(a) The ratio of maximum fluctuation of energy to the work done per cycle is called

(b) A rigid body, under the action of external forces, can be replaced by two masses placed at a fixed distance apart. The two masses form an equivalent dynamical system, if

(c) Angle of ascent of cam is defined as the angle

(d) The centrifugal tension in belts

(e) In a spring controlled governor, when the controlling force ______ as the radius of rotation increases, it is said to be a stable governor.

(f) A rotor supported at A and B carries two masses as shown in the figure given below : [Figure: rotor with masses]. The rotor is

(g) Idler pulley is used

(h) The primary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = mass of reciprocating parts, ω = angular speed of crank, r = radius of crank, θ = angle of inclination of crank with the line of stroke, and n = ratio of the length of connecting rod to radius of crank)

(i) The height of a Watt governor is

(j) When brakes are applied to all the four wheels of a moving car, the distance travelled by the car before it is brought to rest, will be

(a) What are centripetal and tangential components of acceleration? When do they occur? How are they determined? [6]

(b) Describe the procedure to draw velocity and acceleration diagrams of a four link mechanism. In what way are the angular accelerations of the output link and the coupler found? [8]

(a) Define the following terms : [5]
(i) Pitch circle (ii) Pitch diameter (iii) Pitch point (iv) Circular pitch (v) Module

(b) In an epicycle gear, the pitch cycle diameter of the annulus A is to be approximately 324 mm and the module is to be 6 mm. When the annulus is stationary, the three armed spider makes one revolution for every five revolutions of the wheel S. Find the number of teeth for all the wheels and exact pitch circle diameter of the annulus. If the torque of 30 N.m is applied to the shaft carrying S, determine the fixing torque of the annulus. [9]

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 number of teeth are T_C = 28, T_D = 26, T_E = T_F = 18.
(a) Sketch the arrangement.
(b) Find the number of teeth on A and B.
(c) If the arm G makes 100 r.p.m. clockwise and A is fixed, find the speed of B.
(d) If the arm G makes 100 r.p.m. clockwise and wheel A makes 10 r.p.m. counterclockwise, find the speed of wheel B.

(a) Derive the relation $ \frac{T_1}{T_2} = e^{\mu \theta} $ for a flat-belt drive with usual notations. [6]

(b) A belt drive transmits 8 kW of power from a shaft rotating at 240 r.p.m to another shaft rotating at 160 r.p.m. The belt is 8 mm thick. The diameter of the smaller pulley is 600 mm and the two shafts are 5 m apart. The coefficient of friction is 0.25. If the maximum stress in the belt is limited to 3 N/mm², find the width of the belt for (i) an open belt drive and (ii) a cross-belt drive. [8]

(a) Distinguish between brakes and dynamometer. [2]

(b) Discuss the effect of applying the brakes to a vehicle when (i) brakes are applied to the rear wheels only; (ii) brakes are applied to the front wheels only; (iii) brakes are applied to all the four wheels. [4×3=12]

A rotating shaft carries three unbalanced masses of 4 kg, 3 kg and 2.5 kg at radial distance of 75 mm, 85 mm and 50 mm and at the angular position of 45°, 135° and 240° respectively. The second and third masses are in the planes at 200 mm and 375 mm from the plane of the first mass. The angular positions are measured counter-clockwise from the reference line along x-axis and viewing the shaft from the first mass end. The shaft length is 800 mm between bearings and the distance between the plane of the first mass and the bearing at that end is 225 mm. Determine the amount of the counter masses in planes at 75 mm from the bearings for the complete balance of the shaft. The first counter mass is to be in a plane between the first mass and the bearing and the second mass in a plane between the third mass and the bearing at the end.

The arms of a Hartnell governor are of equal length. When the sleeve is in the mid-position, the masses rotate in a circle with a diameter of 150 mm (the arms are vertical in the mid-position). Neglecting friction, the equilibrium speed for this position is 360 r.p.m. Maximum variation of speed, taking friction into account, is to be 6% of the mid-position speed for a maximum sleeve movement of 30 mm. The sleeve mass is 5 kg and the friction at the sleeve is 35 N. Assuming that the power of the governor is sufficient to overcome the friction by 1% change of speed on each side of the mid-position, find (neglecting obliquity effect of arms) the (i) mass of each rotating ball, (ii) spring stiffness and (iii) initial compression of the spring.

