4.3. Body flexibility calculation and experiments

To localize body flexibility, calculations were performed to determine the MR-LF geometry that would yield the same foot flexion as the MR-DF design while limiting the bending in MR-LF to a small region, or flexure, near each foot. The length of the MR-LF flexure was chosen as 2 mm to avoid contact between the foot and compartment, and the diameter was determined using cantilever beam equations. The robots were modeled as a cantilever beam with the midsection fixed and a constant torque applied to the free end, with the assumption that bending was symmetric on both sides of the robot and resulted from a uniform magnetic torque applied on the robot foot. For the MR-DF design, bending was assumed to occur uniformly across the entire half-body length (7.5 mm), whereas, for the MR-LF design, the compartment was assumed to be rigid so bending only occurred in the MR-LF flexure (length: 2 mm). By setting the maximum bending angle of each case to be equal, the diameter of the MR-LF flexure was calculated to be 3.6 mm.
To evaluate the effect of localized flexibility on body flexibility, experiments were performed using physical half-robot models mounted with the midsection face at x = 0 in the magnetic field created by the actuator magnet (see Figure 2B; magnetic field plots in Figure S1). Body flexibility was determined using the maximum and minimum foot flexion angles for the designs. Foot flexion was measured from a video of the half-robot models being actuated through three rotations of the actuator magnet.