Classification of mechanisms – Basic kinematic concepts and definitions – Degree of freedom, Mobility – Kutzbach criterion, Gruebler’s criterion – Grashof’s Law – Kinematic inversions of four-bar chain and slider crank chains – Limit positions – Mechanical advantage – Transmission Angle – Description of some common mechanisms – Quick return mechanisms, Straight line generators, Universal Joint – rocker mechanisms.

1. KINEMATICS OF MACHINES
UNIT-1
BASIC MECHANISM

2. Kinematics
• Kinematics is the branch of classical
mechanics which describes the motion of
points, bodies (objects) and systems of bodies
(groups of objects) without consideration of
the causes of motion.

3. MACHINE

4. RESISTANT BODY

5. LINK or ELEMENT

6. EXAMPLES FOR LINK

7. TYPES OF LINK

8. RIGID LINK

9. FLEXIBLE LINK

10. FLUID LINK

11. STRUCTURE

12. MACHINE Vs STRUCTURE

13. KINEMATIC PAIR

14. CLASSIFICATION OF KINEMATIC PAIRS
• Based on type of Contact
• Based on type of Relative motion
• Based on type of constraint

15. 1. Based on Nature of contact
or
Type of contact

16. 2. Based on Nature of relative motion between them
or
Type of relative motion

17. 3. Based on Type of constraint

18. BASED ON NATURE OF CONTACT
IN KINEMATIC PAIRS
• LOWER PAIR
• HIGHER PAIR

19. LOWER PAIR

20. HIGHER PAIR

21. DEPEND ON RELATIVE MOTION
IN KINEMATIC PAIRS

22. ii) Turning pair

23. iii) Rolling pair

24. iv) Screw pair (helical pair)

25. v) Spherical pair

26. DEPEND ON CONSTRAINING MOTIONS
IN KINEMATIC PAIR

27. TYPES OF CONSTRAINED
MOTIONS

28. 1. COMPLETELY CONSTRAINED MOTION

29. 2.INCOMPLETELY CONSTRAINED MOTION

30. 3.SUCCESSFULLY CONSTRAINED MOTION

31. KINEMATIC CHAIN

32. HOW TO FIND
KINEMATIC CHAIN OR NOT

33. EXAMPLE .1
ARRANGEMENT OF THREE LINKS

34. SOLUTION

35. EXAMPLE-2
ARRANGEMENT OF FOUR LINKS

36. EXAMPLE – 3
ARRANGEMENT OF FIVE LINKS

37. JOINTS

38. 1.Binary joint

39. Checking whether it’s a kinematic chain

40. 2.Ternary joint

41. 3.Quaternary Joint

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

43. DEGREE OF FREEDOM
OR MOBILITY
Degree of Freedom for plane Mechanism m (mobility):
It is defined as the no of input motions, which must be independently controlled
in order to bring mechanism into useful engineering purpose.

44. (a) Siding pair [DOF = 1]
(b) Turning pair (revolute pair) [DOF = 1]

45. (c) Cylindrical pair [DOF = 2]
(d) Rolling pair [DOF = 1]

46. .
(e) Spherical pair [DOF = 3]
Eg. Ball and socket joint
(f) Helical pair or screw pair [DOF = 1]

47. PROBLEMS

48. FIND THE DEGREE OF FREEDOM(MOBILITY) FOR
THE GIVEN DIAGRAMS

49. EXAMPLE-1

50. EXAMPLE-2

51. EXAMPLE - 3

52. EXAMPLE-4

53. EXAMPLE -5

54. INVERSION MECHANISM
• Inversion of a kinematic linkage or mechanism is observing the
motion of the members of the mechanism with fixing different
links as reference frame. Each time when a different link is
chose as the frame link the mechanism shows different
characteristics of the motion.
• KEEPING ANY ONE OF THE LINK FIXED AND
ROTATING OR OSCILLATING OTHER LINKS-
THIS RESULTS DIFFERENT FORM OF MOTION OUTPUT FOR
DIFFERENT USAGE

55. INVERSIONS OF FOUR BAR
CHAIN

56. FIRST INVERSION -

58. SECOND INVERSION

59. COUPLING ROD OF A LOCOMOTIVE – USED TO
TRANSMIT ROTATION FROM ONE WHEEL TO ANOTHER WHEEL
EXAMPLE --- IN TRAIN
• .

61. THIRD INVERSION

62. WATT INDICATOR MECHANISM- USED TO SHOW THE
STEAM PRESSURE IN THE CYLINDER

65. PANTOGRAPH
- USED TO ENLARGE THE SMALL GIVEN DIAGRAM

66. WORKING --- PANTOGRAPH

67. "Pantograph" is a drawing instrument to magnify figures.
Tracing the original figure by moving the red point, we can automatically
obtain the magnified figure with the pen at the blue point. Find the ratio of
magnification when the lengths of the arms are defined in the right figure.

68. ACKERMAN STEERING

69. INVERSIONS OF SINGLE SLIDER
CRANK CHAIN

70. First Inversion

72. Second Inversion

73. .

