THEORY OF MACHINES - 2 MARKS

 

 

 

 

2 MARKS Q & A

ME 3491 – THEORY OF MACHINES

 

 

 

 

 

N.SITHIVINAYAGAM, AP/MECH

II YEAR MECH - A

 

 

DEPARTMENT OF MECHANICAL ENGINEERING

MRK INSTITUTE OF TECHNOLOGY

KATTUMNANNARKOIL – 608301

 

 

ME 3491–THEORY OF MACHINES

UNIT-I

 

1.      1. Differentiate between lower pair and higher pair.(APR/MAY 2023)

A pair of links having surface or area contact between the members is known as a lower pair. The contact surface of the two links is similar. When a pair has a point or line contact between the links, it is known as a higher pair

2.      Name the two methods of finding acceleration in a mechanism. (APR/MAY 2023)

1.      Instantaneous centre method, and

2.      Relative velocity method

3.      Name any four perfect straight line generating mechanism.

1. The peacellier mechanism.

2. The hart mechanism

3. The Scott Russell mechanism

4. a Robert linkages

4.      Differentiate between the structure and mechanism.

SI. No	Structure	Mechanism
1	No relative motion exists between its members.	Mechanism is assemblage of links used to transmit and modify motion.
2	It does not convert the available energy into work.	A mechanism is the skeleton outline of the machine primarily to transmit definite motion between various links.
3	Example: Bridges, Roof trusses	Example: Drafter, typewriter & clocks

                       

5.      Identify whether the kinematic chain with the following link lengths is Grashofian or not 60 mm, 120 mm, 90 mm and 110 mm.

Given: AB = 60mm, BC=120mm, CD=90mm & AD = 110mm

            s = length of shortest link = 60 mm

              l = length of longest link = 120 mm

p & q = length of other two links

Here s +l = 60 + 120 =180 mm and  p + q = 90 + 100 =190 mm

Since (i) s + l ≤ p + q and (ii) any one of the links adjacent to the shortest link is fixed, therefore the given mechanism is crank-rocker mechanism.

6.      Write the different types of kinematic pairs based on the relative motion between them.

            i) Sliding pair;             (ii) Turning pair;

(iii) Rolling pair; and  (iv) Screw pair

 

7.      Differentiate machine and structure.

SI. No	Machine	Structure
1	Relative motion exists between its parts.	No relative motion exists between its members.
2	It transforms available energy into useful work.	It does not convert the available energy into work.
3	Links are meant to transmit motion and forces.	Members are meant for carrying loads having straining action.

8.      Define rigid link and give examples.

SI. No	Rigid links	Example
1	A Rigid link is one which does not undergo any deformation while transmitting motion.	Example : Connecting rod, Piston

9.      List out the inversions of a double slider crank chain.

1) Elliptical trammel. 2) Scotch yoke mechanism.    3) Oldham’s Coupling.

10.  Determine the number of freedom of the mechanism shown in the fig. below.

11.  Write short notes on complete and incomplete constraint in lower and higher pairs, depict your answer with neat sketches.

1. Completely constrained motion. When the motion between a pair is limited to a definite direction irrespective of the direction of force applied, then the motion is said to be a completely constrained motion.

12.  Define Grubler’s criteria for a mechanism.

The grubler’s criterion for plane mechanism is given by      

Where  l           = Number of links in the mechanism, and

                        j           = Number of binary joints.

The Grubler’s criterion applies to mechanisms with only single degree of freedom joints and the overall mobility of the mechanism is unity.

13. Name any two inversion of the 4-bar chain.

Three in versions are possible from a four-bar kinematic chain. They are:

ü  Crank-rocker mechanism or Rotary – oscillating converter.

ü  Double crank mechanism or Rotary – rotary converter.

ü  Double rocker mechanism or Oscillating – oscillating converter.

14. Classify kinematic pairs based on nature of contact. Give examples.

Kinematic pair based on nature of contact:

ü  Lower pair – example :Nut and bolt, Ball and socket joints,

ü  Higher pair – example - Cam and follower, Roller bearing, Ball bearing.

15. When a linkage becomes mechanism?

When one of the links of a kinematic chain is fixed, the chain is known as mechanism. It may be used for transmitting or transforming motion. Ex: Engine indicators, typewriter.

16. State and sketch any two inversions of a double slider mechanism.

PART-2:KINEMATICS OF LINKAGE MECHANISMS

17.  Define instantaneous centre.

ü  Definition:  Instantaneous centre of a moving body is defined as the centre which goes on changing from one instant to another.

ü  In a single slider crank mechanism, there are four links.

Number of instantaneous centres,

18.  State the application of velocity diagrams.

Since the dynamic force are function of acceleration (F=ma) and acceleration are the function of velocities (a=dv/dt), the for the determination of velocity and acceleration of various links become very important in the design of any mechanism.

