This document provides information about the Machine Design-I course including the instructor's details, textbook and reference books, sessional marks distribution, and a note about important topics for exams. It then discusses the topic of shafts, keys, and couplings. Different types of keys like sunk, saddle, and spline keys are described along with their dimensions. The forces acting on sunk keys and formulas for calculating torque transmitted by solid and hollow shafts are provided. Finally, various types of rigid and flexible couplings are defined including sleeve, clamp, flange, bushed pin, universal and Oldham couplings.

1. Machine Design-I
ME-260
Course Teacher:
Gohar Ali
Lecturer
Mechanical Engineering Department
BUITEMS
Text Book: R.S Khurmi and J K Gupta, A Textbook of
Machine Design
Reference: J. E. Shigley, Mechanical Engineering
Design, McGraw-Hill
R L Norton, Machine Design, An Integrated Approach,
McGraw-Hill
1

2. Sessional Marks Distribution
 Class performance/behavior/mobile use = 5 marks
 Attendance = 5 marks
 Presentation = 5 marks
 Assignment/Quiz = 10 marks
Note:
 Problems & Theory covered during class lectures and suggested
problems will be important for the mid term exam as well as the
final exam.
 Please don’t miss mid term exam and your presentation session
coz there wont be any compensation afterwards.
2

3. Topic:
Shaft, Keys and Coupling
3

4. Keys 4
 Key
A key is a temporary fastener usually piece of mild steel inserted between the shaft and
hub or boss of the pulley (gear or flywheel) to connect these together in order to prevent
relative motion between them.
So that motion may transfer form shaft to pulley or vice versa.
It is always inserted parallel to the axis of the shaft.
 Keyway
A keyway is a slot or recess in a shaft and hub of the pulley to
accommodate a key.

5. Types of keys 5
The following are the types of keys
 Sunk key
 Saddle key
 Tangent key
 Round key
 Splines
 Sunk Key
The sunk keys are provided half in the keyway of the shaft and half in the keyway of the
hub or boss of the pulley.
The sunk keys are of the following types
 Rectangular sunk key
 Square sunk key
 Parallel sunk key
 Gib head sunk key
 Feather key
 Wood ruff key
 Rectangular sunk key
It has a rectangular cross section as shown in figure with important dimensions, which insert
half in the keyways of hub and shaft. Taper from up side.
𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 𝑡 =
𝑑
6
𝐵𝑟𝑒𝑎𝑑𝑡ℎ = 𝑏 =
𝑑
4
Where d = diameter of shaft
𝑡𝑎𝑝𝑒𝑟 = 1: 100

6. Sunk Keys 6
 Square sunk key
It has a square cross section as shown in
figure with important dimensions, which also
insert half in the keyways of shaft and hub.
Taper from up side.
 Parallel sunk key
A parallel sunk key may be rectangular
or square in cross section but it has no taper

7. Sunk Keys 7
 Gib head sunk key
It is a rectangular sunk key with a head at one end known as gib head. It is usually
provided to facilitate the removal of key.
𝐵𝑟𝑒𝑎𝑑𝑡ℎ = 𝑏 =
𝑑
4
𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 𝑡 =
𝑑
6
Where d = diameter of shaft

8. Sunk Keys 8
 Feather sunk key
When a parallel sunk key is attached either to the shaft or hub and which
transmits a torque and permits axial movement is known as feather key.
The feather key may be screwed to the shaft or it may have double Gib heads.
The various proportions of a feather key are same as that of rectangular sunk
key and gib head key.
 Wood ruff sunk key
The woodruff key is an easily adjustable key. It is a
piece from a cylindrical disc having segmental cross-
section in front view as shown in Fig.
A woodruff key is capable of tilting in a recess milled
out in the shaft by a cutter having the same curvature
as the disc from which the key is made.

9. Sunk Keys 9
 Forces acting on a Sunk Key
When a key is used in transmitting torque from a shaft to a rotor or hub, the following two
types of forces act on the key:
 Forces due to fit of the key in its keyway, These forces produce compressive stresses in
the key which are difficult to determine.
 Forces due to the torque transmitted by the shaft. These forces produce shearing stress
and crushing stresses.
 Design of key or torque transmitted by key
Let us consider a rectangular sunk key used to transmit torque and connect shaft to the
hub of pulley etc as shown in fig
Let,
T = Torque transmitted by the shaft,
F = Tangential force acting at circumference of shaft,
d = Diameter of shaft,
l = Length of key,
b = Width of key.
t = Thickness of key,
τ = Torsional shear stresses
σc = Crushing stresses for the material of key.

10. Forces acting on a Sunk Key 10
A little consideration will show that due to torque transmitted the key many fail in shearing
and crushing
 Shearing Failure of key
As the key is transmit power therefor the key fail in shear as shown in diagram,
b
t
l

11. Forces acting on a Sunk Key 11
The shearing strength of key is given by
𝐹 = 𝜏𝐴 ………………(i)
Where,
𝐴 = 𝑙𝑏
Put in equation (i) we get
𝐹 = 𝜏𝑙𝑏 ……………(ii)
As key is used to transmit torque therefore,
Torque = force (moment arm)
𝑇 = 𝐹(𝑟)
𝑇 = 𝐹
𝑑
2
Put the value of force form equation (ii)
we get,
𝑻 = 𝝉𝒍𝒃
𝒅
𝟐
…………(A)
The above use to calculate torque transmit
by key in shearing and use in Design of key
b
t
l

