MACHINE ELEMENTS (Phase 2)
PART 1 – INTRODUCTION TO CAM DESIGN
DEFINITION OF TERMS

CAM – A rotating mechanism of irregular shape, as on a wheel on a
machine: used to change the direction of the motion of another part
moving against it, as rotary into reciprocating or variable motion.
COMMON CLASSIFICATION OF CAM ACCORDING TO SHAPE:
 DISK CAM – Cam profile curve is worked in a flat plate as shown in
Figure 1.
 CYLINDRICAL CAM - Cam profile curve is worked around a blank
cylinder.
Figure 2: Cylindrical Cam

Figure 1: Common types of Disk Cam
CAM FOLLOWER – A part with a sliding contact with the cam. Two
(2) types and most common used are Reciprocating and Oscillating
follower.
CLASSIFICATION ACCORDING TO TYPES OF FOLLOWER:
 IN-LINE/RADIAL FOLLOWER – The follower is considered to be inline or radial when its centerline passes through the center of cam
rotation. Seldom used in actual practice since it produces high contact
stresses.
 OFFSET FOLLOWER – The centerline of the follower has an offset
distance with respect to the center of cam rotation.
 OSCILLATING FOLLOWER – Special type cam mechanism with a
follower oscillating at a certain center having a defined distance with
respect to center of cam rotation.
1
CLASSIFICATION BASED ON THE TYPE OF MOTION:




SIMPLE MOTION – The cam profile is generated in reference with
the predefined motion of the follower.
PARABOLIC MOTION – Analytically, the cam profile is generated by
following the motion curve of an equation of a Parabola. Graphical
method will be discussed in the proceeding topics.
HARMONIC MOTION – Cam profile is generated by following the
motion curve of a harmonic motion.
CYCLOIDAL MOTION – Cam profile is generated by following the
motion curve of a cycloid.
Figure 3: Cam Nomenclature (Radial Cam with Roller follower)
CAM NOMENCLATURE:
 BASE CIRCLE – The smallest circle tangent to the cam surface about
the center of cam rotation.
 CAM PROFILE – The actual contacting surface of a disk type cam. Its
curvature is generated using either one of the following
considerations: (1) Assumption of the required motion for the follower
then design the cam profile to give this motion and, (2) Assumption of
the shape of the cam then determine what characteristics of
displacement, velocity and acceleration this contour will give.
Dilemma: After the cam is designed, some contour will be difficult
to manufacture.
Solution: Follow the second method by making the cam
symmetrical and by using shape for the cam contours that can be
generated through machining and other metal working process.
Result: Manufacturing of cams for automotive application that
must be produced cheaply and accurately has been solved.
 STROKE – The distance measured between two extreme position of
the follower.
 TRACE POINT – Is a point on the follower that corresponds to the
contact point of fictitious knife edge follower.
 PITCH CURVE – Is the path of trace point relative to the cam profile.
 PRESSURE ANGLE – The angle between the direction of motion of
the trace point and the common normal (line of action) to the
contacting surfaces. It is also a measure of the instantaneous force
transmission properties of the mechanism. The larger is the pressure
angle, more power is required to operate the cam mechanism.
REMEMBER! Line of action is the axis where the force from rotating
cam profile is ACTUALLY transmitted on the follower.
2
1.0 PROCEDURES IN GENERATING CAM CONTOUR
There are two distinct methods of how Cam contours or cam
profiles are generated. The methods are (1) Graphical Method and (2)
Analytical Method. The first method is of relatively the simplest method
of generating cam contours which uses only graphical techniques
while the second method uses mathematical equations to determine
the curvature of the cam profile.
thus, we need to determine the plot of motion curve as shown in Figure
4. With the corresponding intersection of the motion curve and the
angle corresponding to this displacement, the procedures above will
then follow to generate the required cam contour.

GRAPHICAL METHOD FOR SIMPLE MOTION
To determine the cam contours graphically, it will be necessary to
invert the mechanism and to hold the cam stationary while the follower
moves around it. This will not affect the relative motion between the
cam and the follower, and the procedure is as follows:
1. Rotate the follower about the center of the cam in a direction
opposite to that of the proposed cam rotation.
