536
�KINEMATICS OF MACHINERY.
�accompany the use of toothed-wheels. We have already seen
( 43 to 50) that they may be employed with pair-closure alone,
in such a way, for instance, as is represented in Fig. 366.
Taking first toothed- wheels for which the centroids are circular, we may include them all under the symbol H z , H z or (H z ), which stands for a pair of hyperboloidal toothed- wheels, and consider
K z) K z or (JQ the pair of bevel wheels, and C z , C z or (<7 Z ) do. spur wheels
as special cases under this general class.
The teeth of these wheels are in general formed as ruled surfaces of the same character as the axoids for the motion which they transmit ; they may, however, be made helical, and in that case If z becomes H t . The most general class formed in this way has the higher screw 8 for its tooth form, it would therefore be written H;,H; or (JI~). As special cases under this class we have
(JT.) conic or bevel screw-wheels, and ((7s) cylindric screw-wheels.
The pair of elements 8, 8 or ($,), represented in Fig. 367, is included in the last subdivision. For this pair the symbol (C t ) is generally pre- ferable. The symbol (8,) is, however, valuable, in relation to its higher form ($,) as pointing out that the general closed screw-pair (8) may be looked at as a subdivision of the general class of reciprocally enveloping screws.
We have also to distinguish other and higher classes of toothed-wheels, those namely which have non-circular centroids. Of these we have the general cases
(fii) and (JHJ),
which include as special cases (JQ and (X;), (6 Y Z ) and (Q). The forms (H s ), (JQ, etc., may also be considered as subdivisions under (H;), (K ; ), etc.
The intermediate forms Hl,K z (hyperboloidal face-wheel with bevel wheel (Fig. 36) and H Z) S Z (Fig. 365) may be included under
��FIG. 367.
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