Kinematics of machines Question Papers

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06ME44
USN

Fourth semester B.E. Degree Examination, I)ecemb er 2oll
Kinematics of Machines
Max. Marks:100
Time: 3 hrs.
Note: Answer any FIW full questions, selecting
at least TWO questions ftom eaeh part'

Ci
o
PART -A
o
d
o. I a. Define the following, with sketches:
(08 Marks)
(!
i) Link Mechanism iii) Machine iv) Inversion.
ii)
ad

c)
b. Explain: i) Lower pairs ii) Higher pairs' (06 Marks)

an inversion of a slider
c)
c. Describe with a neat sketch, the crank and slotted lever mechanism,
(06 Marks)
B9 crack mechanism
&. neat sketch' (10 Marks)
d9 2 a. Explain the Whitworth quick return motion mechanism, with a
Explain with a neat sketch,
b. Derive the expression for necessary condition of correct steering.
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d6
,=+ (10 Marks)
.EN the Ackerman steering gear mechanism'
bip
and connecting
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-c !l 3 A single slider crank mechanism shown in Fig.Q3, has the crank cB = 100rnm
has a speed of
oF rod BA : 300;, with eeatre of gravity G-ld0mm ftom B. The crankshaft
3s 75 radlsecand an angular acceleration of 1200 rad/sec'. Find
@(d i) The velocityof G and the angular velocrty of AB'
bE ii) The acceleiation of G and angular acceleration of AB. (20 Marks)

do 6
ot
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>e
26
6r

oP Fis.Q3
Locate all the instantaneous centres ano frna *re angular velocity
of the link BC' The link
-O
qo-
tro. 4 a. and AD:600mm'
o..
oi dimensions of the mechanism are AB = 300mm, BC = BD:360mm
The angle BAD :60". The crank rotates at 100 rpm.lRefer Fig.Qa($l
(10 Marks)
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olt
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coo
ar=
o. iB Fig.Qa(a)
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3L engine are 200mm and
->'
,J< b. The lengths of the crank and the connecting rod o{ a reciprocating
120 rad/sec' when the
-i o'i 700mm r"rpr.rir"ly. rrr. crank rotates in clockwise direction at
c) crank is at 30oC to'iDC, by using the Klein's construction,
determine
and acceleration of the cR'
i) The velocity *a u..*f*ration Jf the piston ii)Angular velocity
o
Z (10 Marks)

o.

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a
06ME44

PART -B
The crank and connecting rod of an engine are 0.3m and 1.5 in length respectively.The crank
rotates at 180 rpm clockwise. Determine the velocity and acceleration of the piston when the
crank is 40o from TDC. Also determine the position of the crank for zero acceleration of the
piston. (20 Marks)

6 a. Derive the expression for the length of arc of contact in a pair of spur gears in a mesh.
(08 Marks)

b. Two mating gears have 20 and 40 involute teeth of module 10mm and 20o pressure angle.
The addendum of each wheel is to be made of such a length that the line of contact on each
side of the pitch point has half the maximum possible length. Determine the addendum
length for each wheel, length of path of contact, arc of contact and contact ratio. (12 Marks)

7 a. Explain with a neat sketch the o'Sun & planet wheel" (04 Marks)

b. In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth,
respectively. If the arm rotates at 150 rpm in the anticlockwise direction about the centre of
gear A which is fixed, determine the speed of the gear B, if the gear A instead of being
fixed, makes 300 rpm in the clockwise direction. [Refer Fie.Q7(b)]. (16 Marks)
Ag

Fie.Q7(b)

8 Construct the profile of a cam to suit the following specifications:
Cam shaft diameter = 40mm Least radius of cam:25mm
Diameter of the roller:25mm -
Angle of lift 120"
:
Angle of fall 150" Lift of the follower = 40mm
No. of pauses are two of equal interval between motion.
During the lift the motion is SHM. During the fall motion is UARM. The speed of camshaft is
uniform. The line of stroke is offset to 12.5mm from the centre of the cam. (20 Marks)

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2 of2

r
06M.E,44

Fourth Semester B.E. Degree Examination, June/July 201,1
Time: 3 hrs. Max. Marks:100
Note: Answer any FIVEfull questions.
selecting atleast TWO from each.parl.
.:

2
PART -A
I a. Define:
i) Kinematic chain
2
ii) Machine
E
iii) Structure
iv) Self closed pair
v) Force closed pair. (10 Marks)
;' b. Sketch and explain any two inversions of four bar chain. (10 Marks)
(,e

