Chap.4 Cam Mechanism
4.1 Introduction
4.2 Classification of Cam Mechanisms
4.3 Cam Nomenclature
4.4 Motion events
4.5 Graphical Synthesis of Cam Contour
4.6 Analysis Synthesis of Cam Contour
4.7 Considerations of Cam Mechanisms
Synthesis
4.1 Introduction
? 1 What is a Cam?
? 2 Cam Mechanisms
? 3 Application
1 What is a Cam?
Simple Cam experiment
Cam and Follower
? A cam may be defined as a machine
element having a curved outline or a
curved groove,which,by its
oscillation or rotation motion,gives
a predetermined specified motion to
another element called the
follower,
2 Cam Mechanisms
? A cam mechanism usually consists of two
moving elements,the cam and the
follower,mounted on a fixed frame,
? Cam Mechanism is a mechanism which is
conveniently used to transform one of the
simple motions,such as rotation,into any
other motions,such as translation,
oscillation,
3 Application
? The cam has a very important function in the operation of
many classes of machines,especially those of the automatic
type,such as printing presses,shoe machinery,textile
machinery,gear-cutting machines,and screw machines,In
any class of machinery in which automatic control and
accurate timing are paramount,the cam is an indispensable
part of mechanism,The possible applications of cams are
unlimited,and their shapes occur in great variety,
? Example (video)
4.2 Classification of Cam Mechanisms
? By Modes of Input/Output Motion
? By the configuration of the follower
? By shape of the cam
? By Force and form closure
? By arrangement of the follower
? By type of motion constrain
? By type of motion program
Modes of Input/Output Motion
1,Rotating cam-translating
follower
2,Rotating cam-Rotating follower
The follower arm swings or
oscillates in a circular arc with
respect to the follower pivot,
3,Translating cam-translating
follower
Follower Configuration
1,Knife-edge follower
2,Roller follower
3,Flat-faced follower
4,Oblique flat-faced follower
5,Spherical-faced follower
Cam Shape
1,Plate cam or disk cam(盘凸轮 ),
The follower moves in a plane perpendicular
to the axis of rotation of the camshaft,A
translating or a swing arm follower must be
constrained to maintain contact with the cam
profile,
2,Grooved cam (槽凸轮 ) or closed cam,
This is a plate cam with the
follower riding in a groove
in the face of the cam,
Cam Shape(ct)
3,Cylindrical cam （圆柱凸轮） or barrel cam,
The roller follower operates in a groove cut on the periphery of a
cylinder,The follower may translate or oscillate,If the cylindrical
surface is replaced by a conical one,a conical cam results,
4,End cam （端面凸轮）,
This cam has a rotating portion of a cylinder,The follower
translates or oscillates,whereas the cam usually rotates,The end
cam is rarely used because of the cost and the difficulty in cutting
its contour,
Force and form closure
1,Force closure:Gravity constraint & Spring constraint,
Weight constraint:the weight of the follower system is
sufficient to maintain contact,
Spring constraint,the spring must be properly designed to
maintain contact,
1,Form closure,
A groove maintains positive action.(Grooved cam mechanism)
A constant-diameter cam or conjugate cam,
a dual or conjugate cam
(共轭凸轮 )
a constant-diameter cam
(等径凸轮 )
a constant-diameter cam
(等径凸轮 )
Follower Arrangement
1,In-line follower,
The center line of the follower passes
through the center line of the camshaft,
2,Offset follower,
The center line of the follower does not pass
through the center line of the cam shaft,
The amount of offset is the distance
between these two center lines,The offset
causes a reduction of the side thrust
present in the roller follower,
By type of motion constrain
? Critical extreme position(CEP)
? Critical path motion(CPM)
Type of motion program
? Rise-fall(RF)
? Rise-fall-dwell (RFD)
? Rise-dwell-fall-dwell (RDFD)
? Please think
Compare with the linkage,what kind of condition
is more suitable to use cam mechanism,
4.3 Cam Nomenclature
（基圆）
（升距）
（凸轮理论廓线）
（凸轮实际廓线）
（凸轮压力角）
(stroke)
（起始圆）
Trace point
Inversion
Inversion of cam mechanism
Real motion Inversion
? Pressure angle,The angle at any
point between the normal to the
pitch curve and the instantaneous
direction of the follower motion,This
angle is important in cam design
because it represents the steepness
of the cam profile,
Dwell-rise-dwell-fall
dwell rise dwell fall（ return）
? When the cam turns through one
motion cycle,the follower executes
a series of events consisting of rises,
dwells and returns,Rise is the
motion of the follower away from
the cam center,dwell is the motion
during which the follower is at rest;
and return is the motion of the
follower toward the cam center,
4.4 Motion events
SVAJ DIAGRAMS
? Motion of the follower
? S—displacement function
? V—the first derivative of the
displacement
? A—the second derivative of the
displacement
? J —the third derivative of the
displacement
Why we care about these?
