Design of a Counter-bending Structure using Topology Optimization

Counter-bending is a bio-inspired passive behavior that has been observed in the whip-like flagella of many microorganisms and cells. Counter-bending beams passively bend toward and conform around applied forces. Counter-bending behavior is particularly interesting in soft robotic grasping as it offers passive adaptability to objects in contact. The mechanism behind counter-bending behavior has been proposed as models and inspired compliant grasper designs in previous works; yet, existing designs only realize 2D counter-bending, which limits the adaptability to one direction. 3D counter-bending fingers can expand their adaptability to objects with wider range of geometries, and the unique constraints enforced by the 3D counter-bending beam can also be exploited in other applications such as coupling mechanisms and underactuated underwater locomotion. However, a physical realization of 3D counter-bending beam has yet to be proposed. In this paper, we employ continuum topology optimization to search for a beam structure capable of 3D counter-bending. The topology optimizer 1) validates existing 2D counter-bending model, and 2) generates a 3D structure that provides insight into prototyping a 3D counter-bending beam. To validate the structure from optimization results, we prototype a 3D counter-bending beam using inextensible wires and soft elastomers, and we assemble 3D counter-bending fingers into an underactuated grasper to demonstrate the adaptability to objects with distinct geometries enabled by the counter-bending capability.