Code No: V0321
R07
SET - 1
II B. Tech II Semester Supplementary Examinations Dec - 2012
KINEMATICS OF MACHINERY
(Com. to MM, AME, ME)
Time: 3 hours
Max. Marks: 80
Answer any FIVE Questions
All Questions carry Equal Marks
1. a) Differentiate between
i) Machine and mechanism
ii) Quick return motion of crank and slotted lever type and that of Whitworth type.
b) Name the two inversions obtained by fixing the crank of a single slider crank chain.
Describe them with neat sketches.
(6M+10M)
2. Sketch Tchebicheff’s mechanism and show that it generates an approximate straight line?
(16M)
3. a) What is coriolis component of acceleration? How is it determined?
b) Explain the procedure to determine the velocity and acceleration of a slider-crank
mechanism by Klein’s construction.
(6M+10M)
4. Derive an expression for the ratio of angular velocities of two shafts connected by a Hooke’s
joint?
(16M)
5. Particulars of a symmetric tangent cam operating a roller follower are:
Least radius of cam=30 mm; roller radius =15 mm; Angle of ascent=75 degrees; total lift =15
mm; speed of the cam shaft =500 r.p.m. Calculate the principal dimensions and the equations
of displacement curve when the follower is in contact with straight flank and circular nose.
(16M)
6. a) Show that involute gears satisfy law of gearing.
b) A pair of 20o full depth involute spur gears having 30 and 50 teeth respectively of module
4 mm are in mesh, the smaller gear rotate at 1000 r.p.m. Determine
i) sliding velocities at
engagement and at disengagement of a pair of teeth and ii) the contact ratio. Take addendum
as one module.
(6M+10M)
7. a) What are the different types of chains used for hoisting and hauling purposes? Give sketches
for each case.
b) A belt is required to transmit 35 kW from a pulley of 150 cm diameter running at 400 r.p.m.
The angle of contact is spread over 11/24 of the circumference of the pulley and coefficient of
friction can be assumed to be 0.28. Determine the width of the belt required for the purpose if
the thickness of the belt is 10 mm, weight of the belt is 0.015 N/cm3 and the allowable stress in
the belt material is 250 N/cm2.
(6M+10M)
8.
a) What is a differential gear of an automobile? Describe its working with the help of a neat
sketch.
b) Explain about different torques in an epicyclic gear train?
(10M+6M)
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R07
Code No: V0321
SET - 2
II B. Tech II Semester Supplementary Examinations Dec - 2012
KINEMATICS OF MACHINERY
(Com. to MM, AME, ME)
Time: 3 hours
Max. Marks: 80
Answer any FIVE Questions
All Questions carry Equal Marks
1. a) Differentiate between
i) Element and Link
ii) Mechanism and machine
iii) Closed pair and unclosed pair
iv) Lower pair and Higher pair
b) Find the distance between the fixed centers of a Whitworth quick return motion mechanism
used in shaping machine if the time ratio of cutting to return stroke=1.5; length of driving link
= 4 cm; length of return stroke = 15 cm. Also find the angles of cutting and return strokes.
(8M+8M)
2.
a) A coupler AB to form a simple Watt mechanism joins two bars OA and O1B. When the
mechanism is in its mean position, the lines OA and O1B are perpendicular to AB. If
OA=16cm, O1B=24cm and AB=12cm, find the position of point P on connecting link which
gives the best straight line motion
b) Sketch and Describe the Scott-Russell and Robert’s straight-line motion mechanisms.
(8M+8M)
3.
a) State and prove the Kennedy’s theorem as applicable to instantaneous centers of rotation of
three bodies.
b) In the slider-crank mechanism shown in fig.1, OA= 450 mm and AB=1200 mm. When the
crank rotates at 40 rad/sec counter-clock wise and the angle AOB= 30 degrees, determine the
acceleration of the slider at B
(6M+10M)
A
O
B
30o
Fig. 1
4. a) Differentiate between Davis and Ackermann steering gears.
b) The angle between the axes of two shafts connected by a Hooke’s joint is 180. The driving
shaft revolves at a uniform speed of 900 rpm. The driven shaft carries a flywheel of mass 25
kg. If the radius of gyration of the flywheel is 120mm, determine the maximum torque on the
driven shaft?
