Kinematics Of Machine

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2021 102503 2020 102503 2020 103503

2021102503

B.Tech Examination, 2021

3 hours70 marks

Instructions

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

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Q1
Choose the correct answer of the following (any seven):

a)
The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is

a)
(i) 1

b)
(ii) 2

c)
(iii) 3

d)
(iv) 4

b)
The number of inversions for a slider crank mechanism is

a)
(i) 10

b)
(ii) 8

c)
(iii) 6

d)
(iv) 4

c)
Balancing of a rigid rotor can be achieved by appropriately placing balancing weights in

a)
(i) a single plane

b)
(ii) two planes

c)
(iii) three planes

d)
(iv) four planes

d)
The Klein's method of construction for reciprocating engine mechanism

a)
(i) is a simplified version of instantaneous centre method

b)
(ii) utilizes a quadrilateral similar to the diagram of mechanism for reciprocating engine

c)
(iii) enables determination of Coriolis component

d)
(iv) is based on the acceleration diagram

e)
In reciprocating engines, primary forces

a)
(i) are partially balanced

b)
(ii) are completely balanced

c)
(iii) are balanced by secondary forces

d)
(iv) cannot be balanced

f)
The ratio of tension on the tight side to that on the slack side in a flat belt drive is

a)
(i) an exponential function of the product of coefficient of friction and lap angle

b)
(ii) proportional to the product of coefficient of friction and lap angle

c)
(iii) proportional to the lap angle

d)
(iv) proportional to the coefficient of friction

g)
In a $6 imes 20$ wire rope, No. 6 indicates the

a)
(i) diameter of the wire rope in mm

b)
(ii) number of wires

c)
(iii) number of strands in the wire rope

d)
(iv) gauge number of the wire

h)
In case of a multiple disc clutch, if $n_1$ is the number of discs on the driving shaft and $n_2$ is the number of discs on the driven shaft, then what is the number of pairs of contact surfaces?

a)
(i) $n_1 + n_2$

b)
(ii) $n_1 + n_2 + 1$

c)
(iii) $n_1 + n_2 - 1$

d)
(iv) $n_1 + 2n_2$

i)
The minimum number of teeth on the pinion to operate without interference in standard full-height involute teeth gear mechanism with $20^\circ$ pressure angle is

a)
(i) 14

b)
(ii) 12

c)
(iii) 6

d)
(iv) 18

j)
Which type of gear is used for shaft axes having an offset?

a)
(i) Mitre gears

b)
(ii) Spiral bevel gears

c)
(iii) Hypoid gears

d)
(iv) Zerol gears

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Q2
Answer the following:

a)
With the help of neat sketch, explain the following: Link, Kinematic pair, Kinematic chain, Mechanism and Machine.

7 marks
b)
Sketch and explain the working principle of Whitworth quick return motion mechanism.

7 marks
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Q3
Answer the following:

a)
Sketch and explain elliptical trammels and Scotch yoke mechanism of a double-slider crank chain.

7 marks
b)
In a crank and slotted lever quick return motion mechanism, the distance between the fixed centres is 240 mm and the length of the driving crank is 120 mm. Find the inclination of the slotted bar with the vertical in the extreme position and the time ratio of cutting stroke to the return stroke. If the length of the slotted bar is 450 mm, find the length of the stroke if the line of stroke passes through the extreme positions of the free end of the lever.

7 marks
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Q4
Answer the following:

a)
With the help of example, explain instantaneous centre method for finding velocity of a point on a link.

6 marks
b)
A mechanism is shown in Fig. 1, with following dimensions: $O_1A = 60$ mm; $AB = 180$ mm; $O_2B = 100$ mm; $O_2C = 180$ mm and $CD = 270$ mm. The crank $O_1A$ rotates clockwise at a uniform speed of 120 r.p.m. The block $D$ moves in vertical guides. Find, by instantaneous centre method, the velocity of $D$ and the angular velocity of $CD$ .

8 marks
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Q5
Answer the following:

a)
Explain how the velocities of a slider and the connecting rod are obtained in a slider crank mechanism.

