GUJARAT TECHNOLOGICAL UNIVERSITY - mytoolbag.inmytoolbag.in/media/GTUPAPERS/1/2/AUTOMOBILE/S3/KOM.pdf · (b) Figure shows the link mechanism of a quick return mechanism of the slotted

GUJARAT TECHNOLOGICAL UNIVERSITY

AUTOMOBILE ENGINEERING (02)

/MECHANICAL ENGINEERING (19) KINEMATICS OF MACHINES

SUBJECT CODE: 2131906

B.E. 3RD

SEMESTER

Type of course: Engineering Science

Prerequisite: Zeal to learn the subject

Rationale: Kinematics of Machines is a fundamental course of mechanisms and machines. It is

intended to introduceessential elements of machines and their functionality and engenders skills for

kinematics analysis of machine elements like linkages, cams, and gears, within the general machine

design context.

Teaching and Examination Scheme:

Teaching Scheme Credits Examination Marks Total

Marks L T P C Theory Marks Practical Marks

ESE

(E)

PA (M) PA (V) PA

(I) PA ALA ESE OEP

3 1 0 4 70 20 10 30 0 20 150

Content:

Sr.

No Topic Lectures Weightage

1 Introduction of Mechanisms and Machines:

Concepts ofKinematics and Dynamics, Mechanisms and Machines,

Planar and Spatial Mechanisms, Kinematic Pairs, Kinematic Chains,

Kinematic Diagrams, Kinematic Inversion, Four bar chain and Slider

Crank Mechanisms and their Inversions, Degrees of Freedom,Mobility

and range of movement - Kutzbach and Grubler’s criterion, Number

Synthesis, Grashof’s criterion

4

10%

2 Synthesis and Analysis of Mechanisms:

Position analysis (Analytical Techniques): Loop closure (Vector

Loop) representation of linkages, Position analysis of Four bar, slider

crank and inverted slider crank mechanisms, Coupler curves, Toggle

and Limit Position, Transmission angle, Mechanical Advantage.

Dimensional Synthesis: Definitions of Type, Number and

Dimensional Synthesis, Definitions ofMotion, Path and Function

generation, precision position, Chebychev spacing, structural error,

Freudenstein’s equation, two and three position synthesis (function

generation only) of four bar and slider crank mechanisms by graphical

and analytical methods.

Velocity and Acceleration Analysis: Velocity and Acceleration

Diagrams, Instantaneous Centre of Velocity, Rubbing Velocity,

Velocity and Acceleration Images, Corioli’s component of

acceleration.

Special Mechanisms: Straight line mechanism, Indicator diagrams,

4

6

6

40%

Hooke’s Joint, Steering Mechanisms. 3

3 Gears and Gear Trains:

Gears:Terminology, Law of Gearing, Characteristics of involute and

cycloidal action, Interference and undercutting, centre distance

variation, minimum number of teeth, contact ratio, spur, helical, spiral

bevel and worm gears, problems.

Gear Trains: Synthesis of Simple, compound & reverted gear trains,

Analysis of epicyclic gear trains.

5

5

25%

4 Cams and Followers:

Introduction: Classification of cams and followers, nomenclature,

displacement diagrams of follower motion, kinematic coefficients of

follower motion.

Synthesis and Analysis: Determine of basic dimensions and synthesis

of cam profilesusing graphical methods, cams with specified contours.

3

6

25%

References:

1. Theory of Machines and Mechanisms (3/e 2009, 2013 Impression) Uicker J J Jr., Pennock G R,

Shigley J E, Oxford Press.

2. Kinematics and Dynamics of Machinery (1/e 2009, 2013 Reprint) Norton R L, McGraw-Hill

3. Mechanism and Machine Theory (2013 Reprint), Ambekar, A G, Prentice Hall

4. Theory of Machines, Singh Sadhu, Pearson Education

5. Theory of Machines, Rattan S S, Tata McGraw-Hill

Web Resources

http://kmoddl.library.cornell.edu/

Course Outcomes:

1. Students will be able to identify functional characteristics various machine elements.

2. Students will demonstrate the ability to synthesize and analyse mechanisms.

3. Students will demonstrate ability to design and analyse cams.

4. Students will demonstrate the ability analyse gear trains.

Tutorials and Project Work:

1. Tutorials should be designed to cover contents of the theoretical portion.

2. In addition to tutorials assignments should be given to students for additional practice and

demonstrate verities in a given topic.

3. Students should be given projects which may include development of computer codes of

analytical methods, computer models and computer aided simulations, and development of

functioning prototypeof various mechanisms.

ACTIVE LEARNING ASSIGNMENTS: Preparation of power-point slides, which include videos,

animations, pictures, graphics for better understanding theory and practical work – The faculty will

allocate chapters/ parts of chapters to groups of students so that the entire syllabus to be covered. The

power-point slides should be put up on the web-site of the College/ Institute, along with the names of

the students of the group, the name of the faculty, Department and College on the first slide. The best

three works should submit to GTU.

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III (NEW) - EXAMINATION – SUMMER 2017

Subject Code: 2131906 Date: 09/06/2017 Subject Name: Kinematics of Machines Time: 10:30 AM to 01:00 PM Total Marks: 70 Instructions:

1. Attempt all questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks.

Marks

Q-1 Short Questions 14 1 Which of the following mechanism is used to enlarge or reduce the size of

drawing?

(a) Pantograph (b) Graphometer (c) Oscillograph (d) Clinograph

2 A cylindrical Pair allows ___ degree of freedom

(a) 2 (b) 3 (c) 4 (d) 1

3 The kinematic chain having N links will have ______inversions

(a) N-1 (b) N (c) N-2 (d) N-3

4 A ball and socket Joint form a ________ pair.

5 A negative degree of freedom for a linkage means

(a) constrained motion (b) Unconstrained motion

(c) Statistically indeterminate structure (d) none of these

6 The total number of instantaneous centres for a mechanism containing n links

is given by _________.

7 The coriolis component of acceleration acts

(a) parallel to sliding surface (b) Perpendicular sliding surface

(c) at 450 to the sliding surface (d) none of these

8 The moment on a pulley which produces he rotation of the pulley called

(a) work (b) Energy

(c) momentum (d) torque

9 State the relation for centrifugal tension in belt.

10 Hour and minute hand are connected in a clock mechanism by means of

(a) simple gear train (b) Epicyclic train

(c) Reverted gear train (d) Non of above

11 The contact ratio for gears is_________.

(a) zero (b) less than one (c) greater than one

12 For gears : Diametral pitch X Circular pitch = _________

13 Define Pitch point for Cam.

14 Define Transmission angle

Q.2 (a) Draw a neat sketch of following mechanism with proper notation of the links.

1. Four bar crank and lever mechanism.

2. Four bar rocker- rocker mechanism.

04

(b) Differentiate between Machine and Structure with suitable example. 04 (c) Explain inversion method of synthesis for four bar mechanism using Two

point and Three Point. 06

OR (c) Explain Relative pole method of synthesis for slider crank mechanism

using Two point and Three Point. 06

Q.3 (a) Derive an empirical relation for the velocity ratio of two shaft connected by

Hook’s Joint. 06

(b) Figure shows the link mechanism of a quick return mechanism of the slotted

lever type the various dimensions of which are

OA= 400 mm, OP = 200 mm, AR = 700 mm, RS = 300 mm.

