kinematics of machinery...kinematics of machinery me6401 dept. of mechanical engg, sri vidya college...

Kinematics of Machinery ME6401

Dept. of Mechanical Engg, Sri Vidya College of Engg & Tech, Virudhunagar – 626005.

UNIT 4 – GEARS AND GEAR TRAINS

PART - A

1. 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, situated on the line joining the centre of rotation of the pair of mating

gears.

2. Define normal and axial pitch in helical gears.

Normal pitch is the distance between similar face of adjacent teeth, along a

helix on the pitch cylinder normal to the teeth.

Axial pitch is the distance measured parallel to the axis between

similar faces of adjacent teeth.

3. What are the advantages and limitations of gear drive? Write any two.

Advantages:

1. Since there is no slip, so exact velocity ratio is obtained.

2. It is more efficient and effective means of power transmission.

Limitations:

1. Manufacture of gear is complicated.

2. The error in cutting teeth may cause vibration and noise during operation.

4. Define interference.

The phenomenon when the tip of tooth undercuts the roots on its mating gear

is known as interference.

5. Define cycloidal tooth profile and involute tooth profile.

A cycloid is the curve traced by a point on the circumference of a circle

which rolls without slipping on a fixed straight line. Involute profile is defined as the

locus of a point on a straight line which rolls without slipping on the circumference of

a circle.



6. Define circular pitch and diametral pitch in spur gears.

Circular pitch (Pc) : It is the distance measured along the circumference of

the pitch circle from a point on one teeth to the corresponding point on the adjacent

tooth.

Pc=πD/T

Diametral pitch (PD) : It is the ratio of number of teeth to the pitch circle diameter.

PD=T/D=π/Pc

7. Define Backslash.

It is the difference between the tooth space and the tooth thickness along the

pitch circle. Backslash = Tooth space – Tooth thickness

8. What is gear train of train of wheels?

Two or more gears re made to mesh with each other to transmit power from one

shaft to another. Such a combination is called a gear train or train of wheels.

9. Write velocity ratio in compound train of wheels?

Speed of last follower - Product of teeth on drivers

Speed of first driver – Product of teeth on followers.

10. Define simple gear train.

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

11. What is reverted gear train?

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

12. Where the epicyclic gear trains are used?

The epicyclic gear trains are used in the back gear of lathe, differential gears of

the automobiles, pulley blocks, wrist watches, etc.

13. Define Contact Ratio.

It is the ratio of the length of arc contact to the circular pitch is known as

contact ratio. The value gives the number of pairs of teeth in contact.



14. Write down the difference between involute and cycloidal tooth profile.

S.No Involute Tooth Profile Cycloidal Tooth Profile

1. Variation in centre distance does

not affect the velocity ratio. The centre distance should not vary.

2. Pressure angle remains constant

throughout the teeth.

Pressure angle varies. It is zero at the

pitch point and maximum at the start and

end of engagement.

3. Interference occurs. No interference occurs.

4. Weaker teeth. Stronger teeth.

15. What is an angle of obliquity in gears?

It is the angle between the common normal to two gear teeth at the point of

contact and the common tangent at the pitch point. It is called as pressure angle.

16. What is bevel gearing? Mention its types.

When the non-parallel (or) intersecting but coplanar shafts connected by gears,

they are called bevel gears and the arrangement is bevel gearing. It is of two types

namely skew bevel gearing and spiral gearing.

17. What are the methods to avoid interference?

1. The height of the teeth may be reduced.

2. The pressure angle may be increased.

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

18. What is the advantage when arc of recess is equal to arc of approach in meshing

gears?

When arc of recess equal to arc of approach, the work wasted by friction is

minimum and efficiency of drive is maximum.

19. What do you know about tumbler gear?

Tumbler gears are those which are used in lathes for reversing the direction of

rotation of driven gears.

20. What you meant by non-standard gear teeth?

The gear tooth obtained by modifying the standard proportions of

gear teeth parameters is known as non- standard gear teeth.

21. What is meant by compound gear train?

When there are more than one gear on shaft, it is called a compound gear train.



22. What is the advantage of a compound gear train over a simple gear train?

The advantage of a compound gear train over a simple gear train is that a much

larger speed reduction from the first shaft to the last shaft can be obtained with small

gears.

23. State the methods to find the velocity ratio of epicyclic gear train.

Two methods are:

1) Tabulation method.

2) Algebraic method.

24. What is the externally applied torques used to keep the gear train in equilibrium?

1) Impart torque on the driving member.

2) Resisting or holding torque on the driven member.

3) Holding or braking torque on the fixed member



UNIT 4 – GEARS AND GEAR TRAINS

PART - B

1. In an ecicyclic gear train shown in figure, the arm A is fixed to the shaft S. The wheel B having

100 teeth rotates freely on the shaft S. The wheel F having 150 teeth driven separately. If the arm

rotates at 200 rpm and wheel F at 100 rpm in the same direction; find (a) number of teeth on the

gear C and (b) speed of wheel B.

C

100 rpm

F150 S

B100

C Arm A

200 rpm

Solution:

TB=100; TF=150; NA=200rpm; NF=100rpm:

Since the mod ule is same for all gears :

the number of teeth on the gears is proportional to the pitch cirlce :

rF rB 2rC TF TB 2TC

150 100 2 TC TC 25 Number of teeth on gears C

The gear B and gear F rotates in the opposite directions:

The Gear B rotates at 350 rpm in the same direction of gears F and Arm



2. The gear train shown in figure 4 is

used in an indexing mechanism of a

milling machine. The drive is from

gear wheels A and B to the bevel gear

wheel D through the gear train. The

following table gives the number of

teeth on each gear.

