Research ArticleMICROROBOTS

Microwheels on microroads: Enhanced translation on topographic surfaces

See allHide authors and affiliations

Science Robotics  31 Jul 2019:
Vol. 4, Issue 32, eaaw9525
DOI: 10.1126/scirobotics.aaw9525
  • Fig. 1 Square-wheeled bicycles can translate smoothly on roads constructed from truncated catenaries.

  • Fig. 2 μWheel translation on flat surfaces.

    (A) A 5-mer (5,2) and a 7-mer (7,6) translate at different velocities in the same applied field. Inset: μWheels of different size (1 < n < 7) and symmetry (2 < ξ < 6). Scale bars, 10 μm. (B) Time-averaged velocity (normalized by the frequency and particle radius) of μwheels of different size (2 < n < 29). Brown dots correspond to μwheels with n > 7. (C) Instantaneous velocity profiles for singlet (1,1), dimer (2,2), trimer (3,3), square (4,4), and 7-mer (7,6) μwheels. Symbols are experimental measurements, and solid lines are calculations based on Eq. 2 and eq. S6, where T is one full rotational period.

  • Fig. 3 μWheel translation on topographic surfaces.

    (A) The calculated commensurate “roads” for μwheels of n = (2,2), (4,4), and (7,6) where optimal spacings d are 6.3a, 3.8a, and 3.1a, respectively. (B) Experimental geometry (measured by AFM along θ = 90°) with minimum spacing of d = 4.4a and blaze angle of γ = 26°; spacing can be readily increased by lowering translation angle θ. Maximum height is 1.7a, and arrow indicates blaze direction. Scale bar, 10 μm. (C) Experimental measurement of displacement of the centers of mass of two dimer lobes with time rolling along θ ~ 90° against the blaze direction. Mode I, rotation with slip; mode II, nonslip flipping. Insets: Fourier transform of the instantaneous velocity. (D) Calculated displacement of the centers of mass of two lobes of a dimer rolling along a textured surface with trapezoidal bumps (fig. S3B). Insets show the Fourier transforms of the instantaneous velocity.

  • Fig. 4 Enhanced μwheel velocities on topographic surfaces.

    (A) The ratio of topographic to flat surface μwheel average translation velocities ν¯p/ν¯ with the ratio of spatial/rotational frequency ωfs. Open and closed symbols represent with and against the blaze direction. The line is a fit from Eq. 3. (B) The dashed line is a fit from Eq. 4 with the blaze, and the solid line is against the blaze direction. Symbols are identical to those of Fig. 2B.

  • Fig. 5 μWheel rectifying on topographic surfaces.

    (A) The ratio of dimer translation velocities on topographic/flat surface ν¯p/ν¯with field frequency. Negative frequencies indicate propulsion direction again the blaze direction. The inset shows the force balance on the μwheel. (B) Illustration of the rectifier effect for dimer (2,2), diamond (4,2), and square (4,4) μwheels.

  • Fig. 6 Separation of μwheel isomers.

    Composite images of diamond and square μwheels translating on a (A) flat surface versus on a (B) textured surface (against the blaze direction) with the same time interval under identical field conditions (movie S8). (C) A diamond and square translating against the blaze under low magnetic field frequency (movie S9).

Supplementary Materials

  • robotics.sciencemag.org/cgi/content/full/4/32/eaaw9525/DC1

    Materials and Methods

    Fig. S1. Experimental setup and the rolling of a μwheel under a 3D magnetic field.

    Fig. S2. μWheels translating on flat surfaces.

    Fig. S3. Schematics for modeling the rolling of a dimer on a textured surface and textured surface with trapezoidal bumps used in the simulations.

    Fig. S4. Calculation of an ideal road for a square (4,4) μwheel translating without slip.

    Movie S1. Translation of a 7-mer and a 5-mer under a 3D magnetic field on a flat surface.

    Movie S2. Translation of a dimer on a flat surface.

    Movie S3. Translation of a dimer under a 3D magnetic field on a topographic surface along the blaze direction.

    Movie S4. The simulated translation (slip and flip) of a dimer on a topographic surface with evenly spaced trapezoidal bumps.

    Movie S5. The simulated translation (sequential flip of two lobes) of a dimer on a flat substrate.

    Movie S6. The simulated translation (continuous flip) of dimer on a topographic surface with trapezoidal bumps spaced by d = 1.39a.

    Movie S7. The rectifier effect for the translation of a dimer under a 3D magnetic field on a topographic surface.

    Movie S8. Comparison of a diamond and square μwheel translation on the flat (top) versus topographic surface against the blaze direction (bottom).

    Movie S9. Translation of a diamond and square against the blaze direction.

  • Supplementary Materials

    The PDF file includes:

    • Materials and Methods
    • Fig. S1. Experimental setup and the rolling of a μwheel under a 3D magnetic field.
    • Fig. S2. μWheels translating on flat surfaces.
    • Fig. S3. Schematics for modeling the rolling of a dimer on a textured surface and textured surface with trapezoidal bumps used in the simulations.
    • Fig. S4. Calculation of an ideal road for a square (4,4) μwheel translating without slip.
    • Legends for movies S1 to S9

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.avi format). Translation of a 7-mers and a 5-mers under a 3D magnetic field on a flat surface.
    • Movie S2 (.avi format). Translation of a dimer on a flat surface.
    • Movie S3 (.avi format). Translation of a dimer under a 3D magnetic field on a topographic surface along the blaze direction.
    • Movie S4 (.mov format). The simulated translation (slip and flip) of a dimer on a topographic surface with evenly spaced trapezoidal bumps.
    • Movie S5 (.mov format). The simulated translation (sequential flip of two lobes) of a dimer on a flat substrate.
    • Movie S6 (.mov format). The simulated translation (continuous flip) of dimer on a topographic surface with trapezoidal bumps spaced by d = 1.39a.
    • Movie S7 (.mp4 format). The rectifier effect for the translation of a dimer under a 3D magnetic field on a topographic surface.
    • Movie S8 (.avi format). Comparison of a diamond and square μwheel translation on the flat (top) versus topographic surface against the blaze direction (bottom).
    • Movie S9 (.avi format). Translation of a diamond and square against the blaze direction.

    Files in this Data Supplement:

Stay Connected to Science Robotics

Navigate This Article