Machinery's Handbook, 31st Edition
2372 CAMS AND CAM DESIGN and R max circles giving the points 2 ′ , 4 ′ , 6 ′ , etc. The R min circle with center at the cam shaft center is drawn through the lowest position of the center of the roller follower and the R max circle through the highest position as shown. The different points on the pitch curve are now located. Point 6 ′″ , for instance, is found by stepping off the y 6 ordinate of the displacement diagram on arc 6 ′ starting at the R min circle.
30
B
C
28
32
36 ′ :0 ′
6 ′
2
26
34
34 ′
4
φ 0
h
6 ′′
y 6
32 ′
h
6 ′ M
36:0
24
D E
A
6 ′′′
y 6
0 2 4
6 8 10
12 14 16 18 20 22 24 26 28 30
36
30 ′
8 ′
100 °
20 °
180 °
60 °
2
22
R min
360 °
28 ′
10 ′
(a)
4
20
26 ′
12 ′
18
6
24 ′
14 ′
(b)
22 ′
16 ′
16
8
20 ′
18 ′
14
10
12
Fig. 12. (a) Time-Displacement Diagram for Cam to be Laid Out; (b) Construction of Contour of Cam with Swinging Roller Follower
Pressure Angle and Radius of Curvature.— The pressure angle at any point on the profile of a cam may be defined as the angle between the direction where the follower wants to go at that point and where the cam wants to push it. It is the angle between the tangent to the path of follower motion and the line perpendicular to the tangent of the cam profile at the point of cam-roller contact. The size of the pressure angle is important because: 1) Increasing the pressure angle increases the side thrust and this increases the forces exerted on cam and follower. 2) Reducing the pressure angle increases the cam size and often this is not desirable because: a) The size of the cam determines, to a certain extent, the size of the machine. b) Larger cams require more precise cutting points in manufacturing and, therefore, an increase in cost. c) Larger cams have higher circumferential speed and small deviations from the theoretical path of the follower cause additional acceleration, the size of which increases with the square of the cam size. d) Larger cams mean more revolving weight and in high-speed machines this leads to increased vibrations in the machine. e) The inertia of a large cam may interfere with quick starting and stopping. The maximum pressure angle α m should, in general, be kept at or below 30 degrees for translating-type followers and at or below 45 degrees for swinging-type followers.These values are on the conservative side and in many cases may be increased considerably, but beyond these limits trouble could develop and an analysis is necessary. In the following, graphical methods are described by which a cam mechanism can be designed with translating or swinging roller followers having specified maximum pressure angles for rise and return. These methods are applicable to any kind of time- displacement diagram.
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