Screw-Based Propulsion Systems

• Screw-based propulsion systems are innovative mechanisms that convert controlled rotational input into axial thrust across fluids, granular, and solid media.
• These systems optimize performance by fine-tuning key geometric parameters such as helix angle, pitch, and blade height to balance thrust, speed, and efficiency.
• They are widely applied in bioinspired robotics, amphibious vehicles, planetary rovers, and microscale active matter where traditional locomotion methods are ineffective.

Screw-based propulsion systems are mechanisms in which the controlled rotation of a helical structure (Archimedes screw, helical rod, or chiral filament) generates net thrust through a medium—liquid, granular, or solid—via the translational coupling of the helix and the medium. Originally inspired by both biological flagellar dynamics and the Archimedean pump, screw-based propulsion is central to bioinspired robotics, amphibious vehicles, planetary rovers, and microscale active matter. These systems excel in domains where conventional wheels or legs are ineffective, offering unique multi-domain mobility, tunable anisotropic coupling, and robust traction in variable environments.

1. Theoretical Foundations

The fundamental operating mechanism is the conversion of rotational input (angular velocity $\omega$) into axial thrust and translational velocity $v$ along the screw’s axis. For a generic screw with mean radius $R$, helix (lead) angle $\alpha$, and axial pitch per revolution $p=2\pi R\tan\alpha$, the ideal no-slip advance per revolution is $v_\mathrm{ideal} = p\,\omega/(2\pi)$. Real-world operation in deformable or fluid media introduces slip, quantified by the slip ratio $s = 1 - v/v_{\text{ideal}}$ (Lim et al., 2023, Joyce et al., 2023, Chen et al., 15 Nov 2025).

Interaction Laws by Medium

• Fluids (Stokesian): For rigid helices in viscous media, resistive-force theory (RFT) or nonlocal slender-body theory yields thrust $$F_p \sim (\xi_\perp - \xi_\parallel)\,\Omega R^2 L \sin\theta\cos\theta$$, where $\xi_\perp$, $\xi_\parallel$ are drag coefficients and $v$0 is the helix angle (Jawed et al., 2015). Hydrodynamic stability (buckling) emerges above a critical rotation rate $v$1.
• Granular media: Screw propagation is dominated by anisotropic frictional forces with coefficients $v$2, $v$3 (normal/tangential), modeled as $v$4; axial velocity scales as $v$5 with $v$6 a function of helix angle and friction ratio $v$7 (Texier et al., 2017).
• Amphibious/multiphase: In transitional or mixed media, dimensionless metrics such as the advance coefficient $v$8, aspect ratio $v$9, and tip speed $R$0 determine optimality; unique rolling or wheeling modes are favored in non-Newtonian or saturated states (Chen et al., 15 Nov 2025).

Mechanical Advantage and Efficiency

Static mechanical advantage is $R$1 (Lim et al., 2023). Locomotive efficiency is $R$2; cost of transport (COT) is commonly used for evaluation.

2. Geometric and Design Parameters

Critical geometric variables include:

• Radius ($R$3): Larger $R$4 increases volumetric engagement but reduces mechanical advantage for a given torque.
• Helix angle ($R$5): Shallow ($R$6–$R$7) optimizes for thrust in granular media; steep ($R$8–$R$9) enhances speed in fluids, but may increase slip and lateral media displacement (Chen et al., 15 Nov 2025, Joyce et al., 2023).
• Pitch ($\alpha$0): More pitch increases ideal speed but lowers static thrust.
• Blade height (BH): Dominant for thrust in granular media (higher BH $\alpha$1 deeper groove, higher normal stress) (Chen et al., 15 Nov 2025).
• Thread starts ($\alpha$2): More starts increase flow rate but can raise drag and torque demand.
• Aspect ratio ($\alpha$3): High $\alpha$4 (less crowded) optimizes thrust in water; low $\alpha$5 required in sand for blade-to-media cohesion (Chen et al., 15 Nov 2025).

Dynamic reconfiguration—e.g., NASU’s tunable origami-inspired lead angle—enables real-time adaptation to speed/efficiency trade-offs, with $\alpha$6 maximizing efficiency and $\alpha$7 maximizing velocity (Joyce et al., 2023).

3. Fluid–Structure and Media Interactions

Viscous Fluid

For flexible rods in viscous fluids under low Reynolds number (Stokes flow), fluid–structure interaction (FSI) models (Kirchhoff rod theory coupled with nonlocal slender-body hydrodynamics) predict a universal phase diagram for propulsion regimes. At sub-buckling rotation rates, the propulsive force follows $\alpha$8; above $\alpha$9, a global buckling instability is triggered, sharply reducing thrust and efficiency (Jawed et al., 2015).

