Three different Methods (I)-(III) are presentet, how to construct nonplanar space curves of constant curvature in the euklidian 3-Space. (I) On the unit sphere let there be given a regular curve c*, which is considerd as a spherical image. Via certain integrations we get from c* the parametrization of a space curve c with constant curvature. If c* is a closed regular curve of class C¹ and the center of mass of c* coincides with the center of the unit sphere, the curve c is a closed space curve of constant curvature. If c is even a nonplanar curve, it is called a twisted circle. Examples of sperical images c* are concidered, which have certain symmetries that garant the coincidision of the center of mass of c* with the center of the unit sphere. In particular a special class of sperical images c* is found, the correspondig twisted circles c of which even can be parametrized with elementary functions. (II) A method is shown, how to complete a given curve c of constant curvature via special complements of its corresponding spherical image c* to a twisted circle. (III) Without using the the spherical image a method is shown, how to get space curves of constant curvature on a cylindrical surface which is given by its profile curve.     «

Three different Methods (I)-(III) are presentet, how to construct nonplanar space curves of constant curvature in the euklidian 3-Space. (I) On the unit sphere let there be given a regular curve c*, which is considerd as a spherical image. Via certain integrations we get from c* the parametrization of a space curve c with constant curvature. If c* is a closed regular curve of class C¹ and the center of mass of c* coincides with the center of the unit sphere, the curve c is a closed space curve o...     »