Pitch Circle. Problem 8.17

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1 Follower Travel, mm Displacement, cm Cam Rotation Angle 90 Pitch Circle 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 Cam Rotation Solution:

2 Total Follow Travel Use the follower diagram subdivisions of 0. 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 Prime Curve Prime Circle Base Circle Cam 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. in. 1.0 Base Circle Station Point Numbers

3 inch Prime circle Problem 8.1 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 0. The follower then dwells for 40 of cam rotation, and the return occurs with parabolic motion for the cam rotation from 60 to 360. The amplitude of the follower rotation is 35, and the follower radius is 1 in. The base circle radius is in, and the distance between the cam axis and follower rotation axis is 4 in. Lay out the cam profile using 0 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 For the first part of the rise, , and = L where L = 35, = 140, and = = 80. For the second part of the rise, 180 0, and

4 = L 1 1 where L = 35, = 140, and = = 80. For 0 60 = 35 For the first part of the return, , and = L 1 where L = 35, = 60, and = =100 For the second part of the return, , and = L 1 where L = 35, = 60, and = =100 The displacement diagram is given below followed by a table of values for at 0 increments of. Theta Follower Angle

5 To lay out the cam, first draw the prime circle which has a radius of.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 (rb +r0) = 4 ( +1) =.646" Identify the point on the pivot circle corresponding to = 0, lay off the radial lines at 0 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

6 inch Problem 8. 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 =

Cams. 774 l Theory of Machines

Cams. 774 l Theory of Machines 774 l Theory of Machines 0 Fea eatur tures es 1. Introduction.. Classification of Followers. 3. Classification of Cams. 4. Terms used in Radial cams. 5. Motion of the Follower. 6. Displacement, Velocity