12. Forces acting on a Sunk Key 12
 Crushing Failure of key
Similarly the key also fail in crushing due to
transmission of torque as shown in diagram. The
crushing strength of key is given by
𝐹 = 𝜎𝑐𝜏𝐴 …………………(i)
Where, 𝐴 = 𝑙
𝑡
2
Put in equation (i)
we get,
𝐹 = 𝜎𝑐𝑙
𝑡
2
𝐴 ………………(ii)
As key is used to transmit torque therefore
Torque = force (moment arm)
𝑇 = 𝐹(𝑟) 𝑇 = 𝐹
𝑑
2
Put the value of force from equation (ii)
we get,
𝑻 = 𝝈𝒄𝒍
𝒕
𝟐
𝒅
𝟐
……………(B)
The above formula show the crushing
strength of key and use in Design of key

13. Torque Transmitted by solid shaft 13
Let us consider a shaft which is used to transmit torque from one portion to another portion as
shown in figure.
We know that according to torsion equation
𝑻
𝑱
=
𝝉
𝒓
=
𝑳𝜽
𝑮
𝑻
𝑱
=
𝝉
𝒓
𝑻 =
𝝉𝑱
𝒓
…………(i)
Where J = Polar moment of inertia for circle =
𝝅
𝟑𝟐
𝒅𝟒
and 𝑟 =
𝑑
2
Put in equation (i)
𝑇 =
𝜏
𝜋
32
𝑑4
𝑑
2
𝑻 =
𝝅
𝟏𝟔
𝝉𝒅𝟑
The above formula is used to calculate the torque transmitted by solid shaft or strength of
solid shaft

14. Torque Transmitted by hollow shaft 14
Let us consider a hollow shaft which is used to transmit torque form one portion to another
portion as shown in figure. We know that according to torsion equation
𝑻
𝑱
=
𝝉
𝒓
=
𝑳𝜽
𝑮
𝑻
𝑱
=
𝝉
𝒓
𝑻 =
𝝉𝑱
𝒓
…………(i)
Where J = Polar moment of inertia =
𝝅
𝟑𝟐
(𝒅𝒐
𝟒 − 𝒅𝒊𝒏
𝟒)
=
𝝅
𝟑𝟐
(𝑫𝟒 − 𝒅𝟒)
and 𝑟 =
𝐷
2
Put in equation (i) 𝑇 =
𝜏
𝜋
32
(𝐷4
−𝑑4
)
𝐷
2
, 𝑇 =
𝜋
16
𝜏𝐷3(1 −
𝑑4
𝐷4)
𝑻 =
𝝅
𝟏𝟔
𝝉𝑫𝟑(𝟏 − 𝒌𝟒)
Where K = ratio between inner and outer diameter,
The above formula is used to calculate the torque transmitted by hollow shaft or strength of
hollow shaft

15. Coupling or Shaft Coupling 15
Coupling is a machine element used to connect two shafts end to end to transfer motion,
torque, or power form one shaft to another shaft.
For example the shaft of motor is connected to generator.
 Purpose of coupling
The following are the some main purpose of coupling
 Easy to connect and dis connect two shafts for repair,
maintenance or alternations
 To connect two shafts so the length may increase.
 To provide for misalignment of the shafts.
 To introduce mechanical flexibility.
 To reduce the transmission of shock loads from one shaft to another.
 Types of Shafts Couplings
Shaft couplings are divided into two groups as follows:
1. Rigid coupling
It is used to connect two shafts which are perfectly aligned (the central axis of both shaft
are in same line).

16. Coupling or Shaft Coupling 16
Following types of rigid coupling are important from the subject point of view
 Sleeve or muff coupling.
 Clamp or compression coupling,
 Flange coupling. lateral misalignment
angular misalignment
2. Flexible coupling
It is used to connect two shafts having both
lateral and angular misalignment.
Following types of flexible coupling are
important from the subject point
of view :
 Bushed pin type coupling,
 Universal coupling,
 Oldham coupling

17. Rigid coupling 17
 Sleeve or Muff coupling
 It is the simplest type of rigid coupling, made of cast iron.
 It consists of a hollow cylinder whose inner diameter is
the same as that of the shaft.
 It is fitted over the ends of the two shafts by means of a
gib head key.
 The power is transmitted from one shaft to the other
shaft by means of a key and a sleeve.
 The usual proportions of a cast iron sleeve coupling are
as follows :
 Outer diameter of the sleeve, D = 2d + 13 mm
 Length of the sleeve, L = 3.5 d

18. Design of Sleeve or Muff coupling 18
 Example 13.4.
Design and make a neat dimensioned sketch of a muff coupling which is used to connect
two steel shafts transmitting 40 kW at 350 r.p.m. The material for the shafts and key is plain
carbon steel for which allowable shear and crushing stresses may be taken as 40 MPa and 80
Mpa respectively. The material for the muff is cast iron for which the allowable shear stress
may be assumed as 15 MPa.
Given:
Power transmitted by shaft = P = 40 kw = 40 ×(10)3𝑤𝑎𝑡𝑡 =40 × (10)3 𝑁−m/s
Speed of shaft = N= 350 rpm = revolution per minute
Allowable shear stress for shaft and key = 𝜏 = 40 MPa
Allowable crushing stress for shaft and key = 𝜎𝑐= 80 MPa
Allowable shear stress for coupling = 𝜏 = 15 Mpa
Required : Design a muff or sleeve coupling = ?
 Step 1 Design of Shaft
 Step 2 Design of muff (Check)
 Step 3 Design of key
From table 13.1, for shaft diameter = 55 mm, we get
Thickness of key = t = 18mm
Breadth of key or width of key = b = 18mm
Length of key = L = length of muff = 195 mm