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

机译：基于3D空间中的Darboux框架的路径约束下的车轮运动状态模型

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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.
机译：目的-现有的三维（3D）路面模型使用近似方法（例如一组离散的三角形斑块），并且无法准确描述沿道路进行几何设计的元素的变化。本文旨在构建结合几何设计不变性的3D路面模型，并将该模型用于分析车轮中心的运动状态。设计/方法/方法-本文将3D路面建模为具有几何设计不变式组合的连续函数。通过介绍微分几何和刚体动力学的理论，构建了车轮模型，在该模型中，固定在Darboux框架上的车轮沿弯曲的路面移动，并且车轮的速度，角速度和加速度随时间的变化随时间变化。研究结果-本文采用Darboux框架来研究车轮的瞬时自旋滚动运动。发现车轮的旋转速度，加速度和几何不变量的大小（包括测地曲率，法向曲率和测地扭率）决定了车轮的瞬时运动状态。 -这项工作为将来的车轮运动状态研究提供了理论基础，例如道路几何设计不变性与行驶安全性，车道变更和其他车辆微行为之间的关系。在道路安全和结合了人工智能的车辆方面获得了新的见识。

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