Fig. 2: Basic bending performances and navigation of ETACs (electromagnetically transitional and actuatable material-based continuums).

a Design principle of the ETACs. Design factors, including the tip length-width ratios and graded stiffness distribution, were considered. b Thermal effects on bending performances. Two series of tests were conducted regarding the thermal effects. The plot legends “2:1”, “6:1”, and “Pure” denote the mass ratio between flexible and rigid PCL (Polycaprolactone) powders, where “Pure” refers to the case without using rigid PCL powders. c Thermal effects on stiffnesses. The time-dependent and temperature-dependent stiffnesses are presented. It will take ~9.5 h to complete a cure cycle after being heated by 60 ° C for 30 min. The softening rate of ETACs is larger than 1000% after being heated. The test was conducted in Helmholtz coils with 12 mT magnetic field strength. The modulus was calculated by the validated numerical model. d Bending performances of ETACs with different length-width ratios were tested in a Helmholtz coil. e Graded stiffness at ETACs’ tip was tested with a constant length-width ratio (\(\frac{{L}_{{{\rm{M}}}}}{C}=\)30) in permanent magnetic (PM) fields at a distance of 4 cm. Experimental and numerical results were compared with agreements. f The validated numerical model was further applied to calculate the maximum bending effect of ETACs with respect to magnetic flux density and material stiffness. g Navigation practices. ETACs were applied to navigate a complex aerodigestive tract under PM fields. ETACs with and without optic fiber cores successfully reached all predefined targets framed in circles. h An ETAC navigated through an ex vivo pig bronchi system. Inserted from the trachea, the continuums successfully reached 32 predefined targets at different bronchus levels under PM controls. The right-side images show the continuums’ deformation status during their navigation at RB2 (right superior lobar bronchus, RSLB), LB7 (left superior lobar bronchus, LSLB), and LB18 (left inferior lobar bronchus, LILB), respectively. In (g, h), the graded stiffness was given to the tested continuum tip pre-heated in a 50 ° C oven for 30 min and cooled down to ambient temperature for 5 min. Scale bar: 1 cm. Source data are provided as a Source Data file.