With the advent of calculators and computers analytical methods are becoming more convenient and popular.  However the graphical methods are essential in developing a conceptual understanding about the subject.

19.  Why storm rotates counter clockwise in northern hemisphere?

Cyclones are shaped by the Coriolis effect. As they rotate, cyclones pull air into their center, or "eye." These air currents are pulled in from all directions. In the Northern Hemisphere, they bend to the right. This makes the cyclone rotate counterclockwise.

20.  What are the types of instantaneous centers?

Three types of instantaneous centers are (refer Fig.1) :

ü  Fixed instantaneous centres: From the Fig.1, I₁₂ and I₁₄ are called the fixed instantaneous centres as they remain in the same place for all configurations of the mechanism.

ü  Permanent instantaneous centres: I₂₃ and I₃₄ are called the permanent instantaneous centres as they move when the mechanism moves, but the joints are of permanent nature.

ü  Neither fixed nor permanent centres: I₁₃ and I₂₃are neither fixed nor permanent instantaneous centres as they vary with the configuration of the mechanism.

21.  Define rubbing velocity at a pin joint.

ü Definition:The rubbing velocity is defined as the algebraic sum between the angular velocities of the two links which are connected by pin joints, multiplied by the radius of the pin.

ü Rubbing velocity at a pin joint when the two links move in the same directions

=

ü Rubbing velocity at a pin joint when the two links move in the opposite directions

=

Where and   = Angular velocities of the link 1 and link 2 respectively, and

                  r                       = Radius of the pin.

22.  What is meant by normal component of acceleration?

ü  Normal (or Radial or centripetal) component is perpendicular to the velocity of the particle at the given instant. In other words, the normal component acts parallel to the link.

 

23.  Define centrode.

ü The locus of the instantaneous centre in space during a definite motion of the body is called the space centrode.

ü The locus of the instantaneous centre relative to the body itself is called the body centrode.

ü The space and body centrodes are illustrated in Fig.l.

 

24. Write the relation between the number of instantaneous centers and the number of links in mechanism.

Definition:  Instantaneous centre of a moving body is defined as the centre which goes on changing from one instant to another.

In a single slider crank mechanism, there are four links.

Number of instantaneous centres,

25.  Depict all the directions of Coriolis component of acceleration that arise in a completed cycle of quick return motion of the crank mechanism.

Coriolis component of acceleration occurs when a point on one link is sliding along another rotating link, such as in quick return mechanism.

                        where              w = Angular velocity of ‘oA’ and

                                                V = Linear velocity of ‘B’.

26.  What is the total number of instantaneous centre that are possible for a mechanism consisting ‘n’ links?

Definition:  Instantaneous centre of a moving body is defined as the centre which goes on changing from one instant to another.

In a single slider crank mechanism, there are four links.

Number of instantaneous centers,

 

27.  Name the mechanism in which corolis component of acceleration  is taken into account.

1) Crank and slotted lever mechanism.

2) Whit worth Quick return mechanism

3) Toggle mechanism

28.  What is a relative pole, with respect to velocity analysis?

Definition:In the relative velocity method, it is based upon the relative velocity of various point of the link of given mechanism. In it is taking a some convenient point may be a ‘o’ or ‘a & q’ is known as relative pole.

29.  What are the different methods used for finding the velocity?

Ø  Instantaneous centre method

Ø  Relative velocity method, and

Ø  Analytical method

30.  State and prove Kennedy’s three centre theorem.

The Kennedy’s theorem states that if three bodies move relatively to each other, they have three instantaneous centers and lie on a straight line.

31.  Sketch the Geneva wheel indexing mechanism and state its application.

            Geneva mechanism is used in rotary tables and indexing turrets in machine tools and in automatic machines. The sketch is shown in Fig.1.

32.  Distinguish normal component of acceleration and tangential component of acceleration.

Normal (or Radial or centripetal) component is perpendicular to the velocity of the particle at the given instant. In other words, the normal component acts parallel to the link.

Tangential component is parallel to the velocity of the particle at the given instant. In other words, it acts perpendicular to the link.

    

PART-3: KINEMATICS OF CAMMECHANISMS

33.  List the effects of Cam sizing.

1.      The pressure angle

2.      Radius of curvature

34.  When undercutting occurs in cams? How it can be eliminated?

Undercutting occurs in the cam because of attempting to achieve too great a follower lift with very small cam rotation with a smaller cam.

It can be eliminated by following methods 1) By decreasing the follower lift. 2) By increasing cam rotation angle.

 

 

35.  Write any two conditions to avoid undercutting in a cam-follower mechanism.

            1) By decreasing the follower lift.

            2) By increasing cam rotation angle.

36.  Draw a sketch to show prime circle in a cam-follower mechanism.

37.  Differentiate between radial cam and cylindrical cams.

radial cam	cylindrical cam
ü  In radial cams, he follower reciprocates or oscillates in direction perpendicullar to the cam axis is shown in Fig.	ü  A cylindrical cam with a follower reciprocates in a direction parallel to the cam axis is shown in Fig.

