Английский язык. Теория механизмов и машин. Профессиональная составляющая языковой подготовки. Горбенко М.В - 99 стр.

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99
R
max
= maximum radius to the cam
pitch curve, inch
r
f
= radius of cam follower roller,
inch
ρ = radius of curvature of cam pitch
curve (path of center of roller
follower), inch
R
c
= radius of curvature of actual
cam surface, in., =
f
r−
ρ
for convex
surface; =
f
r
+
ρ
for concave surface.
Four displacement curves are of the
greatest utility in cam design.
1. Constant-Velocity Motion: (Fig. 4)
T
t
hy =
or
β
φ
=
h
y
(1a)
T
h
d
t
dy
v ==
or
β
ω
=
h
v
(1b)
*
2
2
0==
d
t
yd
a
(1c)
Tt <<
0
* Except at t = 0 and t = T where the acceleration is theoretically infinite.
This motion and its disadvantages were mentioned previously.
While in the unaltered form shown it is rarely used except in very crude
devices, nevertheless, the advantage of uniform velocity is an important
one and by modifying the start and finish of the follower stroke this
form of cam motion can be utilized. Such modification is explained in
the section Displacement Diagram Synthesis.
2. Parabolic Motion: (Fig. 5)
For 0≤t≤T/2 and 0≤φ≤β/2 For T/2≤t≤T and β/2≤φ≤β
22
)/(2)/(2 βφ== hTthy
(2a)
22
/4/4 βωφ== hThtv (2b)
(
)
2
2
/4/4 βω== hTha (2c)
(
)
(
)
]/121[]/121[
2
βφ−−=−−= hTthy (2d)
(
)
(
)( )
βφ−
β
ω
=
−
=
/1/4/1/4 hTtThv (2e)
()
2
2
/4/4 βω−=−= hTha
(2f)
Examination of the above formulas shows that the velocity is zero
when t =0 and y = 0; and when t = T and y = h.
y
t
T
Acceleration=∞
Velocity
h
Acceleration=∞
A
B
Fig. 4. Cam Displacement, Velocity,
and Acceleration Curves for Constant
Velocity Motion

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