2. Move the follower radially outward the correct amount for each
division of rotation.
3. Draw the cam outline tangent to the polygon that is formed by
the various positions of the follower surface.
Unfortunately, in the last step, there is no graphical way of
determining the contact point between the cam and the follower, and it
must be determined by eye with the use of a French curve. The methods
summarized above are applied in all types of disk cam as follows:
1. DISK CAM WITH RADIAL ROLLER FOLLOWER
By following the construction method of cam contour as
summarized above, we may arrive in the desirable contour provided
that we have the data of follower displacement per degree of cam rotation,
Figure 4. Disk Cam with Radial Roller Follower
Design Plate Problems:
1. A disk cam with a radial roller follower is rotating clockwise
through a total displacement of 1½ in. with the following lift figures:
Cam Angle, θ
30
60
90
120
150
180
Lift, in.
0.10
0.37
0.75
1.13
1.40
1.50
Cam Angle, θ
210
240
270
300
330
360
Lift, in.
1.40
1.13
0.75
0.37
0.10
0.00
Layout the cam contour and determine by trial the
maximum pressure angle and the position (angle) to where it will
3
occur provided that the base diameter of the cam is 2in. and a
diameter of roller follower as 5/8in.
2. A radial roller follower disk cam is rotating clockwise through a
total displacement of 30mm. with the following lift figures:
Cam Angle, θ
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
Lift, mm
0.00
0.23
0.90
2.01
3.51
5.36
7.50
9.87
12.40
15.00
17.60
20.13
22.50
24.64
26.49
27.99
29.10
29.77
30.00
Cam Angle, θ
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
Lift, mm
29.77
29.10
27.99
26.49
24.64
22.50
20.13
17.60
15.00
12.40
9.87
7.50
5.36
3.51
2.01
0.90
0.23
0.00
Using CAD Software, layout the cam details and contour.
Determine the maximum pressure angle and the position (angle) to
where it will occur provided that the base circle diameter of the cam
is 20mm. and a diameter of roller follower as 8mm. with a follower
rod diameter of 4mm. Provide square (1.5mmx1.5mm) keyway in
the layout. Assume a cam thickness of 10mm, hub diameter of
15mm, hub thickness of 3mm and a bore diameter of 8mm.
Generate the 3D model of the cam.
2. DISK CAM WITH OFFSET ROLLER FOLLOWER
Consider the same type of cam assembly but this time, the follower
axis has an offset distance from the vertical axis passing through the
cam rotation. The method of construction will be almost the same in an
exception that roller follower is being offset with the specified distance
from the reference axis given. The development of this type of cam has
been integrated to minimize the pressure angle of the contacting
surface, thus, reducing the power requirement during outward rotation
(lifting motion) although there is a large pressure angle in the return
motion.
Figure 5. Disk Cam with Radial Roller Follower
Design Plate Problems:
1. A disk cam with an offset roller follower is rotating clockwise
through a total displacement of 1½ in. with the following lift figures:
4
Cam Angle, θ
30
60
90
120
150
180
Lift, in.
0.10
0.37
0.75
1.13
1.40
1.50
Cam Angle, θ
210
240
270
300
330
360
Lift, in.
1.40
1.13
0.75
0.37
0.10
0.00
Layout the cam contour and determine by trial the maximum
pressure angle during outward and return motion provided that
the base diameter of the cam is 2in. and a diameter of roller follower
as 5/8in. The centerline of the follower has an offset distance of ½in.
from the vertical axis passing through the center of cam rotation.
2. An offset roller follower disk cam is rotating clockwise through a
total displacement of 33mm. with the following lift figures:
Cam Angle, θ
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
Lift, mm
0.00
0.25
1.00
2.21
3.86
5.89
8.25
10.86
13.63
16.50
19.37
22.14
24.75
27.11
29.14
30.79
32.00
32.75
33.00
Cam Angle, θ
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
Lift, mm
32.75
32.00
30.79
29.14
27.11
24.75
22.14
19.37
16.50
13.63
10.86
8.25
5.89
3.86
2.21
1.00
0.25
0.00
Using CAD Software, layout the cam details and contour. Determine
the maximum pressure angle during outward and return motion
provided that the base circle diameter of the cam is 22mm and a
diameter of roller follower as 8.80mm with a follower rod diameter
of 3.3mm. Provide square (1.7mmx1.7mm) keyway in the layout.
