Page 116 - Cam Design Handbook

THB4 8/15/03 1:01 PM Page 104

104 CAM DESIGN HANDBOOK

y"

Cam angle q b

FIGURE 4.10. Gutman’s [1961] 1-3 harmonic
acceleration curve.

Similarly, if we retain the first three terms in the Fourier series expansion of the dis-
placement of the parabolic curve, the equation of Gutman’s fifth-order harmonic curve can
be obtained.

Freudenstein 1-3 Harmonic Curve (Freudenstein, 1960)
hq h Ê 27 2 pq 1 6 pq ˆ
y = - Á sin + sin ˜
b 2 p Ë 28 b 84 b ¯
h Ê 27 2 pq 1 6 pq ˆ
y ¢ = Á1 - cos - cos ˜
b Ë 28 b 28 b ¯
2p h Ê 27 2pq 3 6pq ˆ
y ¢¢ = Á sin + sin ˜
b 2 Ë 28 b 28 b ¯

4p 2 h Ê 27 2pq 9 6pq ˆ
y ¢¢¢ = Á cos + cos ˜ (4.12)
b 3 Ë 28 b 28 b ¯
In agreement with the foregoing design factors stated, Freudenstein’s 1-3 harmonic curve
has a maximum acceleration of about 135 percent of the acceleration of the parabolic
curve, or 85 percent of the acceleration of the cycloidal curve.

Freudenstein 1-3-5 Harmonic Curve (Freudenstein, 1960)
hq hm Ê 2 pq 1 6 pq 1 10 qq ˆ
y = - Ásin + sin + sin ˜ (4.13)
b 2 p Ë b 54 b 1250 b ¯
1125
m =
1192
h È Ê 2 pq 1 6 pq 1 10 pq ˆ˘
m
y ¢ = Í 1 - Ácos + cos + cos ˜ ˙
b Î Ë b 18 b 250 b ¯ ˚