Kinematics Of Machinery Jntu Model Paper{Www.Studentyogi.Com}

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Code No: R05310304
Set No. 1
III B.Tech I Semester Regular Examinations, November 2007
KINEMATICS OF MACHINERY
( Common to Mechanical Engineering, Mechatronics, Production
Engineering and Automobile Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks

1. (a) Enumerate the inversions of a double slider-crank chain. Give examples.
(b) The length of the xed link of a crank and slotted lever mechanism is 300 mm
and that of the crank 110 mm. Determine,
i. the inclination of the slotted lever with the vertical in the extreme posi-
tion.
ii. the ratio of the time of cutting stroke to the time of return stroke and
iii. the length of the stroke, if the length of the slotted lever is 500 mm and
the line of stroke passes through the extreme positions of the free end of
the lever. [6+10]

2. A torque of 75 N-m is applied to the link OA at A of a Gross-Hopper mechanism
shown in gure 2. The link OA makes an angle of 20 degrees with the horizontal.
Find the magnitude of the vertical force exerted at B to overcome the resisting
torque of 75 N-m. The lengths of the links are: OA=40 mm, AC= 60 mm and
CB= 150 mm. If the link OA makes an angle of 10 and zero degrees with the
horizontal, what will be the vertical force at B to overcome the torque of 75 N-m?
[16]

Figure 2
3. (a) State and Explain Kennedy’s theorem as applicable to instantaneous center
of rotation of three bo dies.


Code No: R05310304
Set No. 1
(b) In the mechanism shown in Figure 3. the crank OA makes 400rpm in the
counter clo ckwise direction. Find
i. angular velocity of the link BA and
ii. velocity of the slider at A. The lengths of the links are OA= 60mm, OB=
220 mm and BC= 300mm. [6+10]

Figure 3
4. (a) Derive the fundamental equation for correct steering.
(b) What are the relative merits and demerits of the Ackermann type of steering
gear over that of Davis type?
(c) Two shafts are to be connected by a Hooke’s joint. The driving shaft rotates at
a uniform speed of 500rpm and the speed of the driven shaft must lie between
475 and 525 rpm. Determine the maximum permissible angle between the
shafts. Also determine the maximum and minimum speeds of the driven shaft.
[6+4+6]

5. (a) Derive an expression for displacement, velocity and acceleration of a tangent
cam with roller follower. When roller is in contact with ank.
(b) A tangent cam with straight working faces tangential to a base circle of 120mm
diameter has a roller follower of 48mm diameter. The line of stroke of the roller
follower passes through the axis of the cam. The nose circle radius of the cam
is 12mm and the angle between the tangential faces of the cam 900. If the
speed of the cam is 180rpm, determine the acceleration of the follower when
i. During the lift, the roller just leaves the straight ank.
ii. The roller is at the outer end of its lift, i.e at the top of the nose. [16]

6. (a) What is standard system of gears? How do es it ensure interchangeability of
gears?
(b) Two 200 involute spur gears have a module of 10mm. The addendum is one
module. The larger gear has 50 teeth and the pinion 13 teeth. Do es the
interference occur? If it occurs, to what value should the pressure angle be
changed to eliminate interference? [16]

7. A leather belt 150mm wide 6mm thick and weighing 6 N/m length connects two
pulleys each 1m in diameter and on parallel shafts. The belt is found to slip when
the moment of resistance is 600N.m and the speed is 500 rpm. If the co e cient
of friction between the belt and the pulleys is 0.24, nd the largest tension in the
belt.


Code No: R05310304
Set No. 1
8. (a) Explain about Epicyclic gear train.
(b) In the epicyclic gear train shown in gure 8b, a gear C which has teeth cut
internally and externally is free to rotate on an arm driven by shaft 1. It
meshes externally with the casting D and internally with the pinion B. The
gears have the following number of teeth:
B = 24 C = 32 40 D = 48
Find the velocity ratio between
i. 1 and 2 when D is xed.
ii. 1 and D when 2 is xed. [16]

Figure 8b


Code No: R05310304
Set No. 2

1. (a) Enumerate the inversions of a double slider-crank chain. Give examples.
(b) The length of the xed link of a crank and slotted lever mechanism is 300 mm
and that of the crank 110 mm. Determine,
i. the inclination of the slotted lever with the vertical in the extreme posi-
tion.
ii. the ratio of the time of cutting stroke to the time of return stroke and
iii. the length of the stroke, if the length of the slotted lever is 500 mm and
the line of stroke passes through the extreme positions of the free end of
the lever. [6+10]