6 marks
b)
In a slider crank mechanism as shown in Fig. 2, the crank is 200 mm long and rotates at 40 rad/sec in a CCW direction. The length of the connecting rod is 800 mm. When the crank turns through $60^\circ$ from inner-dead centre, determine— (i) the velocity of the slider; (ii) the velocity of point $E$ located at a distance of 200 mm on the connecting rod extended; (iii) the position and velocity of point $F$ on the connecting rod having the least absolute velocity; (iv) the angular velocity of connecting rod; (v) the velocity of rubbing of pins of crank shaft, crank and cross head having pins diameters 80 mm, 60 mm and 100 mm respectively.

8 marks
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Q6
Answer the following:

a)
Describe with a neat sketch the working of a cone clutch.

6 marks
b)
A conical friction clutch is used to transmit 90 kW at 1500 r.p.m. The semi-cone angle is $20^\circ$ and the coefficient of friction is 0.2. If the mean diameter of the bearing surface is 375 mm and the intensity of normal pressure is not to exceed $0.25\text{ N/mm}^2$ , find the dimensions of the conical bearing surface and the axial load required.

8 marks
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Q7
Answer the following:

a)
Explain the method to determine velocity ratio of a compound belt drive.

6 marks
b)
A leather belt is required to transmit 7.5 kW from a pulley 1.2 m in diameter, running at 250 r.p.m. The angle embraced is $165^\circ$ and the coefficient of friction between the belt and the pulley is 0.3. If the safe working stress for the leather belt is 1.5 MPa, density of leather $1\text{ mg/m}^3$ and thickness of belt 10 mm, determine the width of the belt taking centrifugal tension into account.

8 marks
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Q8
Answer the following:

a)
Discuss the phenomena of interference in involute gear.

4 marks
b)
A pair of involute spur gears with $16^\circ$ 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 r.p.m. When the gear ratio is 1.75, find in order that the interference is just avoided— (i) the addenda on pinion and gear wheel; (ii) the length of path of contact; (iii) the maximum velocity of sliding of teeth on either side of the pitch point.

10 marks
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Q9
A shaft carries four masses $A$ , $B$ , $C$ and $D$ of magnitude 200 kg, 300 kg, 400 kg and 200 kg respectively and revolving at radii 80 mm, 70 mm, 60 mm and 80 mm in planes measured from $A$ at 300 mm, 400 mm and 700 mm. The angles between the cranks measured anticlockwise are $A$ to $B$ $45^\circ$ , $B$ to $C$ $70^\circ$ and $C$ to $D$ $120^\circ$ . The balancing masses are to be placed in planes $X$ and $Y$ . The distance between the planes $A$ and $X$ is 100 mm, between $X$ and $Y$ is 400 mm and between $Y$ and $D$ is 200 mm. If the balancing masses revolve at a radius of 100 mm, find their magnitudes and angular positions.

14 marks
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2020102503

B.Tech Examination, 2020

3 hours70 marks

Instructions

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Ask AI

Q1
Choose the correct answer of the following (any seven):

a)
When a cylinder is located in a vee-block, then number of degrees of freedom which are arrested is

a)
(i) $2$

b)
(ii) $4$

c)
(iii) $7$

d)
(iv) $8$

b)
A planar mechanism has $8$ links and $10$ rotary joints. The number of degrees of freedom of the mechanism, using Grubler's criterion is

a)
(i) $0$

b)
(ii) $1$

c)
(iii) $2$

d)
(iv) $3$

c)
The lengths of the links of a $4$-bar linkage with revolute pairs only are $p, q, r$ and $s$ units. Given that $p < q < r < s$ . Which of these links should be the fixed one, for obtaining a 'double crank' mechanism?

a)
(i) Link of length $p$

b)
(ii) Link of length $q$

c)
(iii) Link of length $r$

d)
(iv) Link of length $s$

d)
The sense of Coriolis component $2\omega V$ is the same as that of the relative velocity vector $V$ rotated

a)
(i) $45^\circ$ in the direction of rotation of the link containing the path

b)
(ii) $45^\circ$ in the direction opposite to the rotation of the link containing the path

c)
(iii) $90^\circ$ in the direction of rotation of the link containing the path

d)
(iv) $180^\circ$ in the direction opposite to the rotation of the link containing the path

e)
If a two-mass system is dynamically equivalent to a rigid body, then the system will not satisfy the condition that the

a)
(i) sum of the two masses must be equal to that of the rigid body

b)
(ii) polar moment of inertia of the system should be equal to that of the rigid body

