22AUT52 – MECHANICS OF MACHINES
QUESTION BANK
UNIT 1
PART A
1. The figure as shown below is a rigid body undergoing planer motion. The absolute tangential
acceleration of the points R and S on the body are 150 m/s2 and 300 m/s2 respectively in
the direction shown. What is the angular acceleration of the rigid body?
2. Calculate the degree of freedom of the given mechanism.
3. An eight-bar linkage is shown in fig. below. Determine the degrees of freedom.
4. Consider a crank and slotted lever quick return mechanism as shown in the figure. The
length of the driving crank length = 75 mm, and the distance between the fixed centre = 200
mm. Find the ratio of time taken on cutting and idle stroke.
PART B
1. The engine mechanism shown in Fig. has crank OB = 50 mm and length of connecting rod
AB = 225 mm. The centre of gravity of the rod is at G which is 75 mm from B. The engine
speed is 200 r.p.m. For the position shown, in which OB is turned 45° from OA, Find 1. the
velocity of G and the angular velocity of AB, and 2. the acceleration of G and angular
acceleration of AB.
2. Identify the types of mechanisms used in the shaper machine and explain them in detail with
a neat sketch. Also, derive an expression for the ratio of times taken in forward and return
stroke and length of stroke for one of these mechanisms.
3. Identify the mechanism that is used to draw the ellipse and the mechanism used to connect
the two parallel shafts separated by a small distance, and explain them briefly with a suitable
sketch.
4. PQRS is a four-bar chain with link PS fixed. The lengths of the links are PQ = 62.5 mm; QR
= 175 mm; RS = 112.5 mm; and PS = 200 mm. The crank PQ rotates at 10 rad/s clockwise.
Draw the velocity and acceleration diagram when angle QPS = 60° and Q and R lie on the
same side of PS. Find the angular velocity and angular acceleration of links QR and RS.
UNIT 2
PART A
1. A cam is rotating with a uniform angular velocity and pushes its roller follower upwards. If
the nature of the upward displacement of the follower with respect to the angle of cam
rotation is SHM, then what is the shape of the velocity and acceleration curve.
2. Consider the cam rotating with a uniform angular velocity 50 rad/s. Follower also moves
with uniform velocity. Lift of the follower is 100 mm. If the angle of ascent, decent and
dwell are same, the find out the angle of ascent.
3. A cam rotating with a uniform angular velocity pushes its flat – faced radial follower
upwards. If the nature of the upward displacement of the follower with respect to the angle
of cam rotation is cycloid, then what is the shape of velocity and acceleration curve?
4. Consider a cam follower in which cam is rotating with uniform angular velocity ω rad/s and
the follower moves in SHM. If the displacement of the follower is given as, y =
𝑠 cos 𝜋
2
(1 − Ɵ𝑜
Ɵ). Where Ɵ is the angle turned by the cam in time, then find out the
maximum velocity of the follower
PART B
1. A disc cam is to give uniform motion to a knife edge follower during an out stroke of 50
mm during the first half of the cam revolution. The follower again returns to its original
position with uniform motion during the next half of the revolution. The minimum radius of
the cam is 50 mm and the diameter of the camshaft is 35 mm. Draw the profile of the cam
when 1. the axis of follower passes through the axis of the camshaft, and 2. the axis of a
follower is offset by 20 mm from the axis of the camshaft.
2. It is required to set out the profile of a cam to give the following motion to the reciprocating
follower with a flat mushroom contact face:
(i) Follower to have a stroke of 20 mm during 120° of cam rotation;
(ii) Follower to dwell for 30° of cam rotation;
(iii) Follower to return to its initial position during 120° of cam rotation; and
(iv) Follower to dwell for the remaining 90° of cam rotation.
The minimum radius of the cam is 25 mm. The out stroke of the follower is performed with
simple harmonic motion and the return stroke with equal uniform acceleration and
retardation.
3. A cam is to give the following motion to a knife-edged follower:
1. Outstroke during 60° of cam rotation;
2. Dwell for the next 30° of cam rotation;
3. Return stroke during the next 60° of cam rotation, and
4. Dwell for the remaining 210° of cam rotation.
The stroke of the follower is 40 mm and the minimum radius of the cam is 50 mm. The
follower moves with uniform velocity during both the outstroke and return strokes. Draw
the profile of the cam when (a) the axis of the follower passes through the axis of the
camshaft, and (b) the axis of the follower is offset by 20 mm from the axis of the camshaft.
