theory of machines - k. k. wagh polytechnic, nashikpoly.kkwagh.edu.in/dept data...
TRANSCRIPT
Theory of Machines
Page | 1 K K Wagh Polytechnic, Nashik-03
CH-1: Fundamentals and type of Mechanisms
2 Marks Questions
1. Define kinematic link and kinematic chain.
2. Enlist the types of constrained motion. Draw a label sketch of any one.
3. Define –(1) Mechanism (2) Inversion of mechanism
4 Marks Questions
1. Define kinematic pair and state its types.
2. Describe with neat sketch the working of a crank and slotted lever quick return
mechanism.
3. Justify with neat sketch elliptical trammel as an inversion of double slider crank
chain…*
4. Define completely constrained motion and successfully constrained motion with neat
sketch. State one example of each…***
5. Explain with neat sketch working principle of Oldham’s coupling…**
6. State inversion of double slider crank chain. Explain Oldham’s coupling with neat
sketch.
7. Draw a labelled sketch of Quick return mechanism of shaper and explain its working.
8. What are the types of kinematic pair ? Give its examples.
9. Define : (i) Spherical pair (ii) Higher pair.
10. State any four inversions of single slider crank chain. Describe any one with neat
sketch.
11. What is a machine ? Differentiate between a machine and a structure…**
12. Describe with neat sketch the working of scotch yoke mechanism.
13. Justify that slider crank mechanism is a modification of the basic four bar mechanism
with neat sketch.
14. State the meaning of sliding pair, turning pair, rolling pair and spherical pair with one
example each.
8 Marks Questions
1. List out the various inversions of double slider crank chain and explain the
working of Oldham’s coupling with the help of neat sketch.
Theory of Machines
Page | 2 K K Wagh Polytechnic, Nashik-03
CH-2: Velocity & Acceleration in Mechanisms
2 Marks Questions
1. Define (i) Pressure angle (ii) pitch point related to cam.
4 Marks Questions
1. State the formula for calculating: i) velocity ii) acceleration of piston and connecting
rod using analytical method.
2. Explain Klein’s construction of determine velocity and acceleration of different links
in single slider crank mechanism.
3. In a four bar chain ABCD, AD is fixed and is 150 mm long. The crank AB is 40 mm
long and rotates at 120 r.p.m clockwise, while the link CD = 80 mm oscillates about
D. BC and AB are of equal length. Find the angular velocity of link CD when angle
BAD = 60°.
4. The crank of a slider crank mechanism rotates clockwise at a constant speed of 300
r.p.m. The crank is 150 mm and the connecting rod is 600 mm long. Determine linear
velocity and acceleration of the midpoint of the connecting rod at a crank angle of 45°
from inner dead centre position.
5. Define linear velocity, angular velocity, absolute velocity and state the relation
between linear velocity and angular velocity.
6. Describe stepwise procedure for determination of velocity and acceleration by Klein’s
construction with suitable data.
7. PQRS is a four bar chain with PS fixed length of links are PQ = 62.5 mm, QR =175
mm, RS = 112.5 mm, PS = 200 mm. The crank PQ rotate at 10 rad/sec. in clockwise
direction. Determine the angular velocity of point R, graphically by using relative
velocity method.
8. Crank OA of a mechanism is hinged at ‘O’ and rotates at an angular velocity of 20
rad/sec. and angular acceleration of 25 rad/sec2. If crank OA is 50 mm long determine
linear velocity, centripetal acceleration and tangential acceleration of a point A.
9. Explain the inter-relation between linear and angular velocity, linear and angular
acceleration with suitable example.
10. Explain the Klein’s construction to determine velocity and acceleration of single
slider crank mechanism.
11. In a slider-crank mechanism, the crank is 480 mm long and rotates at 20 rad/sec in the
counter-clockwise direction. The length of the connecting rod is 1600 mm. when the
crank turns 60° from the inner-dead centre. Determine the velocity of the slider by
relative velocity method.
12. In a slider crank mechanism, crank AB = 20 mm & connecting rod BC = 80 mm.
Crank AB rotates with uniform speed of 1000 rpm in anticlockwise direction. Find (i)
Angular velocity of connecting rod BC (ii) Velocity of slider C. When crank AB
makes an angle of 60 degrees with the horizontal. Draw the configuration diagram
also. Use analytical method.