The length of the ball and sleeve arms of the bell-crank lever of a Hartnell governor are 140 mm and 120 mm respectively. The mass of each governor ball is 5 kg. The fulcrum of the bell-crank lever is at a distance of 160 mm. At the mean speed of the governor which is 270 r.p.m., the ball arms are vertical and the sleeve arms are horizontal. The sleeve moves up by 12 mm for an increase of speed of 4% neglecting friction, determine the (i) spring stiffness, (ii) minimum equilibrium speed when the sleeve moves by 24 mm, (iii) sensitiveness of the governor and (iv) spring stiffness for the governor to be isochronous at the mean speed.

(a) The ratio of maximum fluctuation of energy to the work done per cycle is called

(b) A rigid body, under the action of external forces, can be replaced by two masses placed at a fixed distance apart. The two masses form an equivalent dynamical system, if

(c) Angle of ascent of cam is defined as the angle

(d) The centrifugal tension in belts

(e) In a spring controlled governor, when the controlling force ______ as the radius of rotation increases, it is said to be a stable governor.

(f) A rotor supported at A and B carries two masses as shown in the figure given below : [Figure: rotor with masses]. The rotor is

(g) Idler pulley is used

(h) The primary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = mass of reciprocating parts, ω = angular speed of crank, r = radius of crank, θ = angle of inclination of crank with the line of stroke, and n = ratio of the length of connecting rod to radius of crank)

(i) The height of a Watt governor is

(j) When brakes are applied to all the four wheels of a moving car, the distance travelled by the car before it is brought to rest, will be

(a) What are centripetal and tangential components of acceleration? When do they occur? How are they determined? [6]

(b) Describe the procedure to draw velocity and acceleration diagrams of a four link mechanism. In what way are the angular accelerations of the output link and the coupler found? [8]

(a) Define the following terms : [5]
(i) Pitch circle (ii) Pitch diameter (iii) Pitch point (iv) Circular pitch (v) Module

(b) In an epicycle gear, the pitch cycle diameter of the annulus A is to be approximately 324 mm and the module is to be 6 mm. When the annulus is stationary, the three armed spider makes one revolution for every five revolutions of the wheel S. Find the number of teeth for all the wheels and exact pitch circle diameter of the annulus. If the torque of 30 N.m is applied to the shaft carrying S, determine the fixing torque of the annulus. [9]

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 number of teeth are T_C = 28, T_D = 26, T_E = T_F = 18.
(a) Sketch the arrangement.
(b) Find the number of teeth on A and B.
(c) If the arm G makes 100 r.p.m. clockwise and A is fixed, find the speed of B.
(d) If the arm G makes 100 r.p.m. clockwise and wheel A makes 10 r.p.m. counterclockwise, find the speed of wheel B.

(a) Derive the relation $ \frac{T_1}{T_2} = e^{\mu \theta} $ for a flat-belt drive with usual notations. [6]

(b) A belt drive transmits 8 kW of power from a shaft rotating at 240 r.p.m to another shaft rotating at 160 r.p.m. The belt is 8 mm thick. The diameter of the smaller pulley is 600 mm and the two shafts are 5 m apart. The coefficient of friction is 0.25. If the maximum stress in the belt is limited to 3 N/mm², find the width of the belt for (i) an open belt drive and (ii) a cross-belt drive. [8]

(a) Distinguish between brakes and dynamometer. [2]

(b) Discuss the effect of applying the brakes to a vehicle when (i) brakes are applied to the rear wheels only; (ii) brakes are applied to the front wheels only; (iii) brakes are applied to all the four wheels. [4×3=12]

A rotating shaft carries three unbalanced masses of 4 kg, 3 kg and 2.5 kg at radial distance of 75 mm, 85 mm and 50 mm and at the angular position of 45°, 135° and 240° respectively. The second and third masses are in the planes at 200 mm and 375 mm from the plane of the first mass. The angular positions are measured counter-clockwise from the reference line along x-axis and viewing the shaft from the first mass end. The shaft length is 800 mm between bearings and the distance between the plane of the first mass and the bearing at that end is 225 mm. Determine the amount of the counter masses in planes at 75 mm from the bearings for the complete balance of the shaft. The first counter mass is to be in a plane between the first mass and the bearing and the second mass in a plane between the third mass and the bearing at the end.

