Design of Transmission Tubes for Surgical Concentric Push-Pull Robots

The performance of concentric push-pull robots passing through endoscopes is best if their laser-cut transmission tubes exhibit high axial stiffness, high torsional stiffness, and low bending stiffness. In this paper we simultaneously consider all three output stiffness values in the design problem, explicitly considering axial stiffness, whereas prior work has focused on the bending/torsional stiffness ratio. We show that it is very challenging for existing laser-cut patterns to simultaneously achieve high axial stiffness and low bending stiffness because these stiffnesses are tightly coupled. To break this coupling and balance all three stiffness factors independently, we propose a new laser material removal design approach that leverages local stiffness asymmetry $\left(E{I}_x\ne E{I}_y\right)$ in discrete bending segments separated by segments of solid tube. These discrete asymmetric segments are then rifled down the tube to achieve global stiffness symmetry. We parameterize the design and provide a study of the properties through finite-element analysis. We also consider the effect of interference between the tubes when the discrete segments are not aligned. Results show that our discrete asymmetric segment concept can achieve high axial stiffness and torsional stiffness better than previously suggested laser patterns while maintaining equally low bending stiffness.