Page 160 - Mechatronics with Experiments

146 MECHATRONICS
Pressure
angle
X
Axial cam
X
Radial cam
Linear Cycle
guide
bearing
Follower
Cam θ
0°
90° 270°

180°

Eccentricity
FIGURE 3.9: Rotary to translational motion conversion mechanism: cam mechanism.

dwell; that is, rise, dwell, fall, dwell,or rise, fall, dwell. In addition, a cam function may
be designed such that the follower makes single or multiple cycles per revolution of the
input shaft, that is one, two, three, or four follower cycles per input shaft revolution. It is
common to design rise and fall periods of the cam as symmetric. During the dwell periods,
the follower is stationary. Therefore, during dwell period the follower position is constant,
and speed and acceleration are zero. If symmetric cam functions are used for rise and fall
periods, then we are only concerned with the cam function design for the rise period.
A cam profile is defined by the following relationship,

x = f( ); 0 < < 2 (3.85)

where x is the displacement of the follower, and is the rotation of the input shaft. The
cam function is periodic. The cam follower motion repeats for every revolution of the input
shaft.
In addition to selecting an appropriate cam function, there are three other important
parameters to consider in cam design (Figure 3.7):
1. Pressure angle: measured as the angle between the follower motion axis and the
axis perpendicular to the common tangent line at the contact point between cam and
follower (Figure 3.7). A cam should be machined such that the pressure angle stays
◦
less than about 30 in order to make sure the side loading force on the follower is not
too high.
2. Eccentricity: the offset distance between the follower axis and cam rotation axis in
the direction perpendicular to the cam motion. By increasing eccentricity, we can
reduce the effective pressure angle, and hence the side loading forces on the follower.
However, as the eccentricity increases, the cam gets larger and less compact.
3. Radius of curvature: the radius of the cam function curvature along its periphery. The
radius of curvature should be a continuous function of the angular position of the
cam input shaft. Any discontinuity in the radius of curvature is essentially reflected
as a non-smooth cam surface. In general, the radius of curvature should be at least
2 to 3 times larger than the radius of the follower. The main considerations are the
continuity and ability of the follower to maintain contact on the cam at all times.