Model of the wheel motion state under path constraints based on the Darboux frame in 3D space. Issue 8 (30th October 2018) - Zhang, He
Abstract : Purpose: Existing three-dimensional (3D) road-surface models use approximation methods such as a set of discrete triangular patches and cannot accurately describe changes in the geometrically designed elements along the road. This paper aims to construct a 3D road-surface model with combinations of geometric design invariants and apply the proposed model to analyse the state of motion of a wheel's centre. Design/methodology/approach: In this paper, the 3D road surface is modelled as a continuous function with combinations of geometric design invariants. By introducing the theories of differential geometries and rigid body dynamics, a wheel-road model wherein a wheel fixed to a Darboux frame moves along a curved road surface is constructed, and the wheel time-dependent properties of the velocity, angular velocity and acceleration at an arbitrary point of the surface are described using road geometry design invariants. Findings: This paper adopts the Darboux frame to study the instantaneous spin-rolling motion of a wheel. It is found that the magnitudes of the spin-rolling velocity, the acceleration and the geometric invariants of the road surface, including the geodesic curvature, the normal curvature and the geodesic torsion, determine the instantaneous states of motion of a wheel. Originality/value: This work provides a theoretical foundation for future studies of wheel motion states, such as the relationship between road geometry design invariants and driving safety, vehicle lane changing and other vehicle microbehaviours. New insights are gained in the areas of road safety and vehicles incorporating artificial intelligence.