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Sketch and explain the following :
dt
HoO
a. Whitworth quick return mechanism. (08 Marks)
ts(.) Ratchet and pawl mechanism. (08 Marks)
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-co
b.
c. Toggle mechanism. (04 Marks)
a7
!L

u.d
A four bar chain of links PQ, QR and RS are 62.5 mm, 175 mm ancl 120 mm long
respectively, the link PS of chain PQRS is fixed and having iength of 200 mm. The link PQ
bU makes an angle of 60" rvith PS and rotaies at i0 radl sec ciockwise. Detennine :
6O
BOE
i) Angular veiocity of links QR and RS
ii) Angular acceleration,:f link QR and RS. (20 frIarks)
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4 a. In a reciprocating engine the length of crank is 250 mm and length of connecting rod is
1000 mm. The crank rotates an uniform speed of 300 rpm. Determine the velocity and
3
=
;'i acceleration of piston, when the crank is 30' from inner dead centre, use Klein's
tro. construction" (l0lVlarks)
o"
o-a
b. Locate all instantaneous benters for the following mechanism. (10 Marks)
ao
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bo'
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5E
(r< Fie. Qa&)(ii)
Fig. Qa@Xi)
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o PART B
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5a. Explain the significance of loop closure equation, with example. (05 Marks)
b. The crank of an engine mechanism is 200 mm long and the ratio of connecting rod length to
the crank radius is 4. Determine the acceleration of the piston when crank has turned through
an angle 45o from inner dead centre and rotatin g at a speed of 240 rpm counter clockwise
direction by complex number approach. (15 Marks)
I of2

06M844

6a. What is interference in involute gears? Derive an expression for the length of arc of contact
in a pair of meshed spur gears. (10 Marls)
b. Two gear wheels mesh externally and are to give a velocity ratio of 3 to 1. The teeth are of
involute form module:6 mm, addendum: one module, pressure angle = 20". The pinion
rotates at 90 rpm. Determine :
i) Minimum no. of teeth on each wheel to avoid interference
ii) The number of pair of teeth in contact. (10 Marlis)

An epicyclic gear train consist of a sun wheel S, a stationary intemal gear 'E' and three
identical planet wheels 'P' carried on a stat- shape planet carrier'C'. The size of difterent
toothed wheels are such that the planet carrier C rotates one revolution for every 5
revolutions of the sun wheel S. The minimum number of teeth on any wheel (say P) is 16.
the driving torque on the sun wheel is 100 N -m. Determine
i) Number of teeth on different wheels of the train.
ii) Toque necessary to keep the internal gear stationary. (20 Marls)

Fig. Q7

The following data relate to cam profile in which the roller follower moves with SHM
during ascent and uniform acceleration and retardation motion during descent.
Minimum radium of cam :30 mm
Roller radius :8 mm
Lift =28mm
Offset of follower axis : 12 mm towards right
Angle of ascent :90"
Angle of descent :60o
Angle of dwell between ascent and descent :45o
Speed ofcam :200 rpm
Draw the profile of cam and determine the maximum verocitv and acceleration during
outstroke and return stroke. (20 Marks)

*****

2 of2

USN
06M844

Fourth Semester B.E. Degree Examination, Dec.08 / Jan.O9
Time: 3 hrs. Max. Marks:100

Note : Answer any FIVE questions selecting ot least two from each part.

Part A
a. Define with suitable examples :
i) Structure
ii) Machine
iii) Mechanism
iv) Higher pair (08 Marks)
b. Sketch and explain the following:
i) Beam engine
ii) Gnome engine.
iii) Ellipticaltrammel. (12 Marks)

a. Sketch the crank and slotted lever mechanism. Indicate the (06 Marks) strokes.
b. Sketch and explain Geneva wheel mechanism. (07 Marks)
c. Sketch Ackremann steering mechanism and obtain condition for correct steering. (07 Marks)

A double slider crank mechanism is shown in figure Q3. The crank OA rotates at a constant
angular velocity of 10 radlsec. The links OA, AB and AC are 100 mm, 200mm and 200 mm
long respectively. By drawing the velocity and acceleration polygons determine:
a. Velocity and acceleration of each slider.
b. Angular velocity and angular acceleration of each connecting rod. (20 Marks)

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.7..,"' ?. ',.

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l/
- *
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1

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I
Fig. Q3
Locate all the instantaneous centers for a
i) Four bar mechanism.
ii) Slider crank mechanism. (10 Marks)
b. Determine the velocity and acceleration of the piston by Kleins construction for a steam
engine to the following specifications:
Stroke of piston: 600 mm
Ratio of length of connecting rod to crank length:5
Speed of engine:450 rpm clockwise.
Position of crank: 45" with inner dead centre. (10 Marks)

1 of ?