Theory of Machines
Page | 3 K K Wagh Polytechnic, Nashik-03
13. Draw the labelled displacement, velocity and acceleration diagrams for a follower
when it moves with simple harmonic motion.
14. In a four-link mechanism, the crank AB rotates at 36 rad/sec. The lengths of a link are
AB = 200 mm, BC = 400 mm, CD = 450 mm and AD = 600 mm. AD is the fixed
link. At the instant when AB is at right angles to AD determine the velocity of : (i)
The midpoint of link BC (ii) A point on the link CD, 100 mm from the pin connecting
the link CD & AD.
15. In a slider crank mechanism, the length of crank OB and connecting rod AB are 125
mm and 500 mm respectively. The centre of gravity G of the connecting rod is 275
mm from the slider. The crank speed is 600 rpm close wise. When the crank has
turned 45º from the inner dead centre position, determine: (i) Velocity of slider ‘A’
(ii) Velocity of the point ‘G’ graphically. Draw the configuration diagram also.
16. Define the terms linear velocity, relative velocity, angular velocity and angular
acceleration.
17. For a single slider crank mechanism, state the formulae to calculate by analytical
method – (i) Velocity of slider (ii) Acceleration of slider (iii) Angular velocity of
connecting rod (iv) Angular acceleration of connecting rod. Also, state the meaning of
each term.
18. In a four bar chain ABCD, AD is fixed and is 150 mm long. The crank AB is 40 mm
long and rotates at 120 rpm clockwise. The link CD = 80 mm oscillates about D.BC
and AD are of equal length. Find the angular velocity of link CD when angle BAD =
60°
19. In a single slider crank mechanism, crank AB = 20 mm and connecting rod BC = 80
mm. Crank AB rotates with uniform speed of 1000 rpm in anticlockwise direction.
Find (i) angular velocity of connecting rod BC and (ii) Velocity of slider C when
crank AB makes angle of 60° with the horizontal.
8 Marks Questions
1. 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 is 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.
2. In reciprocating engine the crank is 250 mm long and connecting rod is 1000 mm
long. The crank rotate at 150 rpm. Find velocity and acceleration of piston and
angular velocity and angular acceleration of connecting rod when the crank makes an
angle of 30° to IDC. Use analytical method.
3. In a slider crank mechanism shown in figure 1.
Theory of Machines
Page | 4 K K Wagh Polytechnic, Nashik-03
Calculate : (i) The acceleration of the slider at B (ii) The acceleration of point E. (iii)
The acceleration of link AB. OA rotates at 20 rad/sec counter – clockwise.
4. In a slider crank mechanism, the crank is 480 mm long and rotates at 20 rad/sec in the
counter – closewise direction. The length of the connecting rod is 1.6 m when the
crank turns 60º from the inner-dead centre determine by relative velocity method (i)
Velocity of slider (ii) Velocity of a point E located at a distance 450 mm on the
connecting rod extended. (iii) Angular velocity of the connecting rod.
5. The crank and connecting rod of a reciprocating engine are 200 mm and 700 mm
respectively. The crank is rotating in clockwise direction at 120 rad/s. Draw Klein’s
construction and find (i) Velocity and acceleration of the piston (ii) Angular velocity
and angular acceleration of the connecting rod at the instant when the crank is at 30°
to IDC (inner dead centre)
Theory of Machines
Page | 5 K K Wagh Polytechnic, Nashik-03
CH-3: Cams & Followers
2 Marks Questions
1. Write the classification of follower.
2. Enlist the different type of follower motion.
3. Define : (i) Radial follower (ii) Off-set follower.
4. State any two types of motion of the follower.
4 Marks Questions
1. Why roller follower is preferred over a knife follower ? State two advantages and
application of roller follower…***
2. State different types of cam and follower motion.
3. A cam is to be designed for a knife edge follower with the following data: i) cam lift
= 40 mm during 90° of cam rotation with SHM. ii) Dwell for the next 30° iii) During
the next 60° of cam rotation, the follower returns to its original position with S.H.M.
iv) Dwell during the remaining 18º
4. 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 40 mm.
5. Draw a neat sketch of radial cam with roller follower and show the following on it :
(i) Pitch point (ii) Pressure angle (iii) Prime circle (iv) Trace point.
