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**Given: barrel arbour core diameter 3mm, barrel inner diameter 9mm, mainspring thickness 0.1. Calculate the theoretical length of the mainspring. **

**Pi x (R²-r²)**

2e

3.14 x (4.5²-1.5²)

2 x 0.1

3.14 x (20.25-2.25)

0.2

3.14 x 18

0.2

56.52

0.2

282.6 turns

**Given: centre wheel 80 teeth, third wheel 75 teeth, fourth wheel 70 teeth, escape wheel 15 teeth, third pinion 10 leaves, fourth pinion 10 leaves, escape pinion 7 leaves. Calculate the number of vibrations per hour, per second and the frequency (in Hertz) of the pocket watch.**Vh = Z1•Z3•Z5•(2Ze) = N1

Z2•Z4•Z6

Vh = 80•75•70•(2 x 15) = 18,000

10•10•7

**Given: minute wheel 48 teeth, minute wheel pinion 12 leaves, hour wheel 36 teeth. How many leaves does the cannon pinion have?**Motion work ratio is almost always 12:1

N1 = Z1 Z3

N2 Z2 Z4

1 = 12 x ?

12 48 x 36

1 x ?

4 x 36

1 x ?

144

144/12 = 12

**Given: hour wheel 48 teeth, minute wheel pinion 10 leaves, cannon pinion 12 leaves. Calculate the number of teeth of the minute wheel.**Motion work ratio is almost always 12:1

N1 = Z1 Z3

N2 Z2 Z4

1 = 10 x 12

12 48 x ?

1 x 10

4 x ?

10

120

120/4 = 30

**Given: hour wheel 64 teeth, minute wheel 42 teeth, cannon pinion 16 leaves. Calculate the number of leaves of the pinion.**N1 = Z1 Z3

N2 Z2 Z4

1 = 16 x ?

12 64 x 48

1 x ?

4 x 48

1 x ?

192

192/12 = 16