Continuum Robot: Tendon-Driven Bending

Tendon Actuation

Tendon 1 (0°) 0%

Tendon 2 (120°) 0%

Tendon 3 (240°) 0%

Backbone State

Curvature κ

–

Bend plane φ

–

Tip bend angle

–

Tip offset

–

How it works

Three tendons run the full length of a flexible disc backbone, threaded through holes 120° apart around each disc's rim. Pulling a tendon shortens the backbone on that side while the opposite side stays at rest length, forcing the whole segment to arc smoothly toward the shortened tendon — no discrete joints, just continuous elastic bending, the same principle that curls an elephant's trunk or an octopus arm.

bendVec = Σ τᵢ · (cos φᵢ, sin φᵢ),  φᵢ = 0°, 120°, 240°
κ = |bendVec| · κmax        (curvature, 1/m)
φ = atan2(bendVec)          (bending-plane direction)
P(s) = ((1−cos κs)/κ · cosφ, (1−cos κs)/κ · sinφ, sin(κs)/κ)

The last line is the constant-curvature (PCC) model: it assumes the whole segment bends along a single circular arc of radius 1/κ, in the plane set by whichever tendons are pulled. Combining the three tendons independently lets the tip point in any direction on a full 360° cone — something no single hinge joint can do — which is exactly why continuum backbones are used for surgical endoscopes and pipe-inspection probes threading through tight, curved passages.

Tendon tension — how far each tendon is pulled (0–100%); the vector sum of all three sets both how sharply the backbone curves (κ) and which way it points (φ).
Curvature κ — inverse of the arc's radius; κ = 0 means a straight backbone, larger κ means a tighter bend.
Bend plane φ — the azimuth of the plane the arc bends within, derived purely from the balance of the three tendon pulls.

Backbone discs Tendon 1 Tendon 2 Tendon 3

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.