38.  Define Prime circle and pitch curve of a cam.

Prime circle:The smallest circle drawn tangent to the pitch curve is known as prime circle.

pitch curve : The locus or path of the tracing point is known as the pitch curve. For the purpose of laying out the cam profiles, it is assumed that the cam is fixed and the follower rotates around it.

39.  Define tangent cam.

When the flanks of the cam are straight and tangential to the base circle and nose circle, the cam is known as tangent cam.

40.  Draw the displacement diagram for a follower when it moves with uniform acceleration and retardation.

 

 

 

 

 

 

41.  List the methods used to reduce the pressure angle of cam.

ü  It is the angle between the direction of the follower motion and a normal to the pitch curve.

ü  Best value of the pressure angle is below 30^◦.

ü  The pressure angle increases, the force required to lift the follower increases.

42.  Define trace point of a cam.

It is a reference point on the follower and is used to generate the pitch curve. In case of knife edge follower the knife edge represents the trace point and the pitch curve corresponds to the cam profile.

43.  Define the following with respect to cam and follower mechanism

a.      Pressure angle

Definition:It is the angle between the direction of the follower motion and a normal to the pitch curve.

b.      Pitch circle

It is the circle passing through the pitch point and concentric with the base circle.

44.  State the reason for providing offset in a cam follower mechanism.

The offset causes a reduction of the side thrust present in the follower

45.  Sketch a cylindrical cam, the follower reciprocates in a direction parallel to the cam axis and also a cylindrical cam with oscillation follower.

ü  A cylindrical cam with a follower reciprocates in a direction parallel to the cam axis is shown in Fig.2(a).

ü  A cylindrical cam with oscillating follower is shown in Fig.2 (b).

 

46.  Draw the displacement, velocity, and acceleration diagram for a follower when it moves with simple harmonic motion.

47.  Why a roller follower is preferred to that of a knife-edged follower?

ü Tangent cams are symmetrical and easy to manufacture.

ü They are less costly to manufacture.

ü They are used for operating the inlet and exhaust valves of I.C. engine.

48.  Derive the equation to determine the maximum velocity and the maximum acceleration when the follower has simple harmonic motion.

                      

                  

49.  State the expressions to determine the maximum velocity and acceleration when the follower moves with simple harmonic motion.

Maximum velocity:                           

Maximum acceleration:                

                        Where S = Stroke of the follower,

                                     =  Angular velocity of the cam in rad/s, and

                        θ₀ and θ_R = Angle of ascent and angle of descent.

 

50.  Sketch displacement, velocity and acceleration diagram for simple harmonic motion and indicate the maximum velocity and maximum acceleration position.

51.  Sketch any four types of follower with cam arrangement.

52.  Enumerate any four different types of follower motions of a cam.

53.  State, atleast, one disadvantage of flat faced follower over roller follower in a cam mechanism.

ü  Advantage: Limited space and reduced failure at pin points.

ü  Disadvantage : Comparatively more surface stress and wear rate.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

UNIT – 2 : GEARS AND GEAR TRAINS

1. 3. Two mating spur gears have 74 and 36 teeth. Their common module is 5 mm. Determine the centre to centre distance between the gear axis.(APR/MAY 2023)

Given: T_A=74, T_B=36 ,  m=5 mm

Module, m=

For gear A, D_A= m T_A and

For gear A, D_A= m T_B

Centre Distance, C =

2. Where the epicyclic gear trains are used? (APR/MAY 2023)

Differential gears of automobile, back gear of lathe, wrist watches, etc.

3. Name the gear drives used for each of the following :

(i) Very high speed reduction ratio (100:1) and (ii) intersecting perpendicular shaft axes.

Very high speed reduction ratio (100:1) Double worm reduction gear

Intersecting perpendicular shaft axes. Bevel gear

4. Compare reverted gear train and epicyclic gear train.

Reverted gear train ü  A compound gear train in which the first and last gears are co-axial is called as reverted gear train.

Epicyclic gear train ü  When the axes of rotation of one or more gears is allowed to rotate about another axis then the gear train is known as epicyclic gear train.

5. State the relationship between speed ratio and train value.

6. How the module of a gear influences its size and number of teeth?

Advantages:  No Interference occurs; Stronger teeth; Less wear and tear.

7. State the law of gearing.

The law of gearing states that for obtaining a constant velocity ratio, at any instant of teeth the common normal at each point of contact should always pass through a pitch point (fixed point), situated on the line joining the centres of rotation of the pair of mating gears.

 

8. What do you mean by spiral gear and hypoid gears?

Spiral Gear The two non-intersecting and non parallel shaft connected by gears is called skew bevel gears of spiral gears

Hypoid Gear A hypoid gear is style of spiral bevel gear whose main vaniance is that the mating gear axes do not connect.