Why we care about these?
? Velocity is related to the kinetic energy,
? Force is proportional to force acceleration,
? Large magnitudes of jerk will tend to
excite the natural frequencies of
vibration of the machine or structure,
which is attached and cause increased
vibration and noise levels,
Constant vel,& Constant accel,
Constant vel,Constant accel,
Example:Dwell-Rise-Dwell-Fall
刚性冲击 柔性冲击
The Fundamental Law of Cam Design
? Constraints,
The cam must be continuous
through the first and second
derivatives of displacement across
the entire interval,
? Corollary,
The jerk function must be finite
across the entire interval
Simple Harmonic Motion Cycloidal displacement
Motion events
柔性冲击
Combined functions
? Why
? What should be considered when
you combine the motion functions?
Motion events
? Combined Function
Trapezoidal Acceleration
Modified Trapezoidal Acceleration
Modified Sinusoidal Acceleration
Polynomial Function
Comparision of some motion events
? Table
4.5 Graphical Synthesis of Cam
Inversion
Analyze the follower position
? In-line follower
? Offset follower
00 1200 1800 2700 3600 00 1200 1800 2700 3600
Example
? Radial cam with in-line knife-edge
? Radial cam with offset knife-edge
follower
? Radial cam with offset roller follower
? Radial cam with flat-faced follower
Key steps,
1,Determine the prime radius and eccentricity
2,Find the follower position when the cam
rotates certain angle
Radial cam with offset knife-edge follower
Radial cam with offset roller follower
?Radial cam with flat-faced follower
4.6 Analysis Synthesis of Cam
If in-line,e =0,s0=rp
Position of point B
Position of point B’
22
0
0
0
s i nc o s
c o ss i n
ers
es)(sMNBNy
es)(sKHKNx
p ??
?????
?????
??
??
?
?
c o s)(
s i n)(
sry
srx
p
p
??
??
?
?
c o s'
c o s'
f
f
ryy
rxx
?
?
?
?
4.7 Considerations of Cam Mechanisms Synthesis
? Pressure angle
? Eccentricity
? Prime circle radius
? Radius of the roller follower
? Facewidth of the flat-faced follower
? Base circle radius
4.7 Considerations of Cam Mechanisms Synthesis(1)
? Pressure angle ?
? Acceptable value [?]
?
?
?
d
ds
v
ers
ev
a n c
p
?
??
?
?
22
t a n
? ??? ?m ax
Rule,
Rule,for translating followers to avoid
excessive side load on the sliding
follower,pressure angle should be less
than 300,If the follower is oscillating on
a pivoted arm,a pressure angle up to
350 is acceptable,
4.7 Considerations of Cam Mechanisms Synthesis(2)
? Eccentricity,If a suitably small cam cannot
be obtained with acceptable pressure angle,
then eccentricity can be introduced to
change the pressure angle,
? For a positive ? (anticlockwise),a positive
value of eccentricity will decrease the
pressure angle on the rise but will increase it
on the fall,
? Prime circle radius
4.7 Considerations of Cam Mechanisms Synthesis(3)
If e=0
prs
d
ds
a n c
?
? ?? t a n
22)
t a n
( esd
ds
r p ???
?
?
? ??? ?m ax rp
? Radius of the roller follower
1,The radius of the roller follower
Rf is too large to follow the
locally smaller concave radius –?
on the cam.(Rf>| ? min|)
2,The follower(cutter) radius is
greater than the minimum
convex radius of curvature of
the cam.That can cause
undercutting,
4.7 Considerations of Cam Mechanisms Synthesis(4)
.avi
Undercutting
Generally,| ? min|>(2-3) Rf
? Facewidth of the flat-faced follower
? Base circle radius
4.7 Considerations of Cam Mechanisms Synthesis(5)
Facewidth>
m i nm a x
????????????????? ?? ddsdds
m i n
2
2
m i n
2
2
)(
)(
)('
'
?
?
?
?
?
?
??
d
sd
sr
d
sd
sr
Lsrjjer
Lsrr
b
b
b
j
b
???
???
????
????
?
Summary
Synthesis of a cam mechanism
Choose the type of the cam mechanism
Choose or design the follower motion events
Choose an initial radius of the cam
Synthesis the cam mechanism
Check the pressure angle and others
Homework
? Pp426-427 8-9,8-14
? Pp429 8-39,p8-1
? Pp401 Draw the geometry for the
derivation of the equation for
pressure angle,then derivate the
equation,
4.1 Introduction
4.2 Classification of Cam Mechanisms
4.3 Cam Nomenclature
4.4 Motion events
4.5 Graphical Synthesis of Cam Contour
4.6 Analysis Synthesis of Cam Contour
4.7 Considerations of Cam Mechanisms
Synthesis
4.1 Introduction
? 1 What is a Cam?
