Dimensionless modeling and experimental validation of stick-slip locomotion in a semidefinite vibration-driven system

Abstract

Rectilinear locomotion of a semidefinite vibration-driven system on an inclined surface is studied using a one-coordinate stick-slip model and a physical prototype. The chassis and rotating assembly are treated as separate rigid bodies. General force balances retain angular-acceleration terms, and the rotor equation defines the instantaneous torque required for constant speed. A third balance resolves the two longitudinal support reactions. The reported prototype geometry and corrected mass properties yield a conservative lower bound of 0.130 N for each support-pair reaction over the investigated frequency and inclination ranges at nominal friction, conditional on the prescribed-speed planar model. The equations are transformed using the unbalance mass ratio Π m , frequency parameter Π ω , friction coefficients μ s and μ k , inclination angle α , and the excitation-to-weight ratio Γ . Explicit validity conditions are established for continuous contact and bounded downhill motion, and an analytical condition for forward frictional breakaway is derived. Numerical integration uses an explicit stick-slip state-switching algorithm with transient removal and step-size verification. The frequency- and inclination-dependent predictions are compared with the experimental markers obtained for a prototype driven by a 3650-type DC vibration motor and instrumented with two WitMotion BWT901CL inertial units. The experimentally obtained points give a combined dimensionless-velocity RMSE of 0.00091 and a maximum absolute discrepancy of 0.00266. The resulting model is intended for continuous-contact, predominantly translational regimes and provides dimensionless criteria for selecting excitation and friction parameters.