Ropes as Nested Helices

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A wire rope is an assembly of several (usually six) wire strands wrapped helically around a central core strand. The wire strands are themselves composed of several (usually six) wires wrapped around a central core wire [1].


This Demonstration shows the construction of a typical wire rope consisting of a core strand with seven wires surrounded by six outer strands, each also consisting of seven wires. For a better view, up to five of the outer strands and up to five of the wires in the strands can be hidden.

The wires in the core strand form single helices around a straight center wire. The center wires of the outer strands equally form a single helix.

Coiling a helix around another one creates a new, double helical structure. The outer wires in the outer strands form double helices [2].


Contributed by: Erik Mahieu (June 2015)
Open content licensed under CC BY-NC-SA



A single helix has the parametric equation , where is the helix radius, is the helix angle, and is the winding angle.

A double helix has the parametric equations




where is the double helix radius, is the helix angle, and is the winding angle.


[1] G. A. Costello, Theory of Wire Rope, New York: Springer, 1997.

[2] C. Erdönmez and C. E. Imrak, "New Approaches for Model Generation and Analysis for Wire Rope," in Computational Science and Its Applications—ICCSA 2011: Part IV (B. Murgante, O. Gervasi, A. Iglesias, D. Taniar, and B. O. Apduhan, eds.), Berlin: Springer-Verlag, 2011.

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