SCHOOL OF MECHANICAL ENGINEERING Mechanical Design B Cam mechanisms Learning pack - Version 1.1 Recommended text: You particularly are directed to: “Theory of Machines and Mechanisms” by J E Shigley and J J Uicker, McGraw-Hill, 2nd edition, 1995. This text book covers all the main points on the topic and provides a considerable amount of detail (also good for linkages and gears). Throughout these notes cross references will be made to sections or pages of this book, and it will be referred to as TMM. If designing a cam system, complete design guidance is available in the ESDU Mechanisms notes volumes 3a to 3d. These cover all the course materials plus detailed considerations covering comprehensive design. Many of the figures are taken from Fundamentals of Applied Kinematics by D C Tao, Adison-Wesley, 1967. You may find this and other standard theory of machines texts useful.
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SCHOOL OF MECHANICAL ENGINEERING
Mechanical Design B
Cam mechanisms
Learning pack - Version 1.1
Recommended text:
You particularly are directed to:
“Theory of Machines and Mechanisms” by J E Shigley and J J Uicker, McGraw-Hill, 2nd edition, 1995.
This text book covers all the main points on the topic and provides a considerable amount of detail (also
good for linkages and gears). Throughout these notes cross references will be made to sections or pages of
this book, and it will be referred to as TMM. If designing a cam system, complete design guidance is
available in the ESDU Mechanisms notes volumes 3a to 3d. These cover all the course materials plus
detailed considerations covering comprehensive design. Many of the figures are taken from Fundamentals
of Applied Kinematics by D C Tao, Adison-Wesley, 1967.
You may find this and other standard theory of machines texts useful.
Cam mechanisms
Dr K D Dearn
These notes are regularly interspersed with questions to illustrate the points made and to
understanding. These are highlighted in
INTRODUCTION
The cam is a mechanical component of a machine that is used to transmit motion to another component,
the follower, through a prescribed motion programme by direct contact.
three elements – the cam, the follower and the frame.
They are versatile and can produce any type of motion in the follower. In addition they can convert rotary
motion to linear and vice-versa. The follower as the driven m
- Non-uniform motion
- Intermittent motion
- Reversing motion
Uses of the cam mechanism include:
- Valve timing in internal combustion (IC) engines
- Textile and sewing machines
- Computers
- Printers
- Paper handling devices (photo
- Machine tools
Figure 1 shows four different configurations of cams used for IC engine valve timing.
Try and answer the following: What kind of cams are these? What sort of follower is employed? How is
contact maintained between the cam and follower? How would you expect the contact force to vary as the
engine goes through its cycle? What are the main advantages of cams in this application?
Figure
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The University of Birmingham
These notes are regularly interspersed with questions to illustrate the points made and to
understanding. These are highlighted in italics for clarity.
The cam is a mechanical component of a machine that is used to transmit motion to another component,
the follower, through a prescribed motion programme by direct contact. The cam mechanism consists of
the cam, the follower and the frame.
They are versatile and can produce any type of motion in the follower. In addition they can convert rotary
versa. The follower as the driven member may respond through:
Valve timing in internal combustion (IC) engines
Textile and sewing machines
Paper handling devices (photo-copiers and automatic telling machines)
Figure 1 shows four different configurations of cams used for IC engine valve timing.
What kind of cams are these? What sort of follower is employed? How is
between the cam and follower? How would you expect the contact force to vary as the
engine goes through its cycle? What are the main advantages of cams in this application?
Figure 1 Cam shaft configurations in IC engines
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These notes are regularly interspersed with questions to illustrate the points made and to increase
The cam is a mechanical component of a machine that is used to transmit motion to another component,
The cam mechanism consists of
They are versatile and can produce any type of motion in the follower. In addition they can convert rotary
ember may respond through:
What kind of cams are these? What sort of follower is employed? How is
between the cam and follower? How would you expect the contact force to vary as the
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Cam mechanisms
Dr K D Dearn
NOMENCLATURE
Cams may be categorised by:
(1) The shape of the cam
(2) The shape of the follower
(3) The motion of the follower
(4) The position of the follower relative to the cam
(5) The means by which the follower is held in contact with the cam.