c)
(iii) centre of gravity (c.g.) of the system should coincide with that of the rigid body

d)
(iv) total moment of inertia about the axis through c.g. must be equal to that of the rigid body

f)
Two rotors are mounted on a shaft. If the unbalanced force due to one rotor is equal in magnitude to the unbalanced force due to the other rotor, but positioned exactly $180^\circ$ units apart, then the system will be balanced

a)
(i) statically

b)
(ii) dynamically

c)
(iii) statically as well as dynamically

d)
(iv) neither statically nor dynamically

g)
In spur gears, the circle on which the involute is generated is called the

a)
(i) pitch circle

b)
(ii) clearance circle

c)
(iii) base circle

d)
(iv) addendum circle

h)
If the pressure angle of the rack is $20^\circ$ , then force acting along the line of action between the rack and the gear teeth is

a)
(i) $250\text{ N}$

b)
(ii) $342\text{ N}$

c)
(iii) $532\text{ N}$

d)
(iv) $600\text{ N}$

i)
Which one of the following is not a friction clutch?

a)
(i) Disc or plate clutch

b)
(ii) Cone clutch

c)
(iii) Centrifugal clutch

d)
(iv) Jaw clutch

j)
Total slip will occur in a belt drive when

a)
(i) angle of rest is zero

b)
(ii) angle of creep is zero

c)
(iii) angle of rest is greater than angle of creep

d)
(iv) angle of creep is greater than angle of rest

Ask AI
Q2
Answer the following:

a)
What are kinematic pairs? With the help of example, classify kinematic pairs according to nature of relative motion between pairing elements.

b)
Sketch and explain the working principle of third inversions of a single slider crank chain mechanism.

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Q3
Answer the following:

a)
Sketch and explain any two inversions of a double slider crank chain.

b)
The Whitworth quick return motion mechanism has the driving crank $160\text{ mm}$ long. The distance between fixed centres is $110\text{ mm}$ . The line of stroke of the ram passed through the centre of rotation of the slotted lever whose free end is connected to the ram by a connecting link. Find the ratio of time of cutting to time of return.

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Q4
Answer the following:

a)
State and prove the 'Aronhold-Kennedy's Theorem' of three instantaneous centers.

b)
In a four-bar chain $ABCD$ , $AD$ is fixed and is $165\text{ mm}$ long. The crank $AB$ is $45\text{ mm}$ long and rotates at $120\text{ r.p.m.}$ clockwise, while the link $CD = 80\text{ mm}$ oscillates about $D$ . $BC$ and $AD$ are of equal lengths. Find the angular velocity of link $CD$ when angle $BAD = 65^\circ$ .

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Q5
Answer the following:

a)
With the help of a neat sketch, explain acceleration diagram of a slider crank mechanism.

b)
In a four-bar chain $ABCD$ , link $AD$ is fixed and crank $AB$ rotates at $10\text{ radians per second}$ clockwise. Lengths of the links are $AB = 60\text{ mm}$; $BC = CD = 70\text{ mm}$; $DA = 120\text{ mm}$ . When angle $DAB = 60^\circ$ and both B and C lie on the same side of $AD$ , find—

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Q6
Answer the following:

a)
Describe with a neat sketch the working of a single-plate friction clutch.

b)
A multiplate clutch has three pairs of contact surfaces. The outer and inner radii of the contact surfaces are $100\text{ mm}$ and $50\text{ mm}$ respectively. The maximum axial spring force is limited to $1\text{ kN}$ . If the coefficient of friction is $0.35$ and assuming uniform wear, find the power transmitted by the clutch at $1500\text{ r.p.m.}$

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Q7
Answer the following:

a)
Explain the phenomena of 'slip' and 'creep' in a belt drive.

b)
Determine the width of a $9.75\text{ mm}$ thick leather belt required to transmit $15\text{ kW}$ from a motor running at $900\text{ r.p.m.}$ The diameter of the driving pulley of the motor is $300\text{ mm}$ . The driving pulley runs at $300\text{ r.p.m.}$ and the distance between the centres of two pulleys is $3\text{ metres}$ . The density of the leather is $1000\text{ kg/m}^3$ . The maximum allowable stress in the leather is $2.5\text{ MPa}$ . The coefficient of friction between the leather and pulley is $0.3$ . Assume open belt drive and neglect the sag and slip of the belt.