6. Draw a neat sketch of Radial cam with roller follower and show on it : (i) Base circle
(ii) Pitch point (iii) Prime circle (iv) Cam profile.
7. What are the different types of follower motion ? Also draw displacement diagram for
uniform velocity.
8. Define the following terms as applied to cam with a neat sketch : (i) Base circle (ii)
Pitch circle (iii) Pressure angle (iv) Stroke of the follower.
9. Define the following terms related to cams (i) Trace point (ii) Pitch curve (iii) Prime
circle (iv) Lift or stroke.
10. Give detailed classification of followers.
8 Marks Questions
1. Construct a cam profile with knife edge follower having an offset of 10 mm for the
following data : Outstroke = 60° with SHM Dwell = 30° Return = 60° with
uniform velocity and remaining is dwell period. Minimum radius of cam = 50 mm
Lift of follower = 25 mm Consider the rotation of cam in clockwise direction.
2. A cam is to be designed for a knife edge follower with the following data: i) cam lift
=40 mm during 90° of cam rotation with SHM. ii) Dwell for the next 30° iii) During
the next 60° of cam rotation, the follower returns to its original position with S.H.M.
iv) Dwell during the remaining 18º6
Theory of Machines
Page | 6 K K Wagh Polytechnic, Nashik-03
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 40 mm.
3. Draw the profile of cam operating a roller reciprocating follower with the following
data : Minimum radius of cam = 25 mm, lift = 30 mm, Roller diameter = 15 mm The
cam lifts the follower for 120° with SHM followed by a dwell period of 30°. Then the
follower lowers down during 150° of the cam rotation with uniform acceleration and
deceleration followed by a dwell period.
4. 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 = 120º, Angle of fall = 150º, lift of the follower = 40 mm, number of pauses are
two of equal interval between motions. During the lift the motions is SHM. 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 by 12.5 mm from the
centre of the cam.
5. A cam is to give the following motion to a knife edged follower : (i) Outstroke during
60° of cam rotation. (ii) Dwell for the next 30° of cam rotation. (iii) Return stroke
during next 60° of cam rotation. (iv) Dwell for the remaining 210° of cam rotation.
The stroke of the follower is 40 mm and the minimum radius of the cam is 50 mm.
The follower moves with uniform velocity during both the outstroke and return
stroke. Draw the profile of the cam when the axis of the follower passes through the
axis of the camshaft.
Theory of Machines
Page | 7 K K Wagh Polytechnic, Nashik-03
CH-4: Power Transmission
2 Marks Questions
1. What are the two advantages and disadvantages of chain drive ?
2. Define angle of lap and slip in belt drive.
3. State four conditions under which the ‘V’ belt drive is selected.
4. How are drives classified ?
5. Write any two disadvantages of chain drive.
6. What do you mean by crowning of pulleys in flat belt drive ? State its use.
7. Define slip and creep in belt drive.
8. State any two advantages of V belt drive over flat belt drive.
4 Marks Questions
1. State one application of each. V-belt drive, flat belt drive, gear drive and chain drive.
2. In a flat belt drive the initial tension is 2000 N. The coefficient of friction between the
belt and the pulley is 0.3 and the angle of lap on the smaller pulley is 150°. The
smaller pulley has a radius of 200 mm and rotates of 500 r.p.m. Find the power in KW
transmitted by the belt.
3. State types of gear train and explain any one.
4. Write the equation relating tension on slack and tight side. Explain in brief the term in
it in case of flat belt.
5. Compare cross belt drive and open belt drive on the basis of: (i) velocity ratio (ii)
application (iii) direction of driven pulley (iv) length of belt drive
6. The central distance between two shaft is 4 m having two pulleys with diameter
having 500 mm and 700 mm respectively. Find length of belt required (i) for open
belt drive (ii) for cross belt drive.
7. State the type of power transmission chains. Describe any one with its sketch.
8. Explain the phenomenon of slip and creep in a belt drive. State its effect on velocity
ratio.
