Chapter 1 Introduction of Machine and Mechanism o… · Chapter 1 – Introduction of Machine ... A...

GTU Paper Analysis (New Syllabus)

Kinematics of Machine (2131906) Department of Mechanical Engineering Darshan Institute of Engineering & Technology

Chapter 1 – Introduction of Machine and Mechanism

Sr. No. Questions

De

c –

14

Jun

– 1

5

De

c -

15

Jun

- 1

6

Theory

1. Define and discuss: kinematic link, kinematic pair, and kinematic chain 7 1

2. Sketch and explain Whitworth quick return mechanism. 7

3. Define and classify kinematic pairs with neat sketches. 7

4. Explain all inversions of double slider crank chain with neat sketches. 7

5. Differentiate lower pair and higher pair? 1

6. What is the number of degree of freedom (n) when the mechanism forms a structure? 1 1

7. In a kinematic chain, a quaternary joint is equal to how many binary joints? 1

8. Which type of pair has been made by the lead screw of a lathe with nut? 1

9. Which mechanism is used to enlarge or reduce the size of drawing? 1

10. Write down the equation about the relation between numbers of pairs (p) forming the kinematic chain and the number of links (l).

1

11. Explain the terms: 1. Lower pair 2. Higher pair 3. Kinematic link 3

12. Sketch and describe four bar chain mechanism. 4

13. What are quick return motion mechanisms? Where are they used? Discuss the functioning of any one of them. 7



Chapter 2 – synthesis & Analysis of Mechanism

Sr. No. Questions

De

c –

14

Jun

– 1

5

De

c -

15

Jun

- 1

6

Theory

1. Explain the Freudenstein’s Equation for four bar chain mechanism. 7

2. Explain three position synthesis of four bar chain mechanism by relative pole method. 7

3. Explain two position synthesis of four bar chain mechanism by relative pole method 7

4. What do you understand by synthesis? 1

5. State Grashoff’s criterion 1

6. Explain limitations of Grubler’s criteria 3

7. What do you understand by Type Synthesis? 1

8. Explain the Freudenstein’s method of three point synthesis of mechanisms. 7

Examples

1.

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:

Using Freudenstein‟s Equation find out other link lengths b, c and d. assume link length a = 1.

7

2. Synthesize a four bar chain mechanism by using Freudenstein”s Equation for the following positions of input- 7



fixed link “a” Synthesize the mechanism for following three successive position with length of fixed link =

50mm.

Ɵ1 = 180⁰ Ø1 =90⁰

Ɵ2 = 135⁰ Ø2 = 80⁰

Ɵ3 = 90⁰ Ø3 = 60⁰

3.

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.

4



Chapter 3 – Velocity and Acceleration Analysis

Sr. No. Questions

De

c –

14

Jun

– 1

5

De

c -

15

Jun

- 1

6

Theory

1. Describe Klein’s construction with an example. 7

2. State and prove Aronhold Kennedy’s Theorem’ of three instantaneous centers. 7 4

3. Differentiate Linear acceleration and angular acceleration 1

4. If a point moves along a straight line which is rotating, what will be the tangential component acceleration? 1

5. When crank rotates with uniform velocity then what will be the tangential acceleration? 1

6. Explain path generation. 4

7. Derive the equation of displacement, velocity and acceleration of slider on a slider crank mechanism by analytical method

7

8. Explain angular velocity Theorem 4

9. Derive an expression for the magnitude and direction of Coriolis component of acceleration. 7

Examples

1.

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.

7

2. A crank and rocker mechanism ABCD has the following dimensions. 7



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.

3.

A toggle mechanism is shown in figure-1 along with the dimensions of the links in mm. Find the velocities of

the points B and C and the angular velocities of links AB, BQ and BC. The crank rotates at 50 rpm in the

clockwise direction. Use Relative Velocity Method.

7

4.

The crank and connecting rod of a reciprocating engine are 120 mm and 600 mm respectively. The centre of

gravity (C.G.) of the connecting rod is 240 mm from the crank end. The crank is rotating uniformly at speed of

300RPM clockwise. Find at the instant when the crank is at 30° from inner dead centre 1. Velocity and

acceleration of the piston, 2. Velocity and acceleration of the C.G. of the connecting rod, and 3. Angular

velocity and angular acceleration of the connecting rod. Use Klein’s Construction

7



5.

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

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

7 7

6. A crank and slotted lever mechanism used in shaper has a centre distance of 300mm between the centre of oscillation of the slotted lever and the centre of rotation of crank. The radius of cranks is 120 mm. Find the ratio of the time of cut to the time of return stroke.

4

7.

The length of various links of a mechanism shown in the fig are as follows:

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

The crank AB makes an angle of 45° with the 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 be 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 velocity at the pin C which is 50 mm in diameter.

10



8 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.

7



Chapter 4 – Special Mechanisms

Sr. No. Questions

De

c –

14

Jun

– 1

5

De

c -

15

Jun

- 1

6

Theory

1. Derive the condition for correct steering. Sketch and show the Davis steering mechanism and discuss their

advantages. 7

2. What is straight line motion mechanism & give its classification. Explain any one in brief. 7

3. Derive an expression for the ratio of shafts velocities for Hooke’s joint and draw the polar diagram depicting the salient features of driven shaft speed.

