Page 95 - Cam Design Handbook

THB3 8/15/03 12:58 PM Page 83

MODIFIED CAM CURVES 83

y C – 1 y C – 2
q Ê 1 qˆ q Ê 1 qˆ
Á
h y = h – sin p ˜ h y = h + sin p ˜
Á
b Ë p b¯ b Ë p b¯
q q
b b
y'
y'
h Ê qˆ h Ê qˆ
y' = 1 – cos p ˜ y' = 1 + cos p ˜
Á
Á
b Ë b ¯ b Ë b ¯
q q
y" q
ph Ê qˆ ph Ê qˆ
y" = sin p ˜ y" = – sin p ˜
Á
Á
2
2
b Ë b¯ b Ë b¯
q y"
y C – 3 y C – 4
Ê q 1 q ˆ Ê q 1 qˆ
Á
h y = h 1 – + sin p ˜ h y = h 1 – – sin p ˜
Á
Ë b p b ¯ Ë b p b¯
q q
b b
q q
h Ê q ˆ h Ê q ˆ
Á
y' = 1 – cos p ˜ y' = – 1 + cos p ˜
Á
b Ë b ¯ b Ë b¯
y' y'
q ph Ê q ˆ ph Ê q ˆ
y" = – sin p ˜ y" = sin p ˜
Á
Á
b Ë b ¯ b Ë b¯
2
2
q
y" y"
y C – 5 y C – 6
q Ê 1 qˆ Ê q 1 q ˆ
Á
Á
h y = h – sin 2p ˜ h y = h 1 – + sin 2p ˜
b Ë 2p b ¯ Ë b 2p b¯
q q
b b
y' q
h Ê q ˆ h Ê q ˆ
y' = 1 – cos 2p ˜ y' = – 1 – cos 2p ˜
Á
Á
b Ë b¯ b Ë b¯
q y'
y" y"
2ph Ê q ˆ 2ph Ê qˆ
Á
y" = sin 2p ˜ y" = – sin 2p ˜
Á
q b Ë b¯ q b Ë b¯
2
2
FIGURE 3.16. Cycloidal motion characteristics.
Note: h = total follower displacement for half-curve or full curve action, and
b = cam angle for displacement h.
for blending with curves in general, especially with DRRD cam action. Chapter 4 shows
an elaborate treatment of polynomials.
EXAMPLE A spring-loaded textile machine has a cam that rotates at 720rpm in which
3
the follower rises 1 / 4 inches in 120 degrees. To keep the spring size small, the maximum
positive acceleration is twice the maximum negative acceleration. Design (a) the rise
portion of the DRRD system with harmonic and cycloidal coupling using the simplified