1. KINEMATICS OF MECHANISMS

2. MACHINE
Machine is a device consisting of various machine elements arranged together so as to perform prescribed task.
Machine is a device which receives energy in some form and utilizes it to do some particular work.
Machine is a device consists of fixed and moving parts that modifies energy and transmits it in useful form.
Machine is assembly of fixed and moving links.
Machine can use more than one mechanism to achieve the desirable motion
Egs: Heat Engine, I. C. Engine

3. LOCKED CHAIN OR STRUCTURE
Structure is an assembly of number of resistant bodies which have no relative motion between them and are meant to carry loads
Links connected in such a way that no relative motion is possible.
Roof trusses used in bridges, transmission towers, machines frames, railway platforms etc are examples of structure.
Structures are not used to transmit power and motion.
Structures are used only to take the load / support the applied load (Zero velocity and acceleration)
Assembly of three links form a structure.
DOF = 0

4. Machine Vs Structure Machine Structure
Part of the machine move relative to each other
Members of the structure do not move relative to each other.
Machine transforms available input energy into useful work
In structure no energy is transformed into useful work.
Links of machine may transform both power and motion
Links of structure only transform forces / load acting on the structure

5. KINEMATIC LINK OR ELEMENT
Kinematic Link: Each resistant body in a machine which moves relative to another resistant body is called Kinematic link or element.
A resistant body is which has negligible deformation while transmitting the required force.
Link should be a
- A resistant body
- Should be connected to other parts of the machine.
- Must have relative motion w.r.t other links

6. LINK OR ELEMENT Kinematic links can be divided into three types.
1.      Rigid link- In this type of link there is no deformation while transmitting
motion. (Resistant body has negligible deformation)
Piston and crank can be considered as a rigid link.
2.      Flexible link- In this type of link there is partial deformation while
transmitting the motion.
Belt drive, Ropes, Chains, wires, Spring is an example of flexible link.
3.      Fluid link- In this type of link the motion is transmitted with the help
of fluid pressure. Hydraulic brake is an example of fluid link.

7. LINK OR ELEMENT
Any body (normally rigid) which has motion relative to another.
Rigid link does not deform while transmitting motion i.e. it dimensions remain the same.
Binary link Ternary link Quaternary link

8. Sliding crank mechanism
Examples of links
Sliding crank mechanism
Line of stroke or
sliding path
Link 1 – Cylinder and frame
(Stationary or fixed link)
Link 2 – Crank (Rotating motion)
Link 3 – Connecting Rod
Link 4 Piston Sliding motion
Slider slides in the stationary cylinder.
Crank – Rotates complete revolution
Slider or Piston – Reciprocates
Connecting Rod – Oscillates
Cylinder & Frame - Stationary
Rotary motion of the crank is converted into reciprocating motion of the slider or vice versa

9. Examples of links
Double crank mechanism

10. Kinematic Pair Kinematic Pair:
Two elements or links connected together in such a way that their relative motion is in a definite direction (Successfully Constrained motion) form a kinematic pair.
The geometrical forms by which two members of a mechanism are joined together,
The relative motion between these two is consistent. Such a pair of links is called Kinematic Pair.

11. Kinematic Pair Link 1 – Cylinder and frame (Stationary)
Link 2 – Crank (Rotating motion)
Link 3 – Connecting Rod
Link 4 – Piston Sliding motion
Pair 1 Joint of link 1 and link 2
Pair 2 Joint of link 2 and link 3 (Turning contact Kinematic Pair)
Pair 3 Joint of link 3 and link 4
Pair 4 Joint of link 4 and link 1 (Sliding contact Kinematic Pair)
THERE ARE FOUR LINKS / FOUR JOINTS / FOUR KINEMATIC PAIRS

