Lecture # 30
Course Name : DESIGN OF MACHINE ELEMENTS
Course Number: MET 214
Cams and follower mechanisms:
Means for transforming rotary motion into reciprocating motion.
Cams can be classified based upon the direction of motion of the follower relative to the axis of
rotation of the cam.
Plate Cams:
Follower moves at right angle to axis of rotation of the cam.
Cylindrical Cams:
Follower moves in a direction parallel to cam axis.
Several different types of follower mechanisms exist.
Radial follower: Centerline of follower intersects axis of rotation.
Offset follower: Centerline of follower does not intersect axis of rotation.
Swinging follower: Locating hinge point outside of cam’s surface enables point of contact existing
between cam and follower to describe a circular arc.
Sensitivity of Followers:
Not all followers have the same sensitivity to changes in cam contour. Different followers respond to cam
profiles in different manners creating different paths.
Cams can be found in a variety of applications
Design procedure for use with cam and follower mechanisms
1) Identify motion requirements for follower using displacement diagram. Displacement diagram
displays follower displacement as a function of cam rotation or time.
2) Establish radius of base circle of cam. Radius of base circle is equal to the distance from the lowest
point on the cam periphery to the center of rotation of the cam.
a) diameter of base circle must be at least as large as the diameter of the hub.
b) In cams made integral with shaft, the diameter of the base circle must be at least equal to
shaft diameter.
c) Forces associated with follower motion will generate stresses in the cam shaft which must be
sized to operate safely with the stress loading.
3) Modify radius of base circle using rise from displacement desired from followers as cam shafts
rotates. Method used to modify base circle depends on type of follower.
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Interval from 00 -> 2100 has been divided into 14 subintervals producing an angle increment of ∆Ѳ
= 210/14 = 150 for each subinterval.
Base circle has been divided into corresponding angular increments of 150 with radial lines
emanating from center of base circle every 150 .
Length of any radial line emanating from center of base circle to periphery of cam can be
determined as follows.
l  rb  x
where l  Length of radial line emanating from center of
For subinterval #10
base circle to periphery of cam.
l10  rb  L
rb  radius of base circle
x  rise of cam
L  Lift of cam
Pressure angle:
Angle between the normal to the cam at a point and the radial line passing through the point. Pressure
angle can vary as you move from point to point along the periphery of the cam.
Note:
To prevent the possibility of binding a pointer follower the pressure angle is usually not permitted to
exceed 300 .
Q: At what point is Φ =0 for the previous example?
Given displacement diagram below, assume cam shaft us rotating at 600 rpm and the left L=1in, plot
velocity of follower as a function of time.
Curves resulting in uniform velocities over various subintervals may generate large jumps in the values
of acceleration for the follower.
Shape of displacement curve can be utilized to control velocity and/or acceleration of follower. Shape of
displacement curve can be categorized based upon acceleration characteristics of follower.
1) Harmonic curve (Generates acceleration curve having a cosine dependencies)
2) Cycloidal curve (Generates acceleration curve having sine dependencies)
3) Constant acceleration (also termed parabolic)
Graphical procedures may be utilized to generate displacement diagram for each category of curve.
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Geometry associated with a circle can
be utilized to generate harmonic motion.
2 half circles are used to generate harmonic
motion. One half circle dedicated to rise of follower,
one half circle dedicated to fall of follower.
Diameter of half circles equal lift L.
Half circles are divided into angular increments
which correspond to subinterval generated on
horizontal axis of displacement diagram.
Geometry associated with angular increments
when projected onto displacement diagram generate
harmonic motion.
where
L

X 
2
(1  cos
0
)
X= rise of cam
Ѳ= angle of cam
Ѳ0 = angle of cam at L
Velocity and acceleration accompanying the displacement curve for harmonic motion can be obtained
by utilizing the relationship Ѳ=ωt and differentiating.
Equating describing velocity and/or acceleration for each category of curves as a function of position are
provided in the table below.
Different types of motion can be combined into a displacement curve to achieve motion characteristics
consisted with requirements of application.
Example shown below depicts a displacement diagram possessing intervals exhibiting harmonic
motion, dwelling characteristics and constant velocity motion.
Geometry of a circle can also be utilized to generate cycloidal curves. The geometry must be different
from the configuration used in harmonic motion since the cycloidal curve is different from the harmonic
curve.
2 options are available.
Simplest technique utilizes rolling circle designated as A.
Circumference of circle A is set equal to Lift L of cam
Circumference of circle = 2Πr=L ->Πd=L
where
r= radius of circle
D= Diameter of circle
Circle is rolled up vertical axis without slippage.
Point P on rolling circle is transferred to displacement diagram to generate cycloidal curve.
Vertical axis is divided into subintervals corresponding to subintervals existing on horizontal axis of
displacement diagram to enable proper correspondence to exist for transferring point P to
displacement diagram.
When modifying base circle to generate can profile for use with roller, displacement diagram must be
interpreted as rise associated with center of roller. Periphery of cam is determined from contact points
establish by outside surface of roller.
To develop cam profile, radius of base circle can be modified by an amount equal to radius of roller to
generate a construction circle to serve as reference surface for generating cam profile from rise defined
by displacement diagram.
rc =rb +rr
where
In example shown below, rc =rb +2rr
rc – radius of construction circle
rb- radius of base circle
rr-radius of roller
When generating a cam profile for use with a flat follower, the procedure is similar to the technique
developed for constructing cams for use with roller followers. The base circle is modified and the rise
from the displacement diagram is used to establish the separation distance between the flat face of
the follower and the center of the base circle at various angles corresponding to intervals existing on
horizontal axis of displacement diagram. Cam profile is established by drawing periphery of cam
tangent to the face of the follower at the various angles.