It is obvious, then, that it would be more in accordance with the requirements to proportion the amount of clearance to the diameter of the wheel, so as to keep the clearance as small as possible. This will possess the advantage that the teeth will be stronger, it being obvious that the teeth are weakened both from the loss of thickness and the increase of height due to the clearance.
It is usual in epicycloidal teeth to fill in the corner at the root of the tooth with a fillet, as at c, d, in [Fig. 143], to strengthen it. This is not requisite when the diameter of the generating circle is so small in proportion to the base circle as to produce teeth that are spread at the roots; but it is especially advantageous when the teeth have radial flanks, in which case the fillets may extend farther up the flanks than when they are spread; because, as shown in [Fig. 47], the length of operative flank is a minimum in teeth having radial flanks, and as the smallest pinion in the set is that with radial flanks, and further as it has the least number of teeth in contact, it is the weakest, and requires all the strengthening that the fillets in the corners will give, and sometimes the addition of the flanges on the sides of the pinion, such gears being termed “shrouded.”
The proportion of the teeth to the pitch as found in ordinary practice is given by Professor Willis as follows:—
| Depth to pitch line | 3⁄10 | of the | pitch. |
| Working depth | 6⁄10 | „ | „ |
| Whole depth | 7⁄10 | „ | „ |
| Thickness of tooth | 5⁄11 | „ | „ |
| Breadth of space | 6⁄11 | „ | „ |
The depth to pitch line is, of course, the same thing as the height of the addendum, and is measured through the centre of the tooth from the point to the pitch line in the direction of a radial line and not following the curve of tooth face.
Referring to the working depth, it was shown in [Figs. 42] and [44] that the height of the addendum remaining constant, it varies with the diameter of the generating circle.
Fig. 144.
From these proportions or such others as may be selected, in which the proportions bear a fixed relation to the pitch, a scale may be made and used as a gauge, to set the compasses by, and in marking off the teeth for any pitch within the capacity of the scale. A vertical line a b in [Fig. 144], is drawn and marked off in inches and parts of an inch, to represent the pitches of the teeth; at a right angle to a b, the line b c is drawn, its length equalling the whole depth of tooth, which since the coarsest pitch in the scale is 4 inches will be 7⁄10 of 4 inches. From the end of line c we draw a diagonal line to a, and this gives us the whole depth of tooth for any pitch up to 4 inches: thus the whole depth for a 4-inch pitch is the full length of the horizontal line b c; the whole depth for a 3-inch pitch will be the length of the horizontal line running from the 3 on line a b, to line a c on the right hand of the figure; similarly for the full depth of tooth for a 2-inch pitch is the length of the horizontal line running from 2 to a c. The working depth of tooth being 6⁄10 of the pitch a diagonal is drawn from a meeting line c at a distance from b of 6⁄10 of 4 inches and we get the working depth for any other pitch by measuring (along the horizontal line corresponding to that pitch), from the line of pitches to the diagonal line for working depth of tooth. The thickness of tooth is 5⁄11 of the pitch and its diagonal is distant 5⁄11 of 4 (from b) on line b c, the thickness for other pitches being obtained on the horizontal line corresponding to those pitches as before.