Granular and Transitional Media

In granular beds, the anisotropic frictional forces give rise to an optimal helix angle $p=2\pi R\tan\alpha$0 (typ. $p=2\pi R\tan\alpha$1–$p=2\pi R\tan\alpha$2), achieving up to $p=2\pi R\tan\alpha$3 normalized velocity and $p=2\pi R\tan\alpha$4 efficiency in dry, deep beds. Performance collapses as $p=2\pi R\tan\alpha$5 falls below passive drag loads or the medium yields (Texier et al., 2017, Chen et al., 15 Nov 2025).

In transitional regimes (wet sand, quicksand), the onset of lateral sand ejection or non-Newtonian yielding marks a sharp phase boundary; rolling modes become optimal as screw-propulsion stalls (Chen et al., 15 Nov 2025).

Dimensionless and Scaling Analysis

Cross-media performance is effectively organized by:

• Advance coefficient $p=2\pi R\tan\alpha$6, aspect ratio $p=2\pi R\tan\alpha$7, Reynolds number $p=2\pi R\tan\alpha$8, Froude number $p=2\pi R\tan\alpha$9 (fluid regimes), and granular inertial number $v_\mathrm{ideal} = p\,\omega/(2\pi)$0.
• Empirical fits: In water, $v_\mathrm{ideal} = p\,\omega/(2\pi)$1 peaks at $v_\mathrm{ideal} = p\,\omega/(2\pi)$2 ($v_\mathrm{ideal} = p\,\omega/(2\pi)$3 at $v_\mathrm{ideal} = p\,\omega/(2\pi)$4, $v_\mathrm{ideal} = p\,\omega/(2\pi)$5). In dry sand, optimal $v_\mathrm{ideal} = p\,\omega/(2\pi)$6 at $v_\mathrm{ideal} = p\,\omega/(2\pi)$7, $v_\mathrm{ideal} = p\,\omega/(2\pi)$8, $v_\mathrm{ideal} = p\,\omega/(2\pi)$9.

4. Robotic Implementations and Experimental Systems

Screw-propelled robots leverage modular designs and advanced materials for robust deployment in heterogeneous terrains.

ARCSnake and ARCSnake V2

ARCSnake series robots integrate Archimedes' screws ($s = 1 - v/v_{\text{ideal}}$0–$s = 1 - v/v_{\text{ideal}}$1, pitch $s = 1 - v/v_{\text{ideal}}$2 22°, 2-start or 1-start) with actuated U-joints ($s = 1 - v/v_{\text{ideal}}$3 pitch/yaw), enabling both “tunneling” and “M-configuration” (wheeling) locomotion. Modular designs (BeagleBone Black controllers, ROS, onboard IMUs, closed-loop velocity and torque regulation) achieve up to $s = 1 - v/v_{\text{ideal}}$4, segment-level continuous thrust $s = 1 - v/v_{\text{ideal}}$5, and teleoperation via a 100 Hz curvature-mapped controller (Schreiber et al., 2019, Richter et al., 2021, Wickenhiser et al., 15 Nov 2025).

Key performance traits:

• Efficient, low-slip locomotion in granular media, robust underwater operation (passive buoyancy control, foam-filled shells, IP67 pressurization) (Wickenhiser et al., 15 Nov 2025).
• Adaptive kinematics: mode transitions triggered by sustained slip thresholds or media classification (IMU, motor current).
• Comparative superiority to wheels or legs in loose sand, debris/moisture robustness.

NASU: Reconfigurable Helical Geometry

NASU exemplifies dynamic reconfiguration, using an origami-inspired Kresling mechanism and linear actuation to tune lead angle $s = 1 - v/v_{\text{ideal}}$6–$s = 1 - v/v_{\text{ideal}}$7 on demand. This enables empirical selection of high-thrust/high-efficiency or high-speed states across gravel, sand, grass, and mud. Typical Pareto-optimal results: at $s = 1 - v/v_{\text{ideal}}$8, $s = 1 - v/v_{\text{ideal}}$9, $$F_p \sim (\xi_\perp - \xi_\parallel)\,\Omega R^2 L \sin\theta\cos\theta$$0; at $$F_p \sim (\xi_\perp - \xi_\parallel)\,\Omega R^2 L \sin\theta\cos\theta$$1, $$F_p \sim (\xi_\perp - \xi_\parallel)\,\Omega R^2 L \sin\theta\cos\theta$$2, $$F_p \sim (\xi_\perp - \xi_\parallel)\,\Omega R^2 L \sin\theta\cos\theta$$3 (Joyce et al., 2023).

