Torx
This hexalobular joint is commonly known as the registered name "Torx". Unfortunately data is not public so close assumptions are made here.
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.
# |
Diam. |
# |
Diam. |
# |
Diam. |
# |
Diam. |
# |
Diam. |
T1 |
0.81 mm |
T2 |
0.93 mm |
T3 |
1.10 mm |
T4 |
1.28 mm |
T5 |
1.42 mm |
T6 |
1.70 mm |
T7 |
1.99 mm |
T8 |
2.31 mm |
T9 |
2.50 mm |
T10 |
2.74 mm |
T15 |
3.27 mm |
T20 |
3.86 mm |
T25 |
4.43 mm |
T27 |
4.99 mm |
T30 |
5.52 mm |
T40 |
6.65 mm |
T45 |
7.82 mm |
T50 |
8.83 mm |
T55 |
11.22 mm |
T60 |
13.25 mm |
T70 |
15.51 mm |
T80 |
17.54 mm |
T90 |
19.92 mm |
T100 |
22.13 mm |
Generic lobulars
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)
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Edit conflict - other version:
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)
Edit conflict - your version:
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)
End of edit conflict