Page 109 - Robotics Designing the Mechanisms for Automated Machinery

98 Dynamic Analysis of Drives

where

The complete solution has the following form:

The solution's component s 0, corresponds to the homogeneous case of Equation (3.134)
and is sought in the harmonic form,

Substituting this solution into the corresponding form of Equation (3.134), we obtain

The component Si is the partial solution of the same equation and its shape depends
on the function A Assuming that the external forces acting on the driven mass are a
linear function of time in the form

we must seek s l in an analogous form. Thus,

Substituting Equation (3.136) into Equation (3.134), we obtain

and the complete solution then looks as follows:

For initial conditions, when t = 0, the position of the driven mass 5 = 0, and the initial
speed of the mass s = 0, we have

Finally, we have

For the particular cases when ^ = 0 or « 2 = 0, we obtain from Equation (3.139),
respectively,