The arms of a Hartnell governor are of equal length. When the sleeve is in the mid-position, the masses rotate in a circle with a diameter of 150 mm (the arms are vertical in the mid-position). Neglecting friction, the equilibrium speed for this position is 360 r.p.m. Maximum variation of speed, taking friction into account, is to be 6% of the mid-position speed for a maximum sleeve movement of 30 mm. The sleeve mass is 5 kg and the friction at the sleeve is 35 N. Assuming that the power of the governor is sufficient to overcome the friction by 1% change of speed on each side of the mid-position, find (neglecting obliquity effect of arms) the (i) mass of each rotating ball, (ii) spring stiffness and (iii) initial compression of the spring.

The length of the ball and sleeve arms of the bell-crank lever of a Hartnell governor are 140 mm and 120 mm respectively. The mass of each governor ball is 5 kg. The fulcrum of the bell-crank lever is at a distance of 160 mm. At the mean speed of the governor which is 270 r.p.m., the ball arms are vertical and the sleeve arms are horizontal. The sleeve moves up by 12 mm for an increase of speed of 4% neglecting friction, determine the (i) spring stiffness, (ii) minimum equilibrium speed when the sleeve moves by 24 mm, (iii) sensitiveness of the governor and (iv) spring stiffness for the governor to be isochronous at the mean speed.

Choose the correct answer (any seven):

Answer the following:

The crank of a slider crank mechanism is $15\text{ cm}$ and the connecting rod is $60\text{ cm}$ long. The crank makes $300\text{ r.p.m.}$ in the clockwise direction. When it has turned $45^\circ$ from the inner-dead centre position, determine—

A Porter governor has all four arms $300\text{ mm}$ long. The upper arms are pivoted on the axis of rotation and the lower arms are attached to the sleeve at a distance of $3.5\text{ mm}$ from the axis. The mass of each ball is $7\text{ kg}$ and the mass on the sleeve is $54\text{ kg}$. If the extreme radii of rotation of the ball are $200\text{ mm}$ and $250\text{ mm}$, find the range of speed of the governor.

Two mating spur gears with module pitch of $6.5\text{ mm}$ have $19$ teeth and $47$ teeth of $20^\circ$ pressure angle, and $6.5\text{ mm}$ addendum. Determine the number of pairs of teeth in contact and the angle turned through by the larger wheel for one pair of teeth in contact. Determine also the sliding velocity at the instant (a) engagement commences, (b) engagement terminates and (c) at the pitch point, when the pitch-line velocity is $1.2\text{ m/sec}$.

The wheel B gears with both A and C and is carried on an arm which rotates about the centre of A at $18\text{ r.p.m.}$ If the wheel A is fixed, determine the speed of wheels B and C.

All the arms of a Porter governor are $20\text{ cm}$ long. The lower and upper arms are pivoted to links of $4\text{ cm}$ and $3\text{ cm}$ respectively from the axis of rotation. Each ball weighs $4\text{ kg}$ and central load is $45\text{ kg}$. If the force of friction of the mechanism corresponds to the weight of $3\text{ kg}$ of the sleeve and if the extreme radii of rotations are $10\text{ cm}$ and $12\text{ cm}$, determine the range of speed of governor.

A shaft carries four masses in parallel planes A, B, C and D in the order along its length. The masses at B and C are $18\text{ kg}$ and $12.5\text{ kg}$ respectively and each has an eccentricity of $60\text{ mm}$. The masses at A and D have eccentricity of $80\text{ mm}$. The angle between the masses at B and C is $100\text{ degree}$ and that between the masses at B and A is $190\text{ degree}$. Both being measured in the same direction. The axial distance between the planes A and B is $100\text{ mm}$ and that between B and C is $200\text{ mm}$. If the shaft is in complete dynamic balance, determine—

(a) Piston, piston rod and cross head of a steam engine

(b) Which amongst the following constitutes higher pair?

