Page 43 - Cam Design Handbook

THB2 8/15/03 12:48 PM Page 31

BASIC CURVES 31

Therefore, the area of the acceleration curve for any cam has an area of positive action
(+) equal to the area of the negative action (-). This observation could aid the designer
in developing the optimum cam acceleration curve shape.
˙˙˙ y
• The follower jerk y¢≤ or shall have the smallest values. Note that with industrial cams
the jerk curve is not frequently of design control since the production tolerance is about
±0.001 inch. The jerk curve is sensitive to much smaller deviations. However, in the
automotive cam field the cam operates over a very small distance, requiring higher tol-
erance of about ±0.0001 inch or better. In this case the jerk curve data is pertinent.

EXAMPLE Given the displacement diagram of a pitch curve in Fig. 2.1a, in which the
1
follower has a total rise of / 2 in. in 0.1sec of cam rotation and falls in an additional 0.08
sec, plot the velocity curve and determine the velocity and acceleration after the initial
0.08sec of cam rotation by applying the graphical-slope differentiating method.
Solution At the 0.08sec point, we draw a tangent to the displacement curve. Caution is
suggested. This is the instantaneous slope of the curve which equals the velocity.
˙ y = dy dt
= distance ab distance bc
. 0371
=
. 008
= . 464 ips in a positve direction

Note that the distances ab and bc were arbitrarily chosen for reasonable measurement
accuracy. In the same manner, other velocity points may be found and the curve plotted
as in Fig. 2.1b. Here is the acceleration at 0.08sec:

˙˙ y = ˙ dy dt
= distance de distance ef
15 .8
=-
. 008
=-198 in sec 2
Again, the distances are chosen arbitrarily. Note, the acceleration is negative because the
follower is reversing its acceleration in a minus, downward direction. Also, mathemati-
cally speaking, the slope is to the left (second quadrant), which means a negative value.
The jerk values may be approximated in the same manner by plotting the acceleration
curve and finding the slopes.

2.3 BASIC CURVE CLASSIFICATION

In this chapter we present some basic curves of the DRD type and their kinematic
relationships.
In design, the first step is to sketch a time chart (discussed in Chap. 1). Then the basic
cam curve may be chosen to satisfy the cam-follower requirements.
The basic curves of the rise-fall displacement diagram are primarily of two families:
the simple polynomial and the trigonometric.