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98
because the motion from rest (the horizontal lines) to constant velocity
takes place instantaneously and this means that accelerations become
infinitely large at these transition points.
Types of Cam Displacement Curves: A variety of cam curves are
available for moving the follower. In the following sections only the rise
portions of the total time-displacement diagram are studied. The return
portions can be analyzed in a similar manner. Complex cams are
frequently employed which may involve a number of rise-dwell-return
intervals in which the rise and return aspects are quite different. To
analyze the action of a cam it is necessary to study its time-displacement
and associated velocity and acceleration curves. The latter are based on
the first and second time-derivatives of the equation describing the time-
displacement curve:
y = displacement = )(
t
f
y
=
or )(
φ
=
f
y
φ
ω===
d
dy
velocity
dt
dy
v
2
2
2
2
2
φ
ω===
d
yd
onaccelerati
dt
yd
a
Meaning of Symbols and Equivalent Relations: y=displacement of
follower, inch
h=maximum displacement of follower, inch
t =time for cam to rotate through angle φ, sec, = φ/ω, sec
T=time for cam to rotate through angle β, sec, = β/ω, or β/6N,
sec
φ =cam angle rotation for follower displacement y, degrees
β =cam angle rotation for total rise h, degrees
v=velocity of follower, in./sec
a=follower acceleration, in./sec
2
t/T =φ/β
N=cam speed, rpm
ω =angular velocity of cam, degrees/sec = β/T = φ/t = dφ/dt = 6N
ω
R
=angular velocity of cam, radians/sec = πω/180
W=effective weight, lbs
g = gravitational constant = 386 in./sec2
()
tf = means a function of t
()
ϕf = means a function of φ
R
min
= minimum radius to the cam pitch curve, inch
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