12. KINEMATIC PAIR
Courtesy:

13. Classification of kinematic pairs:
According to type of relative motion between the elements:
a. Sliding pair: When the two elements or kinematic pair are connected such that only sliding motion is possible between the two.
egs: Piston and cylinder, tail stock on lathe machine
Turning pair: When the two elements are connected such that one can only turn or revolve about the fixed axis of other link such pairs are called as turning pairs.
Egs: Shaft with collars, crank shaft in journal bearings.
c. Rolling pair: When two elements are connected such that one rolls over the other fixed link, the pair is called as rolling pair.
egs: Ball and roller bearings
d. Screw pair: When the two elements are connected such that one element can turn about the other by screw threads.
egs: Lead screw of a lathe, nut and bolt

14. Classification of Kinematic pairs
Based on nature of contact between elements
(i) Lower pair : When the two elements have of the pair have surface contact when the relative motion takes place between the two, the pair formed is known as lower pair.
Egs: Sliding pairs, turning pairs, screw pairs.
Sliding Kinematic Pair
Turning Kinematic Pair

15. (ii) Higher pair: When the two elements of the pair have point or line contact when the relative motion takes place between the two such pairs are called as Higher pairs.
Egs: Ball and roller bearings, Cam and follower

16. DEGREES OF FREEDOM (DOF):
It is the number of independent coordinates required to describe the position of a body.

17. Degrees of freedom/mobility of a mechanism
It is the number of inputs (number of independent coordinates) required to describe the configuration or position of all the links of the mechanism, with respect to the fixed link at any given instant.

18. GRUBLER’S CRITERION
Number of degrees of freedom of a mechanism is given by
F = 3(n-1)-2l-h. Where,
F = Degrees of freedom
n = Number of links in the mechanism.
l = Number of lower pairs, which is obtained by counting the number of joints. If more than two links are joined together at any point, then, one additional lower pair is to be considered for every additional link.
h = Number of higher pairs

19. Examples - DOF F = 3(n-1)-2l-h Here, n = 4, l = 4 & h = 0.
I.e., one input to any one link will result in definite motion of all the links.

20. Examples - DOF F = 3(n-1)-2l-h Here, n = 5, l = 5 and h = 0.
I.e., two inputs to any two links are required to yield definite motions in all the links.

21. Based on relative motion between pairing elements
(a) Siding pair [DOF = 1]
(b) Turning pair (revolute pair) [DOF = 1]

22. Based on relative motion between pairing elements
(c) Rolling pair [DOF = 1]
(d) Cylindrical pair [DOF = 2]

23. Based on relative motion between pairing elements
(e) Spherical pair [DOF = 3]
Eg. Ball and socket joint
(f) Helical pair or screw pair [DOF = 1]

24. Degrees of Freedom

25. KINEMATIC CHAIN
When a number of links or elements are connected such that
- Kinematic pairs are connected such that last link is joined to first link.
- Each link or element forms a part of two kinematic pairs.
- i.e. Group of links either joined together or arranged in a manner that permits them to move relative to one another.
- The relative motion of any point on the link w.r.t to any other point on other link follows a definite direction.
- Such arrangement is called a Kinematic Chain.
Egs: Four bar chain
4-Bar

26. Types of joints in Kinematic chain
Binary Joint: When two links are joined together at a connection the joint is known as binary joint.
Ternary Joint: When three links are joined together at a connection the joint is known as binary joint.
Quaternary Joint: When four links are joined together at a connection the joint is known as binary joint.
Binary joint Ternary Joint Quaternary Joint

27. Kinematic Pair Vs Kinematic Chain
Two elements connected together
Four or More than Four elements connected together
Have constrained relative motion w.r.t to each other
Motion of any point on the link w.r.t. any other point follows a definite direction
Each pair has two links
Chain has minimum four links
First link and last link are connected to form a closed chain
Kinematic pair is a part of chain.
Kinematic Chain is not a part of Kinematic pair.
Egs:
Cylinder & Piston
Crank and connecting rod
Piston and connecting rod.
Crank and frame
Four bar chain
Slider crank chain
Double crank chain

28. MECHANISM
Mechanism – Part of a machine, which transmit motion from input point to output point or from one point to another when one of the links is fixed.
Mechanism may or may not transmit force / Power / Energy HENCE ALL MECHANISMS ARE NOT MACHINES.