For the configuration shown, determine the velocity of cutting tool as S and

angular velocity of the link RS. The crank OP rotates at 210 rpm.

08

OR Q.3 (a) Derive law of correct steering for Ackerman Steering Gear mechanism 06

(b) In a slider crank mechanism, the crank is 480 mm long and rotates at 20 rad/s

in the counter clockwise direction. The length of connecting rod is 1.6 m.

When the crank turns 60o from the inner dead centre, determine the

1. Velocity of slider

2. Velocity of point E located at a distance 450 mm on the connecting

rod extended

08

Q.4 (a) State the relation for Displacement, Velocity and Acceleration for following

motion of follower

1. Uniform velocity, 2. Simple harmonic motion

04

(b) A cam with 30 mm as minimum diameter is rotating clockwise as a uniform

speed of 1200 rpm and has to give the motion to the roller follower 10 mm

diameter as defined below:

1. Outward stroke of 25 mm during 120o of cam rotation with equal uniform

acceleration and retardation

2. Dwell for 60o cam rotation

3. Return to its initial position during 90o of cam rotation with equal uniform


4. Dwell for the remaining 90o cam rotation

Layout the cam profile when the roller axis is offset to right by 5 mm.

10

OR Q.4 (a) State the relation for Displacement, Velocity and Acceleration for following

motion of follower

1. Uniform acceleration and retardation

2. Cyclodial motion

04

(b) A cam with 25 mm as minimum diameter is rotating clockwise as a uniform

speed of 500 rpm and has to give the motion to the flat faced follower defined

below:

1. Outward stroke of 20 mm during 120o of cam rotation with simple

harmonic motion

2. Dwell for 30o cam rotation

3. Return to its initial position during 120o of cam rotation with equal uniform


4. Dwell for the remaining 90o cam rotation

5. Layout the cam for the above mentioned motion of follower.

10

Q.5 (a) Derive the empirical relation for minimum number of teeth to avoid 05

interference in gears. (b) If the number of teeth in the gears 1 and 2 are 60 and 40, the module pitch =3

mm, the pressure angle 20o and the addendum = 0.318 of circular pitch

determine the velocity of sliding when the contact is at the tip of the tooth of

gear 2 and the gear 2 rotates at 800 rpm.

09

OR Q.5 (a) Determine the velocity ratio of differential gear box. 05

(b) Figure shows epicyclic gear train. Gear A is fixed to a frame and is therefore

stationary. The arm B and gears C and D are free to rotate on the shaft. Gears

A, C and D have 100,101 and 99 teeth respectively. Pitch circle diameters of

all are same so that the planet gear P meshes with all of them. Determine the

revolutions of gears C and D for one revolution of the arm B.

09


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III(New)• EXAMINATION – WINTER 2016

Subject Code:2131906 Date:09/01/2017

Subject Name:Kinematics of Machines

Time: 10:30 AM to 01:00 PM Total Marks: 70 Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

MARKS

Q.1 Short Questions 14

1 Find the number of degrees of freedom of a cylinder which is located in a V-

block

2 Define completely constrained motion

3 Define Resistant bodies

4 Define Kinematics of Machines

5 Why Roller follower is preferred over knife edge follower?

6 State any two types of motion of the follower.

7 State two applications of Cam and Followers

8 Define Inversion of mechanism

9 Which type of gear box is used in automobiles?

10 Calculate speed of driving shaft in compound gear train, if the drivers have 50,

60, 80 and 100 teeth and followers have 18, 40, 60 and 80 teeth. Speed of

driven shaft is 150 rpm

11 Why is double Hooke's joint used?

12 What do you understand by synthesis?

13 Difference between Velocity and Speed.

14 One quaternary joint is equal to how many binary joints?

Q.2 (a) A double-parallelogram mechanism is shown in the figure. Note that PQ is

a single link. The mobility of the mechanism is

03

(b) Match the items in columns I and II

Column I Column II

P. Higher Kinematic Pair 1. Grubler’s Equation

Q. Lower Kinematic Pair 2. Line contact

R. Quick Return Mechanism 3. Surface contact

S. Mobility of a Linkage 4. Shaper

04

(c) Explain chebyshev spacing method for location precision point position in four

bar chain mechanism. 07

OR

(c) Design a four bar mechanism with input link a, output link c. Angle ɵ and φ for

three successive positions are given in table. Use Freudenstein’s method.

Draw the mechanism in second position.

Position 1 2 3

ɵ 30 50 70

φ 40 75 100

07

Q.3 (a) A simple quick return mechanism is shown in the figure. The forward toreturn

ratio of the quick return mechanism is 2:1. If the radius of crank O1Pis 125

mm, then what will be the distance‘d ’ (in mm) between the crank centre to

lever pivot centre point ?

04

(b) Using relative velocity method to find the absolute velocity of the slider E in

the mechanism as shown in fig., when the crank rotates at 60 rpm.

O1A=5cm, O2B=12cm, AB= 27cm, O2D=9cm, DE= 18cm

10

OR

Q.3 (a) A solid disc of radius ‘r’ rolls without slipping on a horizontal floor

withangular velocity ω and angular acceleration α.

Determine magnitude of theacceleration of the point of contact on the disc.

04

(b) A Quick return mechanism is shown in fig. Link 2 rotates at 20 rad/sec. Draw

the velocity and acceleration diagram. Given BC=25 cm, OA=15 cm.

10

Q.4 (a) Types of Cam with sketch 04

(b) A cam operates an offset follower. The least radius of the cam is 50mm, roller

diameter is 30mm, and offset is 20mm. The cam operates at 360 rpm. The

angle of ascent is 480, angle of dwell is 420 and angle of descent is 600. The

motion is SHM during ascent and uniform acceleration and retardation during

descent. Draw the cam profile. Consider lift of cam as 40 mm.

Also calculate max velocity and acceleration during descent.

10

OR

Q.4 (a) Types of follower with sketch 04

(b) A cam operates a flat-faced follower having uniform acceleration and

retardation during ascent and descent. The least radius of the cam is 50mm.

During descent, the retardation period is half of the acceleration period. The

ascent lift is 37.5mm. The ascent is for 1/4th period, dwell for 1/4th , descent for

1/3th, and dwell for the remaining 1/6th period. The cam rotates at 600 rpm.

Find the max velocity and acceleration during ascent and descent.

Draw the cam profile.

10

Q.5 (a) Comparison between Involute and Cycloidal tooth profile. 03

(b) Fundamental Law of Gearing. 04

(c) Two 200 involute gears in mesh have a gear ratio of 2 and 20 teeth on the pinion. The

module is 5mm and the pitch line speed is 1.5 m/s. Assuming addendum to be equal to

one module, find (a) angle turned through by pinion when one pair of teeth are in

mesh, and (b) maximum velocity of sliding.

07

OR

Q.5 (a) State any three application of Gear Train. 03

(b) How the direction of rotation of driven shaft can be found out if it has even and

odd number of gears in a gear train? Explain with sketch. 04

(c) In a reverted epicyclic gear train, the arm F carries two wheels A and D and a

compound wheel B, C. The wheel A meshes with wheel B and the wheel D

meshes with wheel C. ZA=80, ZD=48 and ZC=72. Find the speed and direction

of wheel D when wheel A is fixed and arm F makes 240 rpm clockwise.

07

***********

1


GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–III(New) EXAMINATION – SUMMER 2016


Subject Name:Kinematics of Machines Time:10:30 AM to 01:00 PM Total Marks: 70 Instructions:


2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks.