9. Compare cross belt drive and open belt drive on the basis of : (i) velocity ratio (ii)
direction of driven pulley (iii) length of belt drive (iv) Application
10. A shaft runs at 80 rpm & drives another shaft at 150 rpm through belt drive. The
diameter of the driving pulley is 600 mm. Determine the diameter of the driven pulley
in the following cases : (i) Taking belt thickness as 5 mm (ii) Assuming for belt
thickness 5 mm and total slip of 4%.
11. Explain epicyclic gear train with neat sketch.
12. State and explain Law of Gearing.
13. Explain steep and creep phenomenon in belts.
14. Define slip and creep with reference to belt drive. Also state their effect on velocity
ratio.
Theory of Machines
Page | 8 K K Wagh Polytechnic, Nashik-03
15. A pulley rotating at 50 m/s transmits 40 kW. The safe pull in belt is 400 N/cm width
of belt. The angle of lap is 170º. If coefficient of friction is 0.24, find required width
of belt.
16. State four advantages and four disadvantages of chain drive over belt drive.
17. Draw neat labelled sketch of spur gear terminology.
18. Draw the neat sketch of epicyclic gear train and explain how it works.
19. 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. Taking μ = 0.25, determine (i) the force required by the man (ii) the power to
raise the casting.
20. State the formulae to calculate the length of open belt drive and cross belt drive. State
the meaning of each term by drawing suitable diagrams in both cases.
21. What is centrifugal tension ? State its formula. Explain its effect on power transmitted
by a belt drive.
8 Marks Questions
1. Explain with sketch working principle of epicyclic gear trains & Compare flywheel
and governor.
2. A belt is required to transmit 10 kW from a motor running at 600 rpm. The belt is 12
mm thick and has a mass density 0.001 gm/mm3. Safe stress in the belt is not to
exceed 2.5 N/mm2, diameter of the driving pulley is 250 mm whereas the speed of the
driven pulley is 200 rpm. The two shafts are 1.25 m apart. The coefficient of friction
is 0.25, determine (1) Angle of contact at driving pulley (2) The width of the belt
3. (i) Define ‘Gear Train’. State its purpose and types of gear train. (ii) Explain the
concept of fluctuation of energy related with turning moment diagram with sketch.
4. Two parallel shafts, connected by a crossed belt, are provided with pulleys 480 mm
and 640 mm in diameters. The distance between the centre lines of the shafts is 3 m.
Find by how much the length of the belt should be changed if it is desired to alter the
direction of rotation of the driven shaft.
5. An epicyclic gear train is shown in figure no. 1. The number of teeth on A and B are
80 and 200. Determine the speed of the arm, ‘a’ (i) if A rotates at 100 rpm clockwise
and B at 50 rpm counter-clockwise. (ii) if A rotates at 100 rpm clockwise and B is
stationary.
6. Two parallel shafts whose centre line are 4.8 m apart, are connected by open belt
drive. The diameter of larger pulley is 1.5 m and that of smaller pulley 1 m. The initial
Theory of Machines
Page | 9 K K Wagh Polytechnic, Nashik-03
tension in the belt when stationary is 3 kN. The mass of the belt is 1.5 kg/m length.
The coefficient of friction between the belt and pulley is 0.3 Taking centrifugal
tension into account, calculate the power transmitted when the smaller pulley rotates
at 400 rpm.
7. In a simple band brake, the band acts on the 3/4th of circumference of a drum of 450
mm diameter which is keyed to the shaft. The band brake provides a braking torque of
225 N.m. One end of the band is attached to a fulcrum pin of the lever and the other
end to a pin 100 mm from the fulcrum. It the operating force is applied at 500 mm
from the fulcrum and the coefficient of friction is 0.25, find the operating force when
