Sunday, 4 August 2013
Monday, 31 December 2012
Let's get Mathematical Part 12
Given: barrel 84 teeth, centre wheel 80 teeth, third wheel 75 teeth, second wheel (fourth wheel) 70 teeth, escape wheel 15 teeth, centre wheel pinion 12 leaves, third wheel pinion 10 leaves, second wheel pinion (fourth wheel) 10 leaves, escape wheel pinion 7 leaves. Calculate the number of turns an escape wheel pinion accomplishes during one turn of the centre wheel.
Z1•Z3•Z5
Z2•Z4•Z6
80•75•70
10•10•7
Answer: 600
Z1•Z3•Z5
Z2•Z4•Z6
80•75•70
10•10•7
Answer: 600
Friday, 28 December 2012
Let's get Mathematical Part 11
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
N1 = Z1 Z3
N2 Z2 Z4
1 = 16 x ?
12 64 x 48
1 x ?
4 x 48
1 x ?
192
192/12 = 16
Thursday, 27 December 2012
Let's get Mathematical Part 10
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
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
Monday, 24 December 2012
Let's get Mathematical Part 9
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
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
Friday, 21 December 2012
Let's get Mathematical Part 8
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
Vh = Z1•Z3•Z5•(2Ze) = N1
Z2•Z4•Z6
Vh = 80•75•70•(2 x 15) = 18,000
10•10•7
Thursday, 20 December 2012
Let's get Mathematical Part 7
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
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
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