Page 263 - Robot Builders Source Book - Gordon McComb

7.5 Feeding of Parts from Bins 251

FIGURE 7.25c) Relative body-tray displacement in
comparison with the bowl oscillations.

A solution for this equation corresponding to the problem E7-1 made in MATHE-
MATICA language is shown below. (To make the solution easier for the computer we
propose to make a following substitution:

f2=x"[t]-8705.5* Sin[314* t]+342+
(-2777.3* Sin[314* t]+5876.4)* Tanh[5* x'[t]]
y2=NDSolve[{f2==0,x[0]==0,x'[0]==0},x[t],{t,0,.06},
MaxSteps->1500]
j2=Plot[Evaluate[x[t]/.y2],{t,0,.06},
AxesLabel->{"t","x"},GridLines->Automatic]
Expressions (7.33) and (7.34) permit calculating the accelerations that cause move-
ment of the item on the tray. When the acceleration S of the tray exceeds S' cr the item
will move up the groove. When S is greater than S cr the movement will be downward
in the tray. By substituting N= 0 into the equations, we calculate the acceleration S
where rebound of the item occurs:

It follows from these expressions that, to obtain movement up the groove without
bouncing (this is important for maintaining orientation of the parts), the acceleration
S must meet the requirements

Vibrofeeders possess certain advantages which explain their widespread use for
automatic feeding. The advantages are:
• Motion of the parts along the tray does not depend on the masses. This means
that, when the device is tuned appropriately, small and large items move at the
same speed.
TEAM LRN