the drum rotates in the
(i) anticlockwise direction and
(ii) clockwise direction
Theory of Machines
Page | 10 K K Wagh Polytechnic, Nashik-03
CH-5: Flywheel & Governors
2 Marks Questions
1. Define fluctuation of speed and fluctuation of energy…***
2. State the function of Governor in an I.C. engine…**
3. State four applications of flywheel.
4. Draw a line diagram of porter governor.
5. Define the sensitivity in relation to governor. State its significance.
6. State the function of flywheel in I.C. Engine.
7. Define stability and hunting of governor.
4 Marks Questions
1. Draw and explain the turning moment diagram of four stroke I.C engine…***
2. Explain with sketch working of hartnell governor.
3. Differentiate between flywheel and governor…***
8 Marks Questions
1. Explain with sketch working principle of epicyclic gear train.
2. Draw the neat labelled sketch of centrifugal governor.
Theory of Machines
Page | 11 K K Wagh Polytechnic, Nashik-03
CH-6: Brakes & Dynamometers
2 Marks Questions
1. State type of brakes.
2. Give the classification of dynamometer. State the function of it.
3. State the application of (i) Disc brake (ii) Internal expanding brake.
4. Draw a neat labelled sketch of internal expanding brake.
5. Compare brakes and dynamometers. (Any two points)
4 Marks Questions
1. Explain with neat sketch construction and working of eddy current
dynamometer…***
2. Explain working of hydraulic brake dynamometer with sketch.
3. Explain the working of rope brake dynamometer with neat sketch.
8 Marks Questions
1. A band brake acts on the ¾th of circumference of a drum of 450 mm diameter which
is keyed to the shaft. The band brake provides a breaking torque of 225 N-M. one end
of the band is attached to a fulcrum pin of the lever and the other end to a pin 100 mm
from the fulcrum. If the operating force is applied at 500 mm from the fulcrum and
the coefficient of friction is 0.25. Find the operating force when the drum rotates in
the i) anticlockwise direction and ii) clockwise direction.
2. A simple band brake is operated by lever 40 cm long. The brake drum diameter is 40
cm and brake band embrance 5/8 of its circumference. One end of band is attached to
a fulcrum of lever while other end attached to pin 8 cm from fulcrum. The coefficient
of friction 0.25. The effort applied at the end of lever is 500 N. Find braking torque
applied if drum rotates anticlockwise and acts downwards.
3. A simple band brake shown in figure 2 is applied to a shaft carrying a flywheel of
mass 250 kg and of radius of gyration 300 mm. The shaft speed is 200 rpm. The drum
diameter is 200 mm and the coefficient of friction is 0.25. The dimensions a and l are
100 mm and 280 mm respectively and the angle β = 135°. Determine (i) the brake
torque when a force of 120 N is applied at the lever end. (ii) the number of turns of
the flywheel before it comes to rest. (iii) the time taken by flywheel to come to rest.
Theory of Machines
Page | 12 K K Wagh Polytechnic, Nashik-03
4. A band brake acts on the 34th of the circumference of a drum of 450 mm diameter
which is keyed to the shaft. The band brake provides a braking torque of 225 N.m.
One end of the band is attached to a fulcrum pin of the lever and the other end to a pin
100 mm from the fulcrum. If the operating force is applied at 500 mm from the
fulcrum and the coefficient of friction is 0.25, find the operating force when the drum
rotates in the (i) anticlockwise direction (ii) clockwise direction.
Theory of Machines
Page | 13 K K Wagh Polytechnic, Nashik-03
CH-7: Clutches & Bearings
2 Marks Questions
1. List out various types of clutches used to transmit the power.
2. List out various types of bearings used.
4 Marks Questions
1. State types of clutch and its applications…***
2. Draw a neat labeled sketch of multiplate clutch and state it’s working.
3. A single plate clutch with both sides effective, has outer and inner diameter 300 mm
and 200 mm respectively. The maximum intensity of pressure at any point in the
contact surface is not to exceed 0.1 N/mm2. If the coefficient of friction is 0.3,
determine the power transmitted by a clutch at a speed 2500 r.p.m.
4. Explain working principle of clutch. State its location in transmission system of an
automobile.
5. A thrust shaft of a ship has 6 collar of 600 mm external diameter and 300 mm internal
diameter. The total thrust from the propeller shaft is 100 kN. If the coefficient of
friction is 0.12 and speed of engine 90 rpm. Find power absorbed in friction at the
thrust block using uniform pressure intensity condition.
6. Explain (i) uniform pressure theory (ii) uniform wear theory in clutches and bearings.
7. A multiplate disc clutch transmits 55 kW of power at 1800 rpm. Coefficient of
friction for the friction surfaces is 0.1. Axial intensity of pressure is not to exceed 160
kN/m2. The internal radius is 80 mm and is 0.7 times the external radius. Find the
number of plates needed to transmit the required torque.