Table
Cams
Easily designed to coordinate large number of
input-output motion requirements
Can be made small and compact
Dynamic response is sensitive to the manufacturing
accuracy of the cam contour
Expensive to produce
Easy to obtain dynamic balance
Subject to surface wear
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(4) The position of the follower relative to the cam
(5) The means by which the follower is held in contact with the cam.
1 Comparison between cams and linkages
Linkages
Easily designed to coordinate large number of Satisfy limited number of input-output motion
requirements
Occupy more space
Dynamic response is sensitive to the manufacturing Slight manufacturing inaccuracy has little effect on
output response
Less expensive
Difficult and complicated analysis involved in
dynamic balancing
Joint wear is non-critical and quieter in operation
Figure 2 Cam nomenclature
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output motion
Slight manufacturing inaccuracy has little effect on
ed analysis involved in
critical and quieter in operation
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Cam mechanisms
Dr K D Dearn
Figure 2 shows the layout of the most common type of cam
rotates on a fixed centre and the follower bears on the edge.
What follower configurations exist (at least 5 types)? What are the advantages and disadvantages of the
different followers? What should be considered when selecting a f
your own notes. In each case indicate how contact is maintained between follower and cam, (in some cases
external means must be used, in others contact is maintained by the geometry). Indicate on the diagram:
conjugate cams, yoke cams, translating cams and cylindrical cams. What is a face cam?
Figure 3 shows a number of different cam and follower types. Note that the follower may be in
the centre of rotation (i.e. radial) or offset from it, the follower may als
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Figure 2 shows the layout of the most common type of cam – a disc cam. In this configuration, the cam
rotates on a fixed centre and the follower bears on the edge.
What follower configurations exist (at least 5 types)? What are the advantages and disadvantages of the
different followers? What should be considered when selecting a follower? See TMM pp 203
your own notes. In each case indicate how contact is maintained between follower and cam, (in some cases
external means must be used, in others contact is maintained by the geometry). Indicate on the diagram:
ams, yoke cams, translating cams and cylindrical cams. What is a face cam?
Figure 3 shows a number of different cam and follower types. Note that the follower may be in
the centre of rotation (i.e. radial) or offset from it, the follower may also oscillate or be translating.
In-line cam followers
Offset cam followers
Pivoted arm followers
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configuration, the cam
What follower configurations exist (at least 5 types)? What are the advantages and disadvantages of the
TMM pp 203-204, make
your own notes. In each case indicate how contact is maintained between follower and cam, (in some cases
external means must be used, in others contact is maintained by the geometry). Indicate on the diagram:
Figure 3 shows a number of different cam and follower types. Note that the follower may be in-line with
o oscillate or be translating.
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Cam mechanisms
Dr K D Dearn
Figure
CAM KINEMATICS
As with previous studies with gears, it is convenient initially to separate the study of kinematics of the
system from its dynamics.
Generally, the output from a cam system is the motion of the follower. When specifying a cam system, the
design engineer will have in mind the requirements of the follower motion and will seek an optimum cam
configuration and profile to achieve this. It is logical, therefore, that a study of cam kinematics should start
with a study of follower motion.
The following discussion will be illustrated with examples largely featuring disc cams and reciprocating
followers. However, the principles may be readily extended to oscillating followers, where the output is an
angle of rotation rather than a linear displacement, and to other cam types whe
rotation or a translation.
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Cylindrical cam
Translating cam
Positive-acting cams
Figure 3 Common cam configurations
studies with gears, it is convenient initially to separate the study of kinematics of the
Generally, the output from a cam system is the motion of the follower. When specifying a cam system, the
nd the requirements of the follower motion and will seek an optimum cam
configuration and profile to achieve this. It is logical, therefore, that a study of cam kinematics should start
strated with examples largely featuring disc cams and reciprocating
followers. However, the principles may be readily extended to oscillating followers, where the output is an
angle of rotation rather than a linear displacement, and to other cam types where the input may be
School of Mechanical Engineering
The University of Birmingham
studies with gears, it is convenient initially to separate the study of kinematics of the
Generally, the output from a cam system is the motion of the follower. When specifying a cam system, the
nd the requirements of the follower motion and will seek an optimum cam
configuration and profile to achieve this. It is logical, therefore, that a study of cam kinematics should start
strated with examples largely featuring disc cams and reciprocating
followers. However, the principles may be readily extended to oscillating followers, where the output is an
re the input may be
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Cam mechanisms
Dr K D Dearn
The input to the system is the cam movement (usually an angle of rotation,
follower movement (usually a displacement or oscillation angle,
Consider a disc cam. During 1 revolution a follower is said to move in three possible ways:
Rise – i.e. move away from the cam centre
Return – i.e. move toward the cam centre
Dwell – i.e. maintain a constant distance from the cam centre
What shape of disc cam would result in a permanent
made to dwell is one of their main advantages.
