Page 81 - Robotics Designing the Mechanisms for Automated Machinery

70 Dynamic Analysis of Drives

Substituting x" = D into Equation (3.27), we obtain

Thus, Equation (3.28) can be rewritten in the form

For initial conditions t= 0, x = x 0, and x = 0, Solution (3.30) gives

Naturally, the initial deformation of the spring^ at the beginning of the motion must
include the deformation caused by the force F which entails the appearance of the
initial coordinate x 0 of the mass location.
The above-considered spring-driven mechanisms can also be rotating in nature,
as in Figure 3.9. Equation (3.27), rewritten in terms of angular motion, takes the form

where
I- the moment of inertia of the rotating body,
CQ = stiffness of the spring lumped to the angular displacement,
T= resisting torque T= Fr,
r = the radius on which the force F acts, and
0 = angle of rotation.
We should not forget that the dimensions here are different from those in Equa-
tion (3.27). The solution of Equation (3.32) has a form analogous to that of Equation
(3.30), as follows:

FIGURE 3.9 Rotating motion caused by a spring.