The document provides an in-depth analysis of the kinematics of cam mechanisms, detailing the definitions, classifications, and applications of cams and followers in mechanical systems. It explores the evolution of cam designs, the basic principles of cam movement, types of cam profiles, and the kinematic terminology used in cam and follower motion. Additionally, it includes examples of cam applications, particularly in engine components, and outlines the mathematical relationships governing follower motion and acceleration.

1. Kinematic of machine(CE 101T)
(Cam analysis)
By:
Poonam Savsani
Department of Mechanical Engineering
School of Technology
1

2. CAM - Definition
• A cam may be defined as a machine element
having a curved outline or a curved groove,
which, by its oscillation, rotation or reciprocating
motion, gives a predetermined specified motion
to another element called the follower .
• It is usually consists of a cam (the driver), the foll
ower (the driven element), and the frame (the su
pport for the cam and the follower).

3. PARTS OF CAM MECHANISM

4. KINEMATIC DIAGRAM FOR CAM MECHANISM

5. LEONARDO DA VINCI
• The first cam designs
were found in Leonardo da
Vinci’s sketches in his
Codex Madrid I.
• Leonardo found cam
mechanisms being very
compact mechanical
devices to transform rotary
motion to linear motion.

6. Cam hammer
Designed around
1497 by
Leonardo da Vinci
The hammer uses
a cam to convert
rotary motion to
oscillating motion.

7. Examples for cam
• In IC engines to operate the inlet and exhaust valves

8. Classification of CAM Mechanism
Based on modes of Input / Output motion
• Rotating cam – Translating follower
• Rotating cam – Oscillating follower
• Translating cam – Translating follower

9. Classification of followers
According to the shape of follower
• Knife edge follower
• Roller follower
• Flat faced follower
• Spherical faced follower

10. According to the path of motion of follower
a) Radial follower
b) Offset follower

11. a) Radial follower
• When the motion of the follower is along an axis p
assing through the centre of the cam, it is known a
s radial followers. Above figures are examples of t
his type.

12. b) Offset follower
When the motion of the follower is along an axis away from t
he axis of the cam centre, it is called off-set follower. Above f
igures are examples of this type.

13. • According to movement
– Reciprocating follower
– oscillating follower

14. Classification of cams
a) Radial or disc cam
b) Cylindrical cam
c) End cam

15. a) Radial or Disc cam
In radial cams, the follower reciprocates or oscillates
in a direction perpendicular to the cam axis.

16. b) Cylindrical cams
In cylindrical cams, the follower reciprocates
or oscillates in a direction parallel to the cams
axis.

17. c) End cams
It is also similar
to cylindrical cams,
but the follower
makes contact at
periphery of the
cam as shown in
fig

18. CAM Nomenclature
• Cam profile is the actual working surface
contour of the cam. It is the surface in conta
ct with the knife-edge, roller surface, or flat
-faced follower.

19. CAM Nomenclature
Base circle is the smallest circle
drawn to the cam profile from the radial
cam center. Obviously, the cam size is
dependent on the established size of
the base circle.
Trace point is the point on the follo
wer located at the knife-edge, roller ce
nter, or spherical-faced center.
TRACE POINT

20. CAM Nomenclature
• Pitch curve : The path
generated by the trace
point as the follower is
rotated about a stationer
y cam.
 Prime circle: The small
est circle from the cam
center through the pitch
curve

21. CAM Nomenclature
Pressure angle: The angle between the direction of the
follower movement and the normal to the pitch curve
PRESSURE
ANGLE
Pitch point: Pitch point corresp
onds to the point of maximum
pressure angle.
PITCH POINT
Pitch circle: A circle drawn from the cam center and p
asses through the pitch point is called Pitch circle
Stroke: The greatest distance o
r angle through which the follow
er moves or rotates

22. Constraints on the Follower
With external down ward force
Without external down ward force

23. In all cam systems it is important that the follower is always in contact a
nd following the motion of the cam.
 Gravity constraint
The weight of the follower system is sufficient to maintain contact.
 Spring constraint
The spring must be properly designed to maintain contact.
Constraints on the Follower
• Positive mechanical constraint
A groove maintains positive action.

26. Application of cam
• Camshaft of an Engine

27. • Camshaft of an Engine incorporating a Rocker
Arm

28. • Oil pump working

29. ANALYSIS OF CAM FOLLOWER MOTION
KINEMATICS OF CAM AND
FOLLOWER

30. Rise - is when the follower is moving away
from the cam centre.
Dwell - is the period when the follower is st
ationary.
Return - is when the follower moves back t
owards the cam centre.
Stroke/Total follower travel/Throw (h) – is t
he greatest distance through which the foll
ower moves.
Kinematics Terminologies of Cam Mechanisms

32. Angle of return / descent
Angle of dwell
Angle of dwell
Angle of rise / ascent / outstroke
Angle of action

33. • Displacement (s) – is the position of the
follower from a specific zero or rest position
in relation to time or the rotary angle of the
cam.
• Velocity (v) – is the speed with which the
cam moves the follower.
• Acceleration (a) – is the rate of change of
the follower’s velocity.

