Kinetostatic design of asymmetric notch joints for surgical robots

Abstract

We present a kinetostatic model for a needle-sized notched tube continuum joint design, and examine the impact that the design parameters have on both stiffness and joint kinematics. The joint is fabricated by removing a series of asymmetric notches from a metal tube. By fixing a cable to the distal end of the tube, and routing this tendon through the tube's lumen, the joint can be actuated in bending. This simple cutting pattern allows for impressive performance compared to other mechanisms of similar size. However, selecting the cutting geometry using kinematics alone results in many redundant solutions. Since the notches significantly affect the overall structure's stiffness, and limit the maximum forces that it can transmit, a stiffness model can be used to constrain the design-space. Further, because the notch geometry represents a non-prismatic beam configuration, modelling the force-deflection behavior is nontrivial. We have approached this problem using a variation of Castigliano's 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> Theorem, experimentally validated its performance with several test specimens, and analyzed the behavior of the model over a design space specific to neurosurgical applications. The outcomes of this study aim to aid in the design of joints given task-specific constraints, particularly within the field of surgical robotics.