MARKS

Q.1 Short Questions: 14

1 What is the number of degree of freedom (n) when the

mechanism forms a structure?

2 In a kinematic chain, a quaternary joint is equal to how many

binary joints?

3 Define Normal Pitch relating to helical gears.

4 What do you understand by Type Synthesis?

5 Which type of gear train is used to connect minute hand to

hour hand in clock mechanism?

6 What is the product of diametral pitch and circular pitch?

7 Which type of gears are used to connect two non-parallel non-

intersecting shaft?

8 Which condition should be fulfilled by pair of gears for

correct gearing?

9 Define: Kinematic Chain

10 Which type of cam follower is extensively used in air-craft

engines?

11 The size of cam depends upon

(a) base circle (b) pitch circle

(c) prime circle (d) pitch curve

12 Which type of pair has been made by the lead screw of a lathe

with nut?

13 Which mechanism is used to enlarge or reduce the size of

drawing?

14 Write down the equation about the relation between number

of pairs (p) forming the kinematic chain and the number of

links (l).

Q.2 (a) Explain the terms:

1. Lower pair 2. Higher pair 3. Kinematic link 03

(b) Sketch and describe four bar chain mechanism. 04

(c) What are quick return motion mechanisms? Where are they

used? Discuss the functioning of any one of them. 07

OR

(c) A crank and slotted lever mechanism used in shaper has a

center distance of 300 mm between the center of oscillation of

the slotted lever and the center of rotation of the crank. The

radius of the crank is 120 mm. Find the ratio of the time of

cutting to the time of return stroke.

07

Q.3 (a) Give a neat sketch of the straight line motion “Hart 03

2

Mechanism”.

(b) In a Davis steering gear, the distance between the pivots of the

front axle is 1.2 meters and the wheel base is 2.7 meters. Find

the inclination of the track arm to the longitudinal axis of the

car, when it is moving along a straight path.

04

(c) Explain the Freudenstein’s method of three point synthesis of

mechanisms. 07

OR

Q.3 (a) What is the condition for correct steering? 03

(b) State and prove ‘Aronhold Kennedy’s Theorem’ of three

instantaneous centres. 04

(c) A four bar chain mechanism is to be designed, by using three

precision point to generate the function

Y = X1.5 for the range 1 ≤ x ≤ 4

Assuming 300 starting position and 1200 finishing position for

the input link and 900 starting position and 1800 finishing

position for the output link, find the value of x , y , ɵ and φ corresponding to three precision point.

07

Q.4 (a) What do you understand by simple, compound, and epicyclic

gear trains? 03

(b) Explain the term “Interference” as applied to gears? 04

(c) In an epiyclic gear train, an arm carries two gears A and B

having 36 and 45 teeth respectively. If the arm rotates at 150

r.p.m. in the anticlockwise direction about the centre of the

gear A which is fixed, Determine the speed of gear B. If the

gear A instead of being fixed, makes 300 r.p.m. in the

clockwise direction what will be the speed if gear B?

07

OR

Q.4 (a) Explain the terms in relation to gears:

(1) Module (2) Circular Pitch (3) Pressure Angle. 03

(b) State and prove the “Law of gearing” 04

(c) A pair of spur gears with involute teeth is to give a gear ratio

of 4:1. The arc of approach is not to be less than the circular

pitch and the smaller wheel is driver. The angle of the

pressure is 14.50 . Find: (1) The least number of teeth that can

be used on each wheel, and (2) The addendum of the wheel in

terms of the circular pitch?

07

Q.5 (a) Define the following terms related to cam.

(i) Base circle

(ii) Pitch circle

(iii) Pressure angle

03

(b) Draw the displacement, Velocity and Acceleration for

follower when its moves with cycloidal motion. 04

(c) A cam drives a flat reciprocating follower in the following

manner:

During first 1200 rotation of the cam, follower moves outward

through a distance of 20 mm with S.H.M. The follower dwells

during next 300 of cam rotation. During next 1200 rotation of

the cam, the follower moves inward with S.H.M. The follower

dwells for the next 900 of cam rotation. The minimum radius

of the cam is 25 mm. Draw the profile of the cam.

07

OR

3

Q.5 (a) Why a roller follower is preferred to that of a knife-edged

followers. 03

(b) Explain with sketches the different types of cams and

followers. 04

(c) Draw the displacement, velocity and acceleration diagrams for

a follower when it moves with (i) Uniform acceleration and

retardation (ii) Cycloidal motion.

07

*************


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III (New) EXAMINATION – WINTER 2015


Subject Name: KINEMATICS OF MACHINES

Time: 2:30pm to 5:00pm Total Marks: 70 Instructions:




MARKS

Q.1 Short Questions 14

1 What do you understand by synthesis?

2 Differentiate lower pair and higher pair.

3 State Grashoff’s criterion

4 Differentiate Linear acceleration and angular acceleration

5 How many degree of freedom a structure have?

6 If a point moves along a straight line which is rotating, what will be the

tangential component of acceleration?

7 When crank rotates with uniform velocity then what will be the tangential

acceleration?

8 Define Conjugate profile

9 Define : Backlash in Gear

10 What is the product of Circular Pitch and Diametral Pitch

11 What will be the minimum value of contact ratio for Gear?

12 In which gear train the axes of the first and last gear are co-axial?

13 Define the term pressure angle in cam

14 Why roller follower is preferred over a knife edge follower?

Q.2 (a) Explain Limitations of Grubler’s Criteria 03

(b) Explain path generation. 04

(c) A four bar chain mechanism is to be designed, by using three precision point to

generate the function y = x1.5 for the range 1 ≤ x ≤ 4

Assuming 300 starting position and 1200 finishing position for the input link

and 900 starting position and 1800 finishing position for the output link, find the

value of x , y , ɵ and φ corresponding to three precision point.

07

OR

(c) Derive the equation of displacement, velocity and acceleration of slider in a

slider crank mechanism by analytical method 07

Q.3 (a) A crank and slotted lever mechanism used in a shaper has a centre distance of

300 mm between the centre of oscillation of the slotted lever and the centre of

Rotation of the crank. The radius of the cranks is 120 mm. Find the ratio of the

Time of cutting to the time of return stroke

04

(b) The length of various links of a mechanism shown in Fig. are as follows:

AB = DE =150 mm, BC = CD = 450 mm, EF = 375 mm

The crank AB makes an angle of 450 with horizontal and rotates about A in the

clockwise direction at a uniform speed of 120 rpm. The lever DC oscillates

about the fixed point D, which is connected to AB by the coupler. The block F

moves in the horizontal guide, being driven by the link EF.

Determine 1. Velocity of the block F 2. Angular velocity of DC, and 3.

Rubbing speed at the pin C which is 50 mm in diameter.

10

OR

Q.3 (a) The hook’s joint connect two shafts whose axes are intersect. If the driving shaft

rotates uniformly at 500 rpm and variation in the speed of driven shaft is not to exceed

6 % of mean speed, find the maximum possible inclination between two shafts.

03

(b) Explain Angular Velocity Theorem 04

(c) Derive an expression for the magnitude and direction of Coriolis component of

acceleration

07

Q.4 (a) Define the following terms related to cam.

(i) Base circle

(ii) Pitch circle

(iii) Pressure angle

(iv) Stroke of the follower

04

(b) Draw the profile of a cam rotating with an oscillating roller follower to the

specification given below:

1. Follower moves outwards through an angular displacement of 200 during

first 120° of cam rotation.

