An Asymmetric Stick–Slip Ground-Reaction Propulsion Concept Using Phase-Locked Counter-Rotating Rotor Sets

This preprint presents a ground-reaction propulsion concept that converts internally generated, time-varying inertial loads into net surface translation by exploiting intentionally asymmetric stick–slip friction at the ground interface.

Overview

The proposed embodiment uses two phase-locked, counter-rotating rotor sets mounted on a frame. Within each rotor set, a fast rotor and a slow rotor are parameterized so their bearing-load magnitudes match, while their relative phase evolves over the cycle. This produces a time-asymmetric frame-load waveform modeled with a Hann-shaped profile that includes constructive and partially canceling destructive portions.

System configuration (example values in the manuscript)

• Frame mass: M = 50 kg

• Per rotor set (nested rotors):

  • Fast rotor: mf = 0.908 kg, rf = 0.10 m, 600 RPM

  • Slow rotor: ms = 1.816 kg, rs = 0.20 m, 300 RPM

• Key ratios: ωf = 2ωs, ms = 2mf, rs = 2rf, implying equal tangential speeds (vf = vs).

Force and impulse model (summary)

Using the example parameters, the manuscript computes approximately equal per-rotor bearing-load magnitude (F0 ≈ 358.46 N) and shows the within-set vector sum can range from near-cancellation to a peak of about Fset,peak ≈ 716.93 N. If both rotor sets add constructively, the peak frame force is estimated as Fframe,peak ≈ 1433.86 N.

To analyze rectification potential, the forcing is approximated as a constructive half-cycle and a scaled, inverted destructive half-cycle with cancellation fraction α. The resulting impulse-per-cycle is given in closed form as
J = (T/4) · Fpeak · (1 − α), with cycle-average force F = ((1 − α)/4) · Fpeak.
A numerical example in the manuscript (M = 50 kg, T = 0.2 s, α = 0.41, one-set Fpeak ≈ 716.93 N) yields an idealized aavg ≈ 2.11 m/s² and Δvcycle ≈ 0.423 m/s (noting practical limits).

Ground-contact rectification (stick–slip asymmetry)

Net motion is attributed to ground contact where the device’s horizontal excitation interacts with static/kinetic friction. The manuscript outlines stick and slip conditions and emphasizes that translation requires intentional asymmetry in the stick–slip cycle, for example via:

• directional friction (anisotropic feet, bristles, one-way rollers),

• normal-force modulation,

• time-asymmetric “load/release,” or

• phase-selective coupling.
  It also notes a traction-limited bound on achievable acceleration (|a| ≲ μg).

Energy and power framing

The manuscript highlights that, for a given average force, the mechanical power delivered to translation scales with speed (P ≈ Fv), and provides an illustrative linear-in-speed relation P(v) ≈ ((1 − α)/4 · Fpeak) v.

Scope / non-claims

This work does not claim free-space thrust: without an external reaction path (e.g., ground contact), the net impulse of a continuously coupled closed system is zero, consistent with momentum conservation.

Suggested next steps (as stated in the manuscript)

Future work priorities include (i) experimentally characterizing the transmitted force waveform, (ii) designing robust asymmetric friction elements, and (iii) measuring displacement per cycle under controlled conditions.

How to cite (template)

Wells III, J. A. (2026). An Asymmetric Stick–Slip Ground-Reaction Propulsion Concept Using Phase-Locked Counter-Rotating Rotor Sets (Version 3) [Preprint]. Zenodo. https://doi.org/10.5281/zenodo.18879381