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Model of the wheel motion state under path constraints based on the Darboux frame in 3D space

He Zhang (School of Highways, Chang’an University, China)
Shaowei Yang (School of Highways, Chang’an University, China)
Zhengfeng Ma (Transport College, Qinghai Nationalities University, Xining, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 30 October 2018

Issue publication date: 27 November 2018

138

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.

Keywords

Citation

Zhang, H., Yang, S. and Ma, Z. (2018), "Model of the wheel motion state under path constraints based on the Darboux frame in 3D space", Engineering Computations, Vol. 35 No. 8, pp. 2883-2903. https://doi.org/10.1108/EC-11-2017-0460

Publisher

:

Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

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