2. Follower returns to its original position during next 120° of cam rotation

3. Follower to dwell during the rest of cam rotation.

The distance between the pivot center and roller center is 120mm, The distance

between the pivot center and cam axis is 130mm , minimum radius of cam is

40mm, radius of roller is 10 mm The displacement of the follower is to take

place with SHM during outward stroke and inward stroke

10

OR

Q.4 (a) Draw the displacement, Velocity and Acceleration for follower when its moves

with cycloidal motion.

04

(b) A cam rotating in clockwise direction at a uniform speed of 1000 rpm is

required to give a roller follower the motion defined below:

1. Follower moves outwards through 50 mm during 120° of cam rotation.

2. Follower dwells for next 60° of cam rotation

3. Follower returns to its original position during next 90° of cam rotation

4. Follower dwells for rest of cam rotation

The minimum radius of the cam is 50 mm and the diameter of roller is 10 mm.

The line of stroke of follower is off-set by 20 mm from the axis of the cam

shaft. If the displacement of the follower is to take place with uniform and

equal acceleration and retardation on both the strokes. Draw the profile of the

cam and find the max velocity and acceleration during the outwards and return

strokes.

10

Q.5 (a) Explain any three terminology of gear tooth with neat sketch. 03

(b) Explain with the neat sketch the “sun and planet wheel”. 04

(c) Figure shows an epicyclic gear train knows as Ferguson’s paradox. Gear A is fixed to

the frame and is, therefore, stationary. The arm B and gears C and D are free to rotate

on the shafts S. Gear A, C and D have 100, 101 and 99 teeth respectively. The planet

gear has 20 teeth. The pitch circle diameters of all are the same so that the planet gear

P meshes with all of them. Determine the revolutions of gears C and D for one

revolution of the arm B.

07

OR

Q.5 (a) What do you understand by the term “interference” as applied to the gear? 03

(b) Explain with a neat sketch the “Differential Gear Box” 04

(c) A pinion having 30 teeth drives a gear having 80 teeth. The profile of gear is

involute with 200 pressure angle, 12 mm module and 10 mm addendum. Find

the contact ratio.

07

***********

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–III • EXAMINATION – WINTER • 2014

Subject Code: 2131906 Date: 30-12-2014

Subject Name: Kinematics of Machines

Time: 02.30 pm - 05.00 pm Total Marks: 70 Instructions:




Q.1 (a) Define and discuss: kinematic link, kinematic pair, and kinematic chain. 07

(b) Sketch and explain Whitworth quick return mechanism. 07

Q.2 (a) Describe Klein‟s construction with an example. 07

(b) The crank of a slider crank mechanism rotates clockwise at a constant speed of

300 rpm. The crank is 150 mm and connecting rod is 600 mm long. Determine

1. Linear velocity and acceleration of midpoint of connecting rod

2. Angular velocity and angular acceleration of the connecting rod, at a

crank angle of 45o from inner dead centre position.

07

OR

(b) A crank and rocker mechanism ABCD has the following dimensions.

AB = 0.75m, BC = 1.25m, CD = 1m, AD = 1.5m, E is the midpoint of the

coupler link BC. AD is the fixed link. Crank AB has a angular velocity of 20

rad/s counter clockwise and deceleration of 280 rad/s2 at the instant angle DAB

= 60o find

1. Instantaneous linear velocity and acceleration of midpoint E of link BC.

2. Instantaneous angular velocity and acceleration of link CD.

07

Q.3 (a) Explain the Freudenstein‟s Equation for four bar chain mechanism. 07

(b) Design a four bar mechanism with input link „a‟ , coupler link ‟b‟ and output link

„c‟. angles θ and Φ for three successive position are given in table below:

1 2 3

θ 20o 35

o 50

o

Φ 35o 45

o 60

o

07

Using Freudenstein‟s Equation find out other link lengths b, c and d. assume link

length a = 1.

OR

Q.3 (a) Explain two position synthesis of four bar chain mechanism by relative pole

method

07

(b) A double Hooke‟s joint is used to connect 2 shafts in the same plane and the

Intermediate shaft is inclined at an angle of 20° to both the shafts. If driving

shaft Rotates of 250rpm, find maximum and minimum speed of intermediate and

driven shafts.

07

Q.4 (a) Enlist different type of gear train .Explain compound gear train with neat sketch

.Also derive the equation of the velocity ratio for compound gear train.

07

2

(b) An Epicyclic gear train is composed of fixed annular wheel “A” having 300

teeth. Meshing with A is wheel X which drives wheel Z through idle wheel Y,

wheel Z being concentric with A. wheels X and Y are carried on an arm E which

revolves clockwise at 120 rpm about the axis of A and Z. if the wheel X and Z

have 50 and 80 teeth respectively .Determine the number of teeth on Y. and rpm

of Y.

07

OR

Q.4 (a) Derive an expression for the length of path of contact for two involutes profile

gear in mesh.

07

(b) A pair 20o

involute gears has module of 5 mm. the pinion has 20 teeth and gear

has 60 teeth. Addendum on the pinion and gear wheel in terms of module is 1.

Find the followings.

(i) Number of pairs in contact

(ii) Angle turned through by the pinion and gear wheel for one pair in

contact.

07

Q.5 (a) Classify followers and explain with neat sketch. 07

(b) Draw the cam operating knife edge follower from following data

(i) Follower to move out through distance of 20mm during 120°.

(ii) Follower to dwell for next 60°.

(iii) Follower to return to its initial position during 90°.

(iv) Follower to dwell for remaining cam rotation

The cam rotates at 500rpm .The minimum radius of cam is 40mm and line of

follower is offset 15mm from the axis of the cam and displacement to take place

with uniform acceleration and retardation both inward and outward stroke .

07

OR

Q.5 (a) Derive the condition for correct steering. Sketch and show the Davis steering

mechanism and discuss their advantages.

07

(b) What is straight line motion mechanism & give its classification. Explain any one

in brief.

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–IV (OLD) - EXAMINATION – SUMMER 2017

Subject Code: 141902 Date: 08/06/2017


Time: 10:30 AM to 01:00 PM Total Marks: 70 Instructions:




Q.1 (a) Define :

(1) Higher Pair

(2) Kinematic Link

(3) successfully Constrained Motion

(4) Degree of freedom

07

(b) Enlist different types of steering gear mechanism of automobile. Explain any

one in detail with neat sketch. 07

Q.2 (a) Explain modified Scott Russell mechanism with the help of neat sketch.

07

(b) Sketch and explain the various inversions of a Double slider crank chain.

07

OR

(b) Explain Klein’s construction method in detail with neat sketch. 07

Q.3 (a) What is gear train? Give classification of it and Explain epicyclic gear train in

detail.

07

(b) Differentiate between involute and cycloidal profile of gear teeth. 07

OR

Q.3 (a) Explain the interference in involute gears. How interference should be

prevented? 07

(b) Derive the expression for the length of path of contact and length of arc of

contact. 07

Q.4 (a) Explain the following terms as applied to cam.

1. Base circle 2. Pitch circle 3. Pressure angle 4. Stroke of follower. 04

(b) A cam rotating clockwise at a uniform speed of 1000 r.p.m. is required to give a

roller follower the motion defined below.

