Short Notes: Cams | Short Notes for Mechanical Engineering PDF Download

 Page 1


Cams
Cam: A cam is a mechanical member used to impart desired motion 
(displacement) to a follower by direct contact (either point or line contact). A cam 
may be rotating or reciprocating whereas the follower may be rotating, 
reciprocating or oscillating.
• Cam mechanisms belong to higher pair mechanism.
• A driver member known as cam.
• A driven member called the follower.
• A frame is one which supports the cam and guides the follower.
Definitions Related to Cam: The following terminologies are used to draw cam 
profile
• Base Circle: The base circle is the smallest circle (with its centre at the cam 
centre) that can be drawn tangential to the cam profile.
• Trace Point: A trace point is a theoretical point on the follower, its motion 
describing the movement of the follower.
e.g., for a knife edge follower, the trace point is at the knife edge. •
• Pitch Curve:lt is the curve drawn by the trace point assuming that the cam is 
fixed and the trace point of the follower rotates around the cam.
• Pressure Angle:lt represents the steepness of the cam profile. The angle 
between the direction of the follower movement and the normal to the pitch 
curve at any point is referred to as the pressure angle.
Key Points
• For a roller follower, the trace point is at the roller centre.
Page 2


Cams
Cam: A cam is a mechanical member used to impart desired motion 
(displacement) to a follower by direct contact (either point or line contact). A cam 
may be rotating or reciprocating whereas the follower may be rotating, 
reciprocating or oscillating.
• Cam mechanisms belong to higher pair mechanism.
• A driver member known as cam.
• A driven member called the follower.
• A frame is one which supports the cam and guides the follower.
Definitions Related to Cam: The following terminologies are used to draw cam 
profile
• Base Circle: The base circle is the smallest circle (with its centre at the cam 
centre) that can be drawn tangential to the cam profile.
• Trace Point: A trace point is a theoretical point on the follower, its motion 
describing the movement of the follower.
e.g., for a knife edge follower, the trace point is at the knife edge. •
• Pitch Curve:lt is the curve drawn by the trace point assuming that the cam is 
fixed and the trace point of the follower rotates around the cam.
• Pressure Angle:lt represents the steepness of the cam profile. The angle 
between the direction of the follower movement and the normal to the pitch 
curve at any point is referred to as the pressure angle.
Key Points
• For a roller follower, the trace point is at the roller centre.
• For a flat-face follower, it is at the point of contact between the follower and 
cam surface when the contact is along the base circle of the cam.
• During a complete rotation, the pressure angle varies from its maximum to its 
minimum value.
• The greater the pressure angle, the higher will be side thrust and consequently 
the changes of the translating follower jamming in its guide will increase.
• It is not desirable to increase the pressure angle.
Pitch Point and Circle
• A pitch point corresponds to the point of maximum pressure angle and a 
circle drawn with its centre at the cam centre; to pass through the pitch point 
is known as the pitch circle.
Prime Circle
• The prime circle is the smallest circle that can be drawn so as to be tangential 
to the pitch curve.
o
A schematic diagramatic vtew of pitch circle
Follower Displacement Diagram
The following terms are used with reference to the angular motion of the cam
• Angle of Ascent (c |> a): It is the angle through which the cam turns during the 
time the follower rises.
• Angle of Dwell (f) Angle of dwell is the angle through which the cam turns 
while the follower remains stationery at the highest or the lowest position.
Follower
displacement
Rise Dwell Return Dwell
—=Z------ --------*+•------------------ M
Displacement diagram
I
MLigt)
Angle of Descent (c^d): Angle of descent is the angle through which the cam 
turns while follower returns to the initial position.
Page 3


Cams
Cam: A cam is a mechanical member used to impart desired motion 
(displacement) to a follower by direct contact (either point or line contact). A cam 
may be rotating or reciprocating whereas the follower may be rotating, 
reciprocating or oscillating.
• Cam mechanisms belong to higher pair mechanism.
• A driver member known as cam.
• A driven member called the follower.
• A frame is one which supports the cam and guides the follower.
Definitions Related to Cam: The following terminologies are used to draw cam 
profile
• Base Circle: The base circle is the smallest circle (with its centre at the cam 
centre) that can be drawn tangential to the cam profile.
