Planar Bending of Flexible Instrument Shafts: Modeling and Experimental Validation

Abstract

The increase in osteoporotic fractures in the complexly shaped pelvis requires innovative, minimally invasive instruments. Conventional instruments often reach their limits when navigating complex bone structures. Flexible, cablecontrolled instruments offer great potential for the precise, three-dimensional guidance of implants. This paper presents a static model for describing the planar bending of cablecontrolled, small-diameter, metallic flexible hollow shafts. For that, the bending behavior of the shafts was studied and implemented using a four-point bending test. In addition to geometric deformation, the model also takes into account friction losses according to the Capstan equation. Validation is carried out on a physical demonstrator. The experimental investigations confirm the correlation of the trajectories of specific marker points with the model. However, high deviations are found in the calculated bending radii, which increase with increasing shaft stiffness. The simulation underestimates the actual bending radius, which is due to unaccounted torsional couplings, varying bending stiffness, and underestimated friction effects. The presented model serves as an initial methodological basis for the design of flexible medical instruments in the low stiffness range.