4. It is required to set out the profile of a cam to give the following motion to the reciprocating
follower with a flat mushroom contact face:
(i) Follower to have a stroke of 20 mm during 120° of cam rotation;
(ii) Follower to dwell for 30° of cam rotation;
(iii) Follower to return to its initial position during 120° of cam rotation; and
(iv) Follower to dwell for the remaining 90° of cam rotation.
The minimum radius of the cam is 25 mm. The out stroke of the follower is performed with
simple harmonic motion and the return stroke with equal uniform acceleration and retardation.
UNIT 3
PART A
1. ln the given figure, four gears are meshing with each other. Given, T1, = 20, T2= 40, T3 =
10, N1, = 100 rpm. Each gear has the same module. Determine the number of teeth on gear
4.
2. A compound gear train, the power is transmitted from a motor shaft to output shaft. The
motor shaft is connected to gear 1 whereas the output shaft is connected to gear 6. The
number of teeth on each gear are given as: T1 =35, T2 = 80, T3 = 45, T4 = 125, T5 = 33, T6 =
75. The motor shaft is rotating at 1126 rpm in a clockwise direction, find the direction and
speed of the output shaft.
3. An external gear with 60 teeth meshes with pinion of 20 teeth, module being 6 mm. What is
the centre distance in mm?
4. In the compound gear train shown in the given fig., gear A and C have equal numbers of
teeth and gear B and D have equal number of teeth. When A rotates at 800 rpm, D rotates at
200 rpm. Determine the rotational speed of the compound gear BC.
PART B
1. Two shafts A and B are co-axial as shown in the fig. A gear C (50 teeth) is rigidly mounted
on shaft A. A compound gear D-E gears with C and an internal gear G. D has 20 teeth and
gears with C and E has 35 teeth and gears with an internal gear G. The gear G is fixed and
is concentric with the shaft axis. The compound gear D-E is mounted on a pin which projects
from an arm keyed to the shaft B. Sketch the arrangement and find the number of teeth on
internal gear G assuming that all gears have the same module. If the shaft A rotates at 110
r.p.m., find the speed of shaft B.
2. An epicyclic reduction gear, as shown in Fig. has a shaft A fixed to arm B. The arm B has a
pin fixed to its outer end and two gears C and E which are rigidly fixed, revolve on this pin.
Gear C meshes with annular wheel D and gear E with pinion F. G is the driver pulley and D
is kept stationary. The number of teeth are : D = 80 ; C = 10 ; E = 24 and F = 18. If the pulley
G runs at 200 r.p.m. ; find the speed of shaft A.
3. Fig. shows diagrammatically a compound epicyclic gear train. Wheels A , D and E are free
to rotate independently on spindle O, while B and C are compound and rotate together on
spindle P, on the end of arm OP. All the teeth on different wheels have the same module. A
has 12 teeth, B has 30 teeth and C has 14 teeth cut externally. Find the number of teeth on
wheels D and E which are cut internally. If the wheel A is driven clockwise at 1 r.p.s. while
D is driven counter clockwise at 5 r.p.s., determine the magnitude and direction of the
angular velocities of arm OP and wheel E.
4. Fig. shows an epicyclic gear train. Pinion A has 15 teeth and is rigidly fixed to the motor
shaft. The wheel B has 20 teeth and gears with A and also with the annular fixed wheel E.
Pinion C has 15 teeth and is integral with B (B, C being a compound gear wheel). Gear C
meshes with annular wheel D, which is keyed to the machine shaft. The arm rotates about
the same shaft on which A is fixed and carries the compound wheel B, C. If the motor runs
at 1000 r.p.m., find the speed of the machine shaft. Find the torque exerted on the machine
shaft, if the motor develops a torque of 100 N-m.
UNIT 4
PART A
1. Outline the significance of the balancing of the rotating part of the high-speed engine.
2. Interpret why only part of the unbalanced force due to reciprocating mass is balanced by
revolving mass.
3. Two masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane.
Another pair of equal masses m1, is attached to the opposite sides of the shaft in the vertical
plane as shown in figure. Consider m = 1 kg, e = 50 mm, e1 = 20 mm, b = 0.3 m, a = 2 m
and a1 = 2.5 m. For the system to be dynamically balanced. Find the mass m1, in kg.
4. How the different masses rotating in different plane are balanced?
PART B
1. A, B, C, and D are four masses carried by a rotating shaft at radii 100, 125, 200 and 150 mm
respectively. The planes in which the masses revolve are spaced 600 mm apart and the mass
of B, C and D are 10 kg, 5 kg, and 4 kg respectively. Find the required mass A and the
relative angular settings of the four masses so that the shaft shall be in complete balance.
