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 引用本文: 王囡囡, 熊佳铭, 刘才山. 自行车动力学建模及稳定性分析研究综述[J]. 力学学报, 2020, 52(4): 917-927.
Wang Nannan, Xiong Jiaming, Liu Caishan. REVIEW OF DYNAMIC MODELING AND STABILITY ANALYSIS OF A BICYCLE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 917-927.
 Citation: Wang Nannan, Xiong Jiaming, Liu Caishan. REVIEW OF DYNAMIC MODELING AND STABILITY ANALYSIS OF A BICYCLE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 917-927.

## REVIEW OF DYNAMIC MODELING AND STABILITY ANALYSIS OF A BICYCLE

• 摘要: 自行车发明于两个多世纪前. 这一看似古老的交通工具在为人们提供出行便利的同时,其独特的运动特性及动力学性质 也吸引了来自数学、物理及力学等多个学科相关学者的兴趣. 大体上,自行车可以描述为具有 7 个自由度和 4 个非完整约束的多刚体系统. 但由于前后车轮之间复杂的运动耦合关系,使得自行车的约束方程和动力学模型变得异常复杂, 导致对自行车的稳定性存在一些模糊认识. 本文针对经典的 Carvallo-Whipple 自行车构型,系统回顾了历史上自行车动力学研究中的相关问题,这些问题包括：(1) 自行车在复杂曲面上的几何约束和非完整约束的数学描述;(2) 自行车系统内在的对称性及守恒量; (3) 自行车动力学的各类建模方法; (4) 自行车运动的相对平衡点及稳定性分析,包括水平面上的匀速直线运动及旋转对称曲面上的匀速圆周运动;(5) 影响自行车自稳定性的结构参数等. 本文最后对自行车动力学实验和控制方面的研究工作进行了回顾,并对自行车今后的研究给出了展望.

Abstract: The bicycle was invented more than two centuries ago. This seemingly ancient vehicle not only provides convenient transportation for people, but also attracts the interest of scholars from mathematics, physics, mechanics and other disciplines due to its unique motion characteristics and dynamic properties. Generally, a bicycle can be described as a rigid multi-body system with seven degrees of freedom, subjected to four nonholonomic constraints. However, due to the complex kinematic coupling between the front and rear wheels of a bicycle, its constraint equations and dynamic model become extremely complicated, leading to some vague knowledge about bicycle self-stability. Aiming at the classic Carvallo-Whipple bike configuration, this paper systematically reviewed the relevant problems in the research of bicycle dynamics in history. These problems include: (1) Mathematical description of geometric constraints and nonholonomic constraints for a bicycle moving on a complex curved surface; (2) The intrinsic symmetries of the bicycle system and the relevant conservation quantities; (3) Various modeling methods of bicycle dynamics; (4) The stability analysis of the relative equilibriums for the bicycle motions in a uniform linear motion on a horizontal surface and in a uniform circular motion on a surface of revolution, respectively; (5) Structural parameters affecting the bicycle self-stability, and etc. Finally, some typical experiments work and the different control strategies of the bicycle are detailedly described, and also several open problems are addressed for future research.

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