(c) A ______ is an assemblage of resistant bodies having no relative motion between them.

(d) The total number of instantaneous centres for a mechanism with n links is

(e) The direction of linear velocity of any point on a link with respect to another point on the same link is ______ to the line joining these points.

(f) The open-belt drive is used when the shafts are arranged ______ and are to rotate in the ______ directions.

(g) Which one of the following is a spring-controlled centrifugal governor?

(h) Two parallel and coplanar shafts are connected by

(i) A ______ is an imaginary circle which by pure rolling action gives the same motion as the actual gear.

(j) A system of several masses revolving in different planes of a shaft can be completely balanced by ______ masses in ______ planes.

(a) What do you mean by inversion of a mechanism? Draw any three inversions of a single-slider crank mechanism.

(b) "Peaucellier mechanism is a straight line generating mechanism." Prove this.

The crank of a slider crank mechanism is 150 mm and the connecting rod is 600 mm long. The crank makes 300 r.p.m. in the clockwise direction. When it has turned 45 degree from inner dead centre position, determine— (a) acceleration of the midpoint of the connecting rod; (b) angular acceleration of the connecting rod. Use space diagram, velocity diagram and acceleration diagram.

(a) What are meant by slip and creep in a belt drive?

(b) A rope drive is required to transmit 1100 kW from a pulley 1·05 m in diameter running at 360 r.p.m. The safe pull in each rope is 2·2 kN and the mass of rope per meter of length is 1·35 kg. The angle of lap is 150 degree, the groove angle is 45 degree and the coefficient of friction between the rope and the groove is 0·3. How many ropes will be required if allowance is made for the centrifugal stress?

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

(b) A cone clutch is to transmit 7·5 kW at 850 r.p.m. The cone has a face angle of 11 degree. The width of the face is half of the mean radius and the normal pressure between the contact faces is not to exceed 0·09 N/mm². Assuming uniform wear and the coefficient of friction between contact faces as 0·2, find the main dimensions of the clutch and the axial force required to engage the clutch.

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

(b) Two involute gears of 20 degree pressure angle are in mesh. The number of teeth on pinion is 30 and the gear ratio is 2. The pitch expressed in module is 5 mm and the pitch line speed is 1.5 m/s. Assuming addendum on standard and equal to one module, find— (i) the angle turned through by pinion when one pair of teeth is in mesh; (ii) the maximum velocity of sliding.

(a) Explain with a sketch, the different types of gear trains depending upon the arrangement of wheels.

(b) An epicyclic gear consists of three wheels A, B and C as shown in figure below. Wheel A has 72 internal teeth, C has 32 external teeth. The wheel B gears with both A and C and is carried on an arm which rotates about the centre of A at 18 r.p.m. If the wheel A is fixed, determine the speed of wheels B and C.

All the arms of a Porter governor are 20 cm long. The lower and upper arms are pivoted to links of 4 cm and 3 cm respectively from the axis of rotation. Each ball weighs 4 kg and central load is 45 kg. If the force of friction of the mechanism corresponds to the weight of 3 kg of the sleeve and if the extreme radii of rotations are 10 cm and 12 cm, determine the range of speed of governor.

A shaft carries four masses in parallel planes A, B, C and D in the order along its length. The masses at B and C are 18 kg and 12.5 kg respectively and each has an eccentricity of 60 mm. The masses at A and D have [...] [incomplete question]

(a) Piston, piston rod and cross head of a steam engine

(b) Which amongst the following constitutes higher pair?

(c) A ______ is an assemblage of resistant bodies having no relative motion between them.

(d) The total number of instantaneous centres for a mechanism with n links is

(e) The direction of linear velocity of any point on a link with respect to another point on the same link is ______ to the line joining these points.

(f) The open-belt drive is used when the shafts are arranged ______ and are to rotate in the ______ directions.

(g) Which one of the following is a spring-controlled centrifugal governor?

