Page 116 - Robotics Designing the Mechanisms for Automated Machinery

3.7 Drive with a Variable Moment of Inertia 105

FIGURE 3.29 Variable moment of inertia caused by changing geometry of
the system: a) Cylindrical manipulator; b) Indexing table with a movable
body. (Here Coriolis acceleration occurs.)

Thus,

and

Integrating this expression further with respect to time, we obtain the relationship
between the angle of rotation and time:

From Equation (3.171) it follows that

Obviously, for the layout shown in Figure 3.28b an expression of the same form can be
derived, the only difference being that in place of moments of inertia we substitute
masses; in place of angular speeds, translational speed; in place of angle of rotation,
translational displacement; and in place of torques, forces. Thus, the assumed depen-
dencies describing the changes in the mass m(f) and the driving force F( V) are obtained
in a form analogous to that of Equation (3.166) and we have