Page:The Kinematics of Machinery.djvu/294

 272 KINEMATICS OF MACHINERY.

here without any general qualitative meaning there is no special connection between the symbols and the links for which they stand. The only direction in which they have a partly general character is in their alphabetic sequence their order, that is, may be not without significance. Where possible we may begin with a at some specially distinctive link, such as the crank in the case supposed, and so greatly facilitate the recollection of the meaning agreed on for the symbols. The applications of this contracted notation, as we shall find in the sequel, prove it to be of the greatest value.

Our method of symbolization, lastly, allows a further and most useful piece of information to be brought into the formula. It is frequently important to indicate that link of the chain to which the driving effort is applied, or through which the mechanism is moved. For it is evident that there is an immense difference between two mechanisms otherwise the same if one be driven by an effort applied to the link a and the other by an effort applied to b. We had a striking example of this in the mechanism of the water-wheel and the lift-wheel. Both would be indicated by the symbol ( C' C x \ F" x ) c, while the transmission of motion in them would be essentially different.

It becomes evident on looking into this matter that this formula is of the nature of a general or indeterminate formula for both mechanisms, which it must be our object to turn into a special or determinate formula for each of them. We may do this, and supply the information that is wanted, by putting the symbol for the driving link as a denominator in the exponent. The latter will then show the fixed link only in the general formula, but in the special formula it will be fractional, its numerator indicating the fixed, and its denominator the driving link. The choice of the fractional form is justified by the analogy with the symbols for force- and chain-closures which were fixed in 57.

Thus for example the mechanism (C") d, if the crank be the

driving link, will be written (C" 4 ')r, in words " C parallel four on d by a," the latter part being a contraction for "placed on d, driven by a" The same mechanism, if driven by the lever, has

for its special formula (C" 4 ')c ; the general formula (C") d being of course common to both mechanisms. The water-wheel will