9. Distinguish cycloid and involutes profiles of gears tooth.

Cycloid ü  Cycloidal teeth wider flank, so its stronger ü  Manufacturing is difficult so rare used in industry

Involute ü  Pressure angle remain constant during engagement and disengagement. ü  Widely used in industry

10. Define module of gears and its relation to circular pitch.

Module is the ratio of the pitch circle diameter to the number of teeth.

Circular pitch .

11. Write the advantages of cycloidal gears.

Advantages:  No Interference occurs; Stronger teeth; Less wear and tear.

12. Define the terms: Module and pitch circle diameter of spur gear.

Module : It is the ratio of the pitch circle diameter to the number of teeth.

Pitch circle : It is an imaginary circle which by pure rolling action, would give the same motion as the actual gear.

13. What is meant by interference and undercutting of gears?

Fig.1 shows a pinion and a gear wheel in mesh. If the addendum of the mating gear is more than the limiting value, it interferes with the dedendum of the pinion and the two gears are locked. (Refer Fig.1(a))

 

 

 

Now, instead of the gear mating with the pinion, a cutting rack is used to cut the teeth in the pinion. Then the portion of the pinion tooth will be removed as shown in Fig.1(b).

A gear having its material removed in this manner is said to be undercut and the process is known as undercutting.

Undercutting will not take place if the teeth are designed to avoid interference. However, when the actual gear meshes with the undercut pinion, no interference occurs.

 interference in gears.

The phenomenon when the tip of tooth undercuts the roots on its mating gear is known as interference.

14. State the relationship between circular pitch and the module.

Circular pitch .

15. Define normal and axial pitch in helical gears.

Normal pitch: It is the distance between similar faces of adjacent teeth, along a het on the pitch cylinder normal to the teeth.

Axial pitch: It is the distance measured parallel to the axis, between similar faces of adjacent teeth.

16. What is the advantage when arc of recess is equal to arc of approach in meshing gears?

                                i.            The height of the teeth may be reduced.

                              ii.            The pressure angle may be increased.

                            iii.            The face of the gear tooth may be relieved.

17. How is the epicyclic gear train works?

When the gears are arranged in such a manner that one or more gears move upon and around another gear, then the gear train is known as epicyclic gear train.

18. What do you understand by the term “interference” as applied to gears?

interference in gears.

The phenomenon when the tip of tooth undercuts the roots on its mating gear is known as interference.

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

ü  Because they share load between several gear meshes, epicyclic trains take up less space and have a lighter weight.

ü  Because they share load between several meshes, epicyclic trains have smaller and stiffer components that lead to reduced noise and vibration while increasing efficiency.

ü  The input and output shafts of epicyclic trains are concentric so no bending moments or torques are created from radial forces that develop from the change of the force’s line of action.

20. Briefly write about reverted gear train with suitable sketch.

When the axes of the first gear (i.e., first driver) and the last gear (i.e., last driven or follower) are co-axial, then the gear train is known as reverted gear train. Refer Fig.2.

 

21. Prove or disprove that in a spur gear pair, pure rolling occurs only at one

    bar— Pitch curve

    point along the path of contact.

We know that in a spur gear pair, at thepitch point there is no sliding. Theaction is pure rolling. We also knowthat the path of contact should alwayspass through the pitch point. Thus thepure rolling occurs only at one pointalong the path of contact.

22. What is meant by an epicyclic gear train? Give a practical example.

ü When the gears are arranged in such a manner that one or more gears move upon and around another gear, then the gear train is known as epicyclic gear train.

ü Examples :Differential gears of automobile, back gear of lathe, wrist watches, etc.

23. Define : (a) normal pitch and (b) axial pitch relating to helical gears.

ü  Normal pitch: It is the distance between similar faces of adjacent teeth, along a het on the pitch cylinder normal to the teeth.

ü  Axial pitch: It is the distance measured parallel to the axis, between similar faces of adjacent teeth.

24.  Define the following terms used in gears : (a) Pitch circle, (b) Circular pitch, (c) Diametral pitch and (d) Module.

(a)   Pitch circle : It is an imaginary circle which by pure rolling action, would give the same motion as the actual gear.

(b)   Circular pitch : It is the distance measured along the circumference of the pitch circle from a point on one tooth to the corresponding point on the adjacent tooth.

(c)   Diameteral pitch : It is the ratio of number of teeth to the pitch circle diameter.

(d)   Module : It is the ratio of the pitch circle diameter to the number of teeth.

25. What is meant by contact ratio in gear? And write the equation to determine this value.

ü  Contact ratio in gear refers to the number of teeth in contact.

ü  Contact ratio =

26. How to change the direction of rotation of the output gear in simple gear train without changing the direction of rotation of input gear?

By using intermediate idle gears.

