BME603 – THEORY OF MACHINE
Section-Wise Solved Answers (2024–25)
SECTION A
Attempt all questions in brief (2 × 7 = 14 marks)
(a) Differentiate between lower pair and higher pair.
In a lower pair, the two elements have surface contact with each other during relative motion, such as sliding or turning. Examples include piston and cylinder, and shaft in a bearing.
In a higher pair, the contact between the two elements is along a line or at a point, such as in cam and follower or gear tooth contact. Lower pairs generally have less wear and smoother motion compared to higher pairs.
(b) Define Grashof’s Law.
Grashof’s Law states that for a four-bar mechanism, if the sum of the shortest and longest links is less than or equal to the sum of the remaining two links, then at least one link will be capable of making a complete rotation.
(c) State Kennedy’s theorem.
Kennedy’s theorem states that for any three bodies in relative motion, the three instantaneous centers of rotation lie on a straight line.
(d) Define pressure angle related to cam.
The pressure angle of a cam is the angle between the direction of motion of the follower and the direction of the force transmitted from the cam to the follower. Smaller pressure angles are preferred for smooth operation and reduced side thrust.
(e) What do you understand by interference?
Interference in gears occurs when the non-involute portion of a gear tooth comes into contact with the mating tooth. This causes improper meshing, noise, and wear, and is avoided by proper gear design.
(f) State D’Alembert’s principle.
D’Alembert’s principle states that a dynamic system can be treated as a static system by introducing an inertia force equal to mass multiplied by acceleration, acting opposite to the direction of acceleration.
(g) Explain the term hunting of governor.
Hunting of a governor is the continuous fluctuation of the governor speed about its mean position. It causes oscillations of the sleeve and results in unstable engine speed.
SECTION B
Attempt any three (7 × 3 = 21 marks)
(a) Slider-crank mechanism velocity analysis
Given:
Crank length = 0.48 m
Angular velocity = 20 rad/s
Connecting rod length = 1.6 m
Crank angle = 60°
The velocity of the slider is determined using velocity polygon or analytical method. The crank velocity is first calculated, then resolved along the line of stroke.
Velocity of point E on the extended connecting rod is found by proportional distances using the velocity diagram. This method gives accurate velocity values for both slider and point E.
(b) Inversions of mechanism and inversions of four-bar chain
Inversion of a mechanism is the process of fixing different links of a kinematic chain one at a time to obtain different mechanisms.
The four-bar chain has three important inversions:
When the shortest link is fixed, a double crank mechanism is obtained.
When a link adjacent to the shortest link is fixed, a crank-rocker mechanism is formed.
When the link opposite to the shortest link is fixed, a double rocker mechanism is obtained. These inversions are used in pumps, engines, and hand tools.
(c) Involute gear teeth and comparison with cycloidal teeth
In involute gears, the tooth profile is generated from the involute of a circle. The major advantage is constant velocity ratio even with small center distance errors.
Cycloidal teeth are generated from cycloids and have less wear but are difficult to manufacture. Involute teeth are easier to manufacture and widely used in modern gear systems.
(d) Balancing of rotating masses (numerical concept)
The balancing mass is found by vectorially adding all existing mass moments and placing an equal and opposite balancing mass at a given radius.
The magnitude is calculated using the polygon of forces and its angular position is determined from the closing side of the polygon.
(e) Self-locking brake and band and block brake
A brake is said to be self-locking when the braking torque is sufficient to hold the load even without external force.
In a band and block brake, blocks are mounted on a flexible band that wraps around a drum. When the brake is applied, friction between blocks and drum produces braking torque.
SECTION C
Attempt any one (7 × 1 = 7 marks)
(a) Coriolis component of acceleration
Coriolis acceleration occurs when a particle moves along a rotating path. It is given by:
ac=2ωva_c = 2 \omega vac=2ωv
where ω is angular velocity and v is relative velocity.
The direction of Coriolis acceleration is obtained by rotating the relative velocity vector through 90° in the direction of rotation.
(b) Quick return mechanisms
Quick return mechanisms are those in which the return stroke takes less time than the forward stroke.
Examples include Whitworth quick return mechanism and crank and slotted lever mechanism. These are commonly used in shaping and slotting machines to improve productivity.
