Internal Gears.—For tooth curves within the pitch lines, divide radius of each wheel by any number not greater than radius of pinion, and look in the table under “flanks.” For curves outside pitch line use lower line of table; or, divide radii by any number and look under “faces.” In applying instrument draw tangents at middle and side of space, for internal teeth.
Involute Teeth.—For tabular values look opposite “Pinion,” under proper number of teeth, for each wheel. Draw setting tangent from “base circle” of involute, at middle of tooth. For this the instrument gives the whole side of tooth at once.
In all cases multiply the tabular value by the pitch in inches.
Bevel-Wheels.—Apply above rules, using the developed normal cone bases as pitch lines. For right-angled axes this is done by using in place of the actual ratio of radii, or of teeth numbers, the square of that ratio; and for number of teeth, the actual number multiplied by the square root of one plus square of ratio or radii; the numerator of ratio, and number of teeth, belonging to wheel sought.
When the first column ratio and teeth numbers fall between those given in the table, the tabular values are found by interpolating as seen in the following examples:
EXAMPLES OF TABULAR VALUES AND SETTING NUMBERS.
Take a pair of 16 and 56 teeth; radii 5.09 and 17.82 inches respectively; and 2 inches pitch.
| Kind of Gearing. | Number of Teeth. | } | Kind of Flank. | Ratio Radii. | First Column Ratio. | Tab. Val. | ||||||
| Flank. | Face. | Flank. | Face. | |||||||||
| Epicycloidal, | } | Small | Radial | . | 29 | Radial | . | 29 | .. | .44 | ||
| Radial Flanks | Large | Radial | 3. | 5 | Radial | 3. | 5 | .. | .44 | |||
| Epicycloidal, | } | Small | Curved 2 deg. | . | .29 | 2 | . | 87 | .63 | .36 | ||
| Curved Flanks. | Large | Curved 3 deg. | } | 3. | 5 | 3 | 7. | .82 | .30 | |||
| Epicycloidal, | } | Small | “Sets,” Divide | 2. | 2 | 2. | .63 | .26 | ||||
| Interchange’bl. | Large | Radii by 2.55 | 7. | 7 | 7. | .40 | .30 | |||||
| Epicycloidal, | } | Pinion | Curved 2 deg. | 2 | Pinion | .63 | .44 | |||||
| Internal. | Wheel | Int. face 7 deg. | 3. | 5 | Pinion | 7 | [8] | .84 | .39 | |||
| Epicycloidal, | } | Pinion | Curved 2 deg. | 2 | Pinion | .63 | .44 | |||||
| Rack & Pinion. | Rack | Parallel | Parallel | Rack | .. | .31 | ||||||
| Involute | } | Small | Face and Flank | Pinion. | .44 | |||||||
| Gearing. | Large | One Curve | Pinion. | .84 | ||||||||
[8] The face being here internal, the tabular value is to be found under “flanks.” If bevels, use ratio radii .082 and 12.25; and teeth numbers 16.6 and 203.8 respectively.
Walker’s Patent Wheel Scale.—This scale is used in many manufactories in the United States to mark off the teeth for patterns, wherefrom to mould cast gears, and consists of a diagram from which the compasses may be set to the required radius to strike the curves of the teeth.