Research ArticleAPPLIED SCIENCES AND ENGINEERING

Pulse-driven robot: Motion via solitary waves

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Science Advances  01 May 2020:
Vol. 6, no. 18, eaaz1166
DOI: 10.1126/sciadv.aaz1166
  • Fig. 1 Our Slinky-robot.

    (A) Schematic showing the locomotive mechanism of an earthworm based on retrograde peristaltic waves (i.e., waves that propagate in the opposite direction to locomotion). (B) Picture of metallic Slinky used in this study. (C and D) Pictures of our Slinky-robot (C) before and (D) after the pneumatic actuator is elongated. (E) Front view of the Slinky-robot showing the electromagnet. Note that several red plastic spheres are glued on to the Slinky to prevent it from rolling. Photo credit: Bolei Deng, Harvard University.

  • Fig. 2 Performance of the Slinky-robot.

    (A) Snapshots taken during a test in which we extend the front 10 loops to Ain = 100 mm while keeping the electromagnet on. (B) Displacement of the head during three cycles for tests in which (i) mh/mtot = 0.23 and we keep the electromagnet on (red line), (ii) mh/mtot = 0.23 and we turn off the electromagnet after stretching (green line), and (iii) mh/mtot = 0.32 and we turn off the electromagnet after stretching (blue line). (C) Snapshots taken during a test in which Ain = 100 mm and we turn the electromagnet off after stretching the front loops. (D) Evolution of uhcycle as a function of mh/mtot for tests in which Ain = 100 mm. The square and triangular markers correspond to mh/mtot = 0.23 and 0.32, respectively. (E) Evolution of uhcycle as a function of Ain for tests in which mh/mtot = 0.32. The triangular marker corresponds to Ain = 100 mm. (F) Static response of the Slinky as measured in a uniaxial test. (G) Evolution of η as a function of Ain for tests in which mh/mtot = 0.32. The triangular markers correspond to Ain = 100 mm. The green dashed line corresponds to the amplitude of the supported soliton, As. (H) Evolution of η as a function of na and Ain for tests in which mh/mtot = 0.32. Photo credit: Bolei Deng, Harvard University.

  • Fig. 3 Wave propagation in the Slinky.

    (A) Experimental setup used to test the propagation of pulses in the metallic Slinky. At t = 0 s, na = 10 loops between the loading plate and the front of the Slinky are stretched to Ain = 100 mm. (B) Snapshots of the propagation of the pulse in the Slinky at t = 0.10, 0.17, 0.24, and 0.34 s. The circular markers indicate the positions of the center of mass of the Slinky. (C) Displacement of the center of mass of the Slinky, uCM, as a function of time. Circular markers correspond to the time points considered in (A) and (B). (D) Spatiotemporal displacement diagram of the propagating pulse. (E) Velocity signals measured at the 10th and 80th loops. (F) Evolution of the cross-correlation of v10 (t) and v80 (t) as a function of the input amplitude Ain. The triangular marker corresponds to Ain = 100 mm. The green dashed line corresponds to the amplitude of the supported soliton, As, predicted by Eq. 10. Photo credit: Bolei Deng, Harvard University.

  • Fig. 4 Mathematical model.

    (A) Schematic of our model. Each nonlinear spring represents the elastic response of an individual loop, whereas each concentrated mass represents its mass. (B) Spatial displacement profiles at t = 0, 0.10, 0.17, and 0.24 s as measured in our experiments (circular markers) and predicted by our analytical solution given by Eq. 7 (solid lines).

  • Fig. 5 Steering and moving over different surfaces.

    (A) Snapshots taken during a test in which we twist the last loop by β = 180° before initiating the wave. The Slinky-robot steers by an angle θ = 13° when the pulse reaches its tail. (B) Evolution of the steering angle θ as a function of the applied twist β. (C) Evolution of uhcycle as a function of the friction coefficient between the Slinky and the substrate, μ. The triangular marker corresponds to Bristol paper—the substrate considered in Fig. 2. Photo credit: Bolei Deng, Harvard University.

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