75. .

79. Third Inversion

80. .

82. .

84. Fourth Inversion

85. Pendulam pump or Bull Engine

87. Hand Pump

88. INVERSIONS OF DOUBLE SLIDER
CRANK CHAIN

89. ,

91. Second Inversion

93. Third Inversion

94. .

97. .

98. Toggle mechanism,
UNIT - I

100. Toggle mechanism
• For a linkage mechanism, the limit position of a link is the
position of a link for which a coordinate which describes its
position relative to an adjacent link is a maximum or a minimum.
• For a mechanism, when one of its links is in a limit position, we
said that it is at the limit position of a mechanism.
• For a four-bar mechanism, if its limit positions are occurred
when the active link is aligned with the connecting rod, this
mechanism is at the toggle position. When the mechanism is
reaching its toggle position, a small input torque can generate an
extremely large output torque, where its mechanical advantage
is being infinitely maximal. At such situation, the mechanism is
called a toggle mechanism.

101. toggle mechanisms
• The toggle mechanisms can be used in the
situation when one needs to output large
force subject to a short stroke, for example,
the stone crushers and mechanical presses,
etc. The shown mechanism has a toggle
position when the two lower links arrange to
be aligned. At this position, the slider can
produce an extremely large power to press
workpiece.

103. .
.

104. Intermittent motion mechanisms
Ratchet and pawl mechanism

105. Application of Ratchet Pawl
mechanism

106. ,
.

107. .
.

108. Intermittent motion mechanisms
Geneva wheel mechanism

109. Snap Action Mechanism
.
• Its known as toggle mechanism or flip flop
mechanisms

110. Motion Adjustment Mechanism
• Its used to adjust the motion of the link

111. .
• .

112. .
.

113. .
.

114. Hooke’s joint

115. Straight line generators
Unit -1

116. Scott Russell straight line Mechanism

117. Arrangement
• The green link is 2 times greater than the
length of blue link. This blue link is pinned as
shown in fig with green link.
• One more requirement is that the slider's
connection pin needs to be sliding in a line
that would intersect the static pivot end of the
short link.

118. Scott Russell straight line Mechanism
The complexity of the mechanisms to generate
exact straight lines can be reduced by
introduction of one or more slider crank linkages.
It is possible to generate an exact straight line
using the slider crank mechanism but the range of
motion is limited.
Based on the geometry of the linkage the output
motion is a simple sine function of the drive link or
a simple harmonic motion. It is evident from the
figure that this mechanism is made up of
isosceles triangles, AB, AC and AO2 are of equal
lengths.

119. Peaucellier Exact Straight Line Mechanism
• Peaucellier linkage can convert an input circular
motion to the exact straight line motion.
• The construction of this mechanism is such that
the point which is connected to the crank moves
in a circular path and the point traversing the
straight line is selected as the output point.
• The linkage has a rhombic loop formed of the
equal length members, 5, 6, 7 and 8. Two equal
length links are connected to the opposite
corners of the rhombus at one end and to a
common fixed point O4 at the other ends.
• The point A of the rhombus is connect to fixed
point O2 through the link 2. The length of the
link 2 is equal to the distance between points
O2 and O4.
• By the constraints of the geometry point A moves
in a circular path and as the point A moves in a
circle point P traverses an exact straight line path
normal to the line joining O2 and O4.

120. Peaucellier Apparatus
• --- For drawing straight lines

121. USAGE
The apparatus in the right figure is
invented by M.Peaucellier in 1864. It
has six pieces or links. There are
two long links of equal length and
four short links that form a rhombus.
Tracing the original figure by
dragging the red point, we can
obtain a transformed figure at the
blue point.

122. .
How to use
• Drag the red point.
• The red point moves on a line when "Line"
option is selected.
• The red point moves on a circle when "Circle"
option is selected.

123. Some important concepts in link
mechanisms are:
• Crank: A side link which revolves relative to the frame is called a crank.
• Rocker: Any link which does not revolve is called a rocker.
• Crank-rocker mechanism: In a four bar linkage, if the shorter side link
revolves and the other one rocks (i.e., oscillates), it is called a crank-rocker
mechanism.
• Double-crank mechanism: In a four bar linkage, if both of the side links
revolve, it is called a double-crank mechanism.
• Double-rocker mechanism: In a four bar linkage, if both of the side links
rock, it is called a double-rocker mechanism.

124. MECHANICAL ADVANTAGE OF
MECHANISM
-------- a quality measure
• Due to more usage of 4 bar mechanism, its necessary to study
some of the advantages of mechanisms.
• Which tell whether the mechanism is good one or not.
• It’s a quality measure of all mechanism

125. MECHANICAL ADVANTAGE
• It’s the ratio of output torque to the input torque
• M.A(ideal) =
• M.A (Actual) =
TA = Driving link torque
TB = Driven link Torque
A
B
A
B
T
T



 
A
B
A
B
T
T




126. Transmission Angle
• The angle between
Coupler and the
follower


127. Effect of Transmission angle on
mechanical advantage