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Q8
Answer the following:

a)
Define the following terms related to gear:

b)
The following data relates to a pair of $20^\circ$ involute gears in mesh: Module $= 6\text{ mm}$ Number of teeth on pinion $= 17$ Number of teeth on gear $= 49$ Addenda on pinion and gear wheel $= 1\text{ module}$ Calculate—

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Q9
A shaft with $3\text{ metres}$ span between two bearings carries two masses of $10\text{ kg}$ and $20\text{ kg}$ acting at the extremities of the arms $0.45\text{ m}$ and $0.6\text{ m}$ long respectively. The planes in which these masses rotate are $1.2\text{ m}$ and $2.4\text{ m}$ respectively from the left end bearing supporting the shaft. The angle between the arms is $60^\circ$ . The speed of rotation of the shaft is $200\text{ r.p.m.}$ If the masses are balanced by two counter-masses rotating with the shaft acting at radii of $0.3\text{ m}$ and placed at $0.3\text{ m}$ from each bearing centres, estimate the magnitude of the two balance masses and their orientation with respect to the $X$-axis, i.e., mass of $10\text{ kg}$ .

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2020103503

B.Tech Examination, 2020

3 hours70 marks

Instructions

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Ask AI

Q1
Choose the correct answer of the following (any seven):

a)
When a cylinder is located in a vee-block, then number of degrees of freedom which are arrested is

a)
(i) 2

b)
(ii) 4

c)
(iii) 7

d)
(iv) 8

b)
A planar mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of the mechanism, using Grubler's criterion is

a)
(i) 0

b)
(ii) 1

c)
(iii) 2

d)
(iv) 3

c)
The lengths of the links of a 4-bar linkage with revolute pairs only are $p$ , $q$ , $r$ and $s$ units. Given that $p < q < r < s$ . Which of these links should be the fixed one, for obtaining a 'double crank' mechanism?

a)
(i) Link of length $p$

b)
(ii) Link of length $q$

c)
(iii) Link of length $r$

d)
(iv) Link of length $s$

d)
The sense of Coriolis component $2\omega V$ is the same as that of the relative velocity vector $V$ rotated

a)
(i) $45^\circ$ in the direction of rotation of the link containing the path

b)
(ii) $45^\circ$ in the direction opposite to the rotation of the link containing the path

c)
(iii) $90^\circ$ in the direction of rotation of the link containing the path

d)
(iv) $180^\circ$ in the direction opposite to the rotation of the link containing the path

e)
If a two-mass system is dynamically equivalent to a rigid body, then the system will not satisfy the condition that the

a)
(i) sum of the two masses must be equal to that of the rigid body

b)
(ii) polar moment of inertia of the system should be equal to that of the rigid body

c)
(iii) centre of gravity (c.g.) of the system should coincide with that of the rigid body

d)
(iv) total moment of inertia about the axis through c.g. must be equal to that of the rigid body

f)
Two rotors are mounted on a shaft. If the unbalanced force due to one rotor is equal in magnitude to the unbalanced force due to the other rotor, but positioned exactly $180^\circ$ apart, then the system will be balanced

a)
(i) statically

b)
(ii) dynamically

c)
(iii) statically as well as dynamically

d)
(iv) neither statically nor dynamically

g)
In spur gears, the circle on which the involute is generated is called the

a)
(i) pitch circle

b)
(ii) clearance circle

c)
(iii) base circle

d)
(iv) addendum circle

h)
If the pressure angle of the rack is $20^\circ$ , then force acting along the line of action between the rack and the gear teeth is

a)
(i) 250 N

b)
(ii) 342 N

c)
(iii) 532 N

d)
(iv) 600 N

i)
Which one of the following is not a friction clutch?

a)
(i) Disc or plate clutch

b)
(ii) Cone clutch

c)
(iii) Centrifugal clutch

d)
(iv) Jaw clutch

j)
Total slip will occur in a belt drive when

a)
(i) angle of rest is zero

b)
(ii) angle of creep is zero

c)
(iii) angle of rest is greater than angle of creep

d)
(iv) angle of creep is greater than angle of rest

Ask AI
Q2
Answer the following:

a)
What are kinematic pairs? With the help of example, classify kinematic pairs according to nature of relative motion between pairing elements.

