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105
of the center of the roller follower. From R
u
lay out R
u
R
y1
= y
1
and
R
u
R
y2
= y
2
; these are equal lengths in this example. Next, if the rotation
of the cam is counterclockwise, lay out ktanτ
1
, to the left, ktanτ
2
to the
right from points R
y1
and R
y2
,
respectively, R
y1
and R
y2
being
the same point in this case.
The specified maximum
pressure angle α
1
is laid out at
E
1
as shown, and a ray (line)
E
1
F
1
is determined. Any point
on this ray chosen as the cam
shaft center will proportion the
cam so that the pressure angle
at a point on the cam profile
corresponding to point P
1
, of
the displacement diagram will
be exactly α
1
.
The angle α
2
is laid out at
E
2
as shown, and another ray E
2
F
2
is determined. Similarly, any point on
this ray chosen as the cam shaft center will proportion the cam so that
the pressure angle at a point on the cam profile corresponding to point
P
2
of the displacement diagram will be exactly α
2
.
Any point chosen within the cross-hatched area A as the cam center
will yield a cam whose pressure angles at points corresponding to P
1
and P
2
will not exceed the specified values α
1
and α
2
respectively. If O
1
is chosen as the cam shaft center, the pressure angles on the cam profile
corresponding to points P
1
and P
2
are exactly α
1
and α
2
, respectively.
Selection of point O
1
also yields the smallest possible cam for the given
requirements and requires an offset follower in which e is the offset
distance.
If O
2
is chosen as the cam shaft center, a radial translating follower
is obtained (zero offset). In that case, the pressure angle α
1
for the rise
is unchanged, whereas the pressure angle for the return is changed from
α
2
to α'
2
. That is, the pressure angle on the return stroke is reduced at
the point P
2
. If point O
3
had been selected, then α
2
would remain
unchanged but α
1
would be decreased and the offset, e, increased.
Fig. 12 shows the shape of the cam when O
1
from Fig. 11 is chosen
as the cam shaft center, and it is seen that the pressure angle at a point
on the cam profile corresponding to point P
1
is α
1
and at a point
corresponding to point P
2
is α
2
.
Fig. 11. Finding Proportions of Cam; Offset
Translating Follower
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