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Problem 8.23<br />
In the sketch shown, the disk cam is used to position the radial flat-faced follower in a computing<br />
mechanism. The cam profile is to be designed to give a follower displacement S for a<br />
counterclockwise cam rotation according to the function S = k 2 starting from dwell. For 60˚ of<br />
cam rotation from the starting position, the lift of the follower is 1.0 cm. By analytical methods,<br />
determine the distances R and L when the cam has been turned 45˚ from the starting position. Also<br />
calculate whether cusps in the cam profile would occur in the total rotation of 60˚.<br />
Solution:<br />
Starting Position<br />
Dwell<br />
<br />
ω<br />
2.5 cm radius<br />
Spring<br />
S<br />
- 329 -<br />
R<br />
<br />
<br />
θ<br />
L<br />
Point of<br />
Contact<br />
Find k first given the values of S and at the given point. Note that must be converted to radians<br />
to ensure consistent units.<br />
S = k 2<br />
Therefore,<br />
k = S 2 =<br />
1<br />
2 = 0.9119<br />
[ /3]<br />
Now,<br />
R = rb + S = rb + k 2 = 2.5+ 0.9119 2<br />
Where rb is the radius of the base circle. Also,<br />
At = 4 ,<br />
and<br />
L = dR<br />
= 2k = 2(0.9119) = 1.8238<br />
d<br />
R = 2.5+ 0.91192 = 2.5 +0.9119 ( 4 ) 2<br />
= 3.063 cm
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