Access this dataset on Dryad; DOI: 10.5061/dryad.kd51c5bm7

This dataset corresponds to the results shown in the manuscript: “Fluidic Torque-Enabled Object Manipulation by Microrobot Collectives”, Science Advances

Data_for_Fig_1.zip

Figure 1 characterizes the azimuthal flow fields generated by a single 300 μm diameter magnetic microrobot spinning at the air–water interface under a rotating magnetic field.

Description of the data and file structure

OVERVIEW

This dataset contains the experimental measurements used to generate:

• Fig. 1C: Flow velocity (u, mm/s) as a function of magnetic field frequency (Omega, Hz) at various normalized distances from the microrobot center.
• Fig. 1D: Normalized flow velocity (u / (omega*R)) as a function of normalized distance (d/R), demonstrating inverse-square scaling consistent with low-Reynolds-number hydrodynamics.

The raw data were extracted from video microscopy experiments in which 3 micrometer tracer particles were used to visualize local fluid velocities around a spinning microrobot.

FILES INCLUDED

1.

u vs omega at 5R.xlsx

Description: Flow velocity as a function of magnetic field frequency measured at d/R = 5.

Columns include: Magnetic field frequency (Hz), measured flow velocity u (mm/s)

This file was used to generate the d/R = 5 curve in Fig. 1C.

2.

u vs omega at 7.5R.xlsx

Description: Flow velocity as a function of magnetic field frequency measured at d/R = 7.5.

Columns include: Magnetic field frequency (Hz), measured flow velocity u (mm/s)

This file was used to generate the d/R = 7.5 curve in Fig. 1C.

3.

u vs omega at 10R.xlsx

Description: Flow velocity as a function of magnetic field frequency measured at d/R = 10.

Columns include: Magnetic field frequency (Hz), measured flow velocity u (mm/s)

This file was used to generate the d/R = 10 curve in Fig. 1C.

4.

u vs distance normalised.xlsx

Description: Normalized velocity data used to generate Fig. 1D.

Columns include: Normalized distance d/R, Magnetic field frequency (Hz), Measured flow velocity u (mm/s), Normalized velocity u / (omega*R)

This file demonstrates the scaling: u is proportional to (omega * R) / (d/R)², which is expected for low-Reynolds-number flow generated by a rotating micro-disk.

EXPERIMENTAL CONTEXT

Microrobot properties: (Diameter: 300 micrometers), (Radius R = 150 micrometers), Located at the air–water interface, Actuated by a rotating magnetic field

Key variables:

Omega = magnetic field frequency (Hz)

omega = microrobot angular velocity (rad/s)

d = distance from microrobot center

R = microrobot radius

u = local flow velocity (mm/s)

Measurements were extracted from 30 frames-per-second recordings using particle tracking techniques. Flow immediately adjacent to the microrobot boundary was not included because it exceeded imaging resolution limits.

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Data_for_Fig_2.zip

Figure 2 quantifies the programmable co- and counter-rotation of concentric ring structures driven by a rotating magnetic microrobot collective.

Description of the data and file structure

OVERVIEW

This dataset contains the experimental and simulation measurements used to generate:

• Fig. 2A: Inner ring angular velocity (omega_ring) as a function of the number of microrobots in the annulus region (N_annulus) for various field frequencies (Omega).
• Fig. 2E: Heat map of experimental inner ring angular velocity across the (N_annulus, Omega) parameter space when N_center = 20.
• Fig. 2F: Heat map of simulated inner ring angular velocity across the same parameter space.
• Fig. 2G: Experimental and simulation comparison of omega_ring versus N_annulus at fixed Omega.
• Fig. 2H: Experimental and simulation comparison of omega_ring versus Omega at fixed N_annulus.

These data quantify how hydrodynamic torque generated by rotating microrobot collectives transfers to passive concentric ring structures.

EXPERIMENTAL PARAMETERS

Key variables:

Omega = magnetic field frequency (Hz)

omega_ring = angular velocity of passive ring (rad/s)

N_annulus = number of microrobots in the annulus region

N_center = number of microrobots in the center region

Unless otherwise stated:

N_center = 20 for heat map experiments

Field frequencies range from 5 Hz to 70 Hz

Each experiment recorded 10 seconds at 30 frames per second

Ring orientation was manually tracked every 10 frames

Angular velocity was calculated from the slope of angular position versus time.

