Page 94 - Robotics Designing the Mechanisms for Automated Machinery

3.3 Electric Drives 83

When there is no resistance torque, i.e., a v = a 2 = 0 we obtain

For the case when a^ - 0 we derive from Expression (3.65) the following formula:

Expression (3.64) allows us to find the dependence of the rotation angle 0 on time. For
this purpose we must rewrite this expression as follows:

Integrating this dependence termwise, we obtain:

and

Now for the particular case when oc 2 - 0:

For

For

In Figure 3.20 the graphic representation of this dependence is shown to be com-
posed of three components. This graph provides us with a tool for determining the
time ^ needed to achieve rotation for the angle 0j.
Let us consider the case where the drive is supplied by a series DC motor with the
characteristics given by Expression (3.47). Because of analytical difficulties, we will