Assume a cam thickness of 11mm, hub diameter of 15.5mm, hub
thickness of 3.30mm and a bore diameter of 8.80mm. The offset
distance of axis of the follower from the vertical axis passing through
the cam rotation is measured as 6mm. Generate the 3D model of the
cam.
3. DISK CAM WITH FLAT-FACED FOLLOWER
Figure 6 shows a typical layout of a Cam with flat-faced follower.
The principal construction of this type of cam are the same as in the
radial roller follower with the exception that the cam profile is drawn
tangent to the various position of the flat face follower.
Figure 6. Disk Cam with Flat-Faced Follower
5
In this case, there is no need to distinguish between radial and offset
followers because they are kinematically equivalent. That is any
follower shaft parallel to the one shown will produce the same output
motion. However, it may be necessary to change the length of the
follower face when the follower is offset.
One important factor of the design of this type of cam is the
determination of the minimum length of follower face to ensure a
smooth contact of the mating surfaces during the operation. This
minimum length can be defined graphically by measuring the
maximum parallel distance between the axis passing through the center
of cam rotation and the normal axis to the point of contact
corresponding to the angle of cam rotation.
Figure 7. Determination of the length of follower face
(Radial symmetrical construction)
From Figure 7, we can determine graphically the length of the
follower face using the equation:
𝑳
𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒇𝒐𝒍𝒍𝒐𝒘𝒆𝒓 𝒇𝒂𝒄𝒆 = 𝟐 [ + 𝒂𝒍𝒍𝒐𝒘𝒂𝒏𝒄𝒆]
𝟐
In case of an offset follower, for symmetrical construction, the
length of the follower face will be determined using the equation:
𝑳
𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒇𝒐𝒍𝒍𝒐𝒘𝒆𝒓 𝒇𝒂𝒄𝒆 = 𝟐 [ + 𝒂𝒍𝒍𝒐𝒘𝒂𝒏𝒄𝒆 + 𝒐𝒇𝒇𝒔𝒆𝒕 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆]
𝟐
Figure 8. Determination of the length of follower face
(Offset symmetrical construction)
6
Design Plate Problems:
1. A disk cam rotating clockwise drive a radial flat-faced follower
through a total displacement of 1.50in. with the following lift
figures:
Cam Angle, θ
30
60
90
120
150
180
Lift, in.
0.10
0.37
0.75
1.13
1.40
1.50
Cam Angle, θ
210
240
270
300
330
360
Lift, in.
1.40
1.13
0.75
0.37
0.10
0.00
Lay out the cam using the following conditions:
a. Base circle diameter of 2in. Add 0.125in (symmetrical
construction) after determining the minimum length of the
follower face.
b. Base circle diameter of 2.50in and a follower offset distance of
0.25in. Add 1/8 in. (symmetrical construction) after
determining the minimum length of the follower face.
2. A Flat-faced follower disk cam is rotating clockwise through a total
displacement of 33mm. with the following lift figures:
Cam Angle, θ
0
10
20
30
40
50
60
70
80
90
100
110
120
130
Lift, mm
0.00
0.04
0.29
1.02
2.16
4.00
6.45
9.46
12.87
16.50
20.13
23.54
26.55
29.00
Cam Angle, θ
140
150
160
170
180
190
200
210
220
230
240
250
260
270
Lift, mm
30.84
32.05
32.71
32.96
33.00
32.96
32.71
32.05
30.84
29.00
26.55
23.54
20.13
16.50
Cam Angle, θ
280
290
300
310
320
Lift, mm
12.87
9.46
6.45
4.00
2.16
Cam Angle, θ
330
340
350
360
Lift, mm
1.02
0.29
0.04
0.00
Using CAD Software, layout the cam details and contour.