27.  State law of gearing

The law of gearing states that for obtaining a constant velocity ratio, at any instant of teeth the common normal at each point of contact should always pass through a pitch point (fixed point), situated on the line joining the centres of rotation of the pair of mating gears.

The law of gearing states that the common normal at the point of contact between a pair of teeth must always pass through the pitch point.

28.  State any two advantages of involute gears.

ü  In volute tooth gears, variation in centre distance does not affect the velocity ratio.

ü  In volute tooth gears are easier to manufacture when compared to cycloidal tooth gears.

29.  Distinguish between simple gear train and epicyclical gear train.

ü  When there is only one gear on each shaft, it is known as simple gear train.

ü  When the gears are arranged in such a manner that one or more gears move upon and around another gear, then the gear train is known as epicyclic gear train.

 

30.  Define the following terms used in gears : (a) Pitch circle, (b) Circular pitch, (c) Diametral pitch and (d) Module.

(e)   Pitch circle : It is an imaginary circle which by pure rolling action, would give the same motion as the actual gear.

(f)    Circular pitch : It is the distance measured along the circumference of the pitch circle from a point on one tooth to the corresponding point on the adjacent tooth.

(g)   Diameteral pitch : It is the ratio of number of teeth to the pitch circle diameter.

(h)  Module : It is the ratio of the pitch circle diameter to the number of teeth.

31.  Define the terms “velocity ratio” and “sliding velocity” in a spur gear pair.

 Velocity ratio : It is the ratio of speed of driving gear to the speed of the driven gear.

Sliding velocity : It is the velocity of one tooth relative to its mating tooth along the common tangent at the point of contact.

32.  Prove or disprove that pure rolling is possible at one point only, on the line of action, between two meshing gear teeth profiles.

This statement is known as law of gearing or conditions of correct gearing. For its proof.

33.  Distinguish, with suitable free hand sketches, a non-reverted gear train and a reverted gear train.

Reverted gear train: If the axes of the first and the last wheels of a compound gear coincide, it is called a reverted gear train. Refer Fig.4.

 

Non -reverted gear train : If the axes of the first and the last wheels of a compound gear do not coincide, it is called a non- reverted gear train. Refer Fig.5.

34.  What is axial pitch of a helical gear?

It is the distance measure parallel to the axis, between similar faces of adjacent teeth.

35.  State the condition for constant velocity ratio of toothed wheels.

The law of gearing states that for obtaining a constant velocity ratio, at any instant of teeth the common normal at each point of contact should always pass through a pitch point (fixed point), situated on the line joining the centres of rotation of the pair of mating gears.

The law of gearing states that the common normal at the point of contact between a pair of teeth must always pass through the pitch point.

36.  Explain the construction of involute teeth and its advantages.

ü  In volute tooth gears, variation in centre distance does not affect the velocity ratio.

ü  In volute tooth gears are easier to manufacture when compared to cycloidal tooth gears.

37. Define module of gears and its relation to circular pitch.

Module is the ratio of the pitch circle diameter to the number of teeth.

Pitch circle, Pc = p x Module

38. Explain briefly the use of differential in an automobile.

The function of a differential gear in an automobile is to :

Transmit motion from engine to rear wheels, and

Rotate the rear wheels at different speeds while the automobile is taking a turn.

39.  Define the law of gearing with the equation.

The law of gearing states that for obtaining a constant velocity ratio, at any instant of teeth the common normal at each point of contact should always pass through a pitch point (fixed point), situated on the line joining the centres of rotation of the pair of mating gears.

40.  What are the principal reasons for the use of non-standard gears?

Non- standard gears are used for obtaining improved performance and for more economic production.

41.  List out the applications of epicyclic gear train.

Differential gears of automobile, back gear of lathe, wrist watches, etc.

42.  Differentiate diametral pitch and circular pitch of a friction wheel.

Pitch circle : It is an imaginary circle which by pure rolling action, would give the same motion as the actual gear.

Circular pitch : It is the distance measured along the circumference of the pitch circle from a point on one tooth to the corresponding point on the adjacent tooth.

43.  What is reverted gear train?

When the axes of the first gear and the last gear are co-axial, then the gear train is known as reverted gear train.

44.  Define interference in gears.

The phenomenon when the tip of tooth undercuts the roots on its mating gear is known as interference.

45.  State the law of gearing.

The law of gearing states that for obtaining a constant velocity ratio, at any instant of teeth the common normal at each point of contact should always pass through a pitch point (fixed point), situated on the line joining the centres of rotation of the pair of mating gears.

46.  What are various types of torques in an epicyclic gear train?

ü  Input torque on the driving member.

ü  Output torque or load torque on the driven member.

ü  Braking torque on the fixed member.

47.  What are the advantages and disadvantages of involute gear tooth profile?

Advantages : Variable centre distance; Constant pressure angle; Easy manufacturing.