34. • Jerk (j) – is the rate of change of the follow
er’s acceleration.
• Angular velocity (ω) – is the speed of the c
am or the ratio of the angular displacemen
t by the cam to the time interval ∆t.
where θ is in radians

35. Follower Displacement Diagram
• A follower displacement diagram is a
graph showing displacement of the followe
r plotted as a function of time.
• Since the cam usually rotates at constant
angular velocity, the t-axis can be consider
as the θ-axis.
• The follower displacement diagram determ
ines the shape of the cam.

36. where:
h is the stroke
t is in seconds
θ is in radians

37. Motion of the Follower
1. Uniform motion ( constant velocity)
2. Simple harmonic motion
3. Uniform acceleration and retardation motion
4. Cycloidal motion

38. a) Uniform motion (constant velocity)
Displacement diagram
Since the follower moves with uniform velocity during its
rise and fall, the slope of the displacement curve must be co
nstant as shown in fig
RISE DWELL RETURN DWELL
ANGLE OF ROTATION
STROKE

39. ω

40. • Generally, this design
is not used for critical
systems because the
high acceleration at
the two ends of the
segment will result in
large forces that will
smooth out in the
cam.

41. • The shock effects inherent from the uniform velocity can be reduces
by modifying the motion.
• The modification is to have the follower undergoing uniform accelera
tion at the start of the constant velocity interval and uniform decelera
tion at the end of the constant velocity interval, so that the velocity c
urve is continuous.
Modified Uniform Velocity

43. • In constructing the cam profile, we employ
the principle of kinematic inversion, imagin
ing the cam to be stationary and allowing t
he follower to rotate opposite to the directi
on of cam rotation.
BASIC PRINCIPLE

44. A cam is to give the following motion to a knife-edged follower :
1. Outstroke during 60° of cam rotation ;
2. Dwell for the next 30° of cam rotation ;
3. Return stroke during next 60° of cam rotation, and
4. Dwell for the remaining 210° of cam rotation.
The stroke of the follower is 40 mm and the minimum radius of the cam is 50 mm.
The follower moves with uniform velocity during both the outstroke and return strokes.
Draw the profile of the cam when cam rotates in clockwise direction.
(a) the axis of the follower passes through the axis of the cam shaft, and
(b) the axis of the follower is offset by 20 mm from the axis of the cam shaft.
PLOT THE DISPLACEMENT DIAGRAM
40mm
60° 30° 60° 210°
A
G H
P
0 1 2 3 4 5 6 0’ 1’ 2’ 3’ 4’ 5’ 6’
B
C
D
EF J
K
L
M
N

45. Profile of the cam when the axis of follower passes through
the axis of cam shaft
60°
60°
30°
40mm
60° 30° 60°
A
G H
0 1 2 3 4 5 6 0’ 1’ 2’ 3’ 4’ 5’ 6’
B
C
D
EF
J
K
L
M
N
1 0
23
4
5
6
0’
1’
2’
3’
4’
5’ 6’
A
B
CDE
F
G
H
I
J
K
L M N
I
210°

46. the axis of the follower is offset by 20 mm from the axis
of the cam shaft.
60°
60°
30°
40mm
60° 30° 60°
A
G H
0 1 2 3 4 5 6 0’ 1’ 2’ 3’ 4’ 5’ 6’
B
C
D
EF
J
K
L
M
N
2345
6
0’
1’
2’
3’
4’
5’
6’
I
210°
A
B
CD
E
F
G
H
I
J
K
L
M
N
OFFSET CIRCLE r=20 mm
BASE CIRCLE r=50 mm

47. Simple Harmonic Motion
• Cams that produces simple harmonic moti
on to the follower are called eccentric cam
s.
• Eccentric cams are circular cams wherein
the axis of rotation does not intersect the
center of the circle.
• The displacement equation of simple harm
onic motion can be written as :

48. SIMPLE HARMONIC MOTION

49. Time required for the out stroke of the
follower in seconds,
tO = θO /ω
Max velocity and acceleration during
outstroke
Max velocity and acceleration during
returnstroke

51. 87
6
5
4
3
2
1 0
s
ϴo ϴR
1 2 3 4 5 6 7 8
ϴd

52. A cam, with a minimum radius of 25 mm, rotating clockwise at a uniform speed
is to be designed to give a roller follower, at the end of a valve rod, motion described be
low :
1. To raise the valve through 50 mm during 120° rotation of the cam ;
2. To keep the valve fully raised through next 30°;
3. To lower the valve during next 60°; and
4. To keep the valve closed during rest of the revolution i.e. 150° ;
The diameter of the roller is 20 mm and the diameter of the cam shaft is 25 mm.
Draw the profile of the cam when
(a) the line of stroke of the valve rod passes through the axis of the cam shaft, and
(b) the line of the stroke is offset 15 mm from the axis of the cam shaft.
The displacement of the valve, while being raised and lowered, is to take plac
e with simple harmonic motion. Determine the maximum acceleration of the valve ro
d when the cam shaft rotates at 100 r.p.m. Draw the displacement, the velocity and the
acceleration diagrams for one complete revolution of the cam.

