Page 80 - Robotics Designing the Mechanisms for Automated Machinery

3.1 Mechanically Driven Bodies 69

FIGURE 3.8 Speed versus displacement for an
oscillating body influenced by dry friction.

and

For the case k = 0, it follows from Equation (3.25) that

Thus, Equation (3.26) coincides with the Formula (3.18) which describes the same sit-
uation k = 0 (as a result of n = 0 in this case).
Let us consider the case in which the resisting force F shown in Figure 3.4b) is con-
stant. Such a case can arise when, for instance, the force of gravity acts on the mass
driven by the spring. This is the situation which occurs in Figure 2.16 where the spring
9 lifts the lever 6, the cutter 7, and the armature of the magnet 5. The following equa-
tion describes this situation:

The solution of this equation consists of two components:

where, x' is the solution of the homogeneous equation and therefore has the form
given in Equation (3.15), while the partial solution x" must be some constant value
jc" = D = const.