29. MECHANISM - A mechanism is a constrained kinematic chain.
- Motion of any one link in the kinematic chain will give a definite and predictable motion relative to each of the others.
- If one of the links or elements of the Kinematic Chain is fixed.
- The arrangement used for transmitting or transforming the motion.
- Such arrangement is called mechanism.
- A mechanism is a Kinematic chain with one link fixed.
- Mechanism can be used to transform rotary into reciprocating, reciprocating into rotary, rotary to oscillating.
Egs. Clock, lock, Type writer, slider crank mechanism etc.
4-Bar

30. MECHANISM Mechanism with four links is called simple mechanism.
Mechanism with more than four link is called compound mechanism.
4-Bar

31. All machines are mechanisms, all mechanisms are not machines
All the machines are made out of more than one mechanism.
Machines transmit power and motion.
Mechanism (Like used in clock) where only relative motion is present but power is not transmitted.
Such mechanisms are not machines.

32. Mechanism Vs Machine Mechanism Machine
1. If one of the link in a chain is fixed we get a mechanism.
Machine is a collection of one or more mechanism to do useful work with desired motion
2. Used to transmit or transform motion
(Transform: Rotary into linear)
2. Transmit or Transforms energy into useful work.
3. Every mechanism is not a machine.
3. Every machine is collection of mechanism
Egs; Lock, Clock, Typewriter, Key board of computer, etc
Egs: I. C. Engine, Shaping machine, hand pump etc.

33. Example for Mechanism

34. Example for Mechanism
Courtesy:

35. Example for Mechanism
Courtesy:

36. Revision till now
Element or Link: It is a Resistant body which has motion relative to other
connected parts is known as link.
Resistant body: A body when performing motion in a mechanism under the influence
of applied force has negligible deformation.
Kinematic Pair: Two elements or links which are connected together in such a way
That their relative motion is in a definite direction (Constrained motion) is called a
Kinematic pair.
Kinematic Chain: When number of links are connected such that each link or element
forms a part of two kinematic pairs or when last link is connected to the first link and
relative motion of any one link follows a definite direction w.r.t. to another.
Mechanism: When one of the link in a kinematic chain is fixed the arrangement can be
used to transmit or transform motion. It is termed as mechanism. (ALL MECHANISMS
ARE NOT MACHINES)
Inversion of mechanism: Different mechanism obtained by fixing different links in a
Kinematic chain are termed as inversions of mechanism.
Machine: It is the collection of one or more mechanisms to convert input energy
into desirable output work.

37. Four bar chain
Four bar chain is the simplest Kinematic chain with four mechanical elements.
Four links form “four turning pair”.
Four links can all be of different lengths.
If one of the link in the four bar chain is fixed it is called as four bar mechanism.
The sum of the shortest and the longest link should be greater than the remaining two links to have continuous relative motion between any two links.
Most of the time motion is provided by a prime mover egs: Electric motor.
A motor has rotary motion hence the link connected to motor should be able to make rotation motion.
The shortest link makes completely rotation is called crank.
Link which can partially rotate or oscillate is called rocker or level.

38. FOUR BAR CHAIN (link 1) frame (Stationary or fixed)
(link 2) crank (Smallest link which rotates)
(link 3) coupler or connecting rod
(link 4) lever or rocker (Partial rotation or oscillates)

39. Inversions of four bar chain
The different types of the mechanisms obtained by fixing each element is called as inversion of a mechanism.
In four bar chain there are four links hence four inversions are possible.
i.e. By fixing one link we get one inversion.

