Fig. 9.

Here the stability metric det H₁₁ of Corollary 3 is shown on the left for a system of three tubes of equal stiffness and circular precurvature which subtend a total arc of 78.2 degrees in the undeformed state. Each tube is assumed to be actuated rotationally at s = 0, and is precurved over the entire length of the tube. If there were only two tubes, no continuous path would exist for the tubes to be rotated fully 360 degrees with respect to one another. With three tubes, however, a continuous path can be found which allows tubes 2 and 3 to be rotated 360 degrees with respect to tube 1. The green line drawn on the left chart shows a chosen stable path in the distal angle space, and the right chart shows how that path transforms to the proximal angles which are actuated. The amount of distortion in the curve is related to the stability measure, with lower stability measures indicating greater distortion.