Disadvantages: Interference occurs; Weaker teeth; More wear and tear.

48.  What are the applications of reverted gear trains?

            The reverted gear trains are used in automobile gear boxes, lathe back gears, industrial speed reducers, etc.

49.  State the law gearing.

The law of gearing states that for obtaining a constant velocity ratio, at any instant of teeth the common normal at each point of contact should always pass through a pitch point (fixed point), situated on the line joining the centres of rotation of the pair of mating gears.

 

PROPOSED QUESTION & ANSWER

1.      What is epicylic gear train? Give a practical example.

ü  When the gears are arranged in such a manner that one or more gears move upon and around another gear, then the gear train is known as epicyclic gear train.

ü  Examples: differential gears of automobile, back gear of lathe, wrist watches, etc.

2.      What is the differential in automobile?

The function of a differential gear in an automobile is to:

(i)     Transmit motion from engine to rear wheels, and

(ii)   Rotate the rear wheels at different speeds while the automobile is taking a turn.

3.      Define the following terms used in gear: (a) Pressure angle (b) Module.

ü  Pressure angle is the angle between the common normal to two gear teeth at the point of contact and the common tangent at the pitch pint.

ü  Module is the ratio of the pitch circle diameter to the number of teeth.

4.      What are the advantages of planetary gear trains?

ü  Because they share load between several gear meshes, epicyclic trains take up less space and have a lighter weight.Because they share load between several meshes, epicyclic trains have smaller and stiffer components that lead to reduced noise and vibration while increasing efficiency.

ü  The input and output shafts of epicyclic trains are concentric so no bending moments or torques are created from radial forces that develop from the change of the force’s line of action.

ü  The input and output shafts of epicyclic trains are concentric so driver and driven equipment can be mounted in line, providing additional space savings.

5.      Define the term ‘arc of contact’ in gears.

The arc of contact is the path traced by a point on the pitch circle for the beginning to the end of engagement of two meshing teeth.

6.      Name two applications of reverted gear train

ü  Back gear of lathes

ü  Automobile gear box

7.      Define gear ratio.

            The gear ratio of a gear train is the ratio of the angular velocity of the input gear to the angular velocity of the output gear.

8.      Write short notes on differentials.

The function of a differential gear of an automobile is:

(i)     to transmit motion from engine to rear wheels, and

(ii)   to rotate the rear wheels at different speeds while the automobile is taking a turn.

9.      State the law of gearing

The law of gearing states that for obtaining a constant velocity ratio, at any instant of teeth the common normal at each point of contact should always pass through a pitch point (fixed point), situated on the line joining the centres of rotation of the pair of mating gears.

10.  What are the methods to avoid interference?

ü  The height of the teeth may be reduced.

ü  The pressure angel may be increased.

ü  The radial flank of the pinion may be cut back (undercutting).

 

UNIT– 3 : FRICTION IN MACHINE ELEMENTS

 

1.       Define co-efficient of friction.(APR/MAY 2023)

The coefficient of friction is defined as the ratio of the limiting friction (F) to the normal reaction (R_N) between the two bodies.

✓Coefficient of friction, μ  =   =

2.       Infer the advantages of wire ropes over fabric ropes. (APR/MAY 2023)

High Strength: Steel wire rope is exceptionally strong and can withstand heavy loads and stresses.  Its high tensile strength makes it suitable for lifting, towing, and other load-bearing applications. Durability: Steel wire rope is highly durable and resistant to wear, abrasion, and corrosion.

3.      What is the effect of centrifugal tension in belt drive?

The tension caused by centrifugal force is called centrifugal tension. The centrifugal tension has no effect on the power transmitted.

4.      What are the advantages of hydraulic brake over other brakes?

Ø  Ease and accuracy of control.

Ø  Multiplication of force.

Ø  Constant force and torque

Ø  Simple, safe and economical

5.      Define lead, and pitch of a screw thread.

ü  The thread pitch is the distance between threads expressed in mm . For example thread pitch of 1.5 means that the distance between one thread and next is 1.5 mm.

6.      State the two assumptions based on which the bearing are designed.

Ø  Considering uniform wear

Ø  Considering uniform pressure.

7.      Differentiae Self-energizing and self locking brakes.

ü  When the moment of frictional force helps to apply the brake, then the brake is said to be self-energising brake.

ü  When the frictional force is great enough to apply the brake with no external force, then the brake is said to be self –locking brake.

8.      What are the disadvantages of V-belts driven over flat?

ü  Power transmitted is more due to wedging action in the grooved pulleys.

ü  V-belt is more compact, quiet and shock absorbing.

ü  The V-belt drive is positive because of negligible slip between the belt and the groove.

ü  High velocity ratio (maximum 10) may be obtained.

 

9.      What are self energizing brakes?

ü 

ü  If f< α, then torque required is negative.