Determine the minimum length of the follower face with a
symmetrical construction allowance of 2mm on both ends. The base
circle diameter of the cam is 25mm and a diameter of roller follower
is 8.80mm with a follower rod diameter of 2.25mm. Provide square
(1.5mmx1.5mm) keyway in the layout. Assume a cam thickness of
11mm, hub diameter of 20mm, hub thickness of 3.30mm and a bore
diameter of 8mm. Generate a 3D model of the cam.
4. DISK CAM WITH OSCILLATING ROLLER FOLLOWER
Figure 9. Disk Cam with an Oscillating Roller Follower
7
Figure 9 shows a typical layout of a disk cam with an oscillating
roller follower. In this type of cam, an oscillating follower move at a
certain degree as the cam rotates and touches the mating surface of the
follower. The principal construction of this type of cam is the same as
in the reciprocating roller follower, only, various condition shall be
established first before doing the layout of the cam contour. These are:
1. Distance between the center of cam rotation and center of
oscillation of the follower,
2. Position of center of oscillation relative to the center of cam
rotation and,
3. Radius of oscillation of the follower.
Design Plate Problems:
1. A disk, cam rotating counterclockwise drives an oscillating roller
follower through a total angle of 200. Lay out the cam using a
minimum diameter of 2in. The center of the hub of the follower is to
be 3in to the right of the center and on the horizontal centerline of
the cam. The diameter of the roller is to be 0.75in and the distance
from the center of the hub to the center of the roller is to be 2.75in.
Using a bore of 0.75in, hub diameter of 1in., and a 0.10in x 0.10 in
key in both cam and follower hub, draw the cam assembly layout
and determine graphically the maximum pressure angle. Use the
following lift figures:
Cam Angle
30
60
90
120
150
180
Follower Angle,
degree
1.50
5.50
10.00
14.50
18.50
20.00
Cam Angle
210
240
270
300
330
360
Follower Angle,
degree
18.50
14.50
10.00
5.50
1.50
0.00
2. A disk, cam rotating counterclockwise drives an oscillating roller
follower through a total angle of 300. Lay out the cam using a CAD
software providing a minimum cam diameter of 33mm. The center
of the hub of the follower is to be 75mm to the right and 15mm above
the center of rotation of the cam. The center of the roller is to be
67.50mm from the center of oscillation. Using a bore of 15mm, hub
diameter of 22.50mm, and a 2.25mm x 2.25mm key in both cam and
follower hub with cam and hub thickness of 10mm and 3mm
respectively, draw the cam contour and generate its 3D model using
the below lift figures. Determine also the maximum pressure angle.
Cam Angle
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
Follower Angle,
degree
0.00
0.22
0.86
1.92
3.35
5.12
7.18
9.47
11.92
14.48
17.06
19.60
22.02
24.25
26.20
27.81
29.01
29.75
30.00
Cam Angle
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
Follower Angle,
degree
29.75
29.01
27.81
26.20
24.25
22.02
19.60
17.06
14.48
11.92
9.47
7.18
5.12
3.35
1.92
0.86
0.22
0.00
8
5. DISK CAM WITH OSCILLATING FLAT-FACED FOLLOWER
Graphically, the construction method in generating the cam contour
of a disk cam with an oscillating flat-faced follower is a combination of
knowledge in a reciprocating and oscillating follower. Review that cam
contour in a flat faced follower is always drawn tangent to the enclosing
polygon generated by following the displacement of the follower with
respect to cam rotation. The concept of finding the minimum length as
in the reciprocating flat face follower is also applied in this type of cam.
The construction is almost similar with the oscillating roller
follower in an exception that cam contour is drawn normal to a flat
surface.
Design Plate Problems:
1. A disk, cam rotating counterclockwise drives a flat-faced follower
through a total angle of 200. Lay out the cam using a minimum
diameter of 2in. The center of the hub of the follower is to be 3in to
the right of the center and on the horizontal centerline of the cam.
