Animation of cycloid and spiral curves in companion with instantaneous center of rotation and radius of curvature

IF 1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY

Journal of the Chinese Institute of Engineers Pub Date : 2023-08-02 DOI:10.1080/02533839.2023.2238768

Jeng-Tzong Chen, Chia-Ying Yang, Y. Chou, Chi-Ning Tsang

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引用次数: 0

Abstract

ABSTRACT In this paper, the animations for the 2D cycloid and the 3D spiral curves are done. The trajectories of instantaneous rotation center and the corresponding radius of curvature are given. We prove that the trajectory of the instantaneous center of rotation is also a cycloid. For a 3D spiral curve, the two radii and the two instantaneous centers of rotation for the spiral curve are also given. It is interesting to find that the two parameters in the Frenet equation have the same meaning of radius of curvature but in different planes. In a similar way of the 2D experience, we also confirm that the trajectory of the instantaneous center of rotation for a spiral curve is also a spiral curve. An example is also given to discuss the Puyuma express incident, a major accident in 2018. The curve of rail is interpolated and the radius of curvature is determined. Discussions on the radius of rail curve and the speed of train for the failure are done. Finally, the animation is implemented by using the MATLAB and the Mathematica software. Not only theoretical derivation for the curvature of a curve but also its real application to rail engineering is proposed.

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具有瞬时旋转中心和曲率半径的摆线曲线和螺旋曲线的动画

本文对二维摆线和三维螺旋曲线进行了动画处理。给出了瞬时旋转中心的轨迹和相应的曲率半径。证明了瞬时旋转中心的轨迹也是一条摆线。对于三维螺旋曲线，给出了螺旋曲线的两个半径和两个瞬时旋转中心。有趣的是，Frenet方程中的两个参数具有相同的曲率半径含义，但在不同的平面上。在类似的二维经验中，我们也确认了螺旋曲线的瞬时旋转中心轨迹也是螺旋曲线。并以2018年发生的重大事故普尤马特快列车事故为例进行了讨论。对钢轨曲线进行插值，确定其曲率半径。对轨道曲线半径和列车运行速度对故障的影响进行了讨论。最后，利用MATLAB和Mathematica软件对动画进行了实现。提出了曲线曲率的理论推导及其在轨道工程中的实际应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the Chinese Institute of Engineers 工程技术-工程：综合

CiteScore

2.30

自引率

9.10%

发文量

审稿时长

6.8 months

期刊介绍： Encompassing a wide range of engineering disciplines and industrial applications, JCIE includes the following topics: 1.Chemical engineering 2.Civil engineering 3.Computer engineering 4.Electrical engineering 5.Electronics 6.Mechanical engineering and fields related to the above.