7 marks
b)
Sketch and explain the working principle of third inversions of a single slider crank chain mechanism.

7 marks
Ask AI
Q3
Answer the following:

a)
Sketch and explain any two inversions of a double slider crank chain.

7 marks
b)
The Whitworth quick return motion mechanism has the driving crank 160 mm long. The distance between fixed centres is 110 mm. The line of stroke of the ram passed through the centre of rotation of the slotted lever whose free end is connected to the ram by a connecting link. Find the ratio of time of cutting to time of return.

7 marks
Ask AI
Q4
Answer the following:

a)
State and prove the 'Aronhold-Kennedy's Theorem' of three instantaneous centers.

6 marks
b)
In a four-bar chain $ABCD$ , $AD$ is fixed and is 165 mm long. The crank $AB$ is 45 mm long and rotates at 120 r.p.m. clockwise, while the link $CD = 80$ mm oscillates about $D$ . $BC$ and $AD$ are of equal lengths. Find the angular velocity of link $CD$ when angle $BAD = 60^\circ$ .

8 marks
Ask AI
Q5
Answer the following:

a)
With the help of a neat sketch, explain acceleration diagram of a slider crank mechanism.

4 marks
b)
In a four-bar chain $ABCD$ , link $AD$ is fixed and crank $AB$ rotates at 10 radians per second clockwise. Lengths of the links are $AB = 60$ mm; $BC = CD = 70$ mm; $DA = 120$ mm. When angle $DAB = 60^\circ$ and both $B$ and $C$ lie on the same side of $AD$ , find— (i) angular velocities (magnitude and direction) of $BC$ and $CD$; (ii) angular acceleration of $BC$ and $CD$ .

10 marks
Ask AI
Q6
Answer the following:

a)
Describe with a neat sketch the working of a single-plate friction clutch.

6 marks
b)
A multiplate clutch has three pairs of contact surfaces. The outer and inner radii of the contact surfaces are 100 mm and 50 mm respectively. The maximum axial spring force is limited to 1 kN. If the coefficient of friction is 0.35 and assuming uniform wear, find the power transmitted by the clutch at 1500 r.p.m.

8 marks
Ask AI
Q7
Answer the following:

a)
Explain the phenomena of 'slip' and 'creep' in a belt drive.

4 marks
b)
Determine the width of a 9.75 mm thick leather belt required to transmit 15 kW from a motor running at 900 r.p.m. The diameter of the driving pulley of the motor is 300 mm. The driving pulley runs at 300 r.p.m and the distance between the centres of two pulleys is 3 metres. The density of the leather is $1000\text{ kg/m}^3$ . The maximum allowable stress in the leather is 2.5 MPa. The coefficient of friction between the leather and pulley is 0.3. Assume open belt drive and neglect the sag and slip of the belt.

10 marks
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Q8
Answer the following:

a)
Define the following terms related to gear: (i) Pitch circle diameter (ii) Angle of obliquity (iii) Circular pitch (iv) Module

4 marks
b)
The following data relates to a pair of $20^\circ$ involute gears in mesh: Module = 6 mm Number of teeth on pinion = 17 Number of teeth on gear = 49 Addenda on pinion and gear wheel = 1 module Calculate— (i) the number of pairs of teeth in contact; (ii) the angle turned through by the pinion and the gear wheel when one pair of teeth in contact; (iii) the ratio of sliding to rolling motion when the tip of a tooth on the larger wheel (1) is just making contact, (2) is just leaving contact with its mating tooth and (3) is at the pitch point.

10 marks
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Q9
A shaft with 3 metres span between two bearings carries two masses of 10 kg and 20 kg acting at the extremities of the arms 0.45 m and 0.6 m long respectively. The planes in which these masses rotate are 1.2 m and 2.4 m respectively from the left end bearing supporting the shaft. The angle between the arms is $60^\circ$ . The speed of rotation of the shaft is 200 r.p.m. If the masses are balanced by two counter-masses rotating with the shaft acting at radii of 0.3 m and placed at 0.3 m from each bearing centres, estimate the magnitude of the two balance masses and their orientation with respect to the X-axis, i.e., mass of 10 kg.

14 marks
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Kinematics Of Machine

B.Tech Examination, 2021

Instructions

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B.Tech Examination, 2020

Instructions

Questions

B.Tech Examination, 2020

Instructions

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