Page 102 - Robotics Designing the Mechanisms for Automated Machinery

3.5 Pneumodrive 91

Supposing, for example, that A(s) = a^ + a 2s; we seek the solution y l in the form

Substituting this expression into Equation (3.105) and comparing the coefficients on
both sides of the equation, we find that

in in,
For initial conditions t= 0 and V= 0, we also have y= 0. (Remember: y = 2V.V}. This
condition gives the following expression for Y:

Finally, the complete solution can be written as

Substituting back the meaning of y we obtain

3.5 Pneumodrive

In general, the dynamics of a pneumomechanism may be described by a system
of differential equations which depict the movement of the pneumatically driven mass
and the changes in the air parameters in the working volume. The work of a pneu-
momechanism differs from that of a hydraulic mechanism in the nature of the outflow
of the air through the orifices and the process of filling up the cylinder volume. Let us
consider the mechanism for which the layout is given in Figure 3.23. Let us suppose
the processes of outflow and filling up are adiabatic, and the pressure p r in the receiver
1 is constant. From thermodynamics we know that the rate of flow of the air through
the pipeline 2 may be described by the formula

where
G = the rate of flow,
a = coefficient of aerodynamic resistance,
2
F p = cross-sectional area of pipe 2 (m ),
p r = air pressure in the receiver 1,
T r = absolute temperature of the air in the receiver,