(SEM VI) THEORY EXAMINATION 2023-24 THEORY OF MACHINE

THEORY OF MACHINE – KME603

Section-wise Important Questions & Ready Answers

SECTION A

(Attempt all – 2 marks each)

(a) Constrained Motion

Constrained motion is the motion of a body that is restricted to follow a definite path due to mechanical constraints. The constraint ensures that the motion occurs in a predetermined direction, such as the sliding motion of a piston in a cylinder.

(b) Kennedy’s Theorem

Kennedy’s theorem states that for any three rigid bodies in relative motion, the three instantaneous centers of rotation lie on a straight line. This theorem is widely used in velocity analysis of mechanisms.

(c) Radial Follower and Offset Follower

In a radial follower, the line of motion of the follower passes through the cam center, whereas in an offset follower, the line of motion is offset from the cam center. Offset followers help reduce pressure angle and wear.

(d) Law of Gearing

The law of gearing states that the common normal at the point of contact of gear teeth must always pass through the pitch point to ensure a constant velocity ratio during meshing.

(e) D’Alembert’s Principle

D’Alembert’s principle converts a dynamic system into an equivalent static system by introducing inertia forces opposite to the direction of acceleration, enabling equilibrium analysis.

(f) Coefficient of Fluctuation of Speed

It is the ratio of the maximum fluctuation of speed to the mean speed of the system. It indicates the uniformity of speed in engines and machines.

(g) Conditions of Secondary Balancing

For complete secondary balancing, the algebraic sum of secondary forces and the algebraic sum of moments of secondary forces about any reference plane must be zero.

(h) Hunting of Governor

Hunting is the continuous oscillation of the governor sleeve and engine speed about the mean position, caused by excessive sensitivity of the governor.

(i) Gyroscope

A gyroscope is a rotating body that resists changes in the direction of its axis due to angular momentum, commonly used in navigation and stabilization systems.

(j) Dynamometer

A dynamometer is a device used to measure power, torque, or force produced by engines and machines during operation.

SECTION B

(Attempt any three – 10 marks each)

1. Instantaneous Center Method for Slider-Crank Mechanism

Instantaneous centers are located using Kennedy’s theorem. By identifying these centers, velocities of various links and angular velocity of the connecting rod are calculated using relative motion principles.

2. Involute Gear Parameters

For involute gears, the length of path of contact is obtained from the geometry of the gear teeth. Arc of contact is calculated from the pitch circle, and contact ratio indicates smoothness of power transmission.

3. Velocity and Acceleration of Piston

The piston velocity depends on crank rotation and connecting rod length. Acceleration has two components: primary and secondary acceleration, derived using kinematic relations.

4. Balancing of Rotating Masses

Complete balancing requires the vector sum of centrifugal forces and moments to be zero. The unknown mass and angular positions are found using graphical or analytical methods.

5. Block or Shoe Brake

A block brake works by friction between the brake shoe and the drum. A brake is self-locking if friction alone can stop the drum, while it is self-energized if applied force is assisted by friction.

SECTION C

Q3(a) Inversion of Mechanism

Inversion is the process of fixing different links of a kinematic chain to obtain different mechanisms. One inversion of the double slider crank chain is the Oldham coupling, used to transmit motion between parallel shafts.

Q3(b) Coriolis Component of Acceleration

Coriolis acceleration occurs when a body moves radially on a rotating link. Its magnitude is given by 2ωv2\omega v2ωv, where ω is angular velocity and v is radial velocity.

Q4(a) Minimum Number of Teeth to Avoid Interference

Interference occurs when non-conjugate portions of gear teeth come into contact. The minimum number of teeth on a pinion is derived using involute geometry to prevent interference.

Q4(b) Cam Profile with SHM Motion

The cam profile is constructed using displacement diagrams based on simple harmonic motion. The base circle, pitch curve, and cam profile are drawn considering roller follower dimensions.

Q5(a) Turning Moment Diagram and Flywheel

The turning moment diagram shows variation of torque over a cycle. From the maximum fluctuation of energy and flywheel inertia, the coefficient of fluctuation of speed is calculated.

Q5(b) Static Equilibrium of Four-Link Mechanism

For static equilibrium, the principle of virtual work is applied. Input torque is calculated by equating work done by applied forces and resisting torques.

Q6(a) Effort and Power of Governor

Effort of a governor is the mean force exerted at the sleeve for a given change in speed. Power of governor is the work done at the sleeve per unit time.

Q6(b) Porter Governor Numerical

Speed range is determined from equilibrium conditions considering centrifugal force and sleeve load. Friction increases the speed range and modifies the equilibrium speeds.

Q7(a) Dynamometers

Absorption dynamometers absorb power through friction, while transmission dynamometers measure power transmitted through a shaft. A torsion dynamometer works by measuring shaft twist.

Q7(b) Gyroscopic Action

Gyroscopic action is the tendency of a rotating body to resist changes in orientation. It is used in ships, aircrafts, and stabilizing devices.