(6M+10M)
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Code No: V0321
R07
SET - 2
5.
Draw the profile of a cam operating a roller reciprocating follower for the following data:
Minimum radius of cam = 40mm, diameter of roller = 12mm, Lift = 30mm, Angle of ascent
= 1050, Angle of descent = 1200, Angle of dwell in the highest position = 500. The follower
moves with simple harmonic motion during ascent and descent.
(16M)
6.
a) Distinguish between involute and cycloid tooth profiles.
b) A pinion of 20 involute teeth and 125 mm pitch circle diameter drives an rack. The
addendum of both pinion and rack is 6.25 mm. What is the least pressure angle that can be used
to avoid interference? With this pressure angle, find the length of the arc of contact and the
minimum number of teeth in contact at a time.
(6M+10M)
7.
a) Compare the relative merits of belt and chain drives.
b) A rope drive transmits 60 kW through a 140 mm diameter 45 degrees grooved pulley
rotating at 200 r.p.m. Coefficient of friction between the ropes and the pulley grooves is 0.27
and angle of lap is 160 degrees. Each rope has a mass of 0.5 kg/m and can with stand a
maximum load of 700 N. considering centrifugal tension, determine a) the number of ropes
required for the drive and (b) initial rope tension.
(6M+10M)
8.
An internal wheel B with 80 teeth is keyed to a shaft F. A fixed internal wheel C with 82 teeth
is concentric with B. A compound wheel D-E gears with two internal wheels. D has 28 teeth
and gears with wheel C, while E gears with B. The compound wheel revolves freely on a pin
which projects from a disc keyed to a shaft A coaxial with F. If all the wheels have the same
pitch and the shaft A makes 600 rpm, what is the speed of F.
(16M)
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Code No: V0321
R07
SET - 3
II B. Tech II Semester Supplementary Examinations Dec - 2012
KINEMATICS OF MACHINERY
(Com. to MM, AME, ME)
Time: 3 hours
Max. Marks: 80
Answer any FIVE Questions
All Questions carry Equal Marks
1.
a) What is Kutzback’s criterion for degree of freedom of plane mechanisms? In what way
Grubler’s criterion is different from it?
b) What are the inversions of quadric cycle chain? Describe any one.
c) Describe briefly the functions of elliptical trammel and scotch yoke.
(6M+5M+5M)
2. a) Describe peaucellier mechanism with a neat sketch.
b) Explain watt mechanism and prove that it generates a straight-line motion.
(6M+10M)
3. In a Whitworth Quick return motion mechanism, a crank AB rotates about a fixed center A.
The end B operates a slider reciprocating in a slotted link, rotating about a fixed center D,
40mm vertically above A. The crank AB which is 90mm long rotates in a clockwise direction
at a speed of 150rpm. Find the angular acceleration of the slotted link for the configuration in
which AB has turned an angle of 45o past its lowest position.
(16M)
4. a) Sketch and explain a Davis steering gear. Mention its disadvantages.
b) Find the maximum permissible angle between the axes of two shafts connected by a
Hooke’s joint if the driving shaft rotates at 1000 rpm, and the total fluctuation of speed is not to
exceed 50 rpm. Determine the maximum and minimum speeds of the driven shaft. (8M+8M)
5. Draw the profile of a cam to raise a knife - edged follower with uniform acceleration and
deceleration and lower with simple harmonic motion for the following data:
Least radius of cam =60mm, Lift of follower = 45mm, Angle of ascent = 800, Angle of dwell at
the highest position = 500, Angle of descent = 900.
(16M)
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Code No: V0321
R07
SET - 3
6. a) Explain the fundamental law of toothed gearing.
b) Discuss the effect of increasing the centre distance on velocity ratio of two gears in contact
with involute profile.
c) Find the minimum number of teeth to avoid the interference when the addendum for the stub
tooth is 0.8 module and when the power component is 0.95 times the normal thrust. The gear
ratio is 3:1. Find the length of arc of contact in terms of the module.
