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Grootte: 130
Commentaar:
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← Versie 15 sinds 2017-03-02 19:42:11 ⇥
Grootte: 1848
Commentaar:
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| Verwijderingen worden op deze manier gemarkeerd. | Toevoegingen worden op deze manier gemarkeerd. |
| Regel 1: | Regel 1: |
| {{attachment:n_lobe_examples.svg}} |
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| Regel 2: | Regel 4: |
| This joint is common under the registered name "Torx". Unfortunately data is not public so an assumption is made here. | This hexalobular joint is commonly known as the registered name "Torx". Unfortunately data is not public so close assumptions are made here. Example of generated curves with this app: For "Torx", shapes are defined with the following ratio's: ||ra = 1||rb ≈ 0,72 ra||rc ≈ 0,1 ra||rd ≈ 0,175 ra|| The size table is close, but data differs slightly on the net. The table relates to designation and diameter, where diameter = 2*ra. You should consider that inside and outside shapes have a constant section over its height, while bits can have a certain slope. Some tolerance between inside and outside shape is mandatory for proper functioning. ||#||Dia. mm (inch)||#||Dia. mm (inch)||#||Dia. mm (inch)||#||Dia. mm (inch)|| ||T3||1,17 (0,046)||T8||2,31 (0,09)||T25||4,43 (0,173)||T50||8,83 (0,346)|| ||T4||1,28 (0,05)||T9||2,5 (0,098)||T27||4,99 (0,195)||T55||11,22 (0,44)|| ||T5||1,42 (0,055)||T10||2,74 (0,107)||T30||5,52 (0,216)||T60||13,25 (0,519)|| ||T6||1,7 (0,066)||T15||3,27 (0,128)||T40||6,65 (0,26)|| ||T7||1,99 (0,078)||T20||3,86 (0,151)||T45||7,82 (0,306)|| = Mathematics = {{attachment:n_lobe.svg||width=350}} With radii ra, rb, rc and number of lobes n given, rd is to be determined. * Corner ae=pi/n radians or 180/n degrees, so for 6 lobes, ae is 30 degrees. * Triangle: * df=ra-rc * dg+dh=rc+rd * di=rb+rd * cos(ae)=j (omitting prefixes) {{{ (c+d)^2=(a-c)^2+(b+d)^2-2(a-c)(b+d)j c^2+d^2+2cd=a^2+c^2-2ac+b^2+d^2+2bd-2jab-2jad+2jbc+2jcd 2cd-2bd+2jad-2jcd=a^2-2ac+b^2-2jab+2jbc rd=(a^2-2ac+b^2-2jab+2jbc)/(2c-2b+2ja-2jc) rd=((a^2+b^2)/2-ac-jab+jbc)/(c-b+ja-jc) }}} In a spreadsheet with A1=j, A2=a, A3=b, A4=c and A5 is calculation of d, A5 is: {{{ =(A2^2-2*A2*A4+A3^2-2*A1*A2*A3+2*A1*A3*A4)/(2*A4-2*A3+2*A1*A2-2*A1*A4)}}} |
Torx
This hexalobular joint is commonly known as the registered name "Torx". Unfortunately data is not public so close assumptions are made here.
Example of generated curves with this app:
For "Torx", shapes are defined with the following ratio's:
ra = 1 |
rb ≈ 0,72 ra |
rc ≈ 0,1 ra |
rd ≈ 0,175 ra |
The size table is close, but data differs slightly on the net. The table relates to designation and diameter, where diameter = 2*ra. You should consider that inside and outside shapes have a constant section over its height, while bits can have a certain slope. Some tolerance between inside and outside shape is mandatory for proper functioning.
# |
Dia. mm (inch) |
# |
Dia. mm (inch) |
# |
Dia. mm (inch) |
# |
Dia. mm (inch) |
T3 |
1,17 (0,046) |
T8 |
2,31 (0,09) |
T25 |
4,43 (0,173) |
T50 |
8,83 (0,346) |
T4 |
1,28 (0,05) |
T9 |
2,5 (0,098) |
T27 |
4,99 (0,195) |
T55 |
11,22 (0,44) |
T5 |
1,42 (0,055) |
T10 |
2,74 (0,107) |
T30 |
5,52 (0,216) |
T60 |
13,25 (0,519) |
T6 |
1,7 (0,066) |
T15 |
3,27 (0,128) |
T40 |
6,65 (0,26) |
||
T7 |
1,99 (0,078) |
T20 |
3,86 (0,151) |
T45 |
7,82 (0,306) |
Mathematics
With radii ra, rb, rc and number of lobes n given, rd is to be determined.
- Corner ae=pi/n radians or 180/n degrees, so for 6 lobes, ae is 30 degrees.
- Triangle:
- df=ra-rc
- dg+dh=rc+rd
- di=rb+rd
- cos(ae)=j
(omitting prefixes)
(c+d)^2=(a-c)^2+(b+d)^2-2(a-c)(b+d)j c^2+d^2+2cd=a^2+c^2-2ac+b^2+d^2+2bd-2jab-2jad+2jbc+2jcd 2cd-2bd+2jad-2jcd=a^2-2ac+b^2-2jab+2jbc rd=(a^2-2ac+b^2-2jab+2jbc)/(2c-2b+2ja-2jc) rd=((a^2+b^2)/2-ac-jab+jbc)/(c-b+ja-jc)
In a spreadsheet with A1=j, A2=a, A3=b, A4=c and A5 is calculation of d, A5 is:
=(A2^2-2*A2*A4+A3^2-2*A1*A2*A3+2*A1*A3*A4)/(2*A4-2*A3+2*A1*A2-2*A1*A4)