Gear A B C D E F

Number of

teeth 72 72 60 30 28 24

Diametral

pitch in mm 08 08 12 12 08 08

D

A

C Arm

B

H G

E

F

How many revolutions does D makes for one

revolution of A under the following situations:

a. If A and B are having the same speed and same direction

b. If A and B are having the same speed and opposite direction

c. If A is making 72 rpm and B is at rest

d. If A is making 72 rpm and B 36 rpm in the same direction

Solution: Gear D is external to the epicyclic train and thus C and D constitute an ordinary train.

Operation

Arm E (28) F (24)

A (72) B (72) G (28) H (24)

C (60)

Arm or C is fixed 28

7

28

7

& wheel A is given 0 -1

+1 -1 +1

6

24

+1 revolution 24 6

Multiply by m 7

7

(A rotates through 0 -m m +m -m +m

m

m revolution) 6 6

Add n revolutions n n - m n

7 m

n + m n - m n + m n

7 m

to all elements

6

6

(i) For one revolution of A: n + m = 1 (1)

For A and B for same speed and direction: n + m = n – m (2) From (1) and (2): n = 1 and m = 0

If C or arm makes one revolution, then revolution made by D is given by:

N D 2 N C

(ii) A and B same speed, opposite direction: (n + m) = - (n – m) (3) n = 0; m = 1

When C is fixed and A makes one revolution, D does not make any revolution



(iii) A is making 72 rpm: (n + m) = 72

B at rest (n – m) = 0 n = m = 36 rpm (iii) A is making 72 rpm and B making 36 rpm

(n + m) = 72 rpm and (n – m) = 36 rpm

(n + (n – m)) = 72; n = 54

D = 108 rpm

3. The fig shows an Epicyclic gear train. Wheel E is fixed and wheels C and D are integrally

cast and mounted on the same pin. If arm A makes one revolution per sec (Counter

clockwise) determine the speed and direction of rotation of the wheels B and F.

Arm

B20

C35

D15

E20

F30

Solution:

Data: tB = 20; tC = 35; tD = 15; tE = 20; tF = 30 NA = 1rps-(CCW)

Compound Gear

Operation Arm B (20) wheel E (20) F (30)

D (15) C (35)

Arm is fixed & 20

20

4

35 7

20

B is given

0

+1

3

20

ONE

3

30

15

15

7

revolution

(CW)

3

Multiply by m 4

4

7

14

m (B rotates 0 +m m m m

through m 3 3

3 9 revolution)

Add n

n

m+

n n 4 m n 4

m 7

m n

n 14 m

revolutions to

3

all elements 3 3 9

Since the wheel E is fixed and the arm A makes 1 rps-CCW

Speed of gear B 0.571rps (CCW )

Speed of gear F 1.667 (CCW )



4. In the gear train shown, the wheel C is fixed, the gear B, is keyed to the input shaft and

the gear F is keyed to the output shaft.

Output

Shaft A E30

B20 F32

C80

Input Shaft

The arm A, carrying the compound wheels D and E turns freely on the out put shaft. If the

input speed is 1000 rpm (ccw) when seen from the right, determine the speed of the output

shaft. The number of teeth on each gear is indicated in the figures. Find the output torque

to keep the wheel C fixed if the input power is 7.5 kW.

Solution:

Data :

tB = 20; tC = 80; tD = 60; tE = 30; tF = 32;

NB = 1000 rpm (ccw) (input speed);

P = 7.5 kW

Input shaft speed = 1000 rpm (ccw) i.e., gear B rotates – 1000 rpm

m n 1000

Gear C is fixed; n 1 m 0

4



B (20)

Compound Gear Operation Arm wheel C (80) F (32)

Input

D (60) E (30)

Arm is fixed & 20

1 1 1

60 1

30

0 +1

B is given +1

3 3

80

3

32 60 3

1

5

revolution

4 16

Multiply by m 1

1

1

5

(B rotates 0 m

m

m

m

m

through m

3

4

16 3

revolution)

Add n n m+n

1 m n 1 m n n 1 m n 5 m revolutions to

3

all elements 3 4 16

Speed of the output shaft F 50rpm (CW )

Input power P 2 N B

TB

60

TB

7500 60 71.59Nm

2 1000

From the energy equation;

TB N B TF N F TC NC 0

TF 1431.8Nm

From the torque equation :

TB TF TC 0

71.59 1431.8 TC 0

TC 1360.21Nm

The Torque required to hold the wheel C = 1360.21 Nm in the same direction

of wheel

5. The gearing of a machine tool. Motor shaft is connected to gear A and rotates at 975

r.p.m. The gear wheels B, C, D and E are fixed to parallel shafts rotating together.

The final gear F is fixed on the output shaft. What is the speed of gear F ?



Solution

6. In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth

respectively. If the arm rotates at 150 r.p.m. in the anticlockwise direction about the

centre of the gear A which is fixed, determine the speed of gear B. If the gear A

instead of being fixed, makes 300 r.p.m. in the clockwise direction, what will be the

speed of gear B ?

kinematics of machinery...kinematics of machinery me6401 dept. of mechanical engg, sri vidya college...

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