WORKSPACE EVOLUTION OF HARD MAGNETIC SOFT ELASTICA

Workspace, the set of all possible positions reached by the end effector, must be large for a continuum robot for safe steerability. Magnetically actuated soft robots have high workspace due to their millimetre-scale size and large flexibility, enabling them to navigate constrained environments. When subjected to an external magnetic field, they undergo large deflections by interacting with magnetic particles. This work develops closed-form (assuming 2D planar) and numerical solutions to rotation and deflection for uniformly magnetised elastica at an angle using Cosserat rod theory. They are derived in terms of the elliptic function and shooting method, respectively, and are in good agreement with the experimental results provided in the literature. Deflection and rotation plots are presented for various input conditions. The analytical solutions show pitchfork bifurcation when the external field is antiparallel to the magnetic direction with a peak normalised half workspace of 0.103. In contrast, perturbed pitchfork bifurcation is observed for the other angles; increasing the workspace to 0.416 is not yet studied in the existing literature.