The radius of oscillation is 2.75in. Using a bore of 0.75in, hub
diameter of 1in., and a 0.10in x 0.10 in key in both cam and follower
hub, draw the cam assembly layout and determine the minimum
length of follower faced (symmetrical construction) by adding a
0.10in allowance in both ends to ensure smooth contact. Use the
following lift figures:
Cam Angle
30
60
90
120
150
180
Figure 10. Disk Cam with an Oscillating Flat-faced Follower
Follower Angle,
degree
1.50
5.50
10.00
14.50
18.50
20.00
Cam Angle
210
240
270
300
330
360
Follower Angle,
degree
18.50
14.50
10.00
5.50
1.50
0.00
2. A disk, cam rotating counterclockwise drives an oscillating flatfaced follower through a total angle of 300. Lay out the cam using a
CAD software providing a minimum cam diameter of 33mm. The
center of the hub of the follower is to be 70mm to the left and 10mm
above the center of rotation of the cam. The radius of oscillation is
to be 65mm. Using a bore of 15mm, hub diameter of 22.50mm, and
a 2.25mm x 2.25mm key in both cam and follower hub with cam
and hub thickness of 10mm and 3mm respectively, draw the cam
contour and generate its 3D model using below lift figures. Upon
constructing the cam contour, determine the minimum length of
9
follower faced (symmetrical construction) by adding a 1mm
allowance in both ends to ensure smooth contact
Cam Angle
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
Follower Angle,
degree
0.00
0.22
0.86
1.92
3.35
5.12
7.18
9.47
11.92
14.48
17.06
19.60
22.02
24.25
26.20
27.81
29.01
29.75
30.00
Cam Angle
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
Follower Angle,
degree
29.75
29.01
27.81
26.20
24.25
22.02
19.60
17.06
14.48
11.92
9.47
7.18
5.12
3.35
1.92
0.86
0.22
0.00
1. PARABOLIC MOTION
Parabolic motion has the lowest theoretical acceleration for a given
rise and cam speed for the motions listed, and for this reason it has been
used for many cam profiles. However, in slow-speed work, this has
little significance. Parabolic motion may or may not have equal
intervals of acceleration and deceleration, depending on requirements.
Parabolic motion may also be modified to include an interval of
constant velocity between the acceleration and deceleration; this is often
spoken of as modified constant velocity.
Although, analytically, the parabolic motion can be constructed
using the displacement formula as S = ½ At2, it can be graphically
constructed as follow:

GRAPHICAL METHOD FOR CAM DISPLACEMENT CURVE
The above discussion introduced us the method of generating the
cam contour but following the real engineering process, before a cam
contour can be determined, it is necessary to select the motion with
which the follower will move in accordance with the requirements of
the system. If operation is to be at slow speed, the motion may be any
one of several common motions, for example, parabolic (constant
acceleration and deceleration), parabolic with constant velocity, simple
harmonic, or cycloidal.
Figure 11. Parabolic Motion
Procedures:
1. Determine the distance of follower displacement and construct
a displacement graph.
2. Divide the right side of the displacement curve by the number
of interval as the cam rotation. (In case of Figure 11, there are
nine (9) intervals)
10
3. Project a construction line (dotted) from the starting motion
(zero (0) degrees) extending to the point of intersection of the
right side of the displacement graph with the interval line.
4. Trace the curve corresponding to the point of intersection of
each construction line generated in procedure 3 with the degree
of cam rotation.
In plotting the displacement-time graph, it is necessary to
determine the inflection point if the motion is parabolic or a
modification thereof. The inflection point for parabolic motion will be
at the midpoint of the displacement scale and of the time scale if the
intervals are equal. The slope of this point of inflection can be used as a
guide in constructing the section of the displacement having a constant
velocity.
Figure 12. Finding the slope in the point of inflection (Method 1)
Figure 13. Finding the slope in the point of inflection (Method 2)
After the inflection points have been determined as, for example, in
Figure 12 and Figure 13, the constantly accelerated portion OA of the
displacement curve is constructed as shown in Figure 11. The
deceleration portion BC of the curve in Figure 12 and 13 is constructed
in a similar manner for its particular displacement and corresponding
time interval.