• Trace Point: A trace point is a theoretical point on the follower, its motion 
describing the movement of the follower.
e.g., for a knife edge follower, the trace point is at the knife edge. •
• Pitch Curve:lt is the curve drawn by the trace point assuming that the cam is 
fixed and the trace point of the follower rotates around the cam.
• Pressure Angle:lt represents the steepness of the cam profile. The angle 
between the direction of the follower movement and the normal to the pitch 
curve at any point is referred to as the pressure angle.
Key Points
• For a roller follower, the trace point is at the roller centre.
• For a flat-face follower, it is at the point of contact between the follower and 
cam surface when the contact is along the base circle of the cam.
• During a complete rotation, the pressure angle varies from its maximum to its 
minimum value.
• The greater the pressure angle, the higher will be side thrust and consequently 
the changes of the translating follower jamming in its guide will increase.
• It is not desirable to increase the pressure angle.
Pitch Point and Circle
• A pitch point corresponds to the point of maximum pressure angle and a 
circle drawn with its centre at the cam centre; to pass through the pitch point 
is known as the pitch circle.
Prime Circle
• The prime circle is the smallest circle that can be drawn so as to be tangential 
to the pitch curve.
o
A schematic diagramatic vtew of pitch circle
Follower Displacement Diagram
The following terms are used with reference to the angular motion of the cam
• Angle of Ascent (c |> a): It is the angle through which the cam turns during the 
time the follower rises.
• Angle of Dwell (f) Angle of dwell is the angle through which the cam turns 
while the follower remains stationery at the highest or the lowest position.
Follower
displacement
Rise Dwell Return Dwell
—=Z------ --------*+•------------------ M
Displacement diagram
I
MLigt)
Angle of Descent (c^d): Angle of descent is the angle through which the cam 
turns while follower returns to the initial position.
• Angle of Action Angle of action is the total angle moved by the cam during th|| 
time between the beginning of rise and the end of return of the follower.
• In a specific interval of time, acceleration must be given to consider the 
velocity.
• The dynamic effect of acceleration limit the speed and effect of jerk (rate of 
change of acceleration) produce vibrations of the system.
• The angle made by follower to the surface of cam at the point of contact 
cannot be reduced from a certain value. So, it exerts minimum lateral 
pressure on the bearing.
• The size of the base circle controls the pressure angle.
Cam with Specified Contours
Followings are the various types of cams, which are symmetrical cams or specified 
contour cams.
• Tangent Cam (with roller follower)
A tangent cam is symmetrical about the centre line.
Where rc = least radius of cam 
r„ = Radius of nose 
rr = Radius of roller
r = Distance between the cam and nose centre.
• Roller on the Flank
The maximum and minimum velocity can be calculated. When the location of roller 
on the flank as
where, rc = least radius of cam 
r„ = Radius of nose 
rr = Radius of roller
r = Distance between the cam and nose centre.
Let be angle turned by the cam from the beginning of the follower motion.
Page 4


Cams
Cam: A cam is a mechanical member used to impart desired motion 
(displacement) to a follower by direct contact (either point or line contact). A cam 
may be rotating or reciprocating whereas the follower may be rotating, 
reciprocating or oscillating.
• Cam mechanisms belong to higher pair mechanism.
• A driver member known as cam.
• A driven member called the follower.
• A frame is one which supports the cam and guides the follower.
Definitions Related to Cam: The following terminologies are used to draw cam 
profile
• Base Circle: The base circle is the smallest circle (with its centre at the cam 
centre) that can be drawn tangential to the cam profile.
• Trace Point: A trace point is a theoretical point on the follower, its motion 
describing the movement of the follower.
e.g., for a knife edge follower, the trace point is at the knife edge. •
• Pitch Curve:lt is the curve drawn by the trace point assuming that the cam is 
fixed and the trace point of the follower rotates around the cam.
• Pressure Angle:lt represents the steepness of the cam profile. The angle 
between the direction of the follower movement and the normal to the pitch 
curve at any point is referred to as the pressure angle.
Key Points
• For a roller follower, the trace point is at the roller centre.
• For a flat-face follower, it is at the point of contact between the follower and 
cam surface when the contact is along the base circle of the cam.
• During a complete rotation, the pressure angle varies from its maximum to its 
minimum value.
