Machinery's Handbook, 31st Edition
CAMS AND CAM DESIGN 2369 For the right end of the straight line AB , the calculations are similar but, in using Formula (5), calculated y values are subtracted from the total rise of the cam ( y 1 + y 2 + y 3 ) to obtain the follower displacement.
M 2
F
y 3
B
y 2
2 φ 1
A
2 y 1
y 1
E
M 1 φ 1
φ 2
φ 3
Fig. 9. Matching a Parabola at Each End of Straight Line Displacement Curve AB to Provide More Acceptable Acceleration and Deceleration
Table 1 shows the computations and resulting values for the cam displacement diagram described. The calculations are shown in detail so that if equations are programmed for a digital computer, the results can be verified easily. Obviously, the intermediate points are not needed to draw the straight line, but when the cam profile is later to be drawn or cut, these values will be needed since they are to be measured on radial lines. The matching procedure when using cycloidal motion is exactly the same as for para bolic motion, because parabolic and cycloidal motion have the same maximum velocity for equal rise (or return) and lift angle (or return angle). Cam Profile Determination.— In the cam constructions that follow an artificial device called an inversion is used. This represents a mental concept which is very helpful in performing the graphical work. The construction of a cam profile requires the drawing of many positions of the cam with the follower in each case in its related location. However, instead of revolving the cam, it is assumed that the follower rotates around the fixed cam. It requires the drawing of many follower positions, but since this is done more or less dia grammatically, it is relatively simple. As part of the inversion process, the direction of rotation is important. In order to pre serve the correct sequence of events, the artificial rotation of the follower must be the reverse of the cam’s prescribed rotation. Thus, in Fig. 10 the cam rotation is counterclock wise, whereas the artificial rotation of the follower is clockwise. Radial Translating Roller Follower: The time-displacement diagram for a cam with a radial translating roller follower is shown in Fig. 10(a). This diagram is read from left to right as follows: For 100 degrees of cam shaft rotation the follower rises h inches ( AB ), dwells in its upper position for 20 degrees ( BC ), returns over 180 degrees ( CD ), and finally dwells in its lowest position for 60 degrees ( DE ). Then the entire cycle is repeated. Fig. 10(b) shows the cam construction layout with the cam pitch curve as a dot and dash line. To locate a point on this curve, take a point on the displacement curve, as 6 ′ at the 6o-degree position, and project this horizontally to point 6 ″ on the 0-degree position of the cam construction diagram. Using the center of cam rotation, an arc is struck from point 6 ″ to intercept the 60-degree position radial line which gives point 6 ′″ on the cam pitch curve. It will be seen that the smaller circle in the cam construction layout has a radius R min equal to the smallest distance from the center of cam rotation to the pitch curve and, similarly, the larger circle has a radius R max equal to the largest distance to the pitch curve. Thus, the difference in radii of these two circles is equal to the maximum rise h of the follower.
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