Page 77 - Robotics Designing the Mechanisms for Automated Machinery

66 Dynamic Analysis of Drives

FIGURE 3.3 Model of gravitation drive on
an inclined tray.

which resists the movement along the tray). The driving force F in this case can be
found from the known formula

The equilibrium equation thus has the form

From Equation (3.9) we obtain

The time t required to displace a part through a distance L equals

[Note: When sin <f> =/cos 0 or/= tan 0, no movement will occur. The time tends to infi-
nitely long values.]
Here we analyze the movement of a mass driven by a previously deformed spring.
The layout of such a mechanism is shown in Figure 3.4a). A spring as a driving source
is described by its characteristic shown in Figure 3.5. This characteristic shows the
dependence of the force P developed by the spring on the values of the deformation
jc (in both the stretched and compressed modes). When this dependence is linear, as
shown in Figure 3.5, parameter c, which is the stiffness of the spring, is constant for
this case. In other words, stiffness of the spring is a proportionality coefficient tying
the deformation of the spring to the force P it develops. It also defines the value of the
slope of the characteristic and can be described as

and

FIGURE 3.4 Spring-driven body: a) Without and
b) With resisting force F.