The ntill-lines which are at a given distance r from a point 0 of the central axis will therefore form one system of generators of a hyperboloid of revolution; and by varying r we get a series of such hyperboloids with a common centre and axis.
If two such W2 0 - - hyperboloids E, F, equal or E T unequal, be placed in the closest possible contact, as in fig.
The motion of two such hyperboloids, turning in contact with each other, has hitherto been classed amongst cases of rolling ~ contact; but that classification is not strictly correct, for, although the corn ponent velocities of a pair of points of G contact in a direction at right angles --- to the line of contact are equal, still, - F as the axes are parallel neither to each - other nor to the line of contact, the velocities of a pair of points of contact FIG have components along the line of contact which are unequal, and their difference constitutes a lateral sliding.
The directions and positions of the axes being given, and the required angular velocity ratio, the following construction serves to determine the line of contact, by whose rotation round the two axes respectively the hyperboloids are generated: In fig.
~ A pair of thin frusta of a pair of hyperboloids are used in practice to communicate motion between a pair of axes neither parallel nor intersect- FIG.
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