Basics of Coordinate Metrology
Unit 4:  Geometric Elements - Torus

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The next standard and less frequent geometrical element is the torus. A torus can be best described as a cylinder whose ends have been bent like a ring until they fit on top of one another. A torus has the following characteristics:
Extension: Radius R of the entire torus, radius r of the "bent cylinder" (minor radius)
Direction given by the torus axis

A torus is determined by at least seven (probing) points (on the surface of the torus). These points are used to determine the center of the torus P(x, y, z), the major radius R, the minor radius r and the direction vector of the torus axis V(x, y, z). 

In practice the diameter (Ø) D is usually used instead of the radius R. It is twice the value of the radius (D = 2 R).

       

Element:
Torus
Display:
Parameters:
point P (x, y, z), 
direction vector V (x, y, z)
major radius R
minor radius r
Required minimum number of probing points:
7 probing points
Example using a part:

(Fastening eyelet)