1. Follower to move outwards through 50 mm during 120° of cam rotation,

2. Follower to dwell for next 60° of cam rotation

3. Follower to return to its starting position during next 90° of cam rotation

4. Follower to dwell for the rest of the cam rotation.

The minimum radius of the cam is 50 mm and the diameter of roller is 10

mm. the line of stroke of the follower is off-set by 20 mm from the axis of

the cam shaft. If the displacement of the follower takes place with uniform

and equal accelerations and retardation on both the outward and return

strokes, draw profile of the cam.

10

OR

Q.4 (a) Discuss relative merits and demerits of belt, rope and chain drive for

transmission of power.

07

2

(b) What are different types of chains? Explain with neat sketches of power

transmission chains. 07

Q.5 (a) Describe the construction and working of a centrifugal clutch 07

(b) A square threaded bolt of root diameter 22.5 mm and pitch 5 mm is tightened by

screwing a nut whose mean diameter of bearing surface is 50 mm. if coefficient

of friction for nut and bolt is 0.1 and for nut and bearing surface is 0.16 , find the

force required at the end of a spanner 500 mm long when the load on the bolt is

10 KN.

07

OR

Q.5 (a) What is centrifugal tension in a belt? How does it affect the power transmitted?

Also explain the phenomena of slip and creep. 07

(b) Derive equation for finding out the limiting tension ratio in a belt drive.

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–IV(OLD) • EXAMINATION – WINTER 2016


Subject Name:Kinematics Of Machines

Time: 02:30 PM to 05:00 PM Total Marks: 70 Instructions:




Q.1 (a) What is meant by inversion of mechanism? Sketch double slider cranks chain &

draw its inversion.

07

(b) Define the following terms.(1)Link(2)Higher pair(3)Ternary Joint(4)Locked

chain(5)constrained Motion(6)Degree of freedom(7)Quaternary link.

07

Q.2 (a) Classify synthesis problems. 07

(b) Explain briefly dimensional synthesis. 07

OR

Q.2 (a)

Write Short Note on Straight-Line Mechanism. 07

07 (b) Explain cariole’s component of acceleration.

Q.3 (a) Explain the Phenomenon of “slip”& “creep” in a belt drive. 07

(b) Explain instantaneous centre method for finding out velocity of a point on link. 07

OR

Q.3 (a) A Crank & rocker mechanism ABCD has the following dimensions.

AB=0.85m,BC=1.35m,CD=1m,AD=1.5m.Eis the midpoint of the coupler link

BC.AD is the fixed link. Crank AB has an angular velocity of 20rad/sec counter

clockwise & a deceleration of 280rad/sec2 at the instant angle

DAB=60°.Find(1)instantaneous linear velocity & acceleration of midpoint E of

link BC.(2) instantaneous angular velocity & acceleration of link CD.

07

(b) State & prove Kennedy’s theorem. 07

Q.4 (a) State & prove the law of gearing. 07

(b) Explain Epicycle gear train with neat sketch. 07 OR

Q.4 (a) Explain terminology of gear tooth with neat sketch. 07

(b) Two parallel shafts, about 60cm apart are to be connected by spur wheels. one

shaft is to run at 360rpm & the other at 120rpm.Design the wheels, if the

circular pitch is to be 25mm

07

Q.5 (a) List different types of gear train. Explain simple gear train with neat sketch.

Derive the equation of velocity ratio for simple gear train.

07

(b) A pinion having 20 teeth of in volute form,20˚pressure angle & 6mm module

drives a gear having 40 teeth. If addendum=module find(1)addendum & pitch

circle radius of the two gears(2)length of path of approach(3)length of path of

contact(4)Arc of contact.

07

OR

Q.5 (a) Classify followers & explain with neat sketch. 07

2

(b) A cam operates a flat faced follower which moves with cycloid motion during

ascent & descent. The further specifications are (1)Min radius of

cam=30mm(2)Angle of ascent=120°(3)Angle of dwell=60(4)Lift of

follower=40mm(5)Angle of decent=90(6)speed of cam=400rpm

Draw cam profile. Find maximum velocity & acceleration during ascent

&decent.

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–IV EXAMINATION – SUMMER 2016

Subject Code:141902 Date:08/06/2016 Subject Name:Kinematics Of Machines Time:10:30 AM to 01:00 PM Total Marks: 70 Instructions:


Q.1 (a) Sketch and explain the various inversions of a slider crank chain. 07

(b) Explain Grubler’s criterion for determining degree of freedom for mechanisms. 07

Q.2 (a) In a slider crank mechanism, the lengths of crank OB and connecting rod AB

are 100 mm and 400 mm respectively. The crank is 450 from IDC position and

rotates clockwise with a uniform speed of 96 rpm. Locate all the instantaneous

centres of the mechanism and find: (1) Velocity of the slider A (2) Angular

velocity of the connecting rod AB.

07

(b) Derive an expression for the magnitude and direction of coriolis component of

acceleration.

07

OR

(b) Explain the kinematic analysis of I.C. engine mechanism by Klien’s

construction when the angular velocity of crank is uniform.

07

Q.3 (a) Following data is given for a rope pulley transmitting 24 kW :

Diameter of pulley = 400 mm, Speed = 110 R.P.M., Angle of groove = 450,

Angle of lap on smaller pulley = 1600, Coefficient of friction = 0.28, Number of

ropes = 10, Mass in kg/m length of ropes = 53C2 and working tension is limited

to 122C2 KN, where C is girth of rope in metres. Find initial tension and

diameter of each rope.

07

(b) Explain with neat sketches, the classification of power transmission chains. 07

OR

Q.3 (a) An open belt running over two pulleys 240 mm and 600 mm diameter connects

two parallel shafts 3 metres apart and transmits 4 kW from the smaller pulley

that rotates at 300 R.P.M. Coefficient of friction between the belt and the pulley

is 0.3 and the safe working tension is 10N per mm width. Determine: (1)

minimum width of the belt (2) initial belt tension (3) length of the belt required.

07

(b) Derive an expression for ratio of driving tensions for a V-belt drive. 07

Q.4 (a) Two involute gears of 200 pressure angle are in mesh. The number of teeth on

pinion is 20 and the gear ratio is 2. If the pitch expressed in module is 5 mm and

the pitch line speed is 1.2 m/s, assuming addendum as standard and equal to one

module. Find: 1. The angle turned through by pinion when one pair of teeth is in

mesh 2. The maximum velocity of sliding.

07

(b) Explain the interference in involute gears. How interference should be

prevented?

07

OR

Q.4 (a) The cutter of a broaching machine is pulled by square threaded screw of 55mm 07

2

external diameter and 10mm pitch. The operating nut takes the axial load of 400

N on a flat surface of 60 mm internal diameter and 90 mm external diameter. If

the coefficient of friction is 0.15 for all contact surfaces on the nut, determine

the power required to rotate the operating nut, when the cutting speed is 6

m/min.

(b) Describe the construction and working of a centrifugal clutch. 07

Q.5 (a) Draw the displacement, velocity and acceleration diagrams for a follower when

it moves with (i) Uniform Velocity (ii) Simple Harmonic Motion

07

(b) Design a profile of cam for operating the exhaust valve of an oil engine. It is

required to give equal uniform acceleration and retardation during opening and

closing of the valve each of which corresponds to 600 of cam rotation. The

valve must remain in the fully open position for 200 of cam rotation.