• The greater the pressure angle, the higher will be side thrust and consequently 
the changes of the translating follower jamming in its guide will increase.
• It is not desirable to increase the pressure angle.
Pitch Point and Circle
• A pitch point corresponds to the point of maximum pressure angle and a 
circle drawn with its centre at the cam centre; to pass through the pitch point 
is known as the pitch circle.
Prime Circle
• The prime circle is the smallest circle that can be drawn so as to be tangential 
to the pitch curve.
o
A schematic diagramatic vtew of pitch circle
Follower Displacement Diagram
The following terms are used with reference to the angular motion of the cam
• Angle of Ascent (c |> a): It is the angle through which the cam turns during the 
time the follower rises.
• Angle of Dwell (f) Angle of dwell is the angle through which the cam turns 
while the follower remains stationery at the highest or the lowest position.
Follower
displacement
Rise Dwell Return Dwell
—=Z------ --------*+•------------------ M
Displacement diagram
I
MLigt)
Angle of Descent (c^d): Angle of descent is the angle through which the cam 
turns while follower returns to the initial position.
• Angle of Action Angle of action is the total angle moved by the cam during th|| 
time between the beginning of rise and the end of return of the follower.
• In a specific interval of time, acceleration must be given to consider the 
velocity.
• The dynamic effect of acceleration limit the speed and effect of jerk (rate of 
change of acceleration) produce vibrations of the system.
• The angle made by follower to the surface of cam at the point of contact 
cannot be reduced from a certain value. So, it exerts minimum lateral 
pressure on the bearing.
• The size of the base circle controls the pressure angle.
Cam with Specified Contours
Followings are the various types of cams, which are symmetrical cams or specified 
contour cams.
• Tangent Cam (with roller follower)
A tangent cam is symmetrical about the centre line.
Where rc = least radius of cam 
r„ = Radius of nose 
rr = Radius of roller
r = Distance between the cam and nose centre.
• Roller on the Flank
The maximum and minimum velocity can be calculated. When the location of roller 
on the flank as
where, rc = least radius of cam 
r„ = Radius of nose 
rr = Radius of roller
r = Distance between the cam and nose centre.
Let be angle turned by the cam from the beginning of the follower motion.
x (rc + rr)
cos 9
— 1
dx dx d9 
'~~dt~~d9~dt
v=aj(rc + rt )
sin#
vm =4,'(r( + O
cos '9 
sin 3
cos* 3
At 0 = j8, (j8 be the angle turned by the cam when the roller loss the flank)
Vm in = 0 At 0 = 0
• Acceleration
/ =
/ =
.4,,
d\• d\• d9 
~dt~~d9 ' ~ d t
x 2(r( + r)
(2 — cos* 9) 
cos" 9
= x 2(rc + rT ) at9 = 0 °
• Roller on the Nose
I = rn + rr 
and n = rc + rr
x = r cos (or- d)
+ yjl1- r: sin: (a - 6 )- n
dx dx d9 
~ d t = ~d9~dt 
dv_dvd9 
~dt~~d9~dt
Roller on the nose 
in cam contours
Circular Arc (convex) Cam (with flat-faced follower) 
Follower Touching Circular Flank
Page 5


Cams
Cam: A cam is a mechanical member used to impart desired motion 
(displacement) to a follower by direct contact (either point or line contact). A cam 
may be rotating or reciprocating whereas the follower may be rotating, 
reciprocating or oscillating.
• Cam mechanisms belong to higher pair mechanism.
• A driver member known as cam.
• A driven member called the follower.
• A frame is one which supports the cam and guides the follower.
Definitions Related to Cam: The following terminologies are used to draw cam 
profile
• Base Circle: The base circle is the smallest circle (with its centre at the cam 
centre) that can be drawn tangential to the cam profile.
• Trace Point: A trace point is a theoretical point on the follower, its motion 
describing the movement of the follower.
e.g., for a knife edge follower, the trace point is at the knife edge. •
• Pitch Curve:lt is the curve drawn by the trace point assuming that the cam is 
fixed and the trace point of the follower rotates around the cam.
• Pressure Angle:lt represents the steepness of the cam profile. The angle 
between the direction of the follower movement and the normal to the pitch 
curve at any point is referred to as the pressure angle.