40. Inversions of four bar chain Beam Engine (Crank and lever mechanism)
Link 4 Lever (Oscillates about the pivot)
Link 3 Coupler or connecting rod
Link 1 Frame and cylinder – Fixed
Link 2 Crank – Rotating
Link 3 Coupler or connecting rod
Link 4 Lever – Oscillates about the pivot
Link 1 Frame and cylinder
Link 2 Rotating crank

41. Inversions of four bar chain Crank and Lever (Beam Engine Mechanism)
Link 1 Frame and cylinder – Fixed
Link 2 Crank – Rotating
Link 3 Coupler or connecting rod
Link 4 Lever – Oscillates about the pivot
Coupler or connecting rod
Crank and Lever (Beam Engine Mechanism)
Rotating Crank
Piston
Reciprocating
Piston rod
lever
Stationary frame
Cylinder
Stationary

42. Inversions of four bar chain
Double Crank Mechanism
(Coupled Wheel locomotive)

43. Inversions of four bar chain Double crank mechanism Coupled wheels of locomotives1 1
Double crank
- Consists of four links.
Link 1 fixed
Link 2 and 4 are of equal lengths are called as Crank (Rotating).
Link 3 acts as a coupling rod for the two crank (or wheels).
Rotary motion from one wheel is transferred to other wheel.
- Converts rotary motion from of one crank (or wheel) to rotary motion of other crank (or wheel).
- Egs: Coupled wheels of the locomotives.

44. CRANK-ROCKER MECHANISM
Link 1 is fixed

45. Ackermann steering gear mechanism (Double lever mechanism)
Transmits oscillatory motion from one lever to another.
Used in automobiles for steering the vehicle to change the direction of movement of the vehicle.
Consists of four links. Link AL and link BM act as a lever and are of equal length.
Link LM connects the two levers.
Link AB is stationary and longer than LM.

46. Ackermann steering gear mechanism (Double lever mechanism)
When vehicle is moving along straight path. (Link AB and LM remain parallel).
Link AL and link BM are inclined at an angle α.
When turning right for Link BM α will increase and for link AL α will decrease.
Link AL and link BM oscillate hence the mechanism is called as double lever mechanism.

47. Slider crank mechanism
Slider crank and four bar mechanisms
The process of fixing different links of a kinematic chain one at a time to produce distinct mechanisms is called kinematic inversion of mechanism.
Here the relative motions of the links of the mechanisms remain unchanged.
First, let us consider the simplest kinematic chain ,i.e., a chain consisting of four binary links and four revolute pairs.
The four different mechanisms can be obtained by four different inversions of the chain.

48. Examples of rigid links
Sliding crank mechanism
Line of stroke or
sliding path
Link 1 – Cylinder and frame
(Stationary or fixed link)
Link 2 – Crank (Rotating motion)
Link 3 – Connecting Rod
Link 4 Piston Sliding motion
Slider slides in the stationary cylinder.
Crank – Rotates complete revolution
Slider or Piston – Reciprocates
Connecting Rod – Oscillates
Cylinder & Frame - Stationary
Rotary motion of the crank is converted into reciprocating motion of the slider or vice versa

49. Slider crank mechanism
Slider Crank Mechanism in I.C. Engines in Automobiles

50. SLIDER CRANK CHAIN

51. lnversions of slider crank chain
crank fixed (b) connecting rod fixed (c) slider fixed
- Fixing Cylinder gives Slider crank mechanism.
Fixing the link 2 (crank) gives Whitworth quick return mechanism.
Fixing connecting rod (link 3) gives Crank and slotted lever quick return mechanism Used in shaping and slotting machines
Fixing the sliding piston we get a hand pump mechanism.

52. Slider crank inversions Whitworth quick return motion mechanism (Fixing crank)

53. Crank and slotted lever quick return motion mechanism (Fixing connecting rod)
Courtesy:

54. Intermittent motion mechanisms
Geneva wheel mechanism

55. Intermittent motion mechanisms
Ratchet and pawl mechanism

56. Application of Ratchet Pawl mechanism