2. (a) Name the mechanisms that generate straight lines.
(b) Prove that the peaucellier mechanism generates a straight-line motion. [4+12]

3. A crank and rocker mechanism ABCD has the following dimensions: AB =0.75m,
BC =1.25 m, CD =1 m, AD =1.5 m and CF = 500 mm. AD is the xed link. F lies
on BC produced. Crank AB has an angular velo city of 30 rad/s counter clo ck-wise
and a deceleration of 200 rad/s2 at the instant angle DAB= 300. Find

(a) The instantaneous linear acceleration of C and F and
(b) The instantaneous angular velocities and accelerations of links BC and CD.
[16]

4. (a) Explain Davis steering gear with a neat sketch.
(b) For a Davis steering gear, derive the expression for the angle of inclination
of the track arms to longitudinal axis of the vehicle in terms of the distance
between the pivots of the front axle and wheelbase.
(c) In a Davis steering gear the distance between the pivots of the front axle is 90
cm and the wheelbase is 220 cm. When the vehicle is moving along a straight
path, nd the inclination of the track arms to the longitudinal axis of the
vehicle. [4+8+4]

5. (a) Explain with the help of displacement, velo city and acceleration diagrams, a
uniform acceleration and uniform retardation pro le cam.
(b) Draw the pro le of a cam operating a roller reciprocating follower and with
the following data:


Code No: R05310304
Set No. 2
Minimum radius of cam = 25mm, Lift = 30mm, roller diameter = 15mm.
The cam lifts the follower for 1200 with SHM followed by a dwell period of 300.
Then the follower lowers down during 1500 of the cam rotation with uniform
acceleration and deceleration followed by a dwell period. If the cam rotates at
a uniform speed of 150 rpm, calculate the maximum velocity and acceleration
of the follower during the descent period. [16]

6. (a) De ne addendum circle, dedendum circle, arc of contact of gears.
(b) Two gears in mesh have a module of 8mm and a pressure angle of 200. The
larger gear has 57 while the pinion has 23 teeth. If the addenda on pinion and
gear wheels are equal to one mo dule, nd
i. the number of pairs of teeth in contact
ii. the angle of action of the pinion and the gear wheel
iii. the ratio of the sliding to rolling velocity at
A. the beginning of contact
B. the pitch point
C. the end of contact
[16]

7. A leather belt 150mm wide 6mm thick and weighing 6 N/m length connects two
pulleys each 1m in diameter and on parallel shafts. The belt is found to slip when
the moment of resistance is 600N.m and the speed is 500 rpm. If the co e cient
of friction between the belt and the pulleys is 0.24, nd the largest tension in the
belt. [16]

8. In an epicyclic gear train of the sun and planet type shown in gure 8, the pitch
circle diameter of annular wheel A is to be nearly equal to 216mm, and the mo dule
is 4mm. When the annular wheel is stationary, the spider which carries three plant
gears P of equal size, has to make one revolution for every ve revolutions of the
driving spindle carrying S gear. Determine the number of teeth on all the wheels
and also the exact pitch circle diameter of A. [16]

Figure 8


Code No: R05310304
Set No. 3

1. (a) What is the di erence between quick return motion of crank and slotted lever
type and that of whit worth type?
(b) Find the distance between the xed centers of a Whitworth quick return mo-
tion mechanism if the length of driving link is 40mm, return stroke is 150mm
and time ratio of cutting to return stroke is 2. [6+10]

2. (a) Name the mechanisms that generate straight lines.
(b) Prove that the peaucellier mechanism generates a straight-line motion. [4+12]

3. In the mechanism shown in Figure 3. The crank OA rotates at 50 rpm and the
lengths of the links are OA= 125 mm, AC= 600 mm, QC= 150 mm, QD= 150
mm, CD= 130 mm, BD= 550 mm and OQ= 625 mm. When the angle AOQ= 45
degrees, determine,

(a) The linear acceleration of the slider at B.
(b) The angular acceleration of the links AC, CQD and BD. [10+6]

Figure 3
4. Describe the working of a Hooke’s joint with a neat sketch. Also prove that the
ratio of angular velo city of the driven shaft to that of the driving shaft with a
Hooke’s joint is cos a 1-sin2 a cos2 , where is the angle turned by the driving shaft at
any instant and is the angle of inclination of driven shaft with driving shaft. [16]


Code No: R05310304
Set No. 3
(b) Draw the pro le of a cam operating a knife-edge follower having a lift of 30mm.
The cam raises the follower with SHM for 1500 of the rotation followed by a
period of dwell for 600. The follower descends for the next 1000 rotation of the
cam with uniform velocity, again followed by a dwell period. The cam rotates
at a uniform velocity of 120rpm and has a least radius of 20mm. What will
be the maximum velocity and acceleration of the follower during the lift and
the return? [16]