06M.F,44

obtain loop closure equation ro, u +-u*P,f,.ltn?oir*. (04 Marks)
Develop equations for the angular velocities and angular accelerations for the links 3 and 4
as shown in figure Q5 O) using complex algebra method.
,tr, (16 Marks)

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,d
/
b.'L h
I

',
l/1 ',
1,.
t0r
, *'[---- I d,
^n Fig. Qs (b)

a. cornpare cycloidal and involute gear tooth profile. (05 Marks)
b. What is rneant by interference? Mention various methods of avoiCing interference in gears.

Two gear wheels have respectively 28 and45 teeth and a standard aaaenoullsf;Tl
module. The pressure angle is 20" and the module of 6 mm Determine : i) length of path
of contact. ii) contact ratio. (i0 Marks)

Sketch and explain:
i) Simple gear train.
ii) Epicyclic geartrain. (06 Marks)
In an epicyclic gear train of sun and planet type, the pitch circle diameter of the Annular
wheel (A) is 425 mm and the module is 5 mm" When the annular wheel is stationary, the
spider which carries 3 planet Gears (P) of equal size has to make one revolution for every d
revolutions of the driving spindle carryrng sun wheel (S). Determirte the number of teeth
on all the wheels. (I,l Marks)

Draw the profile of a cam operating a roller reciprocating foilower and with the following
: :
data: Minimum radius of cam 25 mm, Lift 30 mm; Rolter diameter 15 mm. The cam lifti :
the follower for 120' with SHM followed by a dweil period of 30", then the follower lcwers
down during 150" of the cam rotation with UARM followed by a dwell period. The cam
rotates at a uniform speed of 150 rprn (CW direction). The axis of the follower passes through
the axis of the cam shaft. Calculate the maximum velocity and acceleration of the follower
during the descent period. (20 Marks)

ME44
uix
July 08
Fourth semester B.E. Degree Examination, June /
Kinematics of Machines Max. Marks:100
Time:3 hrs-
Note Answer any FIVE full questions'
z1^.
2. Graphieai questions can be drawn oru drawing sheet'
3. Miising data if any may be suitably assumed'
Differentiate between: i) Lower pair and higher
pair ii) Machine and mechanism'
1a. (05 Marks)
iiD Constrained and unconstrained motion' the entarged or
b. Jil;;JJ ffiffiire working of pantffih and prove that it reproduces
(08 Marks)
reduced size drawings. (06 Marks)
yoke mechanism'
Sketch and explain tle working of scotch
(08 Marks)
mechanisms:
2a. Find the degrees of freedom for the following

Fig. Q2 (a)
slider mechanism'
b. With neat sketches explain the working of all the inversit,.ns of dcuble (12 Marks)
find for the given
If the crank OA rotates at 150 rpm in the antislockwise direction,
I)' (20 Marks)
tnfiguration the velocity and accelerdtion of slider B and
t

K--1€Orayp,

-{
OA: 80 mm
AC: CB : CD = 120 mm

Fig. Q3
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M.E44
4a. state and prove Arnold-Kennedy's theorem. (05 Marks)
b. Locate all the instantaneous centers of the mechanism shown. Find the angular velocity of
link AB. oA:200 mm, AB: 1500 mrn, BC:600 mm, cD:500 *m urrd BE:400 mm.
OA rotates at 120 rpm clockwise. (15 Marks)

- r:
Fig. Qa &)

Ja- Derive an expression for loop closure equation for four bar mechanism. (08 Marks)
b. If the crank and connecting rod are 150 mm and 600 mm long respectively and the crank
rotates at constant speed of 100 rpm, determine
i) Velocity and acceleration of piston and'
ii) Angular velocity and angular acceleration of connecting rod.
The angle, which the crank makes with the inner dead centre, is 30". (12 Marks)
6a. Explain and derive the condition for the law of gearing. (08 Marks)
b. A pinion having 30 teeth drives a gear having 80 teeth. The profile of the gears is involute
with 20' pressure angle, 12 mm module and 10 mm addendum. Find the length of path of
contact, arc ofcontact and contact ratio. (12 Marks)
Figure shows diagrarnmatically a compound epicyclic gear train. Wheels A, D and E are free
to rotate independently on spindle O, while B and C are cornpound and rotate together on
spindle P, on the end of arm OP. All the teeth of different wheeli have 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 rps while D is driven
counterclockwise at 5 rps, determine the magnitude and direction of angular velocities of arm
OP and wheel E. (20 Marks)

