Design Optimization of Asymmetric Patterns for Variable Stiffness of Continuum Tubular Robots

Variable stiffness mechanisms have become popular for improving the performance of meso/microscale robots due to their ability to enable safe, effective, and versatile operation without additional actuators. In minimally invasive surgery (MIS), they can provide low stiffness for adaptability and an extended workspace and high stiffness for stable manipulation. This study aims to optimize the pattern design that maximizes the stiffness ratio while preventing buckling. Longitudinal slits are identified as the ideal shape for maximizing the ratio using topology optimization. The effects of the design parameters are investigated by analytical modeling and finite-element analysis (FEA). Finally, we established a design optimization process to maximize the variable stiffness ratio while ensuring safety. The load and buckling tests of 19 cases are verified in both the experiment and FEA. Buckling occurred in eight cases, consistent with the expected results from the proposed map. Among the tested cases, the tube with the optimal pattern parameter set exhibits the highest stiffness ratio of 2.67 while satisfying the given stiffness constraint (greater than 0.3 times the flexural stiffness of the initial tube) and avoiding buckling. The proposed optimization method potentially enables an extended workspace and more versatile functionality for MIS instruments.