Design Plate Problems:
1. A symmetrical contour disk cam of flat-faced follower having a
minimum diameter of 25mm follows a constantly accelerated
parabolic motion during the first 600 of cam rotation, a constant
velocity motion during the second 600 rotations and a constantly
decelerated parabolic motion during the third 600 of cam
rotation. If the total follower displacement is 50mm, draw the
cam contour and generate its 3D model. Upon constructing the
cam contour, determine the minimum length of follower face
(symmetrical construction) by adding a 1.50mm allowance in
11
both ends to ensure smooth contact. Use a bore of 15mm, hub
diameter of 22.50mm, and a 2.25mm x 2.25mm key with cam and
hub thickness of 10mm and 3mm respectively. Note: Analyze the
cam contour in every 100 of cam rotation.
2. An offset roller follower disk cam is rotating clockwise through
a total displacement of 33mm with the following motion curves:
Cam Angle of
Rotation
0-60
61-120
121-180
181-240
241-300
301-360
overhung in its construction. Less power will also be needed to operate
the cam.
Although, analytically, the harmonic motion can be constructed
using the displacement formula S = r(1-cos(θ)), where ‘r’ is the radius of
the construction circle (r = S/2) and ‘θ’ being the angle of cam rotation,
it can be simply presented graphically as follow:
Motion Curve
Constant Accelerated Parabolic motion
Constant Velocity motion
Constant Decelerated Parabolic motion
Constant Accelerated Parabolic motion
Constant Velocity motion
Constant Decelerated Parabolic motion
Using CAD Software, layout the cam details and contour.
Determine the maximum pressure angle during outward and
return motion provided that the base circle diameter of the cam
is 20mm and a diameter of roller follower as 8.85mm with a
follower rod diameter of 3.3mm. Provide square
(1.5mmx1.5mm) keyway in the layout. Assume a cam thickness
of 11mm, hub diameter of 15.5mm, hub thickness of 3.30mm and
a bore diameter of 8.80mm. The offset distance of axis of the
follower from the vertical axis passing through the cam rotation
is measured as 6mm. Generate the 3D model of the cam. Note:
Analyze the cam contour in every 100 of cam rotation.
2. HARMONIC MOTION
Generally, harmonic motion has the advantage that, with a radial
roller follower, the maximum pressure angle will be smaller than with
parabolic motion with equal time intervals or with cycloidal motion.
This will allow the follower to be less rigidly supported and more
Figure 14. Harmonic Motion
Procedures:
1. Determine the distance of follower displacement and construct
a displacement graph.
2. Draw the construction circle (semicircle, r = S/2) with the center
at the midpoint of zero (0) degree ordinate.
3. Divide the circle radially with the numbers of division to be
used in the displacement graph.
4. Project a horizontal line extending from the intersection of
construction circle and the line generated in procedure 3 up to
the corresponding angle of rotation in displacement graph.
5. Trace the intersection of ordinates in displacement graph and
the line generated in procedure 4.
12
Note: A dwell can also be integrated with the cam design. Dwell in
cam design is defined as the interval of cam rotation (in degrees)
where the follower has no considerable motion or the cam is at rest
position.
Design Plate Problems:
1. Design the contour of an offset roller follower disk cam rotating
clockwise through a total displacement of 33mm following a
simple harmonic motion. Using CAD Software, layout the cam
details and contour. Determine the maximum pressure angle
during outward and return motion and compare the obtained
result in problem 2 under parabolic motion provided that the
base circle diameter of the cam is 20mm and a diameter of roller
follower as 8.85mm with a follower rod diameter of 3.3mm.
Provide square (1.5mmx1.5mm) keyway in the layout. Assume a
cam thickness of 11mm, hub diameter of 15.5mm, hub thickness
of 3.30mm and a bore diameter of 8.80mm. The offset distance of
axis of the follower from the vertical axis passing through the
cam rotation is measured as 6mm. Generate the 3D model of the
cam. Note: Analyze the cam contour in every 100 of cam rotation.
