1. FUNDAMENTALS & TYPES OF MECHANISM

2. Theory Of Machine
Dynamics
Kinematics
Kinetics
Statics

3. The Machine receives
energy it to
in some
do some
available form and uses
particular type of work

4. STATICS
It deals with the study the forces acting on machine in rest.
DYNAMICS
It deals with the study the forces acting on various parts of a machine

5. KINEMATICS
It is the study of motion, quite apart from the forces which produce that motion.
It is the study of position, displacement, rotation, speed, velocity and acceleration.
KINETICS
It is the study of inertia force which arries due to combined effect

6. It is defined as the combination of rigid or resistance bodies assembled they having no relative motion in between them and transmit only forces

7.  An assembly of moving parts performing a complete functional motion.
A mechanism is a device designed to transform input forces and movement into a desired set of output forces and movement.
Mechanisms generally consist of moving components such as gears and gear trains, belt and chain drives, cam and follower mechanisms, and linkages as well as friction devices such as brakes and clutches, and structural components such as the frame, fasteners, bearings, springs, lubricants and seals, as well as a variety of specialized machine elements such as splines, pins and keys.

8. It is defined as a device which receives energy and transforms it into some useful work.
If the mechanism is used to transmit power (or) to do work, then it is known as machine.
We can define machine as a device for transferring and transforming motion and force or power from the input that is, the source to the output that is the load

9. It is a resistant body or assembly of resistant body of a machine connecting other parts of the machine with relative motion between them.
There are three types of links available in order to transmit motion. They are as follows:
» Rigid link
» Flexible link
» Fluid link

10. Rigid link
A rigid link is one which does not undergo any deformation while transmitting motion. Practically rigid link does not exists. Ex : crank shaft, piston etc.,
Flexible link
A flexible link is one which undergoes partial deformation without affecting the transfer motion. Ex : ropes, belts, chains, springs etc.,
Fluid link
A fluid link is a link which has fluid inside the container and motion is transmitted through the fluid by pressure or compression. Ex: fluids used in hydraulic press, hydraulic jack, hydraulic crane etc.,

11. A joint of two links that permits relative motion is called pair.
Types of kinematic pair
Nature of relative motion between the links.
Nature of contact between the links.
Nature of mechanical arrangement.

12. Nature of relative motion
» Sliding pair
» Turning pair
» Cylindrical pair
» Rolling pair
» Spherical pair
» Helical pair
Nature of contact
» Lower pair
» Higher pair
Nature of mechanical constraint
» Closed pair
» Unclosed pair 12

13. 1. According to the type of relative motion between the elements.
Sliding pair
When the two elements of a pair are connected in such a way that one can only slide relative to the other, the pair is known as a sliding pair.
The piston and cylinder, cross-head and guides of a reciprocating steam engine, ram and its guides in shaper, tail stock on the lathe bed etc. are the examples of a sliding pair.

14. Turning pair
When the two elements of a pair are connected in such a way that one can only turn or revolve about a fixed axis of another link, the pair is known as turning pair.

15. Rolling pair
When the two elements of a pair are connected in such a way that one rolls over another fixed link, the pair is known as rolling pair. Ball and roller bearings are examples of rolling pair.

16. Spherical pair
When the two elements of a pair are connected in such a way that one element (with spherical shape) turns or swivels about the other fixed element, the pair formed is called a spherical pair. The ball and socket joint, attachment of a car mirror, pen stand etc., are the examples of a spherical pair.

17. Helical pair or screw pair
When the two elements of a pair are connected in such a way that one element can turn about the other by screw threads, the pair is known as screw pair. The lead screw of a lathe with nut, and bolt with a nut are examples of a screw pair.

18. Lower pair 2. According to the type of contact between the elements.
When the two elements of a pair have a surface contact when relative motion takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair. It will be seen that sliding pairs, turning pairs and screw pairs form lower pairs.