Commonly the relationship between cam rotation and follower response is sketched on a displacement
diagram as shown in figure 4. This figure shows a typical f
common categories (although there is an unlimited number of more complicated
RRR – Rise Return Rise
DRR – Dwell Rise Return
DRD – Dwell Rise Dwell
Indicate below 4b figure the category of response show
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The input to the system is the cam movement (usually an angle of rotation, θ) and the output is the
follower movement (usually a displacement or oscillation angle, y)
ion a follower is said to move in three possible ways:
i.e. move away from the cam centre
i.e. move toward the cam centre
i.e. maintain a constant distance from the cam centre
What shape of disc cam would result in a permanent dwell? The simple way that cam followers may be
made to dwell is one of their main advantages.
Commonly the relationship between cam rotation and follower response is sketched on a displacement
diagram as shown in figure 4. This figure shows a typical follower curve. Follower responses fall into three
common categories (although there is an unlimited number of more complicated
Indicate below 4b figure the category of response shown, and then sketch the other two
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) and the output is the
ion a follower is said to move in three possible ways:
dwell? The simple way that cam followers may be
Commonly the relationship between cam rotation and follower response is sketched on a displacement
ollower curve. Follower responses fall into three
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Cam mechanisms
Dr K D Dearn
Figure 4 Follower Displacement Diagrams
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Cam mechanisms School of Mechanical Engineering
Dr K D Dearn The University of Birmingham
Issue 1.1 Page 8 of 28 Mechanical Design B
Figure 5 Linear Displacement Function
θ (rad)
θ (rad)
θ (rad)
y (min)
y’ (min/rad)
y’’ (min/rad2)
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Dr K D Dearn The University of Birmingham
Issue 1.1 Page 9 of 28 Mechanical Design B
STANDARD DISPLACEMENT CURVES
Assuming the basic follower response is known (periods of dwell, the lift, the time for rise and return); the
next step in cam design is to decide on the exact relationship between input and output. Consider the
common case of the response DRD illustrated in figure 5. Here, the simplest possible relationship between
input and output for the rise and return is shown – i.e. the follower displacement is directly proportional to
cam rotation. In practice this relationship is never used. To understand why, it is necessary to consider the
velocities and accelerations that would be imposed on the follower.
Consider a cam that rotates at constant speed, then the cam angle is directly proportional to time. The
derivative of displacement with respect to the angle is proportional to the velocity, and the second
derivative is proportional to the acceleration.
In other words:
t∝θ , dtdy
ddy ∝
θ and 2
2
2
2
dt
yd
d
yd ∝θ
Sketch, in the space below figure 5, the first and second derivatives of the displacement curve
Note that y’ (used to denote ��/��) takes constant values for the rise and return, and that �” (used to
denote ���/���) is zero except at the instantaneous transition between rise and dwell, where is becomes
infinite. These transitions are manifest on the cam as sharp discontinuities and would result in unsteady
motion, large contact forces and rapid wear. What is required is a smooth rise without sharp variations in
acceleration and hence contact force. Standard solutions to this problem follow.
PARABOLIC MOTION
The simplest approach to solving discontinuity posed by a simple linear relationship is to employ a second
order parabolic relationship between input and output. The resulting curve is a blend of two parabolas,
usually with a point of inflexion at the half way point.
In the following analysis, the total lift during a parabolic rise is denoted by h and the lift takes place during a
cam rotation angle of β.
Let:
� � � �� � ���
Hence:
y’ = C1 + 2C2θ
y = 2C2
Consider the first half of the rise for 0< θ < β/2: