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Consider a parametric arm of a constant length capable of any 3D operation. This Demonstration illustrates three fundamental spatial transformations of such an arm:[more]
1. Flexure—continuous bending from a straight segment to a full circle.
2. Translation—a particular shape (a semicircle) travels along the arm.
3. Extension—two ends of the arm extend or contract.
The operations are controlled by a single parameter .[less]
Contributed by: Machi Zawidzki (February 2014)
Open content licensed under CC BY-NC-SA
 M. Zawidzki and K. Nishinari, "Modular Pipe-Z System for Three-Dimensional Knots," Journal for Geometry and Graphics, 17(1), 2013 pp. 81–87.
Wolfram Demonstrations Project
Published: February 28 2014