Fig. Q7

Construct the profile of a cam to suit:
Cam shaft diameter : 40 mm; Least radius of cam : 25 mm; Diameter of roller : 25 mm;
Angle of lift :120':' Angle of fall: 150"; Lift of the follower: 40 mm;Number of pauses are
two of equal interval between motions.
During the lift the motion is SHM. During the fall the motion is uniform acceleration and
deceleration. The speed of the camshaft is uniform. The line of stroke of the follower is oflset
12.5 mm from the centre of the cam. (20 Marks)

t
*
F ui*
ME44

Fourth semester B.E. Degree Examination, Dec. 07 / Jan. 08
Time:3 hrs. Max. Marks:100
Note z T.Answer any FIVEfull questions'
2.Graphicalsolutionscanbedrawnondrawingsheet.

a. Distinguish between :
pair.
i) Complete constraint and successful constraint ii) Open pair and closed
iii) Structure and kinematic chain iv) Ivlechanism and machine. (08 Marks)
b. Explain with neat sketches, three inversions of double slider crank chain. (12 Marks)

With neat proportionate diagrams explain the principle and working of following
mechanisms'

a. Whitworth mechanism
b. Geneva mechanism
c. Toggle mechanism
(20 Marks)
d. Hooke's joint.
The Fig.3 shows Robert's straight line mechinism in which point'C'moves.in
ahorizontal
and its velocity and
direction. 02 and O+ are tlie fiied points. pzA is a crank 75 mm long
acceleration are Z0 rad./sec and 100 rad/secz respectively, both clockwise.
The dimensions of
:
other links are : AB :75 mm, o+B 75 mm, lozo 4 = 45o, OzO+:
125 mm. The point'c'

traces its path along horizontal line .joininB OzO+. Find the velocities
and accelerations of
point 'C' and link O+ B.

Fig.3 (20 Marks)

The mechanism of a wrapping machine, is as shown in Fig4 has the following
dimensions:

OrA: 100 mm; AC : 700 mm; BC :200 mm; O:C
:200 mm;
OzE:400 mm; OzD:200 mm and BD: 150 mm'
the velocity of the
The crank OrA rotates at uniform angular velocity of 100 rad/sec. Find
point E of the bell crank iever by instantaneous centre method.
€
1?r

i', !6
ti
1 r,i ,srTZ

-:r*J-
I
I
1 i!c.c nLw' l

Fc-i
--
Fig.4 (20 Marks)

I of2

ME+4
Use kineuatic analysis of the slider- crank by complex numbers
and derive the expressions
9rveJ99ttrandaccelerationoftheslider*d.o*i.tingrod.]--_-
The slider-crank of an internal combustion engine shoil in Fig.s(b) includes
a crank of
50.8 mm tength and a connecting rod of 203 rin
length. Th...rril;p;;J;f;;;*;;;
f,gl;f ,h.;"#.;G
constant at 314 rad/s. Determine the acceleration of tf,e *uss r.ri..
rod when &e crank angle is 30o. The mass centre
at A.
93 is located 50.8*J rro", ifr. crank pin

Fig.s(b) (10 Marks)
6a. what is meant by involute irrtrrr"r.n"lrg'J(o'
b. Derive * for the minimum number of teeth on a pinion mating *rh(:'r[[T:
avoid interference.
"*pr"rrion
(06 Marks)
c. Two mating involute gears of 20o pressure angle have a gear ratio of 2. The
number of
teeth on pinion is 20. The speed of pinion is 250 rpm. Takeirodule
as l2 mm.
If the addendum on each wheel is such that the path of approach and path of recess on
eaeh side are of half the maximum possible length each; find:
i) The addendum of pinion and gear ii) The l."gth of*, of contact. (r0 Marks)
a. The FigT shows an epicyclic gear train. Pinion A has 15 teeth and is
rigidly fxed in the
motor shaft- The wheel B has 20 teeth and gears with A and also with aniular
fixed wheel
D' Finion C has 15 teeth qd it integral with B (C and B being a compound
wheel). Gear C
meshes with annular wheel E, 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
runs at 100 rpm, find the speed of the machine shaft. Find also - C. If the motor
the torque exerted on the
machine shaft if the motor develops a torque of 100 N_m.

Fig.7 (20 Marks)
Draw the profile of the cam for the following details :
a. Minimun radius of the cam -20 mm.
b. Rotation-counter clock-wise at 1000 rpm.
c. Oufward stroke - UARM l}0o. -
d. Follower- l0 mm dia roller.
e. Lift ofthe follower- 20 mm.
f. Dwell at tull lift - 60o.
g. Retum stroke - SHM during 120o.
h. offset - foltrower axis 5 mm to the right of the aris of cam.
calculate the maxim,m acceleration during retum stroke. (20 Marks)
2 of2

-: tr. '.'

Page No... I NIT,44

USN

NBW SCHEME
Fourth Semester B.E. Degree Examination, July 2007
Mechanical Engineerin g
Time: 3 hrs.l [Max. Marks:i00
Note : Answer any FIVE full questions.

I a. Define a kinematic chain. Describe various forms of kinematic chain with examples.
(05 Marks)
b. Explain the Grubler's mobility equation for a planar mechanism. Determine the
mobility of a cam with an oscillating follower fitted with a roller. (05 Marks)
c. Sketch and explain the kinematic chain with three lower pairs. (05 Marks)
d. Sketch and explain the elliptical trammel mechanisrn. (05 Marks)

2 a" What is meant by quick-return mechanism? Sketch and explain drag link mechanism"
(06 Marks)
b. Sketch and explain Peaucellier straight line motion mechanism. (06 Marks)
c. A Hooke's joint is used to connect two shafts whose axes are inclined at 200. The
driving shaft rotates uniformly at 6000 rpm. What are the extreme angular velocities
of the driven shaft? Find the maximum value of acceleration and state the angle at
which it will occur? (08 Marks)

3 A double slider-crank rnechanism is shown in Fig.3(a). The crank OA rotates at constant
angular velocity of 10 radlsec. The links OA, AB and AC are 100 mm, 200 mm and 200
mm long respectively. By drawing the velocity and acceleration polygons, determine :
a. Velocity and acceleration of each slider, (10 Marks)
b" Angular velocity and angular acceleration of each connecting rod"
A

Fig.3(a) (20 Marks)

The stroke of,a steam engine is 400 mrn and the length of the connecting rod is 600 mm.
The crank roJates at 300 rpm clockwise direction and the crank is inclined at 300 with the
inner dead center. The center of gravity of the connecting rod is 240 mm away from the
crank end. By Klein's construction determine the following :
a. Velocity and acceleration of the piston.
b. Angularvelocity and angular acceleration of the connecting rod.
c. Velocity and acceleration at the center of gravity of the connecting rod. (20 Marks)
Contd.... 2

Page No... 2 MEl41 -;
.Y:
.

An internal combustion engine has a crank of 150 mm length and a connecting rod of
600 mm length. The crank rotates at a constant speed of 300 rpm counter clockwise.
Determine the position, velocity and acceleration of the slider when the crank angle is
450 Iiom the inner dead center position by complex algebra. (20 Marks)

a. TIie thickness of an involute gear tooth is 4.98 mm at a radius of 50.8 mm and a
pressure angle of 200. Calculate the tooth thickness on the base circie. (05 Marks)
b. The foilowing data refer to the two mating involute gears of 200 pressure angle :
Number of teeth on pinion is 30, gear ratio is 2, module is 12 mm and the speed of
the pinion is 600 rpm.
The line of contact on each side of the pitch point is half the maximum possible
length. Find the height of addendum for each gear wheel and the length of arc of
contact. Also find the maximum velocity of sliding during approach and excess.
(15 Marks)

la. Sketch and describe a bevel gear differentiaL used in automobiles. (06 Marks)
b. A fixed annular gear A and a smaller concentric rotating gear B are connected by a
compound gear CD. The gear C mesh with gear A and D with B. The compound
gears revolved in a pin on the arm R, which revolves about the axis of A and B. The
number of teeth on gears A, B and D are 150, 40 and 100 respectively. Determine the
number of teeth on gear C, if the gears A and C have twice the module of gears B and
D. How many revolutions will B make for one complete revolution of the arm R?
(14 Marks)

A cam with a base circle radius of 35 mm is rotating at a uniform speed of 100 rpm in
anti-slockwise direction. Draw the profile for the disc cam with reciprocating knife edge
follower on the center line of the cam shaft for the following follower motion.
a. Follower to move upward 3C mm with simple harmonic rnotion in 0.1 sec.
b. Follower to dwell in next 0.15 sec.
c. Follower to move upward to another 30 mm u'ith simple harmonic rnotion in
0.15 sec.
d. Follower to return to its starting position with uniform acceleration and retardation in
the remaining period of one complete revolution of the cam shaft. However, the
acceleration period is twice the retardation period.
Determine the maximum velocity and acceleration of the follower during its outward
stroke. (20 Marks)

JgJJC

Kinematics of machines Question Papers

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