19. Higher pair
When the two elements of a pair have a line or point contact when relative motion takes place and the motion between the two elements is partly turning and partly sliding, then the pair is known as higher pair. A pair of friction discs, toothed gearing, belt and rope drives, ball and roller bearings and cam and follower are the examples of higher pairs.

20. 3. According to the type of closure.
Closed pair
When two elements of a pair are held together mechanically, they constitute a closed pair.
Ex : All pair
Un closed pair
When two elements of a pair are not held together mechanically, they constitute a unclosed pair.
Ex : cam and follower

21. Completely Constrained Motion
TYPES OF MOTIONS
Completely Constrained Motion
Constrained Motions
Uncompletely Constrained Motion
Successfully Constrained Motion

22. 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.
For example, the piston and cylinder (in a steam engine) form a pair and the motion of the piston is limited to a definite direction (i.e. it will only reciprocate) relative to the cylinder irrespective of the direction of motion of the crank.

23. 2. Incompletely constrained motion
When the motion between a pair can take place in more than one direction, then the motion is called an incompletely constrained motion.
A circular bar or shaft in a circular hole, as shown in Fig., is an example of an incompletely constrained motion as it may either rotate or slide in a hole. These both motions have no relationship with the other.

24. 3. Successfully constrained motion
When the motion between the elements, forming a pair, is such that the constrained motion is not completed by itself, but by some other means, then the motion is said to be successfully constrained motion.
Consider a shaft in a foot-step bearing as shown in Fig.
The shaft may rotate in a bearing or it may move upwards.
This is a case of incompletely constrained motion.
But if the load is placed on the shaft to prevent axial upward movement of the shaft, then the motion of the pair is said to be successfully constrained motion.
The motion of an I.C. engine valve and the piston reciprocating inside an engine cylinder are also the examples of successfully constrained motion.

25. If the last link is joined to first link to transmit definite motion, then it is known as kinematic chain.
To determine the given assemblage of links form the kinematic chain or not:
The two equations are:
L=2p-4=2(j+2)/3
Where, l = number of links p = number of pairs j = number of joints
LHS>RHS, the chain is locked
LHS=RHS,the chain is constrained
LHS<RHS, the chain is unconstrained

27. The following types of joints are usually found in a chain :
Binary joint. Ternary Joint Quaternary Joint
Binary joint:
When two links are joined at the same connection, the joint is known
as binary joint

28. Ternary joint:
When three links are joined at the same connection, the joint is known as ternary joint.
It is equivalent to two binary joints as one of the three links joined carry the pin for the other two links.

29. It is equivalent to three binary joints.
Quaternary joint:
When four links are joined at the same connection, the joint is called a quaternary joint.
It is equivalent to three binary joints.
In general, when l number of links are joined at the same connection, the joint is equivalent to (l - 1) binary joints.
Quaternary joint:

30. 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
A mechanism with four links is known as simple mechanism, and the mechanism with more than four links is known as compound mechanism.
When a mechanism is required to transmit power or to do some particular type of work, it then becomes a machine.
In such cases, the various links or elements have to be designed to withstand the forces (both static and kinetic) safely.
A little consideration will show that a mechanism may be regarded as a machine in which each part is reduced to the simplest form to transmit the required motion.

31. Mechanisms and Simple Machines
Mechanism: the fundamental physical or chemical processes involved in or
responsible for an action, reaction or other natural phenomenon.
Machine: an assemblage of parts that transmit forces, motion and energy in a predetermined manner.
The term mechanism is applied to the combination of geometrical bodies
which constitute a machine or part of a machine.
A mechanism may therefore be defined as a combination of rigid or resistant bodies, formed and connected so that they move with definite relative motions with respect to one another .
The similarity between machines and mechanisms is that
they are both combinations of rigid bodies
the relative motion among the rigid bodies are definite.
The difference between machine and mechanism is that machines transform energy to do work, while mechanisms do not necessarily perform this function.
All machines are mechanisms. But all mechanisms are not machines.

