Page:The Kinematics of Machinery.djvu/476

 454 KINEMATICS OF MACHINERY.

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Levers, Cranks, Connecting rods.

Levers, whether simple or compound, are kinematic links furnished with pins about which they can swing (see p. 284). The simple lever is one like the link c of the chain ((7J), of which the formula is C + ... \\ ...C + . The compound lever is a compound link formed from the simple one, such, for example, as is represented by the formula

C+ ...II ( ^ + . 11 (... C+

The crank is also a link of the form C + ...\\...C +, but is so arranged that it can turn completely round its pin or shaft ; it corresponds exactly, that is, to the link a of the chain (C") or ((7'g'P- 1 -). The connecting-rod, lastly, is also a link formed of two cylindric elements, generally in the form C~ ...\\...C~. It cor- responds to the coupler b in the trains ((7 4 ) d and (OgP- L ) d . In its kinematic form, therefore, it does not differ from the bedplate Fig. 304 in 12.

We have here, therefore, a series of links before us, which while they are constructively very different, are kinematically precisely similar, and owe their different characteristics entirely to their position in the chain. The compound lever, too, is exactly similar to the compound bedplate ( 112) in which the element C is used in precisely the same relative positions.

118 - Crossheads and Guides,

The common crosshead is simply the link c, the " block," of the chain (C^P-^. It has the formula (7...J....P. The guides in which it works are formed in many different ways. They constitute the element of the pair 4 which is carried by the frame d in the train (C; / P J -) d, Fig. 318, and generally have the form P~, although sometimes they are also made P +. This prism is shown in the slide-bars D D of Fig. 319, where also C is the crosshead, the