ü  If f> α, then torque required is positive, indicating that an effort is applied to lower the load. Such as screw is called self- locking screw.

 

10.  Why self locking screws have lesser efficiency?

and for self – locking screws, f³ α or α £ 1.

            \ Efficiency of self-locking screws,

                       

                                   

From this expression, we see that efficiency of self-locking screws is less than   or 50%

11.  Write the mathematical expression for the maximum efficiency of a screw jack.

For efficiency to tbe maximum sin (2α+f) = 0,

or 

12.  Write mathematical expression for the length of the belt required for two pulleys of diameters d1 and d2 and at distance x apart are connected by means of an open belt drive.

Where d1 and d2 = diameter of the larger and smaller pulleys, and

x = Distance between the centers of two pulleys.

 

13.  Distinguish between brakes and dynamometers?

A dynamometer is a brake incorporating a device to measure the frictional resistance applied. 

 

14.  The coefficient of friction between the belt and the pulley in a belt and the pulley in a belt drive is 0.3. The angle of lap is 165◦. If the tension on the tight side is 3000 N, determine the tension on the slack side.

Given Data :

Solution : We know that,

or                                            

or                                            

 

15.  Prove or disprove that the efficiency of a screw jack is independent of load raised.

                       

                        Thus the efficiency of a screw jack is independent of the load raised.

 

16.   State the condition and the equation for the velocity of the belt for the transmission of maximum power in a flat belt drive.

ü Condition:The power transmitted shall be maximum when the centrifugal tension is one third of the maximum belt tension (T).

Equation: Maximum velocity,

 

17. Obtain an expression for length of an open belt drive.

            Where d₁ and d₂         =          Diameters of the larger and smaller pulleys, and

                                      x        =          Distance between the centres of two pulleys

18. What is the minimum force required to slide a body on a rough horizontal plane?

Refer Fig.2. The minimum force required to slide a body on a rough horizontal plane is

                                               

                                                                        Fig.2.

19. What is the condition for self locking in screws?

A screw will be self – locking if the friction angle (f) is greater than helix angle (α) or coefficient of friction (µ) is greater than tangent of helix angle (tan α).

20.  Find the power transmitted by a flat belt over a pulley of 600 mm in diameter at 200 revolutions per minute. The maximum and minimum tensions in the belt are 2500 N and 124 N.

Given Data : D = 600 mm;     N = 200 rpm;   T₁ = 2500N;                T₂ = 124 N.

Solution:

Power transmitted,

21. Distinguish between simple gear train and epicyclical gear train.

ü  When there is only one gear on each shaft, it is known as simple gear train.

ü  When the gears are arranged in such a manner that one or more gears move upon and around another gear, then the gear train is known as epicyclic gear train.

 

22.  What is the condition for self –locking in screws?

ü  For a screw to be self-locking, friction angle  f must be greater than helix angle α. The efficiency of self-locking screws should be less than 50%.

ü  A screw will be self – locking if the friction angle (f) is greater than helix angle (α) or coefficient of friction (µ) is greater than tangent of helix angle (tan α).

 

23. With a neat sketch show that angle of repose α is equal to the limiting angle of frictionf.( May / June 2006)

W sin α            = F = µ. R_N

                            = µW cos α

 or tan α           = µ = tan f

Thus,   α          = f .

Hence the angle of repose α is equal to the limiting angle of friction f.

 

24.  Define mechanical efficiency of screw and nut assembly.

The mechanical efficiency of screw and nut assembly may be defined as the ratio between the ideal effort (P₀) (i.e., the effort required to move the load, neglecting friction) to the actual effort (P) (i.e., the effort required to move the load taking friction into account).

 

25. In a screw jack, the coefficient of friction between screw and nut is 0.1 and the helix angle of the screw thread is 3.5◦. Find the efficiency of the screw jack. ( May / June 2006)

Given Data :  µ = 0.1; α = 3.5◦

Solution :µ = tan f = 0.1 or f = tan ^-1 (0.1) = 5.71◦

 

26. A force of 80 N is applied to the brake of a bicycle rear wheel and the distance covered by the bicycle before coming to rest is 12.5 metres. If the coefficient of friction is 0.6, find the work done against the friction. ( May / June 2006)

 

Given Data :  F = 80 N; S = 12.5m; µ = 0.6.

Solution :F = µ R_N or R_N = 80/0.6 = 133.33 N

Workdone = R_N x S = 133.33 x 12.5

                        = 1666.6 N.M

 

27. Derive the minimum force required to slide a body on a rough horizontal surface.

 

W sin α            = F = µ. R_N

                            = µW cos α

 or tan α           = µ = tan f

Thus,   α          = f .

Hence the angle of repose α is equal to the limiting angle of friction f.

28.  Write the equation to determine the efficiency of a screw jack.

Where α = Helix angle, and

            f = Friction angle.