(h) Two parallel and coplanar shafts are connected by

(i) A ______ is an imaginary circle which by pure rolling action gives the same motion as the actual gear.

(j) A system of several masses revolving in different planes of a shaft can be completely balanced by ______ masses in ______ planes.

(a) What do you mean by inversion of a mechanism? Draw any three inversions of a single-slider crank mechanism.

(b) "Peaucellier mechanism is a straight line generating mechanism." Prove this.

The crank of a slider crank mechanism is 150 mm and the connecting rod is 600 mm long. The crank makes 300 r.p.m. in the clockwise direction. When it has turned 45 degree from inner dead centre position, determine— (a) acceleration of the midpoint of the connecting rod; (b) angular acceleration of the connecting rod. Use space diagram, velocity diagram and acceleration diagram.

(a) What are meant by slip and creep in a belt drive?

(b) A rope drive is required to transmit 1100 kW from a pulley 1·05 m in diameter running at 360 r.p.m. The safe pull in each rope is 2·2 kN and the mass of rope per meter of length is 1·35 kg. The angle of lap is 150 degree, the groove angle is 45 degree and the coefficient of friction between the rope and the groove is 0·3. How many ropes will be required if allowance is made for the centrifugal stress?

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

(b) A cone clutch is to transmit 7·5 kW at 850 r.p.m. The cone has a face angle of 11 degree. The width of the face is half of the mean radius and the normal pressure between the contact faces is not to exceed 0·09 N/mm². Assuming uniform wear and the coefficient of friction between contact faces as 0·2, find the main dimensions of the clutch and the axial force required to engage the clutch.

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

(b) Two involute gears of 20 degree pressure angle are in mesh. The number of teeth on pinion is 30 and the gear ratio is 2. The pitch expressed in module is 5 mm and the pitch line speed is 1.5 m/s. Assuming addendum on standard and equal to one module, find— (i) the angle turned through by pinion when one pair of teeth is in mesh; (ii) the maximum velocity of sliding.

(a) Explain with a sketch, the different types of gear trains depending upon the arrangement of wheels.

(b) An epicyclic gear consists of three wheels A, B and C as shown in figure below. Wheel A has 72 internal teeth, C has 32 external teeth. The wheel B gears with both A and C and is carried on an arm which rotates about the centre of A at 18 r.p.m. If the wheel A is fixed, determine the speed of wheels B and C.

All the arms of a Porter governor are 20 cm long. The lower and upper arms are pivoted to links of 4 cm and 3 cm respectively from the axis of rotation. Each ball weighs 4 kg and central load is 45 kg. If the force of friction of the mechanism corresponds to the weight of 3 kg of the sleeve and if the extreme radii of rotations are 10 cm and 12 cm, determine the range of speed of governor.

A shaft carries four masses in parallel planes A, B, C and D in the order along its length. The masses at B and C are 18 kg and 12.5 kg respectively and each has an eccentricity of 60 mm. The masses at A and D have [...] [incomplete question]

Choose the correct option/Fill in the blanks (any seven):

Answer the following:

The crank of a slider crank mechanism is $150\text{ mm}$ and the connecting rod is $600\text{ mm}$ long. The crank makes $300\text{ r.p.m.}$ in the clockwise direction. When it has turned $45\text{ degree}$ from inner dead centre position, determine—

Answer the following:

Answer the following:

Answer the following:

Answer the following:

All the arms of a Porter governor are $20\text{ cm}$ long. The lower and upper arms are pivoted to links of $4\text{ cm}$ and $3\text{ cm}$ respectively from the axis of rotation. Each ball weighs $4\text{ kg}$ and central load is $45\text{ kg}$. If the force of friction of the mechanism corresponds to the weight of $3\text{ kg}$ of the sleeve and if the extreme radii of rotations are $10\text{ cm}$ and $12\text{ cm}$, determine the range of speed of governor.

A shaft carries four masses in parallel planes A, B, C and D in the order along its length. The masses at B and C are $18\text{ kg}$ and $12.5\text{ kg}$ respectively and each has an eccentricity of $60\text{ mm}$. The masses at A and D have ...