2. A disk cam of an offset flat-faced follower having a minimum
diameter of 25mm and a follower offset distance of 3mm follows
the following motion curves during its operation:
Cam Angle of
Rotation
0-60
61-120
121-180
181-240
241-300
301-360
Motion Curve
Dwell
Constant Accelerated Parabolic motion
Decelerating Harmonic Motion
Accelerating Harmonic Motion
Constant Decelerated Parabolic motion
Dwell
If the total follower displacement is 55mm, draw the cam contour
and generate its 3D model. Upon constructing the cam contour,
determine the minimum length of follower face (symmetrical
construction) by adding a 2.00mm allowance in both ends to
ensure smooth contact. Use a bore of 15mm, hub diameter of
22.50mm, and a 2.25mm x 2.25mm key with cam and hub
thickness of 10mm and 3mm respectively. Note: Analyze the cam
contour in every 100 of cam rotation. Each half of follower displacement
is divided equally into types of motion curves given.
3. CYCLOIDAL MOTION
Figure 15 shows the construction for cycloidal motion. Although,
analytically, the type of cycloidal motion presented below (other types
will be presented in the preceding topics) can be constructed using the
displacement formula:
𝜃
1
𝜃
𝑠 = 𝑆[ −
𝑠𝑖𝑛2𝜋 ]
𝛽 2𝜋
𝛽
where ‘S’ is the total displacement of the follower, ‘s’ is the specific lift
with respect to cam rotation, ‘θ’ being the angle of cam rotation and ‘β’
is the total angle in consideration. (In the case of Figure 15, β = 1800)
The radius of the construction circle is r = S/2π. The circumference
of this circle is divided into the same number of parts as in the time
scale, in the case of figure 15, eighteen (18) parts. The eighteen (18)
marks on the circumference are projected horizontally onto the vertical
diameter of the circle. The marks on the vertical diameter are then
projected parallel to OA to the corresponding line on the time axis.
Procedures:
1. Determine the distance of follower displacement and construct a
displacement graph.
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Figure 15. Cycloidal Motion
2. Draw the construction circle (r = S/2π) with the center at point
‘O’.
3. Divide the circumference of the construction circle with intervals
equal to the number of division in the displacement graph.
4. Project horizontally the intersection of each constructed line in
procedure 3 up to the zero (0) degree ordinate of the
displacement graph.
5. Construct the line O-A. (From origin and zero (0) degree ordinate
up to displacement ‘S’ and 180 degrees’ ordinate intersection.
6. Project lines parallel with O-A starting from the intersection of
lines constructed in procedure 4 and trace the curve from the
intersection of ordinates and the line constructed in procedure 5
corresponding to the angle division under consideration.
The significance of constructing the types of motion discussed in
this section will be tackled in the preceding topics of cams. This is due
to the fact that different types of motion curve produce dynamic effect
that tends to separate the cam with the follower and produces
significant level of machine vibration that should be avoided.
Design Plate Problems:
1. Design the contour of an offset flat faced follower disk cam
rotating clockwise through a total displacement of 50mm
following a cycloidal motion. Using CAD Software, layout the
cam details and contour. Determine the length of follower face
permitting a 1.5mm allowance on both sides (symmetrical
construction) provided that the base circle diameter of the cam is
25mm. Provide square (1.5mmx1.5mm) keyway in the layout.
Assume a cam thickness of 11mm, hub diameter of 15.5mm, hub
thickness of 3.30mm and a bore diameter of 8.80mm. The offset
distance of axis of the follower from the vertical axis passing
through the cam rotation is measured as 6mm. Generate the 3D
model of the cam. Note: Analyze the cam contour in every 100 of cam
rotation.
2. A disk cam of a roller follower having a minimum diameter of
25mm and a roller diameter of 10mm follows the following
motion curves during its operation:
Cam Angle of
Rotation
0-60
61-120
121-180
181-240
241-300
301-360
Motion Curve
Dwell
Accelerating Cycloidal motion
Decelerating Harmonic Motion
Accelerating Harmonic Motion
Decelerating Cycloidal motion
Dwell
If the total follower displacement is 45mm, draw the cam contour
and generate its 3D model. Upon constructing the cam contour,
determine the maximum pressure angle between the cam and
the follower. Use a bore of 17.50mm, hub diameter of 20mm, and
a 2.25mm x 2.25mm key with cam and hub thickness of 15mm
14
and 5mm respectively. Note: Analyze the cam contour in every 100
of cam rotation. Each half of follower displacement is divided equally
into types of motion curves given.
15