Key Points
• For a roller follower, the trace point is at the roller centre.
• For a flat-face follower, it is at the point of contact between the follower and 
cam surface when the contact is along the base circle of the cam.
• During a complete rotation, the pressure angle varies from its maximum to its 
minimum value.
• The greater the pressure angle, the higher will be side thrust and consequently 
the changes of the translating follower jamming in its guide will increase.
• It is not desirable to increase the pressure angle.
Pitch Point and Circle
• A pitch point corresponds to the point of maximum pressure angle and a 
circle drawn with its centre at the cam centre; to pass through the pitch point 
is known as the pitch circle.
Prime Circle
• The prime circle is the smallest circle that can be drawn so as to be tangential 
to the pitch curve.
o
A schematic diagramatic vtew of pitch circle
Follower Displacement Diagram
The following terms are used with reference to the angular motion of the cam
• Angle of Ascent (c |> a): It is the angle through which the cam turns during the 
time the follower rises.
• Angle of Dwell (f) Angle of dwell is the angle through which the cam turns 
while the follower remains stationery at the highest or the lowest position.
Follower
displacement
Rise Dwell Return Dwell
—=Z------ --------*+•------------------ M
Displacement diagram
I
MLigt)
Angle of Descent (c^d): Angle of descent is the angle through which the cam 
turns while follower returns to the initial position.
• Angle of Action Angle of action is the total angle moved by the cam during th|| 
time between the beginning of rise and the end of return of the follower.
• In a specific interval of time, acceleration must be given to consider the 
velocity.
• The dynamic effect of acceleration limit the speed and effect of jerk (rate of 
change of acceleration) produce vibrations of the system.
• The angle made by follower to the surface of cam at the point of contact 
cannot be reduced from a certain value. So, it exerts minimum lateral 
pressure on the bearing.
• The size of the base circle controls the pressure angle.
Cam with Specified Contours
Followings are the various types of cams, which are symmetrical cams or specified 
contour cams.
• Tangent Cam (with roller follower)
A tangent cam is symmetrical about the centre line.
Where rc = least radius of cam 
r„ = Radius of nose 
rr = Radius of roller
r = Distance between the cam and nose centre.
• Roller on the Flank
The maximum and minimum velocity can be calculated. When the location of roller 
on the flank as
where, rc = least radius of cam 
r„ = Radius of nose 
rr = Radius of roller
r = Distance between the cam and nose centre.
Let be angle turned by the cam from the beginning of the follower motion.
x (rc + rr)
cos 9
— 1
dx dx d9 
'~~dt~~d9~dt
v=aj(rc + rt )
sin#
vm =4,'(r( + O
cos '9 
sin 3
cos* 3
At 0 = j8, (j8 be the angle turned by the cam when the roller loss the flank)
Vm in = 0 At 0 = 0
• Acceleration
/ =
/ =
.4,,
d\• d\• d9 
~dt~~d9 ' ~ d t
x 2(r( + r)
(2 — cos* 9) 
cos" 9
= x 2(rc + rT ) at9 = 0 °
• Roller on the Nose
I = rn + rr 
and n = rc + rr
x = r cos (or- d)
+ yjl1- r: sin: (a - 6 )- n
dx dx d9 
~ d t = ~d9~dt 
dv_dvd9 
~dt~~d9~dt
Roller on the nose 
in cam contours
Circular Arc (convex) Cam (with flat-faced follower) 
Follower Touching Circular Flank
x (rf + r,)(l— cos0) 
dx dx d9 
' ~~dt~~d9~dt 
\=jj(,rf — r c )sin0
v_= 0 at 9 = 0
o m x
= j;(rf - re )sin 3 at 9 = 3 
Acceleration 
f = o ' (r ,- rc)cos<?
/mo= rc)a td = 0
f ^ = a :(-r/ - rPcosP at d = P
• Follower on the Nose
x= rn- rc + r cos(ar - 6) 
v= orsin(a - d) 
vnir.= oat 6 = a
v is maximum when the follower just touches the nose of the cam.
f = -u)2r cos(a-G)
of the cam
Circular Arc (Convex) Cam (with roller follower) 
Follower on the flank
x = (r,+ rt ) cos 6 - {rf + r c) cos d - (r t + r e)