(4M+4M+8M)
7. a) What is meant by centrifugal tension in belts? Why should it not exceed the permissible
limit?
b) A V-belt having a lap of 180 degrees has a cross sectional area of 3 cm2 and runs in a groove
of included angle 45 degrees. The density of the belt is 0.015 N/cm 3, the maximum stress is
limited to 400 N/cm 2 and coefficient of friction is 0.2. Find the maximum power that can be
transmitted, if the wheel has a mean diameter of 30 cm and runs at 1200 r.p.m. (6M+10M)
8. a) What is the sun and planet gear? Give the procedure to analyze such a gear train.
b) An epicyclic gear consists of a pinion, a wheel of 40 teeth and an annulus wheel with 84
internal teeth concentric with the wheel. The pinion gears with the wheel and annulus. The arm
that carries the axis of the pinion rotates at 100 rpm. If the annulus is fixed, find the speed of
the wheel.
(6M+10M)
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Code No: V0321
R07
SET - 4
II B. Tech II Semester Supplementary Examinations Dec - 2012
KINEMATICS OF MACHINERY
(Com. to MM, AME, ME)
Time: 3 hours
Max. Marks: 80
Answer any FIVE Questions
All Questions carry Equal Marks
1.
a) What is a Kinematic pair? Explain different types of Kinematic pairs as classified by
relative motion.
b) The distance between the axes of two parallel shafts is 1cm.The shafts are connected by
Oldham coupling. Find the maximum Kinematic energy of the intermediate piece of mass 5 kg
when the shafts revolve at 300rpm.
(10M+6M)
2.
Sketch a pantograph and show that it can produce paths exactly similar to the ones traced out
by a point on a link on an enlarged or a reduced scale.
(16M)
3.
In a four link mechanism, the crank AB rotates at 40 rad/sec. The length of the links are crank
AB = 200mm, coupler link BC = 400mm, rocker link CD = 450mm, and fixed link AD =
600mm. when the link AB is at right angle to AD, determine the velocity and acceleration of
a) The mid-point of the link BC.
b) A point on the link CD 150mm, from the pin connecting the links CD and AD.
(16M)
4.
a) Describe an Ackermann steering gear with a neat sketch. Explain why it is widely used.
b) Two shafts are connected by a Hooke’s joint and the angle between their axes is 20 0. The
speed of the driving shaft is 200rpm, while the steady load on the driven shaft is 6 KW.
Determine the mass of the flywheel of the driven shaft if its radius of gyration is 160mm and
output torque of the driven shaft is not to vary by more than 12% of the torque on input shaft.
(6M+10M)
5.
A symmetrical cam with convex flanks operates a flat-footed follower. The lift is 8 mm, base
circle radius is 25 mm and the nose radius is 12 mm. If the total angle of cam action is 120 o,
find the radius of the convex flanks. Determine the maximum velocity and the maximum
acceleration when the cam shaft rotates at 350 r.p.m.
(16M)
6.
a) Derive expressions for length of arc of contact for involute gears.
b) Two equal gear wheels having involute profile have standard addendum equal to one
module. Find the least number of teeth on the pinion to avoid interference and the length of
resulting arc of contact in terms of module, if the radial load on bearing is 0.35 times the
normal thrust.
(8M+8M)
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Code No: V0321
R07
SET - 4
7. a) Obtain expressions for the lengths of belt in case of (i) Open belt drive (ii) cross belt drive.
b) Determine the maximum power that can be transmitted through a flat belt drive for the
following data: The cross section of the belt is 300 mm x 15 mm; Ratio of tensions is 2;
Maximum permissible tension in the belt is 2.0 N/ mm 2; Mass density of the belt material is
1200 kg/ m3.
(8M+8M)
8. In the epicyclic gear shown in figure, the internal wheels A and F and a compound wheel C-D
rotate independently about the axis O. The wheels B and E rotate on pins fixed to the arm L.
All the wheels have the same module and the numbers of teeth are: Band E - 18, C - 28 and D 26. If L makes 200 r.p.m (c.w.), find the speed of F when the wheel A makes 10 r.p.m counter
clock-wise.
(16M)
B
A
C
o
D
F
L
E
Fig. Q. No. 8
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