53. Profile of the cam when the line of stroke of the valve rod passes through
the axis of the cam shaft
6030
0
1
2
3
4
5
6
50
1 2 3 4 5 6 0’1’ 2’ 3’ 4’5 6’
120
150
A
B
C
D
E F
G H
J K
L
M
N
P

54. 1
2
3
4
5
6
AB
C
D
E
F
G
H J
K
L
M
N
P

55. Profile of the cam when the line of stroke of the valve rod is offset 15 mm
from the axis of the cam shaft.
120°
30°
60°
0
12
3
4
5
6
0’
1’ 2’
3’ 4’5’ 6’
A
B
CD
E
F
G
H
J K
L
M
N P

56. angular velocity of the cam

57. Follower Moves with Uniform Acceleration and Retardation

58. Maximum Velocity during outstroke and return stroke.
Maximum acceleration during outstroke and return stroke.

59. ϴO° ϴD° ϴR° ϴD°
0 1 2 3 4 5 6 0’ 1’ 2’ 3’ 4’ 5’ 6’
0123456
0’1’2’3’4’5’6’
A
G H
N

60. • A cycloidal curve is the path traced by a p
oint on a circle as the circle rolls on a strai
ght line.
• To create a cycloidal motion in cam design
, involves superimposing cycloidal motion
on constant velocity motion.
• No acceleration discontinuities, therefore it
can be applied to high speeds.
Cycloidal Motion

62. CYCLOIDAL MOTION

63. Displacement equation for the cycloid motion
Maximum velocity during rise and return stroke

64. Maximum acceleration during rise and return stroke

65. Displacement dia for cycloid motion
ϴo
A
B
S = 2п r
r = S/ 2п
12
3
4 5
6
a'
b'
0’ 1’ 2’ 3’ 4’ 5’ 6’
a
b
c
d e

67. A cam drives a flat reciprocating follower in the following manner :
During first 120° rotation of the cam, follower moves outwards through a distance
of 20 mm with simple harmonic motion. The follower dwells during next 30° of ca
m rotation. During next 120° of cam rotation, the follower moves inwards with
simple harmonic motion. The follower dwells for the next 90° of cam rotation. The
minimum radius of the cam is 25 mm. Draw the profile of the cam.

68. 120°
30°
120°
01
2
3
4
5
6
AB
C
D
E
F
G
H
J K
L
M
N
P
Min radius of cam=base circle radius
= 25mm

69. A cam drives a flat reciprocating follower in the following manner :
During first 120° rotation of the cam, follower moves outwards through a distance
of 20 mm with uniform acceleration and retardation. The follower dwells durin
g next 30° of cam rotation. During next 120° of cam rotation, the follower moves i
nwards with uniform acceleration and retardation. The follower dwells for the
next 90° of cam rotation. The minimum radius of the cam is 25 mm. Draw t
he profile of the cam.

70. 120°
30°
120°
01
2
3
4
5
6
AB
C
D
E
F
G
H
J K
L
M
N
P

71. A cam drives a flat reciprocating follower in the following manner :
During first 120° rotation of the cam, follower moves outwards through a distance
of 20 mm with simple hormonic motion. The follower dwells during next 30° of
cam rotation. During next 120° of cam rotation, the follower moves inwards with
uniform acceleration and retardation. The follower dwells for the next 90° of ca
m rotation. The minimum radius of the cam is 25 mm. Draw the profile of t
he cam.

72. Draw a cam profile to drive an oscillating roller follower to the specifications
given below :
(a) Follower to move outwards through an angular displacement of
20° during the first 120°rotation of the cam ;
(b) Follower to return to its initial position during next 120° rotation of
the cam ;
(c) Follower to dwell during the next 120° of cam rotation.
The distance between pivot centre and roller centre = 120 mm ; distance betwe
en pivot centre and cam axis = 130 mm ; minimum radius of cam = 40 mm ; radi
us of roller = 10 mm ; inward and outward strokes take place with simple harmo
nic motion.
s

74. O
A
A1
120° 120°
120°
1
2
3
4
5 6
1’
2’
3’
4’
5’
6’
1
2
3
4
5
6
1’
2’ 3’ 4’
5’
6’
B
C
D
E
F
G
H
J
K
L
M
N