Machinery's Handbook, 31st Edition
CAMS AND CAM DESIGN
2373
B C
P 1 τ 1
τ 2
P 2
h
y 1
y 2
D
E
A
0°
100°
120°
300°
360°
L = 360° = 2 k
Fig. 13. Displacement Diagram Determination of Cam Size for a Radial or an Offset Translating Follower.— Fig. 13 shows a time-displacement diagram. The maximum displacement is preferably made to scale, but the length of the abscissa, L , can be chosen arbitrarily. The distance L from 0 to 360 degrees is measured and is set equal to 2 π k from which k L 2 π = k is calculated and laid out as length E to M in Fig. 14. In Fig. 13 the two points P 1 and P 2 having the maximum angles of slope τ 1 and τ 2 are located by inspection. In this example, y 1 and y 2 are of equal length. Angles τ 1 and τ 2 are laid out as shown in Fig. 14, and the points of intersection with a per pendicular to EM at M determine Q 1 and Q 2 . The measured distances tan tan MQ k MQ k and 1 1 2 2 τ τ = = are laid out in Fig. 15, which is constructed as follows: Draw a vertical line R u R o of length h equal to the stroke of the roller follower, R u being the lowest position and R o the highest position of the center of the roller follower. From R u lay out R u R y 1 = y 1 and R u R y 2 = y 2 ; these are equal lengths in this example. Next, if the rotation of the cam is counterclockwise, lay out k tan τ 1 , to the left, k tan τ 2 to the right from points R y 1 and R y 2 , respectively, R y 1 and R y 2 being the same point in this case.
E
τ 1 τ 2
k tan τ 2 k
Q 2
Q 1
M
k tan τ 1
Fig. 14. Construction to Find k tan τ 1 and k tan τ 2 The specified maximum pressure angle α 1 is laid out at E 1 as shown, and a ray (line) E 1 F 1 is determined. Any point on this ray chosen as the cam shaft center will proportion the cam so that the pressure angle at a point on the cam profile corresponding to point P 1 , of the displacement diagram will be exactly α 1 .
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