Method for constructing bodies that rotate in the same direction and are in contact with one another and computer system for carrying out said method

1. A method for generating a profile of bodies K 1 and K 2 which, while rotating codirectionally at a same rotational speed about two axes of rotation A 1 with regard to body K 1 and A 2 with regard to body K 2 arranged parallel to one another at a distance a, constantly touch one another at at least one point, said method comprising as a first step forming a cross-sectional profile of the body K 1 in a plane E perpendicular to axes of rotation by a constant, segmentally constantly differentiable, closed convex curve {right arrow over (p)}, and as a second step, forming a cross-sectional profile of the body K 2 from the curve {right arrow over (p)}, according to

{right arrow over (q)}={right arrow over (p)}+a·{right arrow over (n)} ({right arrow over ( p )})+ a   (1),

said {right arrow over (q)} being a curve describing the cross-sectional profile of the corresponding body K 2 ,

said curve {right arrow over (p)}, having at any point a radius of curvature p which is smaller than or equal to distance a,

for each point of said curve {right arrow over (p)}, within a constantly differentiable segment, there being a standardized normal vector {right arrow over (n)}({right arrow over (p)}) of length l which at each point is perpendicular to a tangent to said curve {right arrow over (p)}, and points in a direction of a centre portion of a circle of curvature belonging to the respective point of said curve {right arrow over (p)},

{right arrow over (a)} being a vector which leads in a direction from an intersection point S 1 of the axis of rotation A 1 with the plane E to an intersection point S 2 of the axis of rotation A 2 with the plane E and possesses a length equal to the distance a, and

in a case of a kink in said cross-sectional profile of the body K 1 , said cross-sectional profile of the body K 2 having an arc of a circle, the radius of which corresponds to the distance a and an angle of which corresponds to an angle at which tangents to curve segments of said curve {right arrow over (p)}, abut one another at a kink point wherein

said curve {right arrow over (p)} is described by a single mathematical function, the said single mathematical function being selected from the series consisting of the following members:

B-spline function, Bézier function, rational Bézier function, non-uniform rational B-spline function,

or wherein

said curve {right arrow over (p)} is described segmentally by various mathematical functions, at least one of these said various mathematical functions is selected from the series consisting of the following members:

B-spline function, Bézier function, rational Bézier function, non-uniform rational B-spline function.

2. The method according to claim 1 , wherein said point S 1 lies outside said curve {right arrow over (p)}.

3. The method according to claim 1 , wherein said point S 1 lies on or inside said curve {right arrow over (p)}.

4. The method according to claim 3 , wherein said intersection point S 1 lies on an intersection point of at least two axes of symmetry of said curve {right arrow over (p)} or said intersection point S 1 lies at a symmetry point of said curve {right arrow over (p)} or said intersection point S 1 lies on a centre of rotation of said curve {right arrow over (p)}.

5. The method according to claim 1 , wherein said curve {right arrow over (p)}, has one or more kinks.

6. The method according to claim 5 , wherein said curve {right arrow over (p)}, is described at kink points by an arc of a circle with radius eps which merges tangentially into two adjacent curves, eps being a very small positive real number which tends towards 0 (eps<<1, eps→0).

7. The method according to claim 1 , wherein bodies K 1 and K 2 are screw elements.

8. The method according to claim 1 , wherein said cross-sectional profiles are continued helically in an axial direction, the bodies generated in this way being right-handed or left-handed, and a pitch standardized to the distance a lying in a range of 0.1 to 10, and lengths, standardized to the distance a, of bodies K 1 and K 2 lying in a range of 0.1 to 10.

9. The method according to claim 1 , wherein said cross-sectional profiles are segmentally continued linearly in an axial direction, and a length, standardized to the distance a, of the bodies K 1 and K 2 lies in a range of 0.05 to 10.

10. A method for generating screw elements, wherein said, in a first step, generating by a method of claim 1 cross-sectional profiles of bodies which, while rotating codirectionally at the same rotational speed about axes of rotation arranged parallel to one another at a distance a, constantly touch one another at at least one point and, in a second step, introducing plays between the bodies K 1 and K 2 .

11. A computer system for executing a method according to claim 1 .

12. A computer system according to claim 11 , associated with a machine tool for generating calculated bodies.