Page 513 - Cam Design Handbook

THB14 9/19/03 7:59 PM Page 501

SPECIAL CAM MECHANISMS 501

14.28.4 Basic Spiral Cam Constants

Very often it is necessary to control the contours in which a multiple of q 0 is a function
of a multiple of q i. Then it is necessary to compare scales of values. Let the functions
q q
R = i , S = 0 . (14.31)
K K
i 0
Differentiating
dq i = K , dq 0 = K (14.32)
dR i dS 0
where K i and K 0 are arbitrary constants for each of the curves. Dividing
dq 0 = K dS = K 0 gR (14.33)
0
¢().
dq K dR K
i i i
Equation (14.26) gave q o = f(q i); it is now replaced by S = g(R). Substituting Eqs. (14.29)
and (14.30) give the radii of the two contacting cams
c
r = e in (14.34)
0 K
1+ 0 gR
¢()
K i
K
¢()
c e 0 gR
r = K i in. (14.35)
i K
¢()
1 + 0 gR
K i
Equations (14.31), (14.34), and (14.35) yield all the information necessary to construct
any cam fulfilling the relation in which g¢(R) does not equal zero. For information
on fabrication and cutter location, the reader is referred to the excellent discussion by
Hannula (1951).
EXAMPLE It is desired to measure the temperature of a fluid A indirectly by (1) meas-
uring the saturated vapor pressure exerted by another fluid B in a closed system subject
to fluid A, and (2) then converting this pressure measurement into a linear temperature
scale. The saturated vapor pressure corresponding to the temperature has been found to
be of form
P =10 e 6 t m ( t m +470 ) .

It is further assumed that this pressure can be converted to a uniform angular rotation of
a shaft by means of a Bourdon tube or similar device. The range of pressure from 10psi
to 60psi will produce a 45.5° movement of the driver cam, and the full-scale range of
temperatures (0° to 200°F) will be linear over a 30° span.

Solution The center distance between the cams is chosen as 3in, since this is the
largest size that is practical within the space limitations. In the equation for the vapor
pressure,
(
P = and 10 e 6 t m t +470 ) = ().
S
g R
m