7

4. What is the condition for correct steering? Discuss with neat sketch Ackerman steering gear mechanism of automobile.

7 3

5. Give a neat sketch of the straight line motion “Hart Mechanism”. 3

Examples

1. 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 250 rpm, find maximum and minimum speed of intermediate and driven shafts.

7

2. 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.

3



Chapter 5 – Gears

Sr. No. Questions

De

c –

14

Jun

– 1

5

De

c -

15

Jun

- 1

6

Theory

1. Derive an expression for the length of path of contact for two involutes profile gear in mesh. 7

2. What is meant by the term ‘Interference’ in involute gears? Discuss various methods used to avoid

interference. 7

3. Define terms related to gears: (i) Module (ii)Pressure Angle (iii) Circular Pitch (iv) Backlash (v) Tooth Space (vi) Contact Ratio (vii) Length of Path of Contact

7 3

4. Define conjugate profile. 1

5. Define: Backlash in Gear 1

6. What is the product of Circular pitch and Diametral pitch 1 1

7. What will be the minimum value of contact ratio for gear? 1

8. Explain any three terminology of gear tooth with neat sketch. 3

9. Explain with the neat sketch the “sun and planet wheel”. 4

10. What do you understand by the term “interference” as applied to the gear? 3 4

11. Define Normal Pitch relating to helical gears. 1

12. Which type of gears are used to connect two non-parallel non-intersecting shaft? 1

13. Which condition should be fulfilled by pair of gears for correct gearing? 1

14. What do you understand by simple, compound, and epicyclic gear trains? 3

15. State and prove the “Law of gearing” 4



Examples

1.

A pair 20° 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.

7

2.

Two gear wheels mesh externally and are to give a gear 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 R.P.M. Determine: 1. The number of teeth on the pinion to avoid interference on it and the

corresponding number of teeth on the wheel, 2. The length of path and arc of contact, 3.The number of pairs

of teeth in contact, and 4. The maximum velocity of sliding.

7

3. A pinion having 30 teeth drives a gear having 80 teeth. The profile of gear is involute with 20° pressure angle, 12 mm module and 10 mm addendum. Find the contact ratio.

7

4. 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 14.5°. 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?

7



Chapter 6 – Gear Trains

Sr. No. Questions

De

c –

14

Jun

– 1

5

De

c –

15

Jun

- 1

6

Theory

1. 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. 7

2. In which gear train the axes of the first and last gear are co-axial? 1

3. Explain with a neat sketch the “Differential Gear Box”

4. Which type of gear train is used to connect minute hand to hour hand in clock mechanism? 1

Examples

1.

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.

7

2.

An epicyclic gear train is composed of fixed annular wheel A having 150 teeth. Meshing with A is wheel B which drives wheel D through and idle wheel C, wheel D being concentric with A. Wheels B and C are carried on an arm E which resolves clockwise at 100 R.P.M. about the axis of A and D. If the wheel B and D have 25 and 40 teeth respectively, find the number of teeth on C and sense of rotation of C. Also sketch the arrangement.

7

3.

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.

7



4.

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 the gear A which is fixed, Determine the speed of gear B. If the gear A instead of being fixed, makes 300 rpm. in the clockwise direction what will be the speed if gear B?

7



Chapter 7 – Cam and Followers

Sr. No. Questions

Dec

– 1

4

Jun

– 1

5

Dec

- 1

5

Jun

- 1

6

Theory

1. Classify followers and explain with neat sketch 7

2. Explain with sketches the different types of cams and followers. 7 4

3. Draw the displacement, velocity and acceleration diagrams for a follower when it moves with (i) Uniform acceleration and retardation (ii) Cycloidal motion

7 7

4. Why roller follower is preferred over a knife edge follower? 1 3

5.

Define the following terms related to the cam.

(i) Base circle (ii) Pitch circle (iii) Pressure angle (iv) Stroke of the follower

4 3

6. Which type of cam follower is extensively used in air-craft engines? 1

7. The size of cam depends upon (a) base circle (b) pitch circle (c) prime circle (d) pitch curve

1

Examples

1.

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°.

7



(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 .

2.

A cam, with a minimum radius of 50 mm, rotating clockwise at a uniform speed, is required to give a knife edge follower the motion as described below :

1. To move outwards through 40 mm during 1000 rotation of the cam;

2. To dwell for next 800;

3. To return to its starting position during next 900, and

4. To dwell for the rest period of a revolution.

Draw the profile of the cam when the line of stroke of the follower is off-set by 15 mm. The displacement of

the follower is to take place with uniform acceleration and uniform retardation. Determine the maximum

velocity and acceleration of the follower when the cam shaft rotates at 900 R.P.M.

7

3.

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 = 1200; Angle of fall = 1500; 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.

7

4.

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



5. Draw the displacement, Velocity and Acceleration for follower when its moves with cycloidal motion 4 4

6.

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

7.

A cam drives a flat reciprocating follower in the following manner:

During first 120° rotation of the cam, follower moves outward through a distance of 20 mm with S.H.M. The

follower dwells during next 30° of cam rotation. During next 1200°rotation of the cam, the follower moves inward

with S.H.M. The follower dwells for the next 90° of cam rotation. The minimum radius of the cam is 25 mm. Draw

the profile of the cam.

7

Date post:	08-Apr-2018
Category:	Documents
Upload:	lynhi
View:	241 times
Download:	9 times

Chapter 1 Introduction of Machine and Mechanism o… · Chapter 1 – Introduction of Machine ... A...

Documents