Page 473 - Cam Design Handbook

THB14 9/19/03 7:58 PM Page 461

SPECIAL CAM MECHANISMS 461

FIGURE 14.7. Eccentric circle cam—translating roller follower.

y = E Ecos e + M cos cos t - M. (14.2)
t
-
e
Differentiating gives velocity
dt
v = Ew sin e - M sin t . (14.3)
dt
Inspection of the figure shows the angular relationship
E
e
sint = = sin . (14.4)
M
Differentiating and solving yield
dt Ew cos e
= . (14.5)
dt M cos t
Substituting Eq. 14.5 in Eq. (14.3) gives the follower velocity, and differentiating to find
the acceleration we have,

e
E (sin
r = w e - cos tan ) t (14.6)
2
Ê E cos e ˆ
˙˙ y = Ew 2 cos - + sin tant . (14.7)
e
e
Ë M cos t ¯
3
Equations (14.2), (14.6), and (14.7) provide the characteristics of the complete
follower motion. In addition, we observe that angle t always equals the pressure angle