Pitch Circle Problem 8.17 Construct the profile of a disk cam that ...

Follower Travel, mm
Displacement, cm
1.5
1.0
0.5
0 1 2 3 4 5 6 7 8 9 10
Cam Rotation Angle
90˚
Pitch
Circle
0
1
2
3
4
5
10
9
8
7
6
Problem 8.17
Construct the profile of a disk cam that follows the displacement diagram shown below. The
follower is a radial roller and has a diameter of 10 mm. The base circle diameter of the cam is to be
40 mm and the cam rotates clockwise.
30
15
Solution:
0 0˚ 60˚ 120˚ 180˚ 240˚ 300˚ 360˚
Cam Rotation
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Total Follow Travel
Use the follower diagram subdivisions of 20˚. Next draw the cam pitch circle and lay off radial
lines in the counterclockwise direction. The follower displacements can then be taken directly from
the displacement diagram. Draw the pitch curve. Draw the cam follower circles on the pitch curve.
Use a smooth curve to draw the cam profile tangent to the follower circles.
6
5
4
Prime Curve
7
3
8
2
9
Prime Circle
Base Circle
1
0
10
Cam
16
17
15
11
12 13
14
Problem 8.18
Accurately sketch one half of the cam profile (stations 0-6) for the cam follower, base circle, and
displacement diagram given below. The base circle diameter is 1.2 in.
1.0
Base Circle
0 1 2 3 4 5 6 7
11 10 9 8
Station Point
Numbers
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220˚
240˚
260˚
280˚
1 inch
300˚
180˚
200˚
Prime circle
320˚
340˚
0˚
80˚
100˚
120˚
Problem 8.21
Lay out a cam profile assuming that an oscillating, roller follower starts from a dwell for 0˚ to 140˚
of cam rotation, and the cam rotates clockwise. The rise occurs with parabolic motion during the
cam rotation from 140˚ to 220˚. The follower then dwells for 40˚ of cam rotation, and the return
occurs with parabolic motion for the cam rotation from 260˚ to 360˚. The amplitude of the follower
rotation is 35˚, and the follower radius is 1 in. The base circle radius is 2 in, and the distance
between the cam axis and follower rotation axis is 4 in. Lay out the cam profile using 20˚ plotting
intervals such that the pressure angle is 0 when the follower is in the bottom dwell position.
Solution:
The displacement profile can be easily computed using the equations in Chapter 8 using a
spreadsheet or MATLAB program. Remember that the parabolic motion is represented by two
curves in each rise and return region. The curves are matched at the midpoints of the rise and
return. The profile equations are:
For 0 140˚
= 0
For the first part of the rise, 140˚ 180˚ , and
= 2L
2
where L = 35˚, = 140˚, and = 220˚140˚= 80˚.
For the second part of the rise, 180˚ 220˚ , and
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= L 12
1
2
where L = 35˚, = 140˚, and = 220˚140˚= 80˚.
For 220˚ 260˚
= 35˚
For the first part of the return, 260˚ 310˚, and
= L 12
2
where L = 35˚, = 260˚, and = 360˚260˚=100˚
For the second part of the return, 310˚ 360˚, and
= 2L
1
2
where L = 35˚, = 260˚, and = 360˚260˚=100˚
The displacement diagram is given below followed by a table of values for at 20˚ increments of
.
Theta Follower Angle
0.000 0.000
20.000 0.000
40.000 0.000
60.000 0.000
80.000 0.000
100.000 0.000
120.000 0.000
140.000 0.000
160.000 4.375
180.000 17.500
200.000 30.625
220.000 35.000
240.000 35.000
260.000 35.000
280.000 32.200
300.000 23.800
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320.000 11.200
340.000 2.800
360.000 0.000
To lay out the cam, first draw the prime circle which has a radius of 2.0" + 1.0" = 3.0". Next draw
the pivot circle for the follower pivot. The radius of the pivot circle is 4". Draw the follower in the
initial position ( = 0˚ ) to determine the follower length (r 3 ) and the position on the pivot circle
corresponding to = 0˚ . As indicated in Example 8.5, the length r 3 is given by
r3 = r 1 2 (rb +r0) = 4 2 (2 +1) 2 = 2.646"
Identify the point on the pivot circle corresponding to = 0˚ , lay off the radial lines at 20˚
increments from this point, and label the lines in the counterclockwise direction. Draw lines from
the intersections of the radal lines with the pivot circle tangent to the prime circle. Then lay off the
angular displacements from these tangent lines. Locate the center of the follower by the distance r 3
from the pivot circle along these lines. Draw 1" radius circles through the endponts of the distances
layed off along these lines, and fit a smooth curve which is tangent to the circles corresponding to
the roller follower.
The cam profile is shown in the following figure.
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160˚
140˚
120˚
180˚
100˚
1 inch
200˚
80˚
220˚
60˚
240˚
40˚
260˚
20˚
280˚
0˚
300˚
320˚
340˚
Problem 8.22
Lay out the rise portion of the cam profile if a flat-faced, translating, radial follower's motion is
uniform. The total rise is 1.5 in, and the rise occurs over 100˚ of can rotation. The follower dwells
for 90˚ of cam rotation prior to the beginning of the rise, and dwells for 80˚ of cam rotation at the
end of the rise. The cam will rotate counterclockwise, and the base circle radius is 3 in.
Solution:
The displacement profile can be easily computed using the equations in Chapter 8 in a spreadsheet
or MATLAB program. The profile equations are:
For 0 90˚
s = 0
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