Off-Axis Compliant RCM Joint with Near-Isotropic Stiffness and Minimal Parasitic Error

Abstract

This paper presents an off-axis, monolithic compliant Remote Center of Motion (RCM) joint for neuroendoscopic manipulation, combining near-isotropic stiffness with minimal parasitic motion. Based on the Tetra II concept, the end-effector is placed outside the tetrahedral flexure to improve line of sight, facilitate sterilization, and allow rapid tool release. Design proceeds in two stages: mobility panels are sized with a compliance-based isotropy objective, then constraining panels are synthesized through finite-element feasibility exploration to trade stiffness isotropy against RCM drift. The joint is modeled with beam elements and validated via detailed finite-element analyses, including fatigue-bounded stress constraints. A PA12 prototype is fabricated by selective laser sintering and characterized on a benchtop: a 2 N radial load is applied at the end-effector while a 6-DOF electromagnetic sensor records pose. The selected configuration produces a stiffness-ellipse principal axis ratio (PAR) of 1.37 and a parasitic-to-useful rotation ratio (PRR) of 0.63%. Under a 4.5° commanded rotation, the predicted RCM drift remains sub-millimetric (0.015-0.172 mm). Fatigue analysis predicts a usable rotational workspace of 12.1°-34.4° depending on direction. Experiments reproduce the simulated directional stiffness trend with typical deviations of 6-30%, demonstrating a compact, fabrication-ready RCM module for constrained surgical access.

Figures (11)

• Figure 1: (a) Representation of a double parallelogram RCM mechanism. The mutual parallelism of A, B, C, and D forces the prolongation of the EE to pass through the RCM - (b) Representation of a RCM mechanism with circular guides.
• Figure 2: View of dual compliant joint composed of two identical joint connected in series. This joint can move the EE around the RCM along the pitch and roll directions. mariano2026dual
• Figure 3: Isometric view of Tetra II joint composed of nine flexural walls ($p_1, ..., p_9$). The blue panels, obtained connected the nodes $N1, N2, N3$ and $N4$, are responsible for joint motion and are therefore the ones to be modified to have isotropic stiffness behavior. The red panels block the joint’s rotation, constraining the tool from following circular rotations around the RCM.
• Figure 4: Scheme of the line of sight of the surgeon over the entry area. The green cone represents the visible area while the black cone represents the non visible area. In (a) the joint has the EE located at the center of tetrahedral structure, while in (b) the joint has the EE located at the side of tetrahedral structure. The EE is represented with the red line.
• Figure 5: Scheme of the three panels responsible for the joint movement. Highlighted are nodes $N1, N2, N3$ and $N4$, along with the outputs of the optimization $L_1, L_2, L_3, t_1, t_2, t_3, \theta_1$ and $\theta_2$.