The lift of the valve is 37.5 mm and the least radius of the cam is 40 mm. The

follower is provided with a roller of radius 20 mm and its line of stroke passes

through the axis of the cam.

07

OR

Q.5 (a) What is over hauling and self-locking screws? Derive an expression for

efficiency of self-locking screws.

07

(b) Explain the various types of gear trains. 07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–IV EXAMINATION – WINTER 2015

Subject Code: 141902 Date:04/01/2016


Time: 02:30pm to 05:00pm Total Marks: 70 Instructions:




Q.1 (a) Define: Kinematic link, Kinematic chain, Mechanism, Degrees of freedom, Lower

pair, Higher pair, Inversion.

07

(b) What is the condition for correct steering? Sketch and explain any one type of

steering mechanism with its advantages.

07

Q.2 (a) What are straight line mechanisms? Describe one type of exact straight line motion

mechanism with the help of a sketch.

07

(b) Explain with a neat sketch the “Differential gear box”. 07

OR

(b) Explain various inversion of a slider-crank mechanism with the help of sketch. 07

Q.3 (a) State and prove the law of gearing. 07

(b) Two 200 involute spur gear mesh externally and give a velocity ratio of 3. The

module is 3 mm and the addendum is equal to 1.1 modular. If the pinion rotates at

120 rpm, Determine: (1) Minimum number of teeth on each wheel to avoid

interference (2) Contact ratio.

07

OR

Q.3 (a) What is gear train? Give classification of it and Explain reverted gear train with

sketch also define its velocity ratio.

07

(b) Two shafts A and B are co-axial. Gear C (50teeth) 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 rpm find the speed of shaft B.

07

Q.4 (a) The mean diameter of a square threaded screw jack is 50 mm. The pitch of the

thread is 10 mm. The coefficient of friction is 0.15. What force must be applied at

the end of a 0.7 m long lever, which is perpendicular to the longitudinal axis of the

screw to raise a load of 20kN and to lower it?

07

(b) Describe with a neat sketch the working of a single plate clutch. 07

OR

2

Q.4 A cam is to be designed for a knife edge follower with the following data:

1. Cam lift=40 mm during 900 of cam rotation with SHM.

2. Dwell for the next 300.

3. During the next 600 of cam rotation, the follower returns to its original

position with SHM.

4. Dwell during the remaining 1800.

Draw the cam profile when the line of stroke is offset 20 mm from the axis of the

cam shaft.

The radius of the base circle of the cam is 40 mm. Determine the maximum velocity

and acceleration of the follower during its ascent and descent, if the cam rotates at

240 rpm.

14

Q.5 (a) State the criteria of selection of following for transmission of power:

1. Belt Drive 2. Rope Drive 3. Chain Drive 4. Gear Drive

07

(b) A casting weighing 9 kN hangs freely from a rope which makes 2.5 turns round a

drum of 300 mm diameter revolving at 20 rpm. The other end of the rope is pulled

by a man. The coefficient of friction is 0.25. Determine: (1) The force required by a

man (2) The power to raise the casting.

07

OR

Q.5 (a) In a four bar chain ABCD, AD is fixed link. Crank AB rotates in clock wise

direction at an angular velocity of 10 rad/sec. Link AB=60 mm, BC=CD=70 mm,

DA=120 mm. When angle DAB=600 and the points B and D are on one side of the

link AD, Find angular velocity of link BC and link CD.

07

(b) Describe Klein’s construction with an example. 07

*************


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–IV • EXAMINATION – SUMMER-2015

Subject Code: 141902 Date: 03/06/2015 Subject Name: Kinematics of Machines Time: 10.30am-01.00pm Total Marks: 70 Instructions:


Q.1 (a) Write notes on complete and incomplete constraints in lower and higher pairs,

illustrating your answer with neat sketches. 07

(b) Sketch and explain any two inversions of a double slider crank chain. 07 Q.2 (a) State and prove the ‘Aronhold Kennedy’s Theorem’ of three instantaneous

centres. 04

(b) Locate all the instantaneous centres of the slider crank mechanism.The lengths of crank OB and connecting rod AB are 100 mm and 400 mm respectively.If the crank rotates clockwise with an angular velocity of 10 rad/s, find: 1. Velocity of the slider A,and 2. Angular velocity of the connecting rod AB.

10

OR (b) 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.

10

Q.3 (a) A cam is to be designed for a knife edge follower with the following data : 1. Cam lift = 40 mm during 90° of cam rotation with simple harmonic motion. 2. Dwell for the next 30°. 3. During the next 60° of cam rotation, the follower returns to its original position with simple harmonic motion. 4. Dwell during the remaining 180°. Draw the profile of the cam when (a) the line of stroke of the follower passes through the axis of the cam shaft, and The radius of the base circle of the cam is 40 mm. Determine the maximum velocity and acceleration of the follower during its ascent and descent, if the cam rotates at 240 r.p.m.

10

(b) Define the following terms as applied to cam with a neat sketch :- (a) Base circle, (b) Pitch circle, (c) Pressure angle, and (d) Stroke of the follower

04

OR Q.3 (a) Explain briefly the differences between simple, compound, and epicyclic gear

trains. What are the special advantages of epicyclic gear trains ?

07

(b) Derive an expression for the length of the arc of contact in a pair of meshed spur gears.

07

Q.4 (a) An epicyclic gear consists of three gears A, B and C as shown in Fig. 1.The 07 1

gear A has 72 internal teeth and gear C has 32 external teeth. The gear B meshes with both A and C and is carried on an arm EF which rotates about the centre of A at 18 r.p.m.. If the gear A is fixed, determine the speed of gears B and C.

Figure 1

(b) Write a short note on differential gear box used in automobile with neat sketch

07

OR

Q.4 (a) State and prove the law of gearing. Show that involute profile satisfies the conditions for correct gearing.

07

(b) Two mating gears have 20 and 40 involute teeth of module 10 mm and 20° pressure angle. The addendum on 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 height for each gear wheel, length of the path of contact, arc of contact and contact ratio.

07

Q.5 (a) What are straight line mechanisms ? Describe one type of exact straight line motion mechanism with the help of a sketch.

07

(b) What is the condition for correct steering ? Explain in detail Ackerman Steering Mechanism with neat sketch.

07

OR Q.5 (a) Two shafts with an included angle of 160° are connected by a Hooke’s joint.

The driving shaft runs at a uniform speed of 1500 r.p.m. The driven shaft carries a flywheel of mass 12 kg and 100 mm radius of gyration. Find the maximum angular acceleration of the driven shaft and the maximum torque required

07

(b) four bar mechanism is to be designed, by using three precision points, to generate the function y = x1.5 , for the range 1 ≤ x ≤ 4 . Assuming 30° starting position and 120° finishing position for the input link and 90° starting position and 180° finishing position for the output link, find the values of x, y, θ and φ corresponding to the three precision points

07

*************

2

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–IV • EXAMINATION – WINTER • 2014



Time: 02:30 pm - 05:00 pm Total Marks: 70 Instructions:




Q.1 (a) Define Number of degree of freedom and determine the number of degree of freedom

for the mechanisms shown in Fig.1, 2, 3

07

Figure 1 • Figure 2

Figure 3

(b) Determine the condition for Correct Steering and also verify the condition for Davis

Steering Gear. 07

2

Q.2 (a) Define :

1. Space Centrode

2. Body Centrode

3. Fixed instantaneous Centre

4. Permanent instantaneous Centre

04

(b) In the mechanism, as shown in Fig. 4, the crank OA rotates at 20 r.p.m. anticlockwise

and gives motion to the sliding blocks B and D. The dimensions of the various links are

OA = 300 mm; AB = 1200 mm; BC = 450 mm and CD = 450 mm. For the given

configuration, determine: 1. velocities of sliding at B and D, 2. Angular velocity of CD,

3. linear acceleration of D, and 4. angular acceleration of CD.

