Simulative analysis of interlocking polygonal concentric tube robots during rotation

Concentric tube robots (CTR) are highly compact actuation mechanisms that are well suited for minimally invasive, robot-assisted surgery. CTR with non-circular, e.g., octagonal, cross-sections can mechanically interlock their relative orientation, thereby preventing unintended rotation if an external applied moment lies below a defined threshold torque. In this study, a finite-element model of a two-tube polyamide CTR with octagonal profiles is used to assess the propagation of discrete 45° rotation steps from base to tip. Geometric (tube length, radial clearance and fillet radius of octagon corners) and material (friction coefficient) parameters are systematically varied. During contact of the tube surfaces, torsional twist causes the tip to lag behind the imposed rotation. Once contact is lost, the stored strain energy is released and the tip snaps rapidly into the next interlocked configuration. The simulations demonstrate that clearance and friction strongly affect the threshold torque and the tip lag, whereas increasing the tube length to 50 mm or beyond prevents complete propagation of the angular step because the twist cannot be fully relaxed within a 45° base rotation. Fillet radius variations produce effects comparable to clearance adjustments. The analysis confirms that short, shape-interlocked CTR, as proposed for use as active cannulas with straight outer tubes and short transmission segments in several studies, can reliably execute stepwise rotations with a defined torque threshold, suppress inadvertent motion, and thereby improve positioning in minimally invasive applications.