Page 237 - Robot Builders Source Book - Gordon McComb

6.4 Vibrational Transportation 225

acceleration componentry determines the vertical pressure that the body exerts. Obvi-
ously, when A v is positive (directed upwards) the pressure P v can be expressed as

and when the vertical component is negative, we have

The horizontal component A h also becomes positive (rightward) and negative during
the cycle of motion. This component engenders horizontal inertial forces P h which
equal

These forces can be smaller or larger than the frictional force P F. We can now express
the frictional force, through Expressions (6.12) and (6.13), as follows:

Obviously, horizontal displacement of the body relative to the tray will take place when

Analysis of these expressions shows that there are several different possibilities for the
bodies' behavior on the tray. These possibilities can be described qualitatively as
follows:

1. No motion occurs between the body and the tray. This happens when the value
mA h is always smaller than the frictional force.
2. Motion along the tray occurs, because

However, the body does not rebound. It is always in contact with the tray
because

3. Motion along the tray occurs because of both a) condition (6.17) and b)
rebounds during the intervals when A v ^ g and there is no contact between the
tray and the body. Therefore, relative motion of some sort takes place.
4. Relative motion between the tray and the body occurs but the body does not
proceed in any definite direction because the values of the frictional coefficient
are very low. (Balls or rollers on the tray.)

In practice, case 2 is preferable. In this case the body proceeds smoothly along the
tray in the direction shown by the arrow.
Vibrating transporting trays are used because of their simplicity, high reliability,
high transporting speed, simple ways to control this speed, and simple means that are
adequate for stopping the transported bodies (simple mechanical stops are used).
In Chapter 7 we will speak about vibrofeeders and consider the properties of vibro-
conveying in greater detail.
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