8. State any four types of friction clutch, along with its application each.
9. Explain with neat sketch working of a centrifugal clutch.
10. A car engine has a single plate clutch having outside diameter of 25 cm and inside
diameter of 20 cm. If the axial load exerted by springs is 1500 N, determine the power
transmitted by the clutch at 700 rpm. Assume uniform wear μ = 0.3
11. What is the necessity of clutch ? State its types.
12. Draw the neat sketch of single plate clutch and explain its working…**
13. A vertical shaft 150 mm in diameter and rotating at 100 rpm rests on a flat end
footstep bearing. The shaft carries vertical load of 20 kN. Assuming uniform pressure
distribution and coefficient of friction equal to 0.05, estimate power lost in friction.
8 Marks Questions
1. An engine of a car has a single plate clutch developed maximum torque 147 N-m.
External diameter of clutch plate is 1.2 times its internal diameter. Determine the
dimension of clutch plate and axial force provided by the spring. The maximum
pressure intensity of the clutch facing 98 kN/m2 and coefficient of friction is 0.3.
Assume uniform wear condition.
2. A conical pivot with angle of cone as 100°, supports a load of 18 kN. The external
radius is 2.5 times the internal radius. The shaft rotates at 150 rpm. If the intensity of
Theory of Machines
Page | 14 K K Wagh Polytechnic, Nashik-03
pressure is to be 300 kN/m2 and coefficient of friction as 0.05, what is the power lost
in working against the friction ?
3. Determine the power lost in a footstep bearing due to friction if a load of 15 kN is
supported and the shaft is rotating at 100 rpm. The diameter of bearing is 15 cm and
coefficient of friction is 0.05. Assume : (i) Uniform wear condition (ii) Uniform
pressure condition.
4. A single plate clutch with both sides effective has outer and inner diameters 300 mm
and 200 mm respectively. The maximum intensity of pressure at any point in the
contact surface is not to exceed 0.1 N/mm2. If the coefficient of friction is 0.3,
determine the power transmitted by a clutch at a speed of 2500 rpm. Assume uniform
condition.
Theory of Machines
Page | 15 K K Wagh Polytechnic, Nashik-03
CH-8: Balancing
2 Marks Questions
1. What is balancing? What are the methods of balancing?
2. Why is balancing of rotating parts necessary for high speed engines ?
3. State the adverse effect of imbalance of rotating elements of machine.
4. State any two adverse effects of imbalance.
4 Marks Questions
1. Explain the method of balancing of different masses revolving in the same plane.
2. Four masses A, B, C and D are attached to a shaft and revolve in the same plane. The
masses are 12 kg, 10 kg, 18 kg and 15 kg respectively and their radii of rotations are
40 mm, 50 mm, 60 mm and 30 mm. The angular position of the masses B, C and D
are 60°, 135° and 270° from the mass A. Find the magnitude and position of the
balancing mass at a radius of 100 mm.
3. Write the procedure for balancing of a single rotating mass by single masses rotating
in the same plane…****
4. Three masses 10 kg, 20 kg and 15 kg are attached at a point at radii of 20 cm, 25 cm
and 15 cm respectively. If the angle between successive masses is 60° and 90°.
Determine analytically the balancing mass to be attached at radius of 30 cm.
5. A rotor having the following properties :
m1 = 4 kg r1 = 75 mm Ɵ1 = 45°
m2 = 3 kg r2 = 85 mm Ɵ2 = 135°
m3 = 2.5 kg r3 = 50 mm Ɵ3 = 240°
Determine the amount of the countermass at a radial distance of 75 mm required for
the static balance.
6. Four masses are 260 kg, 160 kg, 300 kg and 200 kg. The corresponding radii of
rotation 300 mm, 250 mm, 150 mm and 200 mm respectively. The angle between
successive masses are, 0º, 45º, 90º and 135º. Find the position and magnitude of
balancing mass required, if its radius of rotation is 200 mm by using graphical
method.
7. Four masses m1, m2, m3 and m4 are 200 kg, 300 kg, 240 kg, and 260 kg respectively.
The corresponding radii of rotation are 0.2 m, 0.15 m, 0.25 m and 0.3 m respectively
and the angles between successive masses are 45°, 75° and 135°. Find the position
and magnitude of balance mass required, if its radius of rotation is 0.2 m.