6. (a) Explain ’law of gearing’.
(b) A pair of spur gears have 16 and 18 teeth, a module of 13mm, addendum of
13mm, and pressure angle of 14 50. Show that the gears have interference.
Determine the amount by which the addendum must be reduced to eliminate
the interference. [16]

7. (a) Discuss about selection of belt drive.
(b) A shaft runs at 80 rpm and drives another shaft at 150rpm through belt drive.
The Diameter of the driving pulley is 600mm. Determine the diameter of the
driven pulley in the following cases:
i. Neglecting belt thickness.
ii. Taking belt thickness as 5mm.
iii. Assuming for case (ii) a total slip of 4% and
iv. Assuming for case (ii) a slip of 2% on each pulley. [16]

8. An epicyclic gear train consists of three gears 1,2 and 3 as shown in gure 8. The
internal gear 1 has 72 teeth and gear 3 has 32 teeth. The Gear 2 meshes with both
gear 1 and gear 3 and is carried on an arm A which rotates about the centre 2 at
20 rpm. If the gear 1 is xed, determine the speed of gears 2 and 3. [16]

Figure 8


Code No: R05310304
Set No. 4

1. (a) What is a Kinematic chain? What is the relation between the number of links
and number of pairs in a kinematic chain?
(b) Give diagrammatic sketches of the following mechanisms and state on which
Kinematic chain each mechanism is based:
i. Oscillating cylinder engine
ii. Oldham shaft coupling
iii. Pendulum pump
iv. Scotch yoke mechanism
v. Watt’s indicator. [6+10]

2. (a) Explain Scott Russell mechanism through a neat sketch. Show that it gener-
ates a straight-line motion.
(b) What are the limitations of Scott Russell mechanism. [12+4]

3. The crank OP of a crank and slotted lever mechanism shown in gure 3. rotates at
200 rpm in the counter-clockwise direction. Various lengths of the links are OP =
90 mm, OA = 300 mm, AR = 480 mm and RS= 330mm. The slider moves along
an axis perpendicular to AO and is 120 mm from O. Determine the velocity of the
slider when the angle AOP is 135o and also the maximum velo city of the slider.
[16]

Figure 3
4. (a) Sketch Ackermann steering gear and explain its advantages.


Code No: R05310304
Set No. 4
(b) For an Ackermann steering gear, derive the expression for the angle of incli-
nation of the track arms to longitudinal axis of the vehicle.
(c) The driving shaft of a Hooke’s joint rotates at a uniform speed of 300 rpm. If
the total maximum variation in speed of the driven shaft is 8 percent of the
mean speed, determine the greatest permissible angle between the axes of the
shaft. Also nd the maximum and minimum speeds of the driven shaft.
[4+7+5]

5. (a) With the help at neat sketches explain the types of cams.
(b) A cam is to operate an o set roller follower. The least radius of the cam is
50mm, roller diameter is 30mm, and o set is 20mm. The cam is to rotate at
360rpm. The angel of ascent is 480, angle of dwell is 420, and angle of descent
is 600. The motion is to be SHM during ascent and uniform acceleration and
deceleration during descent. Draw the cam pro le.
Also calculate the maximum velocity and acceleration during descent. [16]

6. (a) Sketch a pair of gears and represent meshing on it.
(b) An internal spur gear having 200 teeth meshes with a pinion having 40 teeth
and a module of 2.5mm. Determine:
i. the velo city ratio if the pinion is the driver.
ii. the centre distance, and
iii. if the centre distance is increased by 3mm, nd the resulting pressure
angle. [16]

7. A machine which is to rotate at 400 rpm is run by an engine turning at 1500rpm,
through a silent chain, having a pitch of 15mm. The number of teeth on a spro cket
should be from 18 to 105. The linear velocity of chain drive is not to exceed 10m/s.
Find the suitable number of teeth for both the sprockets. [16]

8. (a) Explain about automotive di erential.
(b) An epicyclic gear consists of a pinion, a wheel of 40 teeth and an annulus
with 84 internal teeth concentric with the wheel. The pinion gear with the
wheel and the annulus. The arm that carries the axis of the pinion rotates at
100rpm. If the annulus is xed, nd the speed of the wheel; if wheel is xed,
nd the speed of the annulus. [16]

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Kinematics Of Machinery Jntu Model Paper{Www.Studentyogi.Com}