MECHANICAL ENGINEERING DEPARTMENT
THEORY OF MACHINES-I
III SEMESTER
QUESTION BANK

Explain the difference between machine and mechanism.

Define ‘inversion’ of a mechanism. Name the inversions of double slider crank chain.

Prove how the grublers criterion is an extension of kutzbach’s theory.

What is instantaneous centre of rotation ?

.Why transmission angle is important ?

Prove that the minimum number of links required to form a mechanism is three.

State grashoff’s law. What is its significance in linkage design ?

Draw neat sketch of any one intermittent motion mechanism.

What is the significance of toggle positions in linkages ?

Describe with neat sketch whitworth quick return mechanism using suitable dimension and find
its
1. mobility
2.Time Ratio.

Draw any class II four bar chain (assume your own link lengths). Why it is a class II four bar
chain ? Draw neat sketch showing the extreme positions of i/p and o/p links when the shortest
link is fixed.

Find the degree of freedom of the following mechanisms shown in fig. 2.1, 2.2 and 2.3 :-
In a whitworth quick return motion as shown in fig. 3, OA is a crank rotating at 50 rpm in clockwise
direction. The dimensions of various links are OA = 150 mm. OC = 100 mm, CD = 125 mm and DR =
500 mm. determine the acceleration of slotted lever CA.

Synthesise a four bar chain in which forward stoke requires 30% more time than return stroke
during which output link of 6 cm log oscillates 450. Also find the maximum and minimum
transmission angles and show the toggle positions of the mechanism.
1.Explain type, number and dimensional synthesis.
2.Explain paucellier mechanism with a neat sketch.

A flat faced mushroom follower is operated by a uniformly rotating cam. The follower is raised
through a distance of 30 mm in 1300 rotation of cam, remains at rest for the next 200 and lowered
during further 1300 rotation of cam. The raising of the follower takes place with cycloidal motion
and lowering with equal uniform acceleration and deceleration. The least radius of cam is 25 mm
which rotates at 400 rpm in clockwise direction. Draw:-
(i) Displacement diagram
(ii) Cam profile
And determine the values of the maximum velocity and maximum acceleration during rising and
maximum velocity and uniform acceleration and deceleration during lowering of follower.
(i)
The following particulars refers to a symmetrical circular arc cam operating a flat faced
follower whose centre line passes through cam centre:-
Least Radius =3.2 cm
Nose Radius =0.7 cm
Distance between cam shaft centre and nose centre =5.00 cm
Angle of action of cam =1600
Camshaft speed =1440 rpm.
Assuming no dwell between rise and return,calculate:(i) The lift of the valve.
(ii) The flank radius.
(b) What is the condition for constant velocity Ratio? Prove it for gears.
Compare involute profile with cycloidal profile with gears.
(b) Define interference in involute gears. How it can be avoided?
Method of avoiding interference:
(c) The two 200 involute spur gears are in mesh ,having
Gear ratio =3
No. of teeth on pinion =16
Module =5 mm
Pinion speed =400 rpm
In order to avoid interference ,find:
(i) The maximum addendum
(ii) The contact ratio
(iii)Velocity of sliding.
(i) maximum addendum
(ii) contact ratio =
(iii) velocity of sliding

In an epicyclic gear train shown in Fig. 9(a) ,the wheel C is keyed to shaft B and wheel F is keyed
to shaft A. The wheels D and E rotate together on a pin fixed to the arm G. The number of teeth
on wheels C ,D ,E and F are 35, 65, 32, and 68 respectively.
If the shaft A rotates at 60 rpm and shaft B rotates at 30 rpm in opposite direction, find speed and
direction of rotation of arm G.
(b) Explain with the help of neat sketch a reverted gear train. Explain its applications.
Q.10.(a) The centre distance between two meshing spiral gears in 280 mm and angle between the shafts
650. The normal circular pitch is 14 mm and gear has a helix angle of 350. Find :(i) The no. of teeth on each wheel
(ii) The exact centre distance.
(b) For a pair of helical gears with following data, determine:(i) tooth numbers
(ii) pitch diameters
(iii) modules and normal circular pitch and axial pitch.
Data : No. of teeth of pinion =16
Speed of pinion =1800 rpm
Speed of gear =400 rpm
Centre distance =275 mm
Helix angle =220
Normal pressure angle =200

Define kinematic chain. State various types of kinematic chain?

