The forces on one given screw,
With motion on a second,
In general some work will do,
Whose magnitude is reckoned
By angle, force, and what we call
The coefficient virtual.
Rotation now to force convert,
And force into rotation;
Unchanged the work, we can assert,
In spite of transformation.
And if two screws no work can claim,
Reciprocal will be their name.
Five numbers will a screw define,
A screwing motion, six;
For four will give the axial line,
One more the pitch will fix;
And hence we always can contrive
One screw reciprocal to five.
Screws--two, three, four or five, combined
(No question here of six),
Yield other screws which are confined
Within one screw complex.
Thus we obtain the clearest notion
Of freedom and constraint of motion.
In complex III., three several screws
At every point you find,
Or if you one direction choose,
One screw is to your mind;
And complexes of order III.
Their own reciprocals may be.
In IV., wherever you arrive,
You find of screws a cone,
On every line in complex V.
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