2. A four cylinder vertical engine has cranks 150 mm long. The planes of rotation of the first,
second and fourth cranks are 400 mm, 200 mm and 200 mm respectively from the third
crank and their reciprocating masses are 50 kg, 60 kg and 50 kg respectively. Find the mass
of the reciprocating parts for the third cylinder and the relative angular positions of the
cranks in order that the engine may be in complete primary balance.
3. A shaft carries four masses in parallel planes A, B, C and D in this order along its length.
The masses at B and C are 18 kg and 12.5 kg respectively, and each has an eccentricity of
60 mm. The masses at A and D have an eccentricity of 80 mm. The angle between the masses
at B and C is 100° and that between the masses at B and A is 190°, both being measured in
the same direction. The axial distance between the planes A and B is 100 mm and that
between B and C is 200 mm. If the shaft is in complete dynamic balance, determine : 1. The
magnitude of the masses at A and D ; 2. the distance between planes A and D ; and 3. the
angular position of the mass at D.
4. The three cranks of a three cylinder locomotive are all on the same axle and are set at 120°.
The pitch of the cylinders is 1 metre and the stroke of each piston is 0.6 m. The reciprocating
masses are 300 kg for inside cylinder and 260 kg for each outside cylinder and the planes of
rotation of the balance masses are 0.8 m from the inside crank. If 40% of the reciprocating
parts are to be balanced, find :
1. the magnitude and the position of the balancing masses required at a radius of 0.6 m ; and
2. the hammer blow per wheel when the axle makes 6 r.p.s.
UNIT 5
PART A
1. The length of the upper arm of a Watt governor is 400 mm and its inclination to the
vertical is 30°. Find the percentage increase in speed, if the balls rise by 20 mm.
2. In a Hartnell governor, the mass of each ball is 2.5kg. Maximum and minimum
centrifugal forces on the balls are 2000 N and 100 N, corresponding to radii 20 cm and
15 cm respectively. Length of the vertical and horizontal arms of the ball-crank levers
are the same, then what is the spring stiffness in N/cm?
3. Compare the important functions of governor and flywheel.
4. Calculate the vertical height of a Watt governor when it rotates at 60 r.p.m.
PART B
1. The arms of a Porter governor are each 250 mm long and pivoted on the governor axis. The
mass of each ball is 5 kg and the mass of the central sleeve is 30 kg. The radius of rotation
of the balls is 150 mm when the sleeve begins to rise and reaches a value of 200 mm for
maximum speed. Determine the speed range of the governor. If the friction at the sleeve is
equivalent of 20 N of load at the sleeve, determine how the speed range is modified.
2. A Hartnell governor having a central sleeve spring and two right-angled bell crank levers
moves between 290 r.p.m. and 310 r.p.m. for a sleeve lift of 15 mm. The sleeve arms and
the ball arms are 80 mm and 120 mm respectively. The levers are pivoted at 120 mm from
the governor axis and mass of each ball is 2.5 kg. The ball arms are parallel to the governor
axis at the lowest equilibrium speed. Determine : 1. loads on the spring at the lowest and the
highest equilibrium speeds, and 2. stiffness of the spring.
3. In a spring controlled governor of the type, as shown in Fig. the mass of each ball is 1.5 kg
and the mass of the sleeve is 8 kg. The two arms of the bell crank lever are at right angles
and their lengths are OB = 100 mm and OA = 40 mm. The distance of the fulcrum O of each
bell crank lever from the axis of rotation is 50 mm and minimum radius of rotation of the
governor balls is also 50 mm. The corresponding equilibrium speed is 240 r.p.m. and the
sleeve is required to lift 10 mm for an increase in speed of 5 per cent. Find the stiffness and
initial compression of the spring.
4. A spring-loaded governor is shown in Fig. The two balls, each of mass 6 kg, are connected
across by two springs . An auxiliary spring B provides an additional force at the sleeve
through the medium of a lever which pivots about a fixed centre at its left hand end. In the
mean position, the radius of the governor balls is 120 mm and the speed is 600 r.p.m. The
tension in each spring is then 1 kN. Find the tension in the spring B for this position. When
the sleeve moves up 15 mm, the speed is to be 630 r.p.m. Find the necessary stiffness of the
spring B, if the stiffness of each spring A is 10 kN/m. Neglect the moment produced by the
mass of the balls.
