Concentric Push–Pull Robots: Planar Modeling and Design

Concentric push-pull robots (CPPR) combine the simplicity, miniaturization potential, and open lumen of concentric-tube robots with the kinematic advantages and stability of push-pull multibackbone designs. A CPPR segment is made from a pair concentric tubes with notches asymmetrically cut into their sides in opposing directions. The two tubes are attached to one another at their tips, and push-pull translation of the tube bases relative to each other changes the curvature along the length of the combined tube pair. Custom, variable-curvature shapes are possible by varying the notch parameters along the tubes. In this article, we present a planar, variable-curvature mechanics model for the actuated segment shape and a method for designing the notch pattern to achieve a desired planar, variable-curvature shape with maximal stiffness within specified strain limits. Experiments validate accuracy for various shapes, materials, and cross sections, showing that the design method achieves a variety of desired shapes. We also demonstrate a multisegment robot made from multiple tube pairs that can independently rotate and actuate, increasing the robot DOF.