4.2. Robot fabrication
Robots were cast in 3D-printed molds (Form3, Formlabs) from addition-cure silicone (Dragon Skin™ 10 Medium, Smooth-On) with pigment (Silc Pig™, Smooth-On) added to aid visualization. Separate molds were used for the MR-DF, MR-LF, and MR-LF-S designs. Before casting, the molds were coated with a release agent. The silicone was mixed at a 1:1 ratio (w/w, parts A:B) in a planetary centrifugal mixer (AR-100, Thinky) for 60 seconds at 2000 rpm, then injected into the molds using a syringe and dispensing tip. After casting, magnets (R422-N52, K&J Magnetics) were glued into cavities in each foot using a silicone adhesive (Sil-Poxy™, Smooth-On) and cured overnight. Magnets were aligned coaxially with opposite polarity (i.e., both north poles pointing out). The two-part rigid compartment in MR-LF was 3D printed (Form3, Formlabs), assembled, and placed into the MR-LF molds before casting. The flexure was joined to the compartment by having silicone from the flexure extend into a cavity at the end of the compartment during casting. The overall length (25 mm), foot diameter (12 mm), and foot length (5 mm) were the same for all robots. The body length and diameter of MR-DF were 15 mm and 5 mm, respectively. The body geometry of MR-LF was as follows: flexible segment length 2 mm, flexible segment diameter 3.6 mm, compartment length 11 mm, and compartment diameter 8 mm. The compartment's outer diameter was designed to be small enough to prevent undesired contact between the robot body and channel. The MR-LF-S had the same geometry as MR-LF and was fabricated with the methods described above, except the feet, flexures, and compartment were cast as a single unit from the silicone. Half-robot models for body flexibility tests were fabricated using the same methods as described above using half-robot molds. The single magnet was glued (with the north pole out) into the foot, and the midsection face was glued to a custom 3D-printed PLA mount using the silicone adhesive and cured overnight. All full-robot models were fabricated with the same batch of silicone to avoid variation due to material properties. Similarly, all half-robot models were made from the same silicone mixture.
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 torque applied on the robot foot. For the MR-DF design, bending was assumed to occur 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 the overall 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 (Figure \ref{882568}B; magnetic field plots in Figure S1, Supporting Information). 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. The θa data in Figure \ref{882568} and S2, Supporting Information, were adjusted to represent θa during a representative rotation of the actuator magnet.