? 2 Cam Mechanisms
? 3 Application
1 What is a Cam?
Simple Cam experiment
Cam and Follower
? A cam may be defined as a machine
element having a curved outline or a
curved groove,which,by its
oscillation or rotation motion,gives
a predetermined specified motion to
another element called the
follower,
2 Cam Mechanisms
? A cam mechanism usually consists of two
moving elements,the cam and the
follower,mounted on a fixed frame,
? Cam Mechanism is a mechanism which is
conveniently used to transform one of the
simple motions,such as rotation,into any
other motions,such as translation,
oscillation,
3 Application
? The cam has a very important function in the operation of
many classes of machines,especially those of the automatic
type,such as printing presses,shoe machinery,textile
machinery,gear-cutting machines,and screw machines,In
any class of machinery in which automatic control and
accurate timing are paramount,the cam is an indispensable
part of mechanism,The possible applications of cams are
unlimited,and their shapes occur in great variety,
? Example (video)
4.2 Classification of Cam Mechanisms
? By Modes of Input/Output Motion
? By the configuration of the follower
? By shape of the cam
? By Force and form closure
? By arrangement of the follower
? By type of motion constrain
? By type of motion program
Modes of Input/Output Motion
1,Rotating cam-translating
follower
2,Rotating cam-Rotating follower
The follower arm swings or
oscillates in a circular arc with
respect to the follower pivot,
3,Translating cam-translating
follower
Follower Configuration
1,Knife-edge follower
2,Roller follower
3,Flat-faced follower
4,Oblique flat-faced follower
5,Spherical-faced follower
Cam Shape
1,Plate cam or disk cam(盘凸轮 ),
The follower moves in a plane perpendicular
to the axis of rotation of the camshaft,A
translating or a swing arm follower must be
constrained to maintain contact with the cam
profile,
2,Grooved cam (槽凸轮 ) or closed cam,
This is a plate cam with the
follower riding in a groove
in the face of the cam,
Cam Shape(ct)
3,Cylindrical cam （圆柱凸轮） or barrel cam,
The roller follower operates in a groove cut on the periphery of a
cylinder,The follower may translate or oscillate,If the cylindrical
surface is replaced by a conical one,a conical cam results,
4,End cam （端面凸轮）,
This cam has a rotating portion of a cylinder,The follower
translates or oscillates,whereas the cam usually rotates,The end
cam is rarely used because of the cost and the difficulty in cutting
its contour,
Force and form closure
1,Force closure:Gravity constraint & Spring constraint,
Weight constraint:the weight of the follower system is
sufficient to maintain contact,
Spring constraint,the spring must be properly designed to
maintain contact,
1,Form closure,
A groove maintains positive action.(Grooved cam mechanism)
A constant-diameter cam or conjugate cam,
a dual or conjugate cam
(共轭凸轮 )
a constant-diameter cam
(等径凸轮 )
a constant-diameter cam
(等径凸轮 )
Follower Arrangement
1,In-line follower,
The center line of the follower passes
through the center line of the camshaft,
2,Offset follower,
The center line of the follower does not pass
through the center line of the cam shaft,
The amount of offset is the distance
between these two center lines,The offset
causes a reduction of the side thrust
present in the roller follower,
By type of motion constrain
? Critical extreme position(CEP)
? Critical path motion(CPM)
Type of motion program
? Rise-fall(RF)
? Rise-fall-dwell (RFD)
? Rise-dwell-fall-dwell (RDFD)
? Please think
Compare with the linkage,what kind of condition
is more suitable to use cam mechanism,
4.3 Cam Nomenclature
（基圆）
（升距）
（凸轮理论廓线）
（凸轮实际廓线）
（凸轮压力角）
(stroke)
（起始圆）
Trace point
Inversion
Inversion of cam mechanism
Real motion Inversion
? Pressure angle,The angle at any
point between the normal to the
pitch curve and the instantaneous
direction of the follower motion,This
angle is important in cam design
because it represents the steepness
of the cam profile,
Dwell-rise-dwell-fall
dwell rise dwell fall（ return）
? When the cam turns through one
motion cycle,the follower executes
a series of events consisting of rises,
dwells and returns,Rise is the
motion of the follower away from
the cam center,dwell is the motion
during which the follower is at rest;
and return is the motion of the
follower toward the cam center,
4.4 Motion events
SVAJ DIAGRAMS
? Motion of the follower
? S—displacement function
? V—the first derivative of the
displacement
? A—the second derivative of the
displacement
? J —the third derivative of the
displacement
Why we care about these?
