Three tendons run the length of a stacked-disc backbone, 120° apart. Pulling one tendon shortens that side and leaves the rest at full length, so the segment arcs toward it. The left panel is a side profile of that arc (radius from the axis vs. height); the right panel is a top-down view showing which way the arc points and tracing the backbone's footprint on the ground plane.
bendVec = Σ τi * (cos φi, sin φi), φi = 0°, 120°, 240°
κ = |bendVec| * κmax (curvature, 1/m)
φ = atan2(bendVec) (bending-plane azimuth)
r(s) = (1-cos(κs))/κ, y(s) = sin(κs)/κ
This is the constant-curvature (PCC) model: the whole segment bends along one circular arc of radius 1/κ, in the plane set by φ. Because the three tendons act independently, the tip can point anywhere on a full 360° cone — the same principle used to steer surgical endoscopes and pipe-inspection probes through tight, curved passages.
- Tendon tension — how far each tendon is pulled (0-100%); the vector sum sets both κ and φ.
- Curvature κ — inverse of the arc radius; 0 is straight, larger is a tighter bend.
- Bend plane φ — azimuth of the plane the arc bends within.