Performance in Amphibious and Multi-domain Platforms

Experimental testbeds (linear-rail or mobile platforms) systematically characterize thrust, velocity, slip, and efficiency across fluid, granular, and transitional regimes (Lim et al., 2023, Chen et al., 15 Nov 2025). Two-screw counter-rotating configurations reduce slip variance and cost of transport ($$F_p \sim (\xi_\perp - \xi_\parallel)\,\Omega R^2 L \sin\theta\cos\theta$$4–$$F_p \sim (\xi_\perp - \xi_\parallel)\,\Omega R^2 L \sin\theta\cos\theta$$5 for counter-rotating screws).

5. Design Guidelines and Media-Dependent Optimization

General Media-Dependent Recommendations

Medium	Optimal $$F_p \sim (\xi_\perp - \xi_\parallel)\,\Omega R^2 L \sin\theta\cos\theta$$6	Optimal BH	Typical $$F_p \sim (\xi_\perp - \xi_\parallel)\,\Omega R^2 L \sin\theta\cos\theta$$7	Design Guidance
Water	$$F_p \sim (\xi_\perp - \xi_\parallel)\,\Omega R^2 L \sin\theta\cos\theta$$8–$$F_p \sim (\xi_\perp - \xi_\parallel)\,\Omega R^2 L \sin\theta\cos\theta$$9	$\xi_\perp$015 mm	$\xi_\perp$1–$\xi_\perp$2	Minimize BH; maximize $\xi_\perp$3 for v; low $\xi_\perp$4
Dry/Wet Sand	$\xi_\perp$5–$\xi_\perp$6	$\xi_\perp$7 shell radius	$\xi_\perp$8–$\xi_\perp$9	Max BH; moderate $\xi_\parallel$0, $\xi_\parallel$1–$\xi_\parallel$2
Mixed Regimes	$\xi_\parallel$3	$\xi_\parallel$4 mm	Variable*	Variable $\xi_\parallel$5, axial grading, adaptive shell
Saturated Sand	—	—	—	Use rolling mode (not screw propulsion)

*Variable $\xi_\parallel$6: e.g., inner shell for sand, outer shell for water (Chen et al., 15 Nov 2025).

• In granular media, maximize BH for thrust within structural limits, use moderate to low $\xi_\parallel$7 to avoid failure via lateral ejection or deep cutting.
• For rapid amphibious transition, adaptive blades (e.g., variable pitch, Kresling origami) and real-time slip or current-based control optimize operational efficiency and avoid stalling (Chen et al., 15 Nov 2025, Joyce et al., 2023).
• Avoid high-α, high-ψ screws in dense granular media; switch to rolling tread on loss of shear support.

Practical Trade-Offs

• Shallow angles maximize static thrust but trade off speed.
• Larger radii increase swept volume and interaction force, which can tax drive-train torque and mass constraints.
• Multi-start threads enhance engagement but also friction and torque cost.

Empirical testbeds are essential for calibrating models, as slip, efficiency, and COT are affected by environment and implementation-specific energy losses (Lim et al., 2023).

6. Extensions: Bioinspired Active Matter and Microscale Phenomena

Active screw mechanics extend to microscale chiral swimmers, e.g., bacterial flagella, magnetically actuated colloidal helices, and crawling rods (Banerjee et al., 2024). The coupling between longitudinal spinning ($\xi_\parallel$8) and transverse rolling ($\xi_\parallel$9) yields emergent chiral flows and collective "active nematic" phases. The ratio $v$00, and in Myxococcus xanthus, this chiral activity is measurable but subdominant (typically $v$01). Engineering microscale screws therefore requires consideration of both principal and transverse pitch, to tune collective properties such as chiral mixing or topological flow control (Banerjee et al., 2024).

7. Limitations, Open Challenges, and Future Directions

• Surface dependency: Ineffective propulsion on rigid surfaces with insufficient blade engagement—handled by switching to rolling or wheel-like modes (e.g., ARCSnake’s “M-configuration”) (Richter et al., 2021, Wickenhiser et al., 15 Nov 2025).
• Energy and mass trade-offs: High BH, high-radius designs increase robot mass and energy overhead; efficiency management is critical for field deployment.
• Media transitions: Rapid domain-shifts (granular $v$02 aquatic) require active sensing and control, as high-α screws can quickly stall or induce catastrophic slip in unsupportive environments (Chen et al., 15 Nov 2025).
• Future enhancements: Integration of sensor fusion (IMU+motor current), closed-loop slip and thrust regulation, modular actuation, autonomous media classification, and onboard adaptive geometry remain active areas (Wickenhiser et al., 15 Nov 2025, Joyce et al., 2023). At the microscale, future designs may exploit engineered chiral activity for programmable matter or synthetic collective behaviors (Banerjee et al., 2024).

References: (Jawed et al., 2015, Schreiber et al., 2019, Richter et al., 2021, Lim et al., 2023, Joyce et al., 2023, Banerjee et al., 2024, Chen et al., 15 Nov 2025, Wickenhiser et al., 15 Nov 2025, Texier et al., 2017).