Page:The Kinematics of Machinery.djvu/285

 CONTRACTED FORMULAE. 263

we should have had to substitute for Z. the symbol f. The rest of the formula is clear from what has gone before. Put into words, the whole stands thus : " Kinematic chain consisting of two unequal revolutes connected by an endless band touching them externally, each being provided with a con-axial cylindric spindle, and the two spindles working in parallel bearings in a stationary supporting piece."

The simple spur-gearing of Fig. 183 is written,

C+ ... | ... Ct, C+ ... I ... CtO- ...|| ... C-

The links coming first in the formula are the two spur-wheels with their shafts, the last is the (fixed) bar carrying the bearings. The annular gear of Fig. 184 is written :

C+...\...Ct,C7...\...C+C- ...||... C-

The first link is here the wheel a having external teeth, the second is the annular wheel b, and the third is again the bar c, the latter being supposed fixed.

59. Contracted Formulae.

If once the separation of a chain into links and the special ex- amination of the latter has been completed so that they may be assumed to be already known the formula or symbolic description of the chain may be in many cases greatly shortened. There are several possible forms of contraction, which we shall examine in order.

Firstly, in the case of the lower pairs, and of some others in which the partner elements have the same name-symbol, one letter may frequently be made to suffice for a pair of elements if it be used along with some distinguishing mark. For this purpose a paren- thesis can be used, so that we may employ as contractions :

(S) for the twisting pair

(C) turning CtC-

(P) sliding PP~

(C z ) for a pair of spur wheels C Z) Cz

(*i) bevel KK