<r OO 
in, 
; 
| 
TOOTHED GEARING 387 
The objection to the teeth shown in Fig. 599 is that when at work 
there is a side pressure which tends to push 
the wheels out of gear. To overcome this 
difficulty, the double helical teeth shown in 
Fig. 600 were introduced, and are now 
largely used. To ensure the proper’ bearing 
of the teeth on one another, the shaft of 
one of a pair of wheels having double heli- 
eal teeth should have a slight amount of 
end play. Fia. 600. 
. Exercises XXIII. 
1. A toothed wheel has 95 teeth, whose diametral pitch is } inch. Find the 
diameter of the pitch circle and the circular pitch. 
2. Taking the ordinary proportions for teeth, height above pitch line=0 3p, 
and depth below pitch line=0-4p, where p is the circular pitch, express these in 
terms of the diametral pitch p’. 
3. A wheel A, having 28 teeth, gears with a wheel B, having 35 teeth. How 
teeth on A will come in contact with a particular tooth on B? Also, how 
many revolutions will A make before the same pair of teeth are again in contact ? 
Further, what will the answers be (1) when A has 28 teeth and B 36 teeth, (2) 
when A has 29 teeth and B 35 teeth? 
In the following exercises, 4 to 15, there are given in each two wheels or a wheel and rack 
ingear. Draw, full size, a side elevation of a portion of the pair in gear, in the neighbour- 
hood of the pitch point, sufficient to show four teeth on each completely. Show clearly in 
cach case the path of approach and the path of recess, the are of approach and the are of 
recess, also the maximum obliquities of action during approach and during recess, 
4. Two spur wheels in external contact. Diameters of pitch circles, 10 inches 
and 16 inches, Numbers of teeth, 15 and 24. Cycloidal teeth. Rolling circle, 
5 inches diameter for all curves. 
5. Spur wheel and rack. Diameter of pitch circle of wheel,15 inches. Number of 
teeth onwheel, 20, Cycloidal teeth, Rolling circle, 5 inches diameter for all curves. 
6. Two spur wheels in internal contact. Diameters of pitch circles, 10 inches 
and 20 inches. Numbers of teeth, 20 and 40. Cycloidal teeth. Rolling circle, 
5 inches diameter for all curves. 
7. Same as Exercise 4, but with involute teeth. 
8. Same as Exercise 5, but with involute teeth. 
9. Same as Exercise 6, but with involute teeth. 
10. Two wheels in external contact. Diameters of pitch circles, 10 inches 
and 15 inches. The smaller wheel to have 16 pins ? inch diameter. 
11. Two wheels in internal contact. Diameters of pitch circles, 10 inches and 
30 inches. The smaller wheel to have 16 pins # inch diameter. 
12. Two wheels in internal contact. Diameters of pitch circles, 10 inches and 
30 inches. ‘The larger wheel to have 48 pins }# inch diameter. 
_ 13. Two wheels in internal contact. Diameters of pitch circles, 6 inches and 
12inches. The smaller wheel to have 6.pins }$ inch diameter. 
_ 14 Wheeland rack. Diameter of pitch circle of wheel, 10 inches. Wheel 
has 20 teeth. Rack has pins } inch diameter. 
15. Wheel and rack. Diameter of pitch circle of wheel, 10 inches. Wheel 
has 20 pins } inch diameter. 
16, Design for a spur wheel with cycloidal teeth. Diameter of pitch circle, 
6 feet. Speed, 70 revolutions per minute. Power transmitted, 350 horse-power. 
For strength of teeth use the rule P = 200np?, where P is the driving force at pitch 
circle, nm the ratio of breadth of teeth to pitch, and p the pitch. Take n=2°75. 
Diameter of shaft, 74 inches, enlarged to 84 inches inside the nave of the wheel. 
17. Design for a bevel wheel with cycloidal teeth. Base angle of pitch cone, 30°. 
Mean diameter, 5 feet. Speed, 80 revolutions per minute. Power transmitted, 400 
horse-power. For strength of teeth use the rule P=200np*, where P = driving force 
at mean pitch circle, n= ratio of breadth of teeth to pitch at mean pitch circle, and 
or pitch at mean pitch circle. Take n=3. Wheel to have fourarms of T section. 
Diameter of shaft, 74 inches. Diameter of wheel seat on shaft, 8} inches. 
