# 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
`=(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)`