Example.- Suppose a screw is required to he cut containing 25 threads in an inch, and the leading screw, as before, having two threads in an inch, and that a wheel of 60 teeth is fixed upon for the end of the spindle, 20 for the pinion in contact with the screw-wheel, and 100 for that in contact with the wheel on the end of the spindle; required the Dumber of teeth in the wheel for the end of the leading screw.

25 ÷ 2 = 12.5, and 60 x 12.5 X 20 / 100 = 150 teeth.

Or suppose the spindle and screw wheels to be those fixed upon, also any one of the stud-wheels, to find the number of teeth in the Oilier.

60 x 12.5 / 150 X 100 = 20 teeth, or 60 x 12.5 X 20 / 150 = 100 teeth.

Table of Change Wheels for Screw-cutting; the leading Screw being ½ inch pitch, or containing 2 threads in an inch.

Number of threads in inch of screw.

Numb. of teeth in

Lathe spindle-wheel.

Leading screw-wheel.

1

80

40

1¼

80

50

1½

80

60

1¾

80

70

2

80

90

2¼

80

90

2½

80

100

2¾

80

]10

3

80

120

3¼

80

130

3½

80

140

3¾

80

150

4

40

80

4¼

40

85

4½

40

90

4¾

40

95

5

40

100

5½

40

110

6

40

120

6½

40

130

7

40

140

7½

40

150

8

30

120

Number of threads in inch of screw.

Number of teeth in

Lathe spindle-wheel.

Wheel in contact with spindle-wheel

Pinion in contact with screw-wheel.

Leading screw-wheel.

8¼

40

55

20

60

8½

90

85

20

90

8¾

60

70

20

75

9½

90

90

20

95

9¾

40

60

20

65

10

60

75

20

80

10½

50

70

20

75

11

60

55

20

120

12

90

90

20

120

12¾

60

85

20

90

13

90

90

20

130

13½

60

90

20

90

13¾

80

100

20

110

14

90

90

20

140

14¼

60

90

20

95

15

90

90

20

150

16

60

80

20

120

16¼

80

100

20

130

16½

80

110

20

120

17

45

85

20

90

17½

80

100

20

140

18

40

60

20

120

18¾

80

100

20

150

Number of threads in inch of screw.

Number of teeth in

Lathe spindle-wheel

Wheel in contact with spindle-wheel

Pinion in contact with screw-wheel.

Leading screw-wheel.

19

50

95

20

100

19½

80

120

20

130

20

60

100

20

120

20¼

40

90

20

90

21

80

120

20

140

22

60

110

20

120

22½

80

120

20

150

22¾

80

130

20

140

23¾

40

95

20

100

24

65

120

20

130

25

60

100

20

150

25½

30

85

20

90

26

70

130

20

140

27

40

90

20

120

27½

40

100

20

110

28

75

140

20

150

28½

30

90

20

95

30

70

140

20

150

32

30

80

20

120

33

40

110

20

120

34

30

85

20

120

35

60

140

20

150

36

30

90

20

120

Table by which to determine the Number of Teeth, or Pitch of Small Wheels, by what is commonly called the Manchester Principle.

Diametral Pitch.

Circular Pitch.

3

1.047

4

.785

5

.628

6

.524

7

.449

8

.393

Diametral Pitch.

Circular Pitch.

9

.349

10

.314

12

.262

14

.224

16

.196

20

.157

Example 1. - Required the number of teeth that a wheel of 16 inches diameter will contain of a 10 pitch.

16 X 10 = 160 teeth, and the circular pitch = .314 inch.

Example 2. - What must be the diameter of a wheel for a 9 pitch of 126 teeth ?

126 ÷ 9 = 14 inches diameter, circular pitch .349 inch.

Note. - The pitch is reckoned on the diameter of the wheel instead of the circumference, and designated wheels of 8 pitch, 12 pitch, etc.

Strength of the Teeth of Cast Iron Wheels at a given Velocity.

Pitch of teeth in inches.

Thickness of teeth in inches.

Breadth of teeth in inches.

Strength of teeth in horse-power at

3 feet per second.

4 feet per second.

6 feet per second.

8 feet per second.

3.99

1.9

7.6

20.57

27.43

41.14

54.S5

3.78

18

7.2

17.49

23.32

34.98

46.64

3.57

1.7

6.8

14.73

19.65

29.46

39.28

3.36

1.6

6.4

12.28

16.38

24.56

32 74

3.15

1.5

6.

10.12

13.50

20.24

26.98

2.94

1.4

5.6

8.22

10.97

16.44

21.92

2.73

1.3

5.2

6.58

8.78

13.16

17.54

2.52

1.2

4.8

5.18

6.91

10.36

13.81

2 31

1.1

4.4

3.99

5.32

7.98

10.64

2.1

1.0

4.

3.00

4.00

6.00

8.00

1.S9

.9

3.6

2.18

2.91

4 36

5.81

1.68

.8

3.2

1.53

2.04

3.06

3.08

1.47

.7

2.8

1027

1.37

2.04

2.72

1.26

.6

2.4

.64

.86

1.38

1.84

l.t)5

.5

2.

.375

.50

.75

1.00