32. Planar mechanisms: When all the links of a mechanism have plane motion, it is called as a planar mechanism. All the links in a planar mechanism move in planes parallel to the reference plane.

33. Planar mechanisms
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ero Engg, DSCE 24

34. Spatial mechanisms:
When all links of mechanism are lie in different plane, the mechanism is known as spatial mechanism.
Courtesy:

35. 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.
Kutzbach criterion : Number of degrees of freedom of a mechanism is given by
Where
n = total degrees of freedom in the mechanism
l = number of links (including the frame)
j = Number of equivalent binary joints
h = number of higher pairs (two degrees of freedom)
This equation is called Kutzbach criterion for movability of a mechanism having plane motion.

36. The mechanism, as shown in Fig
The mechanism, as shown in Fig. (a), has three links and three binary joints, i.e. l= 3 and j = 3.
n = 3 (3-1)-2x3=0
The mechanism, as shown in Fig. (b), has four links and four binary joints, i.e. l= 4 and j = 4.
N = 3 (4-1) -2x4 = 1
The mechanism, as shown in Fig. (c), has five links and five binary joints, i.e. l = 5, and j = 5.
n = 3(5-l)-2x5 = 2

37. Number of links, l = 7
Number of Equivalent binary joints, Jb = 8 Number of Higher pairs, h = 0
dof = 3(l -1) – 2Jb –h
= 3(7-1) – 2x8 – 0
= 18 – 16
= 2
Number of links, l = 9
Number of Equivalent binary joints, Jb = 10 Number of Higher pairs, h = 0
dof = 3(l -1) – 2Jb –h
= 3(9-1) – 2x10 – 0
= 24 – 20
Hareesha=N G4, Dept of Aero Engg, DSCE
2/5/2016 28

38. Number of links, l = 7
Number of Equivalent binary joints, Jb = 8 Number of Higher pairs, h = 0
dof = 3(l -1) – 2Jb –h
= 3(7-1) – 2x8 – 0
= 18 – 16
= 2
Number of links, l = 9
Number of Equivalent binary joints, Jb = 10 Number of Higher pairs, h = 0
dof = 3(l -1) – 2Jb –h
= 3(9-1) – 2x10 – 0
= 24 – 20 28

39. Number of links, l = 4
Number of Equivalent binary joints, Jb = 4 Number of Higher pairs, h = 1
dof = 3(l -1) – 2Jb –h
= 3(4-1) – 2x4 – 1
= 9 – 8 – 1
= 0
Number of links, l = 8
Number of Equivalent binary joints, Jb = 10 Number of Higher pairs, h = 1
= 3(8-1) – 2x10 – 0
= 21 – 20 – 0
= 1 29

40. Number of links, l = 11
Number of Equivalent binary joints, Jb = 15
Number of Higher pairs, h = 0 dof = 3(l -1) – 2Jb –h
= 3(11-1) – 2x15 – 0
= 30 – 30 – 0
= 0
Number of links, l = 4
Number of Equivalent binary joints, Jb = 3
Number of Higher pairs, h = 1 dof = 3(l -1) – 2Jb –h
= 3(4-1) – 2x3 – 1
= 9 – 6 – 1
= 2

41. Try these (a) Number of links, l =
Number of Equivalent binary joints, Jb = Number of Higher pairs, h =
dof = -1
Try these
(b)
Number of links, l =
Number of Equivalent binary joints, Jb =
Number of Higher pairs, h =
dof = 1
(c)
Number of links, l =
Number of Equivalent binary joints, Jb = Number of Higher pairs, h =
dof = 0

42. 2/5/2016
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44. Grubler’s criterion:

45. Types of Kinematic Chains
The most important kinematic chains are those which consist of four lower pairs, each pair being a sliding pair or a turning pair.
The following three types of kinematic chains with four lower pairs are important from the subject point of view :
Kinematic Chain
Four bar chain
Slider crank chain
Double crank chain

