Page:The Kinematics of Machinery.djvu/278

 256 KINEMATICS OF MACHINERY.

= equal, >> greater than, < less than, oo infinite ; / crossed obliquely ; -|~ crossed at right angles ; ^ equal and con- axial, ^ equal and parallel ; is coincident;
 * coiiaxial, || parallel, Z. oblique, _L normal ;

D conplane, lying in the same plane, Z. anti-parallel (in a quadrilateral),

^ isosceles, or having adjacent arms equal (in a quadri- lateral).

The relations expressed by these signs may exist either between the elements of a pair or the links of a chain. In the former case the comma between the two elements is omitted, and the symbol itself is printed in a smaller type than in the latter.

If a hollow cylinder be paired with a geometrically equal solid cylinder they are equal and con-axial, so that the comma would have to be replaced by the sign 4=- If however such bodies, being equal, are to be paired, they must also by necessity be con-axial, so special indication of that relation may be omitted without any loss of distinctness, and we may write the pair Ct^~. If this be a closed turning-pair, the conditions as to the prevention of cross-motions by a proper sectional profile ( 15) must be fulfilled. We shall here always presuppose that two elements, the symbols for which are connected by the sign for pairing, form a closed pair, unless the contrary be expressly stated. We shall see further on that in cases where they are not closed the notation of the chain itself always makes it possible to do this. The three lower pairs, then, twisting pair, turning pair, and sliding pair, have for their symbols :

The curved discs in the triangular, quadrilateral, etc., hollow prisms, (Chap. Ill), can be indicated generally by the formula C+,P- ; they fall therefore in one and the same class of pairs. With respect to the simple turning pair, Rt R~, in which the most various profile forms may be used so long as the pair-closure remains, it will be noticed that as far as the relative motions of its elements are concerned it does not differ from the closed cylinder pair CtC~. In most cases it is therefore allowable to write C+C~, instead of B R~. The idea is somewhat simpler, the cylinder instead