linkages and explain D'Alembert's principle and its significance in dynamic analysis.

Determine the input torque on crank AB for static equilibrium of a slider-crank mechanism under a given piston load.

Explain dynamic analysis of a four-bar linkage and dynamic analysis of the slider-crank mechanism.

Determine the magnitude of the joint reaction at $O_2$ given the component of force at joint A along AB.

Define cam terminology — base circle, prime circle, pitch circle, pressure angle, cam profile, lift/stroke of follower and period of dwell — with a neat sketch, and explain why a smaller pressure angle is preferable.

Calculate maximum velocity and acceleration during SHM rise and SHM return for a radial knife-edge cam with given lift, angles and speed.

Draw cam profile for roller reciprocating follower with SHM lift and uniform acceleration-deceleration descent, and calculate maximum velocity and acceleration during descent.

What are cams and how are cams classified, with neat sketches?

In a symmetrical tangent cam operating a roller follower, the least radius of the cam is $30$ mm and roller radius is $18$ mm. The angle of ascent is $80^{\circ}$ and the total lift is $18$ mm. The speed of the camshaft is $800$ r.p.m. Calculate:

Draw cam profile for knife-edge follower with SHM rise and uniform-velocity return, and find maximum velocity and acceleration during lift and return.

Discuss factors influencing cam design including pressure angle, base circle radius and undercutting, and explain critical path motion and torque on the cam shaft.

Explain the classification / types of followers with neat diagrams.

Draw cam profile for central knife-edge follower with SHM outstroke and return, and draw displacement, velocity and acceleration diagrams.

Give cam motion specification for knife-edge follower with outstroke, dwell, return and dwell periods at given speed.

For an eccentric circular cam with flat-faced follower, derive follower acceleration vs rotation angle and determine camshaft speed at which follower jumps/lifts off.

Calculate belt tensions on tight and loose sides and stress in open and crossed belt drives

Explain the construction and working principle of a single-plate clutch.

Determine the torque transmitted by a single-plate clutch given radii, axial force, friction coefficient under uniform wear.

The layout of a crossed flat leather belt drive is shown in Figure 2. The belt,$6mm$ thick, transmits $7.5kW$ and operates at a velocity of $13m/s$. The coefficient of friction between the belt and pulley surface is $0.3$ and the permissible tensile stress for the belt material is $1.75N/mm2$. The density of leather is $0.95g/cm^{3}$. Neglecting the sag and slip of the belt, calculate

(a) The length and width of the belt.

Describe the various friction devices used in power transmission, including pivots and collars, power screws, and clutches, with classifications and applications.

Derive the ratio of maximum to minimum tension in a band and block brake as $T_0/T_n = ((1+\mu \tan\theta)/(1-\mu \tan\theta))^n$.

Determine the maximum, minimum and average pressure in a plate clutch given axial force and radii under uniform wear.

Determine power transmitted by a belt drive from pulley size, speed, angle of lap, friction and maximum tension/stress

Explain kinematics of flat and V-belt pulley systems, friction, efficiency and condition for maximum power transmission

Find the power transmitted by a belt drive given pulley diameter, speed, coefficient of friction, angle of lap and maximum belt tension.

Discuss the various types of brakes with a neat sketch.

Estimate the motor power required to drive a power screw against a given axial load at a given speed from thread geometry and friction.

State and prove/explain the law of gearing and explain conjugate tooth profiles and their role in maintaining constant velocity ratio, including involute profile.

Explain with neat sketches the longitudinal, transverse and torsional types of free vibration.

Design a spur gear drive for strength given power, speed, ratio, centre distance and materials.

Check the design for dynamic load and wear.

Explain static balancing and dynamic balancing and the balancing of rotating masses in the same plane and in different planes.

Define a single degree of freedom (SDOF) system and derive the equation of motion for undamped free vibration.

For a mass-spring system displaced and released from rest, determine natural frequency, maximum velocity and maximum acceleration.

Explain the differences between simple, compound, and epicyclic gear trains and state the special advantages of epicyclic gear trains.

Determine the minimum number of teeth on pinion and gear for a given gear ratio with arc of approach constraint, and the wheel addendum in terms of circular pitch.

Determine the magnitude and angular position of a single balance mass to statically balance four rotating masses in the same plane.

State and prove/derive the law of gearing (law of gear tooth action) for constant velocity ratio.

Determine suitable numbers of teeth for sun, planet and ring in a sun-and-planet epicyclic gear with stationary ring to give a required speed ratio.

Write a short note on any two: