Page 100 - Robotics Designing the Mechanisms for Automated Machinery

3.4 Hydraulic Drive 89

Let us now try to define the operation time of the piston in the hydromechanism
under consideration. For this purpose, we will rewrite Equation (3.100) in the form

where Vis the speed of the mass.
Let us assume that A can be taken as a constant value. Then Equation (3.101) can
be rearranged as

Integrating Equation (3.102), we obtain

where C is the constant of the integration.
The initial conditions are that when t = 0, V = 0; thus, C = 0, and we can finally write

where

From Equation (3.103) we obtain the following expression for the speed:

From equation (3.104) we derive an expression describing the dependence s(£). We
rewrite correspondingly:

and

Now, finally, we obtain