Figure 4

10

OR

(b) In Fig. 5, the angular velocity of the crank OA is 600 rpm. Determine the linear velocity

of the slider D and the angular velocity of the link BD, when the crank is inclined at an

angle of 75° to the vertical. The dimensions of various links are: OA = 28 mm; AB = 44

mm; BC = 49 mm; and BD = 46 mm. The centre distance between the centres of

rotation O and C is 65 mm. The path of travel of the slider is 11 mm below the fixed

point C. The slider moves along a horizontal path and OC is vertical.

Figure 5

10

Q.3 (a) Define Centrifugal tension for flat belt also discuss the effect of centrifugal tension on

power transmission.

05

3

(b) A pulley used to transmit power by means of ropes has a diameter of 3.6 metres and has

15 grooves of 45° angle. The angle of contact is 170° and the coefficient of friction

between the ropes and the groove sides is 0.28. The maximum possible tension in the

ropes is 960 N and the mass of the rope is 1.5 kg per metre length. What is the speed of

pulley in rpm and the power transmitted if the condition of maximum power prevail?

09

OR

Q.3 (a) Derive the expression for length of the chain with usual notation. 05

(b) A belt drive is required to transmit 10 KW from motor running at 600 rpm. The belt is

12 mm thick and has a mass density of 0.001 gm/mm3. Safe stress in the belt is not

exceeding 2.5 N/mm2. Diameter of the driving pulley is 250 mm whereas the speed of

the driven pulley is 220 rpm. The two shafts are 1.25 m apart. The coefficient of friction

is 0.25. Determine the width of the belt.

09

Q.4 (a) Define Interference for Involute Gears and derive expression the minimum number of

teeth.

05

(b) A pair of involute spur gears with 16° pressure angle and pitch of module 6 mm is in

mesh. The number of teeth on pinion is 16 and its rotational speed is 240 rpm. When the

gear ratio is 1.75, find in order that the interference is just avoided; 1. The addenda on

pinion and gear wheel; 2. The length of path of contact; and 3. The maximum velocity

of sliding of teeth on either side of the pitch point.

09

OR

Q.4 (a) Derive the expression for the length of path of contact and length of arc of contact. 05

(b) Two 20o involute spur gears have a module of 10 mm. the addendum is one module.

The larger gear has 50 teeth and the pinion 13 teeth. Does the interference occur? If it

occurs, to what value should the pressure angle be changed to eliminate interference?

09

Q.5 (a) Explain the working of Cone clutch with neat sketch. 04

(b) Construct the profile of a cam to suit the following specifications :

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

S.H.M. During the fall the motion is uniform acceleration and deceleration. The speed

of the cam shaft is uniform. The line of stroke of the follower is off-set 12.5 mm from

the centre of the cam.

10

OR

Q.5 (a) Explain the working of Multi-plate clutch with neat sketch. 04

(b) Draw the profile of a cam operating a knife edged follower having lift of 30 mm. the

cam raises the follower with simple harmonic motion for 150o of its rotation followed

by a period of dwell for 60o. The follower descends for the next 100o rotation of cam

with uniform velocity, again followed by a dwell period. The cam rotates at a uniform

velocity of 120 rpm and has least radius of 20 mm. what will be the maximum velocity

and acceleration of the follower during the lift and the return?

10

**************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–IV • EXAMINATION – SUMMER • 2014



Time: 10:30 am - 01:00 pm Total Marks: 70 Instructions:




Q.1 (a) Discuss with neat sketch different types of steering gear mechanism of

automobile in detail.

07

(b) Explain “The common normal at the point of contact between a pair of teeth

must always pass through the pitch point”

07

Q.2 (a) Explain various inversion of a slide-crank mechanism with the help of example. 07

(b) Explain Hart straight line motion mechanism with the help of neat sketch and

prove that tracing point describes a straight line path.

07

OR

(b) Derive analytical expression for the displacement and velocity analyses of a

slider crank mechanism.

07

Q.3 (a) Define Clutch. Explain with neat sketch, working of a clutch generally used in

commercial four wheel drive.

07

(b) Two shafts whose centres are 1 m apart are connected by a V-belt drive. The

driving pulley is supplied with 100 kW and has an effective diameter of 300

mm. It runs at 1000 r.p.m. while the driven pulley runs at 370 r.p.m. The angle

of groove on the pulleys is 40. The permissible tension in 400 mm cross-

sectional area belt is 2.1 MPa. The density of the belt is 1100 kg/m. The

coefficient of friction between the belt and pulley is 0.28. Estimate the number

of belts required.

07

OR

Q.3 (a) What are different types of chains? Explain with neat sketches, the power

transmission chains.

07

(b) A multiple disc clutch transmits 75 kW of power at 2000 rpm. Coefficient of

friction for the friction surfaces is 0.2. Axial intensity of pressure is not to

exceed 180 kN/m2. Internal radius is 100 mm and is 0.8 times the external

radius. Find the number of plates needed to transmit the required torque.

Assume uniform wear conditions.

07

Q.4 (a) Derive the expression for limiting tension ratio in case of flat belt drive. 07

(b) Two parallel shaft 6m apart are to be connected by a belt running over a pulley

of dia 600 mm and 400 mm respectively. Find exact and approx lengths of belt

when belt is open and when belt is crossed.

07

OR

Q.4 (a) Explain degree of freedom with neat sketch. Also explain Grumbler’s criterion.

07

(b) Two mating involute spur gear of 20 degree pressure angle have a gear ratio of

2. The number of teeth on the pinion is 20 and its speed is 250 rpm. Module

pitch of the teeth is 12 mm. Find: (1) The addendum for pinion (2) The

addendum for gear wheel & (3) The length of the arc of contact. Assume

pinion to be the driver.

07

2

Q.5 (a) Classify followers and explain with neat sketch. 07

(b) Draw a cam profile to drive an oscillating roller follwer to the specifications

given below.

(1)Follower to move outwards through an angular displacement of 20º during

the first 120 rotation of the cam;

(2)Follower to return to its initial position during next 120º rotation of the cam.

(3)Follower to dwell during the next 120º of cam rotation.

The distance between pivot centre and roller centre=120mm;distance between

Pivot centre and cam axis =130mm;minimum radius of cam=40mm;radius of

roller=10mm Inward and outward strokes take place with simple harmonic

motion.

07

OR

Q.5 (a) Enlist different types of gear train. Explain compound gear train with neat

sketch. Also derive the equation of the velocity ratio for compound gear train.

07

(b) Differentiate between overhauling and self locking of screw. 07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–IV • EXAMINATION – WINTER 2013

Subject Code: 141902 Date: 26-12-2013 Subject Name: Kinematics of Machines Time: 02:30 pm to 05:00 pm Total Marks: 70 Instructions:


Q.1 (a) Describe briefly Types of Constrained Motions 07

(b) Sketch and explain any two inversions of double slider crank chain 07

Q.2 (a) Explain Types of Instantaneous Centres and also state Aronhold Kennedy (or Three Centres in Line) Theorem

05

(b) Locate all the instantaneous centres of the slider crank mechanism as shown in Fig.1.The lengths of crank OB and connecting rod AB are 100mm and 400 mm respectively.If the crank rotates clockwise with an angular velocity of 10 rad/s,find:1.Velocity of the slider A,and2.Angular velocity of the connecting rod AB.