Fluidic torque (tau) was estimated using the low-Reynolds-number drag torque approximation:

tau = 8 * pi * eta * R_ring³ * omega_ring

where:

eta = dynamic viscosity of water

R_ring = ring radius

omega_ring = measured angular velocity

FILES INCLUDED (TYPICAL CONTENTS)

The ZIP archive contains processed numerical datasets corresponding to:

1.

Experimental angular velocity vs N_annulus for multiple Omega values used to generate Fig. 2A.

Columns include: N_annulus, Omega (Hz), omega_ring (rad/s)

Experimental heat map data (N_center = 20)

Used to generate Fig. 2E.

Columns include: N_annulus, Omega (Hz), omega_ring (rad/s)

2.

Simulation heat map data (N_center = 20) used to generate Fig. 2F.

Columns include: N_annulus, Omega (Hz), omega_ring (rad/s)

3.

Comparison datasets for fixed Omega (e.g., Omega = 70 Hz) used to generate Fig. 2G.

Columns include: N_annulus, omega_ring_experiment (rad/s), omega_ring_simulation (rad/s)

4.

Comparison datasets for fixed N_annulus (e.g., N_annulus = 30) used to generate Fig. 2H.

Columns include: Omega (Hz), omega_ring_experiment (rad/s), omega_ring_simulation (rad/s)

All reported values are steady-state angular velocities measured after the system reached dynamic equilibrium.

DATA PROCESSING

Experimental data were obtained using:

• Video recordings at 30 frames per second
• Manual tracking of ring angular position using a circular marker
• Linear regression of angular position versus time to compute angular velocity
• MATLAB used for interpolation and heat map generation

Heat maps were generated by interpolating discrete measurements over the (N_annulus, Omega) parameter space using MATLAB interpolation functions.

Simulations were performed using a low-Reynolds-number hydrodynamic interaction model of microrobots and passive rings.

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Data_for_Fig_3.zip

Figure 3 demonstrates functional exploitation of fluidic torque generated by microrobot collectives, including gear actuation, 3D object rotation, dynamic self-assembly of ring structures, and absorption/expulsion of passive particles by a dense collective.

OVERVIEW

This dataset contains experimental measurements used to generate:

• Fig. 3A: Angular velocities of mechanically coupled gears driven by a microrobot collective.
• Fig. 3B: Angular position and angular velocity of a 3D floating object actuated by microrobots.
• Fig. 3C: Collective radius of dynamically self-assembling ring structures as a function of magnetic field frequency.
• Fig. 3D: Distribution of passive particle distances to arena boundaries under different field frequencies (absorption vs. expulsion behavior).

These data quantify how fluidic torque can be harnessed for multi-body actuation and collective manipulation.

EXPERIMENTAL PARAMETERS

Key variables:

Omega = magnetic field frequency (Hz)

omega = angular velocity (rad/s or deg/s depending on dataset)

theta = angular orientation (degrees or radians)

N_microrobots = number of microrobots in the collective

N_objects = number of passive objects

General conditions: Experiments recorded at 30 frames per second, Steady-state behavior measured after approximately 20 seconds of driving at the frequency of interest, Microrobots operate below step-out threshold (< 120 Hz)

FILES INCLUDED

The ZIP archive contains processed numerical datasets corresponding to:

1.

Gear Actuation Data (Fig. 3A)

Description: Angular velocities of two mechanically coupled gears.

Columns include: Time (s), Angular velocity of left gear (rad/s), Angular velocity of right gear (rad/s)

The left gear is directly driven by a microrobot collective.

The right gear is actuated through mechanical contact.

Instantaneous angular velocities were computed from frame-to-frame angular displacement.

2.

3D Object Actuation Data (Fig. 3B)

Description: Angular orientation and angular velocity of a floating 3D object driven by microrobots located in a thin liquid film on top of the object.

Columns include: Time (s), Angular orientation (degrees), Angular velocity (deg/s)

The object mass is approximately 45,000 times greater than a single microrobot.

3.

Dynamic Self-Assembly Data (Fig. 3C)

Description: Collective radius of ring structures driven by embedded microrobots.

Columns include: Magnetic field frequency Omega (Hz), Collective radius (mm), Number of rings or microrobots

These measurements quantify how collective morphology changes as a function of driving frequency.

At low frequencies, rings cluster.

At higher frequencies, rings form a rotating circular structure with increasing collective radius.

4.

