Theory of Machines

1. S4’s Polytechnic Ghogaon,Karad
NAME:- MR.BHOSALE BHARATRAJ Y.
(Lecturer in Mechanical department)

2. The power is transmitted from one shaft
to another shaft, which are at considerable distance
apart, through a belt, rope or chain & gear when the
distance between the two shaft is small.
Types of Drives for power transmission :-
•Belt Drive
•Chain Drive
•Gear Drive
•Rope Drive
POWER TRANSMISSION

3. BELT DRIVE
The Belts are classified as :
1.Flat Belt: This type of belts are used on flat
pulley and at a distance more than 8 meters.
Slip occurs due to flat surface
2.‘V’ Belt: This type of belts are used in grooved
pulley & distance between the pulley is very small.
Belts are trapezoidal in cross section and the
angle of groove pulley is 340 to 380.
3.Circular or Rope Belt: This type of belts are used
where the dist between two pulleys are more
than 8 meters. Rope drive is used for large
amount of power transmission.

4. V-BELT AND PULLEY

5. Types of Belt Drives
1.Open belt Drive 2.Cross belt Drive 3.Compound belt Drive

6. FLAT BELT DRIVES WITH PARALLEL SHAFTS

7. FLAT BELT DRIVES WITH PERPENDICULAR SHAFTS

8. Tight side (T1) and slack side (T2) of Belt
When the part of belt moves from driven pulley to the
driving pulley is known as tight side of belt having tension T1 and
the part of belt moves from driving to the driven pulley is known
as slack side of belt having tension T2 . Both the tensions are
different in magnitude (T1 >T2) .

9. Angle of Lap or Contact & length of Open
Belt drive:

10. Formulae (Open belt)
• Angle of Lap or Contact (θ)
θ = (180-2α) …..in Degree
= (180-2α) x П/180 …..in radians
where,
α = sin-1 [ (r1 - r2)/x ]
• Length of belt (L)
L= П (r1+r2) + 2x + [(r1- r2)2/x]
Where ,
X= central distance between two pulleys

11. Angle of Lap or Contact & length of
Cross Belt drive :

12. Formulae (Cross belt)
• Angle of Lap or Contact (θ)
(θ) = (180+2α) …..in Degree
= (180+2α) x П/180 …..in radians
where,
α = sin-1 [ (r1+r2)/x ]
• Length of belt (L)
(L)= П (r1+r2) + 2x + [(r1+r2)2/x]
Where,
X= central distance between two pulleys

13. Slip of Belt
Definition:-
The motion of belt & pulley is due to firm frictional grip between the belt
and pulley but sometimes frictional grip became insufficient so this may causes:
i) The forward motion of the driver pulley without carrying belt with it.
ii)The forward motion of belt without carrying the driven pulley with it.
This is called slip of belt and it is expressed in percentage. The slip of belt decrease the
velocity ratio.
where,
S1 = percentage slip between driver pulley and belt.
S2= percentage slip between belt and driven pulley.
S = S1 + S2 =total percentage of slip.
v = linear velocity of belt per minute.
d1 & d2 = diameters of driving and driven pulley.
t = thickness of the belt.

14. Derivation - Slip of Belt

15. Creep of Belt
Definition:-
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.
where ,
σ1 and σ2 = Stress in the belt on the tight and slack side respectively,
E = Young’s modulus for the material of the belt.

16. Velocity Ratio
It is the ratio between the velocities of the driver and the follower or driven.
It may be expressed, mathematically, as discussed below :
Let ,
d1 = Diameter of the driver,
d2 = Diameter of the follower,
N1 = Speed of the driver in r.p.m., and
N2 = Speed of the follower in r.p.m.
When the thickness (t) of the belt is considered

17. Centrifugal Tension
• Since the belt continuously runs over the pulleys, therefore, some
centrifugal force is caused, whose effect is to increase the tension on both,
tight as well as the slack sides. The tension caused by centrifugal force is
called centrifugal tension.
• At lower belt speeds (less than 10 m/s), the centrifugal tension is very
small, but at higher belt speeds (more than 10 m/s), its effect inconsiderable
and thus should be taken into account.
Let, m = Mass of the belt per unit length in kg,
v = Linear velocity of the belt in m/s,
r = Radius of the pulley over which the belt runs in meters, and
Tc= Centrifugal tension acting tangentially at P and Q in Newton
Formula……….
Tc = mV2

18. LOCATION OF IDLER PULLEYS

19. CHAIN DRIVE
In belt and rope drives that slipping may occur. In order to
avoid slipping, steel chains are used. The chains are made up of rigid
links which are hinged together in order to provide the necessary
flexibility for warping around the driving and driven wheels.
The chains are mostly used to transmit motion and power from
one shaft to another, when the distance between the centers of the
shafts is short such as in bicycles, motor cycles, agricultural machinery,
road rollers, etc.

20. CHAINS
ROLLER CHAIN TERMINOLOGY

21. • Advantages & Disadvantages of Chain Drive:
• Advantages
1. As no slip takes place during chain drive, hence perfect
velocity ratio is obtained.
2. Since the chains are made of metal, therefore they occupy
less space in width than a belt or rope drive.
3. The chain drives may be used when the distance between
the shafts is less.
4. The chain drive gives a high transmission efficiency (up to 98
per cent).

22. 5. The chain drive gives less load on the shafts.
6. The chain drive has the ability of transmitting motion to
several shafts by one chain only.
• Disadvantages
1. The production cost of chains is relatively high.
2. The chain drive needs accurate mounting and careful
maintenance.
3. The chain drive has velocity fluctuations especially when
unduly stretched.

23. SPROCKETS

24. GEAR-TEETH TERMS

25. MESHING OF GEAR TEETH