09

Fig No.1 OR

(b) In the mechanism shown in Fig. 2, the slider C is moving to the right with a velocity of 1 m/s and an acceleration of 2.5 m/s2. The dimensions of various links are AB = 3 m inclined at 45° with the vertical and BC = 1.5 m inclined at 45° with the horizontal. Determine: 1.The magnitude of vertical and horizontal component of the acceleration of the point B, and 2.the angular acceleration of the links AB and BC.

Fig No.2

09

2

Q.3 (a) What are straight line mechanisms? Describe one type of exact straight line motion mechanism with the help of a sketch.

07

(b) Sketch and show the Davis steering mechanism and discuss their advantages and disadvantages.

07

OR Q.3 (a) State and prove the law of gearing 07

(b) Explain any five terminology of gear tooth with neat sketch. 07

Q.4 (a) The mean diameter of the screw jack having pitch of 10mm is 50mm. A load of 20000N is lifted through a distance of 170mm. Find the work done in lifting the load and efficiency of the screw jack when

1. The load rotates with the screw, and 2. The load rests on the loose head which does not rotate with the screw.

The external and internal diameter of the bearing surface of the loose head are 60mm and 10mm respectively. The co-efficient of friction for the screw as well as the bearing surface may be taken as 0.08.

07

(b) A single plate clutch, effective on both sides, is required to transmit 25kW at 3000R.P.M. Determine the outer and inner radii of frictional surface if the co-efficient of friction is 0.255, the ratio of radii is 1.25 and the maximum pressure is not to exceed 0.1 N/mm2. Also determine the axial thrust to be provided by springs. Assume the theory of Uniform Wear.

07

OR Q.4 (a) A pulley is driven by a flat belt, the angle of lap being 1200. The belt is 100mm

wide by 6mm thick and density 1000kg/m3. If the coefficient of friction is 0.3 and the maximum stress in the belt is not to exceed 2MPa, find the greatest power which the belt can transmit and the corresponding speed of the belt.

07

(b) In a reverted epicyclic gear train, the arm A carries two gears B and C and a compound gear D-E. The gear B meshes with gear E and the gear C meshes with gear D. The number of teeth an gears B, C, and D are 75, 30 and 90 respectively. Find the speed and direction of gear C when gear B is fixed and the arm A makes 100 R.P.M. clockwise.

07

Q.5 (a) Explain with a neat sketch the “Differential Gear Box” 05 (b) A cam is to be designed for a knife edge follower with the following data:

1. Cam lift = 40mm during 900 of cam rotation with simple harmonic motion.

2. Dwell for the next 300. 3. During the next 600 of cam rotation, the follower returns to its original

position with uniform velocity. 4. Dwell during the remaining 1800.

Draw the profile of the cam when the line of stroke of the follower passes through the axis of the cam shaft. The radius of the base circle of the cam is 40mm.

09

OR Q.5 (a) Derive an expression for the length of the path of contact in a pair of meshed

spur gears. 07

(b) Explain with sketches the different types of cams and followers. 07

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GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–IV • EXAMINATION – SUMMER 2013

Subject Code: 141902 Date: 14-06-2013 Subject Name: Kinematics of Machines Time: 10.30 am - 01.00 pm Total Marks: 70 Instructions:


Q.1 (a) Define : (1) Lower Pair (2) Kinematics Chain (3) Completely Constrained Motion (4) Angle of friction

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(b) Derive the equation for finding out the ratio of angular velocities of two shafts of Hooke’s joint.

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Q.2 (a) What is straight line motion mechanism? Explain Hart’s straight line motion mechanism with neat sketch.

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(b) What is inversion? Explain the inversions of double slider crank chain with neat sketch.

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OR (b) What is steering gear mechanism? Derive the relation for correct steering for

Devis steering gear mechanism. 07

Q.3 (a) Fig-1 shows the mechanism of a radial valve gear. The crank OA turns uniformly at 150 rpm and is pinned at A to rod AB. The point C in the rod is guided in the circular path with D as centre and DC as radius. The dimensions of various links are: OA = 150 mm; AB = 550 mm; AC = 450 mm; DC = 500 mm; BE = 350 mm. Determine velocity and acceleration of the ram E for the given position of the mechanism.

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OR Q.3 (a) Explain the terms used in cam.

(1) Trace point. (2) Pressure angle (3) Pitch circle. 07

(b) Determine a cam for operating the exhaust valve of an oil engine. It is required to give simple harmonic motion during opening and closing of the valve each of which corresponds to 60o of cam rotation. The valve must remain in the fully open position for 30o of cam rotation. The lift of the valve is 40 mm and the least radius of the cam is 40 mm. The follower is provided with a roller of radius 15 mm and its line of stroke passes through the axis of cam. Find out the maximum value of velocity and acceleration of follower if the cam rotates at 120 rpm.

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Q.4 (a) Derive the equation for finding out the torque required to lift the load by a screw jack.

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(b) A belt 100 mm wide and 100 mm thick is transmitting power at 900 m/min. the driving tension is 2.8 times the tension on the slack side. If the safe permissible stress for the belt is 1.8 N/mm2, calculate the maximum power that can be transmitted at this speed. Assume the density of leather belt is 1000 kg/m3. Consider the initial tension in the belt; also calculate the greatest power that can be transmitted by this belt and its corresponding speed.

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OR Q.4 (a) Derive the equation for maximum efficiency of a screw jack for raising a load. 07

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(b) In an epicyclic gear train, the internal wheels A and B and 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. (1) Find the number of teeth on A and B. (2) If the arm G makes 100 rpm clockwise and A is fixed, find the speed of B. (3) If the arm G makes 100 rpm clockwise and wheel A makes 10 rpm counterclockwise, find the speed of wheel B.

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Q.5 (a) Derive the equation for finding out the length of path of contact for a pair of involute gears.

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(b) A pair 20o involute gears has module of 5 mm. The pinion has 20 teeth and gear has 60 teeth. Addendum on the pinion and gear wheel in terms of module is one. Find the followings: (1) Number of pairs in contact. (2) Angle turned through by the pinion and gear wheel for one pair in

contact.

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OR Q.5 (a) Derive equation for finding out the limiting tension ratio in a belt drive. 07

(b) An open belt drive connects two pulleys 1.2 m and 0.5 m diameter, on parallel shafts 3.6 m apart. The mass of the belt is 1 kg/m length and the maximum tension is not to exceed 2000 N. The coefficient of friction is 0.3. The 1.2 m pulley, which is the driver, runs at 200 rpm. Due to slip on one of the pulleys, the velocity of the driven shaft is only 450 rpm. Calculate (1) The torque on each of the two shafts, (2) The power transmitted, and (3) Power lost in friction.

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Figure – 1 Figure – 2

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GUJARAT TECHNOLOGICAL UNIVERSITY - mytoolbag.inmytoolbag.in/media/GTUPAPERS/1/2/AUTOMOBILE/S3/KOM.pdf · (b) Figure shows the link mechanism of a quick return mechanism of the slotted

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