29. What do you mean by friction angle?

The friction angle (f) is the angle at which the resultant reaction R makes with the normal reaction R_N. tan f = µ.

30. What are the significance of fiction with regard to power transmission devices like clutches and bearings?

The power transmission devices like clutches and bearings work on the principle of friction. When two friction surfaces are brought in contact with each other and pressed, they are united due to the friction between them.

31. Which type of screw thread is preferable in power transmission?

Square thread. Example: Lead screw in lathe.

 

32. What is the condition of maximum efficiency of a screw jack?

For efficiency to tbe maximum sin (2α+f) = 0,

or 

33. What are the advantages of wire ropes over fabric ropes?

ü  High strength to weight ratio.

ü  More reliable in operation.

ü  Silent operation even at high working speeds.

34. Diagrammatically represent the forces acting on a body when it slides either up or down on an inclined plane without considering the effect of friction.

35. List out any four desirable characteristics of brake lining material.

ü  A high and uniform coefficient of friction.

ü  Ability to withstand high temperatures, together with high heat dissipation capacity.

ü  Adequate mechanical and thermal strengths.

ü  High resistance to wear.

36. What is creep in the case of belt?

When the belt passes from the slack side to the tight side, a certain portion of the belt extends. And it contracts again when the belt passes from the tight side to slack side. Due to these changes of length, there is a relative motion between the belt and the pulley surfaces. This relative motion is termed as creep.

37. How centrifugal tension affects the power transmission in belt drive?

During operation, as the belt passes over a pulley the centrifugal effect due to its self weight tends to lift the belt from the pulley surface. This reduces the normal reaction and hence the frictional resistance. The centrifugal force produce additional tension in the belt.

38. Define the term “Limiting friction”.

The limiting angle of friction (f) is defined as the angle at which the resultant reaction ‘R’ makes with the normal reaction ‘R_N’.

39. What is the apparent coefficient of friction in belt drives?

‘µ cosec β’ in the tension ratio equation is known as the apparent coefficient of friction.

40.  Distinguish between sliding and rolling friction.

            Sliding friction occurs in between two sliding surfaces whereas rolling friction occurs in between two rolling surfaces.

41. What do you mean by self-locking screw?

If f< α, then torque required is negative.

If f> α, then torque required is positive, indicating that an effort is applied to lower the load. Such as screw is called self- locking screw.

42. Give the effect of centrifugal tension in belt drives.

Centrifugal tension has no effect on the power transmitted. However the centrifugal tension will increase the tension on both tight and slack sides. Its effect is considerable at higher belt speeds (> 10m/s).

43. What is the difference between sliding friction and rolling friction? Give example.

            Sliding friction occurs in between two sliding surfaces whereas rolling friction occurs in between two rolling surfaces.

44. What is limiting angle of friction?

The limiting angle of friction (f) is defined as the angle at which the resultant reaction ‘R’ makes with the normal reaction ‘R_N’.

45. State the functional difference between a clutch and a brake.

The functional difference between a clutch and a brake is that a clutch connects two moving members of a machine, whereas a brake connects a moving member to a stationary member.

PROPOSED QUESTION & ANSWER

1.  What are the advantages and disadvantages of V-belt drive over flat belt drive?

ü  Power transmitted is more due to wedging action in the grooved pulleys.

ü  V-belt is more compact, quiet and shock absorbing.

ü  The V-belt drive is positive because of negligible slip between the belt and the groove.

ü  High velocity ratio (maximum 10) may be obtained.

2. Define anti – friction bearing.

            An antifriction bearing, also known as a rolling contact bearing, is used when very little friction is needed for low differential surface speeds.

3.  Differentiate multiplate clutch and cone clutch.

            A cone clutch serves the same purpose as a multiplate clutch. However, instead of mating two or more spinning disks, the cone clutch uses two conical surfaces to transmit torque by friction. The cone clutch transfers a higher torque than plate or disk clutches of the same size due to the wedging action and increased surface area.

4. Define velocity ratio

It is defined as the ratio between velocity of the driver and the follower (or) driven.

5. What is maximum efficiency of the screw jack?

Where

6. What is the effect of centrifugal tension in belt drives?

ü  Centrifugal tension will increase the tension on both tight and slack sides.

ü  Centrifugal tension has no effect on the power transmitted by the belt drive.

 

7. What is the condition to be satisfied for self-locking of screw jack?

For a screw to be self-locking, friction angle  f must be greater than helix angle α. The efficiency of self-locking screws should be less than 50%.

8. What is the function of brake?

ü  Brake is a mechanical device by means of which motion of a body is retarded for slowing down or to bring it to rest, by applying artificial frictional resistance.

9. State the functional difference between a brake and a clutch.

A clutch connects two moving members of a machine, whereas a brake connects a moving members to a stationary member.

10. Differentiate a brake and a dynameters 

A  Dynameters is a brake incorporating a device to measure the frictional resistance applied.