Why we care about these?
? Velocity is related to the kinetic energy,
? Force is proportional to force acceleration,
? Large magnitudes of jerk will tend to
excite the natural frequencies of
vibration of the machine or structure,
which is attached and cause increased
vibration and noise levels,
Constant vel,& Constant accel,
Constant vel,Constant accel,
Example:Dwell-Rise-Dwell-Fall
刚性冲击 柔性冲击
The Fundamental Law of Cam Design
? Constraints,
The cam must be continuous
through the first and second
derivatives of displacement across
the entire interval,
? Corollary,
The jerk function must be finite
across the entire interval
Simple Harmonic Motion Cycloidal displacement
Motion events
柔性冲击
Combined functions
? Why
? What should be considered when
you combine the motion functions?
Motion events
? Combined Function
Trapezoidal Acceleration
Modified Trapezoidal Acceleration
Modified Sinusoidal Acceleration
Polynomial Function
Comparision of some motion events
? Table
4.5 Graphical Synthesis of Cam
Inversion
Analyze the follower position
? In-line follower
? Offset follower
00 1200 1800 2700 3600 00 1200 1800 2700 3600
Example
? Radial cam with in-line knife-edge
? Radial cam with offset knife-edge
follower
? Radial cam with offset roller follower
? Radial cam with flat-faced follower
Key steps,
1,Determine the prime radius and eccentricity
2,Find the follower position when the cam
rotates certain angle
Radial cam with offset knife-edge follower
Radial cam with offset roller follower
?Radial cam with flat-faced follower
4.6 Analysis Synthesis of Cam
If in-line,e =0,s0=rp
Position of point B
Position of point B’
22
0
0
0
s i nc o s
c o ss i n
ers
es)(sMNBNy
es)(sKHKNx
p ??
?????
?????
??
??
?
?
c o s)(
s i n)(
sry
srx
p
p
??
??
?
?
c o s'
c o s'
f
f
ryy
rxx
?
?
?
?
4.7 Considerations of Cam Mechanisms Synthesis
? Pressure angle
? Eccentricity
? Prime circle radius
? Radius of the roller follower
? Facewidth of the flat-faced follower
? Base circle radius
4.7 Considerations of Cam Mechanisms Synthesis(1)
? Pressure angle ?
? Acceptable value [?]
?
?
?
d
ds
v
ers
ev
a n c
p
?
??
?
?
22
t a n
? ??? ?m ax
Rule,
Rule,for translating followers to avoid
excessive side load on the sliding
follower,pressure angle should be less
than 300,If the follower is oscillating on
a pivoted arm,a pressure angle up to
350 is acceptable,
4.7 Considerations of Cam Mechanisms Synthesis(2)
? Eccentricity,If a suitably small cam cannot
be obtained with acceptable pressure angle,
then eccentricity can be introduced to
change the pressure angle,
? For a positive ? (anticlockwise),a positive
value of eccentricity will decrease the
pressure angle on the rise but will increase it
on the fall,
? Prime circle radius
4.7 Considerations of Cam Mechanisms Synthesis(3)
If e=0
prs
d
ds
a n c
?
? ?? t a n
22)
t a n
( esd
ds
r p ???
?
?
? ??? ?m ax rp
? Radius of the roller follower
1,The radius of the roller follower
Rf is too large to follow the
locally smaller concave radius –?
on the cam.(Rf>| ? min|)
2,The follower(cutter) radius is
greater than the minimum
convex radius of curvature of
the cam.That can cause
undercutting,
4.7 Considerations of Cam Mechanisms Synthesis(4)
.avi
Undercutting
Generally,| ? min|>(2-3) Rf
? Facewidth of the flat-faced follower
? Base circle radius
4.7 Considerations of Cam Mechanisms Synthesis(5)
Facewidth>
m i nm a x
????????????????? ?? ddsdds
m i n
2
2
m i n
2
2
)(
)(
)('
'
?
?
?
?
?
?
??
d
sd
sr
d
sd
sr
Lsrjjer
Lsrr
b
b
b
j
b
???
???
????
????
?
Summary
Synthesis of a cam mechanism
Choose the type of the cam mechanism
Choose or design the follower motion events
Choose an initial radius of the cam
Synthesis the cam mechanism
Check the pressure angle and others
Homework
? Pp426-427 8-9,8-14
? Pp429 8-39,p8-1
? Pp401 Draw the geometry for the
derivation of the equation for
pressure angle,then derivate the
equation,
