Machinery's Handbook, 31st Edition
CAMS AND CAM DESIGN 2377 the profile cannot be represented by a simple formula, the graphical method may be the only practical solution. However, for some of the standard cam profiles utilizing radial translating roller followers, the following formulas may be used to determine key cam dimensions before laying out the cam. These formulas enable the designer to specify the maximum pressure angle (usually 30 ° or less) and, using the specified value, to calculate the minimum cam size that will satisfy the requirement. The following symbols are in addition to those starting on page 2364 . α max = specified maximum pressure angle, degrees R α max = radius from cam center to point on pitch curve where α max is located, inches (m) φ p = rise angle, in degrees, corresponding to α max and R α max α = pressure angle at any selected point, degrees R α = radius from cam center to pitch curve at α , inches (m) φ = rise angle, in degrees, corresponding to α and R α For Uniform Velocity Motion (6a) (6b) If α max is specified, the minimum radius to the lowest point on the pitch curve, R min , is: α h 180 ° πβ α R [ ] h 180 πβ min R [ ] ° α α φ ° = 0 max
tan h 180 ° πβ α
φ ° = 0
(6c)
min
max
For Parabolic Motion
R h (1 − φ ⁄ β ) 720 ° πβ [ ] α R h φ 720 ° πβ 2 [ ] α h 360 ° πβ α R [ ]
(7a)
α
0 9 φ 9 β / 2
φ
α
at radius R α to pitch curve at angle φ , where β / 2 ≤ φ ≤ β .
and α = arctan
(7b) If α max is specified, then the minimum radius to the lowest point of the pitch curve is: (7c) For Simple Harmonic Motion (8a) α α + tan h h 360 2 max ° πβ α − ; E φ ° = 0 α h 90 ° β α R [ ( )] sin φ 180 ° β α φ
[ ( arccot
)] tan α max
180 ° β ( )
180 ° β
(8b)
,
φ
φ
α
2
φ
p
sin h <
cos 2 180 180 ° d d
F
n
β
°
φ
= α max and φ = φ max
(8c)
p
n
α max
β
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