1000-Microrobot Collective Absorption/Expulsion Data (Fig. 3D)

Description: Nearest distance of passive particles to arena boundary under different frequencies.

Columns include: Frequency Omega (Hz), Particle index, Distance to nearest arena edge (mm)

At low frequency (e.g., 5 Hz): Particles are expelled toward the arena boundary.

At high frequency (e.g., 70 Hz): Particles are distributed throughout the arena.

Histograms in Fig. 3D were generated from these distance measurements.

DATA PROCESSING

Gear and 3D object angular positions were manually tracked frame-by-frame.

Angular velocities were computed using: omega = d(theta)/dt

Dynamic self-assembly collective radius was computed by measuring: Centroid of ring structures, Average radial distance of rings from centroid

Particle-boundary distances were calculated using geometric distance measurements from particle centroid to nearest arena edge.

MATLAB was used for: Histogram generation, Statistical analysis, Plot generation

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Data_for_Fig_4.zip

Figure 4 examines how fluidic torque generated by microrobot collectives couples back to collective morphology and object geometry, leading to transitions between dispersed encapsulation and aggregated crawling behaviors.

Description of the data and file structure

OVERVIEW

This dataset contains experimental measurements used to generate:

• Fig. 4F: Angular velocity of circular, gear-shaped, and rod-shaped objects across a range of field frequencies.
• Fig. 4G–I: Rotation of aggregating circular objects driven by a 100-microrobot collective.
• Fig. 4J: Heat map of angular velocity across the (N_obj, Omega) parameter space.
• Fig. 4K: Angular velocity comparison between single circular objects and aggregates of comparable area.

These data quantify how object shape, size, and aggregation influence rotation rate and collective state (crawling vs encapsulation).

EXPERIMENTAL PARAMETERS

Key variables:

Omega = magnetic field frequency (Hz)

omega_obj = angular velocity of passive object (deg/s)

theta = angular orientation (degrees)

N_obj = number of aggregated circular objects

Object diameter or length (mm)

General conditions:

• Experiments recorded at 30 frames per second
• Objects have characteristic length ~4 mm unless otherwise stated
• Microrobot collective size ~100 microrobots for these experiments

Collective behavior classified as:

• Crawling state (aggregated clusters along object boundary)
• Encapsulation state (dispersed rotation surrounding object)
• Angular velocity was computed from linear regression of angular position vs time during steady-state motion.

FILES INCLUDED

The ZIP archive contains processed numerical datasets corresponding to:

1.

Object Angular Velocity vs Frequency (Fig. 4F)

Description: Angular velocity of circular, gear, and rod-shaped objects across multiple frequencies.

Columns include: Frequency Omega (Hz), Angular velocity of circular object (deg/s), Angular velocity of gear-shaped object (deg/s), Angular velocity of rod-shaped object (deg/s)

Hollow markers in Fig. 4F correspond to crawling state.

Filled markers correspond to encapsulation state.

2.

Aggregated Object Rotation Data (Fig. 4G–I)

Description: Angular velocity of aggregates formed by circular objects.

Columns include: N_obj (number of objects in aggregate), Frequency Omega (Hz), Angular velocity (deg/s)

Each dataset corresponds to steady-state measurements over a 10-second interval.

3.

Heat Map Data Across N_obj – Omega Parameter Space (Fig. 4J)

Description: Angular velocity values measured across combinations of N_obj (number of aggregated circular objects) and Omega (Hz)

Columns include: N_obj, Omega (Hz), Angular velocity (deg/s)

Heat map was generated in MATLAB using interpolation across discrete measured points.

4.

Area-Matched Object Comparisons (Fig. 4K)

Description:

Angular velocity comparison between:

• Single circular object (diameter 4 mm)
• Single circular object (diameter 7.5 mm)
• Aggregate with N_obj = 20
• Aggregate with N_obj = 60

Columns include: Frequency Omega (Hz), Angular velocity (deg/s)

These datasets demonstrate how concave aggregate boundaries shift the frequency threshold for crawling-to-encapsulation transition.

DATA PROCESSING

Object angular position was tracked manually or via image processing.

Angular velocity was calculated as: omega_obj = d(theta)/dt

Collective state (crawling vs encapsulation) was determined visually based on microrobot spatial distribution:

Crawling: clustered microrobots moving along one side of object

Encapsulation: dispersed microrobots surrounding object perimeter

Heat maps were generated using MATLAB interpolation functions applied to discrete measurements.