Page 90 - Cam Design Handbook

THB3 8/15/03 12:58 PM Page 78

78 CAM DESIGN HANDBOOK

250

200
150

y Acceleration (in/sec) 2 50 10 20 30 40 50 60
100

0

.. –50 Cam rotation (degrees)
–100
–150

–200
–250
(c) Acceleration.

Cycloidal
Modified Sine
Modified Trapezoidal
FIGURE 3.10. Continued

perpendicular to DM. This procedure results in the modified cycloidal curve having a
maximum acceleration about 7 percent lower than that of the basic cycloidal curve.

3.9 DWELL-RISE-RETURN-DWELL MOTION

Now, let us consider the dwell-rise-return-dwell curve, using a combination of curves to
improve the high-speed action. To analyze the action, we shall use the symmetrical
cycloidal curve (Fig. 3.13), although any of the high-speed shapes, such as trapezoidal and
modified trapezoidal, introduce the same problem. A difficulty arises that did not prevail
in the dwell-rise-dwell action, that is, an abrupt change or dip in the acceleration curve
occurs at the maximum rise point. This dip is undesirable, because it produces sudden
inertia loads and vibrations.
In Fig. 3.13, the problem is eliminated by blending a parabolic curve to the cycloidal
curve portions. A modified total curve is produced. Also, a smoother, more desirable
acceleration curve is developed with lower peak accelerations. An alternative solution,
necessitating less mathematical work, is to employ polynomial equations as shown in
Chap. 4.