Page 196 - Robotics Designing the Mechanisms for Automated Machinery

184 Feedback Sensors

Thus, we can express the gas velocity within each nozzle as it is accepted for dropping
liquids:

Substituting Expressions (5.16) into Equation (5.14), we obtain

From Equation (5.17) and the second assumption it follows that

The area/j is obviously

We assume that the area^ can be calculated for the model given in Figure 5.12b) in a
relatively simple way. In this scheme 1 is an enlarged diagram of nozzle II (see Figure
5.12a)) and 2 is the surface of an element, the position of which is to be measured. The
distance between this surface and the face of the nozzle is s. Experiments show that,
if it is true that

or

then for f 2 we can use the formula for the area of the side of a cylinder, namely:

Substituting (5.21) and (5.19) into (5.18) we obtain

The latter formula shows the dependence of the pressure h on the distance s. Below
are shown some examples of the use of pneumatic measurements of distances and
linear dimensions. The main advantages of this kind of sensor are:
1. The possibility of carrying out the measurements without direct mechanical
contact between the sensor and the surface of the checked element, if necessary.
2. The relatively high sensitivity of this method, which is about 0.001 mm or even
better.
These advantages permit, for instance, carrying out the checking of dimensions
during rotation of the measured part, saving time and money.