46. Four Bar Chain or Quadric Cycle
We have already discussed that the kinematic chain is a combination of four or more kinematic pairs, such that the relative motion between the links or elements is completely constrained.
The simplest and the basic kinematic chain is a four bar chain or quadric cycle chain, as shown in Fig.
It consists of four links, each of them forms a turning pair at A, B, C and D. The four links may
be of different lengths.
A very important consideration in designing a mechanism is to ensure that the input crank makes a complete revolution relative to the other links. The mechanism in which no link makes a complete revolution will not be useful.
In a four bar chain, one of the links, in particular the shortest link, will make a complete revolution relative to the other three links. Such a link is known as crank or driver.
In Fig. AD (link 4 ) is a crank. The link BC (link 2) which makes a partial rotation or oscillates is known as lever or rocker or follower and the link CD (link 3) which connects the crank and lever is called connecting rod or coupler. The fixed link AB (link 1) is known as frame of the mechanism.
When the crank (link 4) is the driver, the mechanism is transforming rotary motion into oscillating motion.

47. A mechanism is one in which one of the links of a kinematic chain is fixed.
Different mechanisms can be obtained by fixing different links of
the same kinematic chain.
These are called as inversions of the mechanism.
By changing the fixed link, the number of mechanisms which can be obtained is equal to the number of links.
Except the original mechanism, all other mechanisms will be known as inversions of original mechanism.
The inversion of a mechanism does not change the motion of its links relative to each other.

48. The method of obtaining different mechanisms by fixing different links in a kinematic chain, is known as inversion of the mechanism.

49. Watt’s Indicator Mechanism
First inversion
Beam Engine
second Inversion
Coupling rod of locomotive
Watt’s Indicator Mechanism
Pantograph
Third Inversion

50. Beam engine

54. Coupling rod of a locomotive

57. Watt’s indicator mechanism

59. Pantograph

62. Oscillating cylinder engine
Reciprocating engine
Whitworth quick return mechanism
Rotary or Gnome engine
SINGLE SLIDER CRANK CHAIN
Crank and slotted lever mechanism
Oscillating cylinder engine
Bull engine

63. First Inversion Bull Engine Oscillating cylinder engine second
Fourth Inversion
Reciprocating engine
Whitworth quick return mechanism
Third
Inversion
Rotary engine
Oscillating cylinder engine
second
Inversion
Crank and slotted lever mechanism
First Inversion
Bull Engine

68. CRANK AND SLOTTED LEVER QUICK RETURN MECHANISM

72. Double Slider Crank Chain
Elliptical Trammel
Scotch Yoke Mechanism
Oldham Coupling

79. Oldham's Coupling

80. COMMON MECHANISM Geneva Mechanism Ackermann Steering Mechanism
Bicycle rear wheel sprocket mechanism Foot operated air pump mechanism
COMMON MECHANISM

82. Application of the Geneva drive
One is movie projectors : the film does not run continuously through the projector. Instead, the film is advanced frame by frame, each frame standing still in front of the lens for 1/24 of a second

83. ACKERMANN STEERING

88. The Grashof’s condition for a four-bar linkage states that “If the sum of the shortest and longest link of a planar four bar linkage is less than or equal to the sum of the remaining two links, then the shortest link can rotate fully with respect to a neighbouring link.
Condition
S+L ≤ P+Q
where S is the shortest link, L is the longest, and P and Q are the other links.
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89. TEST (29/7/20) 1. Explain the following terms:
a) lower pair b) higher pair c) kinematic chain d) Inversion
2. The withworth quick return mechanism has the driving crank 150mm long. The driving crank is 75mm. The line of stroke of the ram passes through the center of rotation of slotted lever whose free end is connected to the ram by a connecting link. Find the ratio of time of cutting to time of return.
3. Sketch and describe four bar mechanism.
4. Apply Kutzbach’s criterion to find degree of freedom of the following mechanism.