Page 117 - Robot Builders Source Book - Gordon McComb

106 Dynamic Analysis of Drives

and the final result for displacement s(f) will have the form

Case 2 (Figure 3.29a) and b))

Analyzing these systems, we must also take into consideration Expression (3.165).
Thus the equation of motion describing the rotation of the column (Figure 3.29a)
appears as follows:

where
m = the mass moving along the beam, during the rotation of the column,
co(t) = the angular speed of the column,
r(t) = the position of the mass m along the beam,
T(co) = the column driving torque.
Let us suppose that:

Substituting the chosen functions (3.176) into Equation (3.175) and rearranging the
equation, we obtain

or, rewriting this equation, we arrive at the form

Denoting:

we can rewrite Equation (3.178) in the form

For this equation the solution is sought as

The integral in the latter expression cannot be solved in a nonnumerical way.
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