Fig. 150.
This, however, is not absolutely necessary so long as the joints are so arranged as to occur in the middle of tooth spaces, and not in the thickness of the tooth. This sometimes necessitates that the rim sections have an unequal length of arc, in which event the pattern is made for the longest segment, and when these are cast the teeth superfluous for the shorter segments are stopped off by the foundry moulder. This saves cutting or altering the pattern, which, therefore, remains good for other wheels when required.
When the teeth of wheels are to be cut in a gear-cutting machine the accurate spacing of the teeth is determined by the index plate and gearing of the machine itself; but when the teeth are to be cast upon the wheel and a pattern is to be made, wherefrom to cast the wheel the points of division denoting the thickness of the teeth and the width of the spaces are usually marked by hand. This is often rendered necessary from the wheels being of too large a diameter to go into dividing machines of the sizes usually constructed.
To accurately divide off the pitch circle of a gear-wheel by hand, requires both patience and skilful manipulation, but it is time and trouble that well repays its cost, for in the accuracy of spaces lies the first requisite of a good gear-wheel.
It is a very difficult matter to set the compasses so that by commencing at any one point and stepping the compasses around the circle continuously in one direction, the compass point shall fall into the precise point from which it started, for if the compass point be set the 1⁄200th inch out, the last space will come an inch out in a circle having 200 points of divisions. It is, therefore, almost impossible and quite impracticable to accurately mark or divide off a circle having many points of division in this manner, not only on account of the fineness of the adjustment of the compass points, but because the frequent trials will leave so many marks upon the circle that the true ones will not be distinguishable from the false. Furthermore, the compass points are apt to spring and fall into the false marks when those marks come close to the true ones.
Fig. 151.
In [Fig. 151] is shown a construction by means of which the compass points may be set more nearly than by dividing the circumference of the circle by the number of divisions it is required to be marked into and setting the compasses to the quotient, because such a calculation gives the length of the division measured around the arc of the circle, instead of the distance measured straight from point of division to point of division.
The construction of [Fig. 151] is as follows: p p is a portion of the circle to be divided, and a b is a line at a tangent to the point c of the circle p p. The point d is set off distant from c, to an amount obtained by dividing the circumference of p p by the number of divisions it is to have. Take one-quarter of this distance c d, and mark it from c, giving the point e, set one point of the compass at e and the other at d, and draw the arc d f, and the distance from f to c, as denoted by g, is the distance to which to set the compasses to divide the circle properly. The compasses being set to this distance g, we may rest one compass point at c, and mark the arc f h, and the distance between arc h and arc d, measured on the line a b, is the difference between the points c, f when measured around the circle p p, and straight across, as at g.