n-tuple complex helical geometry modeling using parametric equations

Complex helical structures are difficult to model in three-dimensional form to conduct finite element analysis. In general, parametric mathematical equations for single and double helical geometries are readily available in existing literature. However, more complex forms such as triple or in general n-tuple helical structures are still not widely studied. In this paper, at first, definitions of single and double helical structures are presented in parametric mathematical forms. Centerlines, curvatures, and torsions of these geometries are found, and these two helical geometries are visualized in three-dimensional structures. Next, one of the untouched helical models, the triple helical geometry, is investigated and a procedure to find the centerline of the triple helical geometry is presented. In addition, the first three-dimensional generated solid model of a triple helix geometry is presented. Finally, the steps used to create triple helix geometry are generalized to find parametric mathematical equations for n-tuple helical geometries.