| 主权项 |
1. A method for generating a profile of bodies K1 and K2 which, while rotating codirectionally at a same rotational speed about two axes of rotation A1 with regard to body K1 and A2 with regard to body K2 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 K1 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 K2 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 K2, 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 S1 of the axis of rotation A1 with the plane E to an intersection point S2 of the axis of rotation A2 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 K1, said cross-sectional profile of the body K2 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 whereinsaid 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 whereinsaid 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. |
