Page 182 - Cam Design Handbook

THB6 8/15/03 2:40 PM Page 170

170 CAM DESIGN HANDBOOK

y

Radius of
curvature r C
Tangent

p Normal

x
FIGURE 6.8 Curvature of a curve.

The radius of curvature is positive (+) for convex cam surfaces and negative (-) for
concave cam surfaces (see Fig. 6.9).

6.4.2 Undercutting of Cam-Roller Follower

Undercutting is a phenomenon in which the constructed cam profile has a faulty shape.
Cam undercutting is dependent on the radius of curvature, the follower acceleration, and
the size of the cam. The easiest way to avoid undercutting is to make a larger cam. To
investigate for undercutting one must find the radii of curvature at every point in the cam
profile. For concave cams using roller followers the acceleration at the initial point of rise
generally controls. In convex profiles utilizing either the roller or flat-faced followers the
maximum negative acceleration controls.
Let
r k = radius of curvature of pitch curve, in
r c = radius of curvature of cam profile, in
R r = radius of follower roller, in

Figure 6.10 shows the different possibilities of roller action. At point (a) on the figure
the concave segment of the curve has proper action where the radius of curvature
r k > 0. At point (b) on the convex segment curve we have a condition r k = R r and
the center of the roller radius R r moves on the pitch curve about a single point on the
cam profile. A sharp point is produced which is not acceptable because of excessive
stresses.