Differentiate between Machine and Mechanism giving example of each?

Explain Robert’s law of cogent linkage?

Differentiate between class I and class II four-bar chain with Harding notation?
 What is Corroli’s component of acceleration and represent it?
 Why tangent cam is not used with flat-faced follower?
 State the difference between cycloidal and involute tooth profile?
 Define inversion and state the inversion of double - Slider crank-chain?
 State Grubler’s criteria with equation?
 Find the degree of freedom of mechanism showing fig. 2.1, 2.2, 2.3?

Derive freudenstein’s equation and explain its significance in the context of four bar mechanism?
 The following data relate to cam profile in which the follower moves the SHM during
ascent and moves with uniform acceleration and declaration during descent.
 What is pressure angle in CAM? Explain its significance.
 A symmetrical tangent cam with a least radius of 25 mm operates a roller follower of
radius 10 mm. The angle of ascent is 60˚ and total lift is 15 mm.
 Draw the coupler curves for Four-bar-Mechanism for fixing different link and give its
application?
 What is contact ratio in gears? Derive the expression for finding contact-ratio.
 Two gears are in mesh having module. 8 mm and pressure angle of 20. The larger gear
has no. of teeth 57 and smaller gear has 23 no. of teeth. The addenda on pinion and gear
wheel are equal to one module.
 What is interference in gear? Explain the method of avoiding it.
 A standard gear pair has teeth of 6 mm module and pressure angle 20. No of teeth are 15
and 60 for two gears.
Determine:1.Is interference present,
2.What is maximum permissible addendum with same pressure angle?
3.Find maximum sliding velocity of smaller wheel rotates at 1200rpm.
 Explain in brief various classification of gears.
 What is a worm gear? How is it useful?
 In epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth
respectively. If arm rotates at 250 rpm in anticlockwise direction about centre of gear A
which is fixed.
 Determine speed of gear If gear A instead being fixed, makes 300 rpm in clockwise
direction, what will be speed of gears?

Draw a neat sketch of mechanism with a higher pair having minimum number of links?

With simple example explain how structure is converted into a mechanism?

Draw neat sketch of a crank rocker four bar mechanism. Show the extreme positions of follower
and show on the fig a angle of oscillation of follower?

Explain how sliding pair is an extension of turning pair?

How many instantaneous centers a four bar chain many have? Show all four instantaneous
centers of a four bar mechanism?

With a neat sketch explain a situation in which coriolis component of acceleration will present?

With a neat sketch explain how a handpump mechanism is an inversion of single slider crank
chain?

Define couple curve. Give atleast one example of a mechanism where coupler curve is used.

What are cognates?

what is the significance of free body, diagram in static force analysis? How three force members
is dealt with in the static force analysis?

. For the fig. shown draw kinematic diagram and identity links, pairs and mobility.

What is mobility? Derive the relation for mobility of a mechanism (Kutzback’s criterion). Give at
least one example which is an exceptional case to above.

Fig (3-a) shows a kinematic diagram of a slidercrank linkage. In the position shown determine
the velocity of point of interest X in fig. when the slider drives upward at a speed of 900 m/s. Also
determine the acceleration of point C (all dim. In mm).

Draw neat sketch of any two:i) Whitworth quick return mechanism.
iii) stone crusher’s mechanism :iv) Ackerman’s steering gear.

Cam with 40 mm as minimum diameter is rotating clockwise at a uniform speed of 1000 rpm and
has to give the motion to the reciprocating roller follower 10 mm diameter as defined below :-

What is the pressure angle in cams? What is its significance? What is pitch point? Explain with a
sketch.

What are cams with specified contour? What are their applications and advantages?

With a kinematic sketch explain how a tangent cam with flat faced follower is converted into a
structure.

Compare cycloidal profile of gear with involute profile of gear teeth.

Define interference in involute gears. Also explain the various methods used in practice to avoid
interference.

The following particular refers to spur gears in mesh:

It is required to replace a gear pair consisting of 200 full depth spur gear of 30 and 75 teeth
having a module 4 mm, by helical gears of 4 mm normal module and 200 full depth. Design the
gear pair.

The following data refer to a spiral gear drive:-
Shaft angle = 900, normal module = 4 mm, Gear ratio = 2.5, Approximate centre distance = 18 cm.
For the maximum efficiency of the drive calculate,
i)
spiral angle, ii) the circular pitch of each gear, iii) no. of tooth on gears, iv) the exact centre
distance.

Explain with neat sketch the various classifications of gear trail?

. An epicyclic gear train shown in fig. (10b) is composed of a fixed annular wheel A having 150
teeth. The wheel A is meshing with wheel B which drive wheel D through an idler wheel C, D
being concentric with A. the wheels B and C are carried on an arm which revolves clockwise at
100rpm. About the axis of A and D. if the wheels B and D have 25 teeth and 40 teeth respectively,
find the number of teeth on C and speed and sense of rotation of C.

Show that the minimum number of link to form a mechanism with constrained mention is equal
to 3.

What are class I and class II dour bar chins state at last four practical application of four bar
mechanism.

what is corolis component of acceleration ? How will you decide the direction of corolis
component ?

Which follower has zero pressure angles? Justify your answer with suitable sketch.

Why tangent cam’s and
flat faced followers are
not used together ?

What are the advantages
of helical gears over spur gears?

What should be the value of minimum contact ratio in gears ? why ?

What do you understand by single enveloping and double enveloping in a worm gear set ? explain
with sketches.

What is transmission angle? Explain its significance.

What do you mean by type, number and dimensional synthesis of mechanisms? Explain with
suitable examples.

For the given mechanisms as shown in figs. 1 and 2 find the degree of freedom.

Define ‘inversion’ of mechanism. Sketch any two inversions of double slider crank chain giving
their practical applications.

Draw a straight line mechanism using Harding’s notations and find it’s mobility.

Link 2 in fig. 3 rotates counterclockwise at a velocity of 40 rad/s and accelerates at a rate of 300
rad/S2
Determine:1. velocity of points B and C
2. the rotational velocity of links 3 and 4
3. the acceleration of points B And C
4. the rotational acceleration of links 3 and 4
 Synthesize a crank-rocker mechanism with time ratio of 1.2 and rocker 7.5 cm long
oscillating though an angle of 1000 .
(i) Determine the maximum and minimum transmission angles, and state whether these are
satisfactory.
(ii) Find out the values of transmission angles in both the toggle position of the synthesized
mechanism.
 Draw neat sketch of transmission angles in both the toggle positions of synthesized
mechanism.
 What are ‘cognates’? State Robert’s law of cognate linkages.
 e four bar linkage shown in fig. 4 has a crank 2 driven by an input torque M12. An external
load p=120 N acts at angle of 400at point q on link 4. For the input particulars position of
the state its direction.
O2A=6 cm, AB = 18
cm, O4B=12cm,
O2O4 =8cm, O4Q=5 cm.
Q.6) it is required to
set out the profile of a cam to give
the following motion to
the follower :-
i) Follower to move
outwards through 31.4 mm during
1800 of cam rotation,
with cycloidal motion,
ii) Follower to return with cycloidal motion during 1800 of cam rotation.
Determine the maximum velocity and acceleration of the follower during outstroke when the
cam rotates at 2400rpm clockwise.
The base circle of the cam is 60 mm diameter and the roller diameter of the follower is 10 mm.
the axis of the roller is offset by 7.5 mm to the right. Draw the displacement diagram and
construct the cam profile.
Q.7) a. Draw a neat sketch :
i) circular arc cam with roller follower.
ii) Tangent cam with knife edge follower.
iii) Eccentric cam with flat face follower.
Q.7) b. What is undercutting in cam ? what is its significance in cam design ?
 why cycloidal motion is preferred over others in cams?
Q.8) a. What are the advantages of cycloidal gears over involute gears ?
 State and prove law of gearing.
 Two involute spur gears have a pressure angle of 200 and a module of 10 mm. the
addendum is one module. The larger gear has 50 teeth and pinion has 13 teeth. Does the
interference occur ? if it occurs, to what value the pressure angle be changed to eliminate
the interference ?
 Two shafts are to be connected by spiral gears with a velocity ratio of 3:1. The angle
between the shafts is 450 and the least distance between the shafts is 22.5 cm. the norml
module is 5 mm and the pinion is to have 20 teeth. determine the pitch circle diameters
and the spiral angle if they are of same hand.
 Two helical gears on parallal shafts havea normal circular pitch of 15 mm and a pitch line
vel. Of 4500 mm/s. if the rotational speed of pinion is 800 rpm and number of pinion teeth
is 20, what must be the helix angle ?
 In an epicyclic gear train, the internal wheels A and B and the compound wheels C and D
rotate independently about axis O. the wheels E and F rotate on pins fixed to the arm G.
E gears with A and C and F gears with B and D. All the wheels have the same module and
the numbers of teeth are
TC = 28, TD = 26, TE = TF = 18
i)
Sketch the arrangement.
ii)
Find the no. of teeth on A and B.
iii) If the rm G makes 100 r.p.m. clockwise and A is fixed, find the speed of B.
iv) If the arm G makes 100 r.p.m. clockwise and wheel A makes 10 r.p.m. counter clockwise
find the speed of wheel B.
 . What is train value? What are applications of epicyclic gear trains ?

Define degree of freedom of a mechanism? How is it determined?

Define Grashof’s law? State haw it is useful in classifying the four link mechanisms

Explain the concept of Transmission Angle?

What are the required of high speed cam?

What is a displacement diagram? Why is it necessary to draw it before drawing a cam profile?

What is the difference between Double helical and Herringbone gear?

What is pressure line and pressure angle of a gear?

What is kuzback’s Critrion for degree of freedom of plane mechanisms? In what way Grubler’s
criterion is crank mechanism?

With neat sketches explain the various inversions of slider crank mechanisms?

The following date relate to a cam operating an oscillating roller follower:-
Minimum radius of cam = 44mm
Diameter of roller = 14mm
Length of follower arm = 40mm
Distance of fulcrum centre from cam centre = 60mm
Angle of Ascent = 75
Angle of Descent = 105
Angle of dwell for follower in the highest position = 60
Angle of oscillation of follower = 28
Draw the profile of the cam if the Ascent and Descent both take place with SHM?

What are cognates? State Robert’s law of cognate linkages?

State and prove the kenedy’s theorem as applicable to I – centre of rotation of three bodies? How
is it helpful in locating various I – centers of a mechanism?

What is path of contact? Derive relation for its magnitude?

What are the main tooth profiles of gear teeth profiles of gear teeth which fulfill the law of
gearing?

What is meant by ‘Interference’ in involutes gears? Explain?

A two state worm rotating at 800 rpm drive a 26 tooth worm gear the worm has a pitch diameter
of 54 mm and a pitch of 18 mm If the coefficient of friction
is 0.06. Find:-
The helix angle of worm.
The speed gear.
The centre distance.
The lead angle for maximum efficiency.
The efficiency.
The maximum efficiency.

In the epicyclic gear train shown in fig. (8), the compound wheels ‘A’ and ‘B’ as well as internal
wheels ‘C’ and ‘D’ rotate independently about the fixed axis O. The wheels E and F rotate on the
pins fixed to arm all the wheels are of the same module. The numbers of teeth on the wheels are
( C and E are in mesh and F and D are in mesh Determine the speed of ‘C’ if :1. The wheel D is fixed and the arm (a) rotates at 200 rpm clockwise